EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

CERN-PH-EP/2004-XXX May-2004

The pseudoscalar states in the 1.4-1.5 GeV/c^{2} mass region

A. Masoni^{(a)}, C. Cicalò^{(b)} and G.L. Usai^{(c)}

(a) CERN PH Division, 1211 Geneva 23, Switzerland and INFN - Sezione di Cagliari, Cagliari, Italy

(b) INFN - Sezione di Cagliari, Cagliari, Italy

(c) Dipartimento di Fisica - Università di Cagliari, and INFN - Sezione di Cagliari, Cagliari, Italy

Abstract

Glueballs represent a key requirement of QCD as a non-abelian field theory. Their search provides one of the strongest motivations for meson spectroscopy. The first glueball candidate was identified in 1980 in J/Ψ radiative decay Its discovery actually dates back to 1963 and for four decades about thirty experiments, using six different production mechanisms, where dedicated to the study of the pseudoscalar states laying in the 1.4-1.5 GeV/c^{2} mass region. Finally the presence of two pseudoscalar states and an axial vector can now be considered established and is reported in the 2004 issue of the Review of Particle Properties. This article aims at reviewing the experimental effort related to this long search that can constitute a sort of paradigm for light quark spectroscopy.

NOPACS: Keywords: Glueballs, light quark spectroscopy, pseudoscalars.

submitted to European Physics Journal C

1 Introduction

According to Quantum Chromodynamics (QCD) hadrons are described as bound states of quarks which interact through colour forces mediated by gluons. Since gluons bring colour they are subject to self coupling and can be constituents of the hadronic matter [1, 2]. These quarkless states, glueballs, can consist of two or more gluons and represent a direct consequence of the non-abelian nature of the theory. The experimental discovery of such states has fundamental importance for the verification of QCD but their unambiguous identification is a formidable task from the experimental point view and requires the combined effort of many experimental measurements.

The Constituent Quark Model [3], successfully describes the meson and the baryon spectrum in terms of composite objects made of constituent valence-quarks. Mesons are described as quark-antiquark (\overline{q}q) pairs and baryons are made of three quarks. They arrange themselves into multiplets according to their J^{P C} [4]. A non-\overline{q}q state simply does not fit the J^{P C}pattern. Therefore the identification of a glueball must proceed through a complete understanding of the conventional mesons in order to rule it out as a standard state. The richness of the meson spectrum and the limits in the theory predictions of the hadron properties make this task a true challenge.

On the basis of our present understanding of the meson properties, and, in particular, of their production and decay mechanisms the following guidelines can be established.

A) The state must be an extra state, i.e. it must lay outside the corresponding J^{P C} nonet.

B) Being SU(3) singlets, glueballs do not carry charge, therefore they do not couple directly to photons.

C) For the same reason as B) glueballs have no flavour. This implies that glueballs do not couple particularly to any specific quark pair and their decay mode should be, at least in principle, flavour blind. Anomalous decay modes are also expected.

D) Glueballs should be produced copiously through gluon rich mechanisms.

Point A sets the most basic condition, i.e. the presence of a set of meson states, with a defined J^{P C}, exceeding the number of available slots in their nonet.

This condition allows to set up the case for the possible presence of a non \overline{q}q state. In order to disentangle the gluonium candidate against the standard mesons, the combined information of points B, C and D, together with the help of the predictions from theoretical models, is definitely needed.

Point B is extremely important since it indicates a way to discard a glueball candidate. A clear signal in γγ collision provides a strong argument against the glueball interpretation.

On the contrary (point D) production mechanisms such as the J/Ψ radiative decay, where the initial state couples to the final one dominantly by the emission of two gluons, are expected to strongly favour glueball enhancement.

Another interesting process, in this respect, is the double pomeron exchange in central production. As the pomeron is expected to have a large gluonic component one can expect glueballs to be produced [5].

Also antinucleon-nucleon annihilation can favour glueball production. In this case, through the annihilation process, quarks and gluons are produced, within a volume corresponding to the radius of strong interactions.

The decay mode (point C) provides other means to distinguish conventional mesons from non \overline{q}q states. The information from theoretical models can help in classifying the ordinary mesons within the nonets and in identifying the intruders [2, 6].

Actually the situation is even more difficult since ordinary \overline{q}q states can mix with gluons and the decay pattern becomes even more complex.

In summary, a well established experimental meson spectrum is the basic assumption for glueball search. The compared analysis of experimental results from different production mechanisms and the study of different decay modes is a mandatory requirement to establish a glueball candidate.

The case of the η(1405), once called the E or ι. is a case in itself in the glueball search. Its outstanding production in J/Ψ radiative decay, in 1980 [7, 8, 9], granted it the title of the first glueball candidate. It has been studied through six different production mechanisms by more than thirty experiments for a period spanning four decades. For many years the nature (and the number) of the states present in the 1.4-1.5 GeV mass region remained unclear and the experimental results look contradictory giving rise to the so called E/ι puzzle[10, 11]. More than 70 experimental results are now quoted within the Review of Particle Properties [12].

The purpose of this article is to perform a review of this great experimental effort trying to extract a comprehensive and coherent picture from this vast, somewhat contradictory, set of experimental results.

We will first present an overview of the most relevant results in a chronological order, then a more detailed discussion of all the different production mechanisms and the observed final states will follow. We will then try to organize the experimental results within a coherent framework.

In forty years names have changed and this can give rise to some confusion. We will use the historical names E and ι for the older experiments.

Following the PDG notation from 1986[13] until 2002 [11] we will refer to the η(1440) to indicate either one pseudoscalar or the two pseudoscalar states. In some cases, when the two pseudoscalar states are separately identified, we will refer to them as η(1405) and η(1475), following the notation of the 2004 PDG issue[12].

2 Experimental Overview

The history of the experimental search of the pseudoscalar and vector states in the 1.4-1.5 GeV/c^{2} is long and quite complex. Here we will trace the essential steps.

The first observation of the E meson dates back to 1963 in a bubble chamber experiment of the CERN-College de France collaboration[14].

The process was \overline{p}p → K_{S}K^{±}π^{∓}π^{+}π^{−}. The data were extremely clean and the peak showed well and almost background free, in the K_{S}K^{±}π^{∓} invariant mass distribution, with mass M = 1426 ± 7 MeV/c^{2} Γ = 80 ± 10 MeV/c^{2}. This state was named E in honour of Europe. Later on, a full spin parity analysis of these data [15], showed the state was a pseudoscalar J^{P C} = 0^{−+} decaying 50% to \overline{K}^{∗}K + c.c. and 50% to a_{0}(980)π (at that time the a_{0}(980) was not yet known but it was observed that the (\overline{K}K) system resonated around 1 GeV/c^{2}). This pseudoscalar was first identified as the η isoscalar partner. The discovery of the η′ and its identification as the missing member of the pseudoscalar nonet gave rise to an interpretation problem and alternative spin assignments were considered.

It is therefore not surprising that the identification of an axial vector, in the same mass region, with a higher statistics π^{−}p → K_{S}K^{±}π^{∓}n bubble chamber experiment [16] led to the conclusion the E meson was a J^{P C} = 1^{++} state.

In the same years, the Mark II experiment identified a peak at a mass of around 1440 MeV[7] and, two years later, the Crystal Ball experiment [8, 9] associated it to a pseudoscalar state. The E meson was definitely considered a 1^{++} state [10] and the new pseudoscalar was called iota˙. Its mass and width were M = 1440±20 MeV/c^{2} Γ = 55±30 MeV/c^{2}, its dominant decay mode was a_{0}(980)π.

These two experiments observed the signal in J/Ψ radiative decay with a very high branching ratio. This fact was one of the strongest arguments in favour of its glueball interpretation [17, 18, 19, 20].

In the eighties several experiments were performed but the situation, instead of being clarified, seemed to become more complicated. The MARK III experiment [21] confirmed, with higher statistics, the pseudoscalar identification but with a higher mass (1458 ± 5MeV/c^{2}) and a larger width (Γ = 98 ± 10MeV/c^{2}) with respect to the results of [8, 9].

The resonance shape was asymmetric and the decay pattern indicated that both a_{0}(980)π and \overline{K}^{∗}K + c.c. contributions were present (as in the original \overline{p}p experiment [15]).

The relative contribution of the two decay modes seemed to depend on the mass interval. The a_{0}(980)π was preferred selecting lower mass values while the \overline{K}^{∗}K + c.c. mode seemed to dominate at higher masses.

All these elements indicated the presence of a more complex structure.

The a_{0}(980)π decay mode was another source of confusion. In the eighties the a_{0}(980) was known to decay mainly to ηπ . Therefore the ι signal was expected to be found in the ηππ final state also [22].

The MarkIII and the Crystal Ball experiment searched for the ι signal in the ηππ channel, but without success.

In the mid eighties a set of contradictory results were obtained in peripheral and central hadro-production at Brookhaven and at CERN.

At Brookhaven the channel π^{−}p → K_{S}^{0}K^{±}π^{∓}n was studied . The statistics was ten times higher with respect to the bubble chamber experiment [16]. The conclusion of their spin parity analysis [23, 24] was totally different. A dominant pseudoscalar contribution, decaying to a_{0}(980)π was found, with mass and width parameters in agreement with the old bubble chamber data[15]. The axial vector was found to contribute at the 10% level only. This result was confirmed, by the same group, with 6.6 GeV/c antiproton data [25].

At the very moment when the mere existence of the axial vector was questioned by the Brookhaven data, a new set of results from the WA76 experiment at CERN provided strong evidence for a 1^{++} state in the E/ι mass region. The WA76 experiment studied π^{+}p collision at 85 GeV/c, the so called central production. Central production, (see Sect. 1), is considered a gluon rich environment. Therefore, within the framework where the ι(1440) was considered a glueball candidate, its strong production was expected. On the contrary the WA76 experiment reported decisive evidence for a 1^{++} state at a mass M = 1425 ± 2MeV/c^{2} and width Γ = 62 ± 5MeV/c^{2} while the pseudoscalar was not seen [26]. The observed dominant decay mode was \overline{K}^{∗}K + c.c.. After the Brookhaven result[23], indicating the pseudoscalar dominance, the WA76 Collaboration performed a new analysis[27] and collected new data with 300 MeV/c incident protons[29]. The 1^{++} state was definitely confirmed. A possible 0^{−+} contribution, at a 14% level, was reported.

In the WA76 papers [27, 29] the analysis model adopted by the Brookhaven experiment [23, 24, 25] was criticized. In particular it was remarked that, because of the incoherent K^{∗}production and the large background present in the data, the analysis performed in [23, 24, 25] could have easily confused a 1^{++} state with a 0^{−+} state decaying to a_{0}(980)π and \overline{K}^{∗}K + c.c.

This argument raises one of the most critical points in the whole set of the E/ι experimental data i.e. the need for a clean, background-free data sample.

Here the word background takes a general meaning and includes several, different, categories. The background originating from other contaminating channels depends essentially on the detector performances, in particular on the detector sensitivity to the channels of interest. Besides this, the combinatorial background and the phase space contribution must be taken into account.

However the most difficult contamination to deal with is the contribution from other resonating states, that lie in the same mass region, and need to be disentangled in order to unambiguously identify a resonance’s parameters. In order to overcome this last difficulty, sophisticated spin parity analysis techniques need to be employed.

Nevertheless, despite the level of accuracy of the adopted analysis, the best procedure is to study different decay modes and different production mechanisms.

The use of different production mechanism enables accessing different J^{P C} states. This way the searched resonance can be put in evidence against a background of other resonances with different J^{P C}s crowded within the same mass region.

The study of different decay modes enables disentagling states with the same J^{P C} having different decay modes.

Two production mechanisms, γγ fusion and \overline{p}p annihilation, represent a powerful tool to select the J^{P C}of the final states.

The γγ reaction can act as a spin filter on spin one states by tagging the virtual photon (see Sect. 3.3).

In 1986 two experiments at SLAC, TPC/2γ [30, 31] and MARKIII [32, 33] showed a prominent signal at a mass of 1420 MeV in the tagged data sample, where spin 1 and spin 0 states are allowed and no signal in the untagged data sample, where spin 1 objects are forbidden. This led to two very important conclusions.

• First the absence of pseudoscalar production in the 1.4-1.5 GeV mass region in γγ collision.

• Second the identification of a 1^{++} signal.

The absence of pseudoscalar contributions allowed an unambiguous determination of the 1^{++} state parameters and enforced the idea of the glueball hypothesis for the E/ι pseudoscalar since glueballs do not couple to photons and their production is expected to be suppressed in photon-photon collision.

Antiproton-proton annihilation at rest provided the first evidence for the E/ι pseudoscalar. Only few partial waves are involved in \overline{p}p at rest, allowing for a much simpler spin parity analysis with respect to hadroproduction. The bubble chamber data[15] were extremely clean but the statistics was limited. It was necessary to wait about twenty years, when, at the end of the eighties, the advent of the Low Energy Antiproton Ring (LEAR) at CERN, made possible high statistics experiments with \overline{p}p at rest. The Asterix experiment first, repeated the original bubble chamber measurement but with a hydrogen gaseous target [34]. Again the statistics was limited and did not allow a spin parity analysis. Nevertheless this experiment showed the power of a technique suitable to disentangle different spin contributions in the same mass region (see Sect. 3.4). By changing the density of the hydrogen target it is possible to select the initial angular momentum state from which the \overline{p}p annihilation occurs. It is therefore possible to discriminate different final state contributions. This technique was exploited later, with high statistics data samples, by the Obelix and the Crystal Barrel experiment in the second generation of LEAR experiments (see below and Sect. 3.4).

At the end of the eighties the existence of a pseudoscalar and an axial vector seemed established but several inconsistencies in the pseudoscalar parameters were present. Moreover the analysis of the K\overline{K}π MarkIII data [21] suggested a more complex structure in the pseudoscalar wave in the E/ι mass region. The possibility that two pseudoscalar states could be present, to explain the discrepancies among the different experiments was considered[35].

This complex structure was confirmed by a Brookhaven experiment in π^{−}p → K_{S}^{0}K_{S}^{0}π^{0}n at 21.4 GeV/c [36] and by the MARKIII [37] and the DM2 [38] experiments in J/Ψ → γK_{S}^{0}K^{±}π^{∓}. These three experiments reported the presence of two pseudoscalars and an axial vector in the 1.4 − 1.5 GeV/c^{2} mass region. They all agreed that the axial vector and one pseudoscalar decay \overline{K}^{∗}K + c.c., while the other pseudoscalar decays to a_{0}(980)π. However according to the DM2 analysis the lower mass pseudoscalar decayed \overline{K}^{∗}K + c.c., while the higher mass one decayed to a_{0}(980)π [38]. For the other two experiments [36, 37] it was the opposite.

This picture could explain several inconsistencies in the previous data but it certainly showed a complex scenario with a mass spectrum crowded with resonances difficult to discriminate with the spin parity analysis.

As shown above the γγ reaction could provide a way to discriminate and study the axial vector in an ideal environment, without the pseudoscalar contributions.

Antiproton annihilation at rest in liquid hydrogen (see Sect. 3.4) could do the opposite by selecting the pseudoscalar production and suppressing the axial vector. Moreover, according to the proposed decay mode scenario, two pseudoscalars should be present in the K\overline{K}π final state, while only one should show up in the ηηπ final state.

This scenario was confirmed by the Crystal Barrel and the Obelix experiments at LEAR.

The first one studied the ηηπ final state with a liquid hydrogen target showing evidence of a pseudoscalar state at a mass M = 1409 ± 3 MeV/c^{2} and width Γ = 86 ± 10 MeV/c^{2} [39], in agreement with the other results in ηππ from hadroproduction and J/Ψ decay[40, 41, 42, 43].

The Obelix experiment performed a wide experimental program studying the K\overline{K}π final state at different target densities. First a liquid hydrogen target was employed. In these conditions the axial vector production is expected to be suppressed and it is therefore the ideal environment for the study of the pseudoscalar states. Two pseudoscalars with masses M_{1} = 1416 ± 2 MeV/c^{2}, M_{2} = 1460 ± 10 MeV/c^{2} and widths Γ_{1} = 50 ± 4 MeV/c^{2}, Γ_{2} = 105±15 MeV/c^{2} were reported [44]. The lower mass pseudoscalar decaying dominantly to a_{0}(980)π and the higher mass one decaying \overline{K}^{∗}K + c.c.. Masses, widths and decay mode were in substantial agreement with the MARKIII[37] result but with ten times higher statistics. This result was confirmed on a successive, refined analysis, performed on a higher statistics cleaner data sample[45].

Measurements with different target densities allowed to prove the presence of the axial vector [46, 47] and to confirm the dominant pseudoscalar production from S-states[48].

A BES experiment in Beijing studied again the K\overline{K}π final state in J/Ψ radiative decay [49]. Only one pseudoscalar was reported but it must be noted that their statistics is much lower (a factor six) with respect to the MARKIII experiment [37]. It is therefore not surprising that the data do not show evidence for two pseudoscalar states.

Another important contribution came again from γγ collision at LEP. The L3 experiment[50] studied both the K\overline{K}π and ηππ final states. They observed a signal consistent with the higher mass pseudoscalar in the K\overline{K}π channel while no signal, at the E/ι mass, is observed in ηππ.

The evidence of two pseudoscalars and an axial vector was further confirmed in π^{−}p → K^{+}K^{−}π^{0}n by the E753 experiment at Brookhaven[51].

In summary, five different experiments, using three different production mechanisms, reported evidence for two pseudoscalars and an axial vector in the E/ι mass region.

These states are now called η(1405), η(1475) and f_{1}(1420) [12].

In the next section we will examine, in more detail, the experimental results according to their production mechanism.

Figure 1: J/Ψ radiative decay, MarkII experiment[7], K_{S}K^{±}π^{∓} invariant mass distribution

3 Production Mechanisms

3.1 J/Ψ decay

The J/Ψ radiative decay is considered the perfect environment for glueball production. According to perturbative QCD the final state couples to the initial c\overline{c} pair dominantly through the emission of two gluons.

If the two gluons coming from the c\overline{c} pair annihilation form a bound state, a resonance is observed in the final state invariant mass distribution. This state has a strong probability to have a large gluon content.

In 1980, the MarkII experiment at SPEAR , the Stanford e^{+}e^{−} accumulation ring, produced the first evidence of a resonant state in the K_{S}^{0}K^{±}π^{∓} invariant mass distribution[7]. The statistics was limited and it did not allow a spin parity analysis but the peak stood out, almost background free, very clearly around 1440 MeV/c^{2} (see fig. 1). In absence of a quantum number identification the state was identified as the E 1^{++} meson[7].

The branching ratio turned out to be extremely high, definitely higher than any radiative decay, with the exception of J/Ψ → γη_{c}, which does not involve the annihilation of the c\overline{c} pair. It is therefore not surprising that this state was interpreted as a glueball [17, 18, 19, 20].

In 1982 the Crystal Ball experiment at SLAC collected a statistics sufficient to perform a spin parity analysis and identified this state as a pseudoscalar[8] (see fig. 2 ). Its mass and width was determined as: M = 1440 ± 20 MeV/c^{2} Γ = 55 ± 30 MeV/c^{2} . The dominant decay mode was a_{0}(980)π.

The E meson was definitely considered a 1^{++} state [10] and the pseudoscalar reported in \overline{p}p annihilation[15] was far in time. Therefore a new pseudoscalar was reported and called iota. Only one year later (see [9]) the Crystal Ball collaboration considered the possibility that the iota was actually the same state observed in bubble chamber by the

Figure 2: J/Ψ radiative decay, Crystal Ball experiment[8], partial wave analysis

CERN-College de France collaboration[15] and originally called E. But the names were already established, the name iota was associated to the pseudoscalar and the name E to the axial vector[10].

The quantum number determination further enforced the glueball hypothesis. The η′ already filled the place for the η isoscalar companion, the pseudoscalar nonet was full and the iota was the outsider[17, 18, 19, 20].

Since the iota dominant decay mode was a_{0}(980)π and the a_{0}(980) decay to ηπ was known to be larger than the K\overline{K} mode, the J/Ψ → γηππ reaction was studied, to search for the iota signal. The first results, from the Crystal Ball experiment at SLAC, were negative[52]. The ηππ mass spectrum around 1.45 GeV did not show any clear resonant activity (see fig. 3). A possible shoulder could be present in the ηπ^{+}π^{−} invariant mass distribution (see fig. 3 a)) but the signal, if any, should be certainly much lower with respect to the K\overline{K}π data. On the contrary, on the basis of the a_{0}(980)\frac{ηπ}{K\overline{K}} relative width, one would have expected a larger signal with respect to the K\overline{K}π case. The obtained relative branching ratio was \frac{J/Ψ→(γι)(ι→ηππ)}{J/Ψ→(γι)(ι→K\overline{K}π)} < 0.5 with 90% confidence level.

This problem can be understood taking into account the presence of two pseudoscalars: if only one of the two contributing pseudoscalars is present (since the other decays dominantly \overline{K}^{∗}K + c.c.), the peak is correspondingly reduced and shifted to lower masses. Moreover, differently from the K\overline{K}π case, in ηππ the phase space shape has a steep increase in the 1.3÷1.5 mass region. This makes the identification of a signal and the evaluation of its contribution, more difficult. Only later, when higher statistics data sample were available, a signal was identified, in J/Ψ → γηππ also (see below).

At that time, however, this apparent contradiction further incremented the E/ι puzzle.

As remarked in Sect. 2, the existence of the axial vector, now named f_{1}(1420) was considered established since 1980[10] but the situation for the ι(1440), or η(1440) remained unclear. We will now refer to the pseudoscalar states using the name η(1440) as in the PDG from 1986[13] until the 2002 issue[11]. The possibility that two pseudoscalar states could actually be present within the η(1440) has been considered since 1986[35] in order Figure 3: J/Ψ radiative decay, Crystal Ball experiment[52], ηππ invariant mass distribution to explain the discrepancies among the different experimental results in the K\overline{K}π and ηππ final states.

A fundamental contribution to the solution of the puzzle and the understanding of the number and the nature of the states present in the 1.2 ÷ 1.5 mass region came from the MarkIII and the DM2 experiments.

The MarkIII experiment at SLAC and the DM2 experiment at Orsay performed an extensive study of the K\overline{K}π and ηππ final states, from J/Ψ radiative decay, in the 1.2÷1.6 GeV/c^{2} mass region.

In 1990 the MarkIII experiment presented the result of a spin parity analysis on a set of about 2400 J/Ψ → K_{S}^{0}K^{±}π^{∓}γ events (about 700 events in the region of interest).

The statistics was much higher with respect to the previous J/Ψ data.

Since the J/Ψ radiative decay branching ratio is 10^{−3} ÷ 10^{−4}, statistics plays a crucial factor. The higher statistics allowed to show that the η(1440) could not be adequately described as a single resonance but rather as a superposition of several states. Already looking at the K_{S}^{0}K^{±}π^{∓} invariant mass, where an asymmetric shape was clearly visible, it was possible to have a hint of a complex structure (see fig. 4a). Another interesting feature was that, selecting the lower region in the K_{S}^{0}K^{±}π^{∓} mass spectrum, the corresponding Dalitz plot (see fig. 4b)), showed a cluster of events in the region of low K_{S}^{0}K^{±} mass, while the Dalitz plot associated to the higher K_{S}^{0}K^{±}π∓ masses (see fig. 4c)) exhibited very clearly the K^{∗} bands. The higher mass Dalitz plot in fig. 4c) showed the typical shape for a pseudoscalar decaying to \overline{K}^{∗}K + c.c..

A partial wave analysis was performed. The amplitudes were constructed using the Zemach tensor formalism[53] and the Flatte’ model[54] was employed to parameterise the a_{0}(980). The process was described within the isobar model framework[55], i.e. as a sequence of two body decays.

The partial wave intensity spectra obtained selecting 1.35 < M_{K_{S}^{0}K^{±}π^{∓}} < 1.6 GeV/c^{2} (see fig. 5) indicated the presence of three states. Their decay modes, masses, widths and branching ratios (J/Ψ → (γX)xX → (K_{S}^{0}K^{±}π^{∓}) are reported in table 1. The analysis Figure 4: J/Ψ radiative decay, MarkIII experiment[37], a) K_{S}K^{±}π^{∓} invariant mass distribution, b) Dalitz plot for 1.35 < M_{K_{S}^{0}K^{±}π^{∓}} < 1.45 GeV/c^{2} c) Dalitz plot for 1.45 < M_{K_{S}^{0}K^{±}π^{∓}} < 1.55 GeV/c^{2}

results showed a lower mass pseudoscalar, at a mass around 1.41 GeV/c^{2} decaying to a_{0}(980)π; a second pseudoscalar, at a mass of 1.49 GeV/c^{2}, decaying through \overline{K}^{∗}K + c.c.; an axial vector, at a mass of 1.44 GeV/c^{2}, decaying through \overline{K}^{∗}K + c.c..

The branching ratios were compatible with the other K\overline{K}π and the ηππ results. In particular the suppression factor (\frac{J/Ψ→(γι)(ι→ηππ)}{J/Ψ→(γι)(ι→K\overline{K}π)} < 0.5) found by the Crystal Ball experiment[52], resulted compatible with the ratio between the lower mass pseudoscalar branching ratio and the total pseudoscalar contribution as reported in table 1.

It must be noted that the K_{S}^{0}K^{±}π^{∓} data sample was exceptionally good: thanks to the 5C kinematical fit it was almost free from other contaminating channels and thanks to Nature the two pseudoscalars and the axial vector dominated the spectrum, accounting

Amplitude decay

\begin{matrix}Mass \\ (MeV/c^{2}) \end{matrix} \begin{matrix}Width \\ (MeV/c^{2}) \end{matrix}

Branching ; ratio (10^{−3})
1^{++}  \overline{K}^{∗}K + c.c. 1443_{−6−2}^{+7+3}  68_{−18−9}^{+29+8}  0.87_{−0.14−0.11}^{+0.14+0.14}
0^{−+}  a_{0}(980)π  1416_{−8−5}^{+8+7}  54_{−21−24}^{+37+13}  0.66_{−0.16−0.15}^{+0.17+0.24}
0^{−+}  \overline{K}^{∗}K + c.c. 1490_{−8−16}^{+14+3}  91_{−31−38}^{+67+15}  1.03_{−0.18−0.19}^{+0.21+0.26}

Table 1: J/Ψ radiative decay, MarkIII experiment[37], states, decay modes, masses, widths and branching ratios obtained from the fit Figure 5: J/Ψ radiative decay, MarkIII experiment[37], acceptance-corrected partial wave intensities for 75% of the signal.

MarkIII further confirmed the pseudoscalar presence in J/Ψ → γηπ^{+}π^{−} [43].

In ηππ the situation is more complex with respect to the K\overline{K}π case. The presence of a rising phase space background (see fig. 4 c)) makes the signal identification more difficult. Nevertheless the 0^{−+} contribution appears quite clearly in the PWA analysis (see fig. 6 b),e)). The determined mass and width were M = 1400 ± 6MeV/c^{2} and Γ = 47 ± 13MeV/c^{2}. These values were in agreement with the results obtained in hadroproduction in the ηπ^{+}π^{−} final state[40, 41] (see section 3.2). The measured branching ratio was:

B(J/Ψ → (γη(1400))B((η(1400)

→ a_{0}(980))B(a_{0}(980) → ηπ) = (3.38 ± 0.33 ± 0.64)x10^{−4}

The DM2 experiment at Orsay collected a similar statistics and investigated the same MarkIII channels. In ref.[42] the results of the analysis of J/Ψ radiative decay data into K_{S}^{0}K^{±}π^{∓}, K^{+}K^{−}π^{0}, ηπ^{+}π^{−} and γρ were presented.

About 700 K_{S}^{0}K^{±}π^{∓} events, selecting 1.35 < M_{K_{S}^{0}K^{±}π^{∓}} < 1.6 GeV/c^{2} were used. In addition a similar statistics of K^{+}K^{−}π^{0} events was also used. The K\overline{K}π mass spectrum showed a clearly asymmetric peak, quite similar to that of MarkIII[37] reported in fig.4a). However, the authors explicitly remarked that, despite the fact the K\overline{K}π spectrum could indicate a more complex structure, the possibility that more than one state may contribute to the η(1440) signal was not considered in the analysis.

The conclusion of the analysis of the K\overline{K}π data was that a resonant pseudoscalar state, associated to the η(1440), was identified. Its decay through \overline{K}^{∗}K + c.c. was established. The authors recognized that an important a_{0}(980) decay contribution could also be present Figure 6: J/Ψ radiative decay, MARKIII experiment[43], acceptance corrected intensity distributions using the channel η → γγ: a) 1^{++} a_{0}(980)π; b) 0^{−+} a_{0}(980)π; c) phase space; d)-f) are the same as a)-c) but for the η → π^{+}π^{−}π^{0} channel

but the analysis did not allow to take a definitive conclusion on this aspect.

A signal, at a mass around 1.40 GeV/c^{2} was observed in the J/Ψ → γηπ^{+}π^{−} reaction also[42]. Its mass and width were M = 1398 ± 6 MeV/c^{2} and Γ = 53 ± 11 MeV/c^{2}. The mass (see the spectrum in fig. 7 ) was definitely lower with respect to the results obtained in K\overline{K}π[42]. The difference was such that the authors concluded that the pseudoscalar observed in ηππ was not the same identified in K\overline{K}π (see ref.[42]).

Two years later the DM2 experiment presented a new analysis of their data on J/Ψ radiative decay into K_{S}^{0}K^{±}π^{∓}, K^{+}K^{−}π^{0} and ηπ^{+}π^{−}[38]. It was the same data set of ref. [42], but, this time, the analysis took a different approach and the possibility that more than one state could contribute to the η(1440) signal was considered. As already remarked above, the statistics was similar to that collected by MarkIII and the invariant K_{S}^{0}K^{±}π^{∓} mass spectrum showed an asymmetric shape (see fig. 8 ), similar to the MarkIII data reported in fig. 4 a). Also the analysis approach was similar to that of MarkIII[37]. In the DM2 case, in addition to the K_{S}^{0}K^{±}π^{∓} data, also a K^{+}K^{−}π^{0} data set was available. These data had a lower statistics and a higher background but the results of the PWA were consistent with the K_{S}^{0}K^{±}π^{∓} data. Therefore the two data sets were combined together in a coupled channel analysis. The ηππ data sample was treated separately. The results of their fit are reported in table 2. As in the MarkIII case two 0^{−+} states, decaying one to a_{0}(980)π and the other to \overline{K}^{∗}K + c.c. plus an axial vector decaying to \overline{K}^{∗}K + c.c.were reported. Unlike the MarkIII case the \overline{K}^{∗}K +c.c. decay mode was associated to the lower mass pseudoscalar (M = 1421 ± 14 MeV/c^{2} Γ = 63 ± 18 MeV/c^{2}) and the a_{0}(980)π mode to the higher mass pseudoscalar (M = 1459 ± 5 MeV/c^{2} Γ = 75 ± 9 MeV/c^{2}). The authors recognized a possible feedthrough between the two pseudoscalars and declared that an a_{0}(980)π component, at 25% level, in the lower mass pseudoscalar, was possible. In order to treat the two overlapping pseudoscalars properly, another, more sophisticated, analysis was carried out, allowing the two pseudoscalar waves to interfere. The results of this analysis showed an important destructive interference between the two pseudoscalar Figure 7: J/Ψ radiative decay, DM2 experiment[42], ηππ invariant mass distribution before (a) and after (b) the a_{0}(980)π cut

states and the fit did not describe well the two 0^{−+} signals. According to this analysis the mass and width of the pseudoscalar decaying to a_{0}(980)π were: M = 1410 ± 2 MeV/c^{2} Γ = 41±8 MeV/c^{2} and for the pseudoscalar decaying to \overline{K}^{∗}K +c.c. were: M = 1409±2 MeV/c^{2} Γ = 34 ± 7 MeV/c^{2}. With this solution the pseudoscalar decaying to a_{0}(980)π had mass and width parameters in agreement with the MarkIII result and consistent with the ηππ results [37, 40, 41, 38, 42]. However the authors tended to disfavour this solution because the fit quality was poor.

The J/Ψ → γηπ^{+}π^{−} data were treated separately. The presence of a state with mass and width M = 1385 ± 15 MeV/c^{2} Γ ≈ 50 MeV/c^{2} decaying through a_{0}(980)π observed in the previous analysis[42] was confirmed. The analysis did not enable taking a firm conclusion on the spin assignment: both 0^{−} or 1^{+} solutions were possible. The identification of this state as the lower mass pseudoscalar observed by MarkIII in K\overline{K}π[37] and in hadroproduction in ηππ[40, 41] would have been the natural choice. However the analysis of the K\overline{K}π data in the same paper (see above) and the uncertainties in the spin assignment, prevented the authors from taking any conclusion on this point[38].

In summary the J/Ψ radiative decay analyses of MarkIII[37] and DM2[38] drew two

Amplitude decay

\begin{matrix}Mass \\ (MeV/c^{2}) \end{matrix} \begin{matrix}Width \\ (MeV/c^{2}) \end{matrix}

Branching ; ratio (10^{−3})
1^{++}  \overline{K}^{∗}K + c.c. 1462 ± 20  129 ± 41 0.76 ± 0.15 ± 0.21
0^{−+}  a_{0}(980)π  1459 ± 5  75 ± 9  1.78 ± 0.21 ± 0.33
0^{−+}  \overline{K}^{∗}K + c.c. 1421 ± 14  63 ± 18  0.83 ± 0.13 ± 0.18

Table 2: J/Ψ radiative decay, DM2 experiment[38], states, decay modes, masses, widths and branching ratios obtained from the fit Figure 8: J/Ψ radiative decay, DM2 experiment[38], K_{S}^{0}K^{±}π^{∓} (a) and K^{+}K^{−}π^{0} (b) invariant mass distributions important, contrasting, conclusions:

• they showed evidence for the presence of two pseudoscalars and an axial vector states in the 1.4 ÷ 1.5 GeV/c^{2} mass region

• they showed that the interference due to the resonances’s overlap and the dynamics related to the opening of the K^{∗}(890)\overline{K} threshold around 1.4 GeV/c^{2} made the spin parity assignments and the resonances’s properties classification an extremely difficult task.

In conclusion, the MarkIII and DM2 experiments[37, 38, 43] provided a set of high quality results showing the first hint of a coherent framework to understand the structure of the pseudoscalar and axial vector states present in the 1.4 ÷ 1.5 GeV/c^{2} mass region. Nevertheless, despite the high quality of the collected data, higher statistics, refined analysis methods and further contributions from other production mechanisms appeared to be necessary to achieve a more complete understanding of the E/ι puzzle[56].

A set of new J/Ψ radiative decay data became more recently available with the advent of BES. The main problem with these data is the limited statistics. The J/Ψ → γηπ^{+}π^{−} data[57] provided further confirmation of a pseudoscalar state at a mass M = 1385 ± 5 MeV/c^{2} and width Γ = 34±7 MeV/c^{2} decaying dominantly a_{0}(980)π with a 30% of direct ησ decay. In the case of the K\overline{K}π data the authors reported the presence of one 0^{−+} state only, in the 1.35 ÷ 1.55 GeV/c^{2} mass region[49]. However, as apparent from fig. 9, the available statistics was much lower with respect to the MarkIII or DM2 data[37, 38], about the same level of the old Crystal Ball data[8]. Therefore, despite a more sophisticated and advanced analysis method, the limited statistics was clearly not sufficient to disentangle

Figure 9: J/Ψ radiative decay, BES experiment[49], invariant mass distribution

two pseudoscalars and therefore their results could not improve the understanding of the pseudoscalar signal.

The MARKIII and DM2 experiments searched for the η(1440) also in the 4π and γρ^{0} channels. The MarkIII original analysis of the J/Ψ → γπ^{+}π^{−}π^{+}π^{−} indicated that the η(1440) could account for a fraction of the pseudoscalar component of their ρρ signal, but they did not fit any mass value[58]. The DM2 experiment reported the presence of three pseudoscalars at masses around 1500, 1800 and 2100 MeV/c^{2}[59]. Six different fits, using different Breit-Wigner, phase space and background forms, were applied. The masses and widths assignment were strongly dependent on the fit choice. For the lower mass pseudoscalar the values ranged from 1456 to 1553 MeV/c^{2} for the mass and from 100 to 160 MeV/c^{2} for the widths. The authors considered unlikely the association of this state to the η(1440)[59]. On the PDG[12] the reported values for these DM2 data, estimated from the various fits, are: M = (1489 ± 12) MeV/c^{2} and Γ = (144 ± 13) MeV/c^{2}.

Several years later, Bugg et al.[60], underlined the need to introduce the ππ S-wave into the data analysis both for the DM2 and the MarkIII data. A reanalysis of the MarkIII data was performed showing that the η(1440) contribution was required. The fit results gave a mass and width parameters: M = (1420 ± 20) MeV/c^{2} and Γ = (160 ± 30) MeV/c^{2}[60]. The width was definitely larger with respect to the other measured values[103]. According to the authors such a large width could be ascribed to several reasons. Centrifugal barrier effects, suppressing the amplitude below the ρρ threshold, could make the width due to ρρ not apparent in other decay channels. Also further 0^{−} contributions, from higher masses, not resolved by the fit could contribute to the observed width. It must be noted that also the DM2 fits, for this channel[59], report a large width, whose value is consistent with the results obtained in the analysis of Bugg et al.[60].

The 4π invariant mass distribution fitted by Bugg et al. from the MarkIII data is reported in fig.10. The DM2 spectrum has a similar shape. It is apparent that these data are certainly not the best possible ones for the study of the η(1440) pseudoscalars and it is therefore not surprising if it was quite hard to extract a consistent and solid information from the 4π data.

Figure 10: J/Ψ radiative decay, MarkIII experiment[58], π^{+}π^{−}π^{+}π^{−} invariant mass distribution, fit performed by Bugg et al.[60],

A state at a mass M = 1401 ± 18 MeV/c^{2} and width Γ = 174 ± 44 MeV/c^{2} decaying to γρ^{0} was reported by the DM2 experiment[42]. Also the MARKIII experiment observed a state, with a mass of M = 1432 ± 8 MeV/c^{2} and width Γ = 90 ± 26 MeV/c^{2}, in their analysis of the J/Ψ → γγρ^{0} data[62]. In both cases however the statistics is extremely limited and the analysis could not perform an unambiguous spin assignment. In the DM2 case no partial wave analysis was performed[42] while in the MarkIII case this state could be either a 0^{−+} or a 1^{++} or even a mixture of the two [62].

In conclusion, both J/Ψ → γγρ and γ4π data did not provide clear and unambiguous information on the 4π and γρ decay modes of the η(1440). Even if the identification of a pseudoscalar signal seems asserted, its mass and width parameters remain affected by large incertitude.

MarkIII and DM2 studied also the J/Ψ hadronic decay mode. Differently for the J/Ψ radiative decay the J/Ψ hadronic decay is not expected to produce gluonic states. Both MarkIII[61] and DM2[42] data on J/Ψ → ϕK\overline{K}π and J/Ψ → ωK\overline{K}π did not show any evidence of a ι signal.

3.2 Hadro-production

Peripheral and central hadroproduction contributed with a large, perhaps the largest, set of measurements to the whole light meson spectroscopy sector.

In peripheral hadroproduction a pion or kaon beam interacts with a nucleon target by the one-particle exchange and then moves forward. An excited meson state, decaying further to two or more stable particles, is produced in the forward direction while the recoiling nucleon decays at large angle. A typical parameter is the squared four-momentum exchanged t. For example pion exchange dominates the π^{−}p reaction at small t values. In pion exchange only even^{++} or odd^{−−} states are allowed. In order to produce 0^{−+}states it is necessary to proceed, at higher t values, through neutral 0^{++} or ρ^{+} exchange.

Experimentally, by measuring the momentum of the recoiling nucleon at large angles, it is possible to select different t regions and therefore to access different J^{P C} states for the produced mesons detected in forward direction.

This process is not expected to be particularly sensitive to glueball production since, in this reaction, most momentum goes to quarks rather than to gluons[1].

Experimentally this process is interesting because it allows collecting high statistics and, by the selection on t, it is possible to perform a form of selection on the accessible J^{P C}s.

On the other hand the huge hadronic background and the number of partial waves involved make the work of disentangling the different resonant states present in the mass spectrum a complex task.

While, in peripheral production, the beam and the target particle interact by means of an exchange particle, in central hadro-production the interaction proceeds trough the collision between the exchange particles from beam and target. At high energies this process is dominated by a double pomeron exchange, where the pomerons are considered multi-gluon objects. Therefore a state X, originating from a double-pomeron collision, is expected to have a large gluon content.

Central production is therefore generally believed as a possible source of glueballs[1, 5]. Experimentally the process is selected by requiring the detection of a slow and fast

proton in the process pp → p_{fast}(X)p_{slow}.

The first high statistics study of the E/ι puzzle came from a peripheral hadroproduction experiment at CERN in 1980. In 1980, almost twenty years after its first observation in \overline{p}p annihilation at rest[14], the E(1420) was still considered an unclear object[63]. Originally identified as a J^{P C} = 0^{−+} state[15], its spin assignment was questioned, by several other experiments, in π^{−}p interaction and \overline{p}p annihilation at 0.7 and 0.76 GeV/c[64, 65, 66, 67]. These experiments indicated that the E(1420) was an axial vector rather than a pseudoscalar but their statistics was poor and the data were not as clean as in the case of \overline{p}p at rest[14, 15]. Therefore the question about the nature of the E(1420) stayed open. In 1980 the result of the analysis of more than 3000 π^{−}p → K_{s}^{0}K^{±}π^{∓}n events was presented[16]. The data were obtained using a π^{−} beam of 3.95 GeV/c, incident on the CERN hydrogen bubble chamber. A peak centred at 1430 MeV/c^{2}, immediately associated with the E(1420), appeared quite clear in the K_{s}^{0}K^{±}π^{∓} mass spectrum, even if on a fast rising phase space background (see fig.11). The f_{1}(1285) peak also was apparent in the spectrum. No special t dependence was observed.

The result of the partial wave analysis indicated unambiguously a J^{P C} = 1^{++} assignment for the E(1420)[16]. The decay mode was dominantly \overline{K}^{∗}K + c.c.. It must be remarked that, in these data also, a much higher background level is present with respect to the case of the \overline{p}p at rest[14, 15]. Nevertheless the higher statistics of the π^{−}p[16] data, combined with the cumulative evidence from the other experiments[64, 65, 66, 67], determined a revise of the E(1420) spin assignment that was then identified as an axial vector[10]. This was the reason why, when a pseudoscalar was discovered, a few years Figure 11: π^{−}p → K_{s}^{0}K^{±}π^{∓}n data from π^{−} at 3.95 GeV/c with the CERN bubble chamber[16], K_{s}^{0}K^{±}π^{∓} invariant mass distribution.

Figure 12: π^{−}p → K_{s}^{0}K^{±}π^{∓}n MPS spectrometer data from π^{−} at 8.0 GeV/c [23], K_{s}^{0}K^{±}π^{∓} invariant mass distribution. later at the same mass in J/Ψ decay[8], it was given a different name (see Sect. 3.1) giving rise to the E/ι puzzle.

As shown above central production is expected to favour glueball enhancement. The ι(440) pseudoscalar observed in J/Ψ decay [8], being a glueball candidate [17, 18, 19, 20], was expected to be seen in central production. On the contrary the WA76 experiment at CERN, studying the centrally produced K_{s}^{0}K^{±}π^{∓} system at 85 GeV/c incident momentum, provided strong evidence for a 1^{++} state at a mass M = 1425 ± 2MeV/c^{2} and width Γ = 62±5MeV/c^{2}while the pseudoscalar was not seen[26]. The observed dominant decay mode was \overline{K}^{∗}K + c.c.. This result provided, with higher statistics, a substantial confirmation of the CERN bubble chamber result in peripheral reaction[16].

The controversial state of the E/ι spin assignment motivated further studies, in hadroproduction, by several Brookhaven experiments. The first one studied the K_{s}^{0}K^{±}π^{∓} system using an incident 8 GeV/c π^{−} beam[23]. The statistics was about ten times higher with respect to the previous π^{−}p CERN experiment[16]. The K_{s}^{0}K^{±}π^{∓} mass spectrum showed a clear peak at 1420 MeV/c^{2}(see fig.12).

The mass and width determination: M = 1421 ± 2 MeV/c^{2} Γ = 60 ± 10 MeV/c^{2} were in agreement with the E(1420) ones but the spin parity analysis results indicated that the state was a pseudoscalar with a dominant a_{0}(980)π decay. A contribution could be possible but the pseudoscalar signal was the dominant one. The same experiment performed another measurement, with the same apparatus, using a 300 GeV/c antiproton beam that confirmed these results[25].

Once more the statistics, the analysis approach and the phase space background played a crucial role. The Brookhaven experiments performed a partial wave analysis using 40 MeV bins, while the analysis made by the CERN bubble chamber group[16] and the WA76 experiment[26], was done in one, 100 MeV mass bin. According to the analysis of[23, 25], using one 100 MeV mass bin, the 1^{++} turned out to be as important as the 0^{−+} or even dominant.

The same Brookhaven group made a further study[24] of the K_{s}^{0}K^{±}π^{∓} system, using a statistics three times higher with respect to the previous one[23]. This time the analysis suggested that the η(440) pseudoscalar and the f_{1}(1420) axial vector (in the PDG-86 notation[13]) could be present at the same time.

After the Brookhaven result[23], indicating the pseudoscalar dominance, the WA76 experiment at CERN performed a new data analysis[27]and collected new data with 300 MeV/c incident protons[29]. The 1^{++} state was definitely confirmed. A possible 0^{−+} contribution, at a 14% level, was reported.

In the WA76 papers [27, 29, 28] the analysis model adopted by the Brookhaven experiment [23, 25, 24] was criticized. In particular it was remarked that, because of the incoherent K^{∗}production and the large background present in the data, the analysis performed in [23, 25, 24] could have easily confused a 1^{++} state with a 0^{−+} state decaying to a_{0}(980)π and \overline{K}^{∗}K + c.c..

In the following years further central production data, from the WA76 and WA102 experiments at CERN, confirmed the f_{1}(1420) axial vector dominance, decaying to \overline{K}^{∗}K+ c.c., and excluded a 0^{−+} contribution in the 1.4 ÷ 1.5 GeV/c^{2} mass region [69, 70, 71, Figure 13: π^{−}p → K_{s}^{0}K_{s}^{0}π^{0}n data from π^{−} at 20 GeV/c at Brookhaven[36], K_{s}^{0}K_{s}^{0}π^{0}invariant mass distribution.

72, 73].

Having asserted the presence of the f_{1}(1420) axial vector several open issues remained on the η(1440) pseudoscalar.

In 1986 a model was presented suggesting that the ι(1440) (η(1440)) could hide two, overlapping, pseudoscalar states[35]

In 1989 the E769 experiment at Brookhaven presented an analysis indicating that, possibly, two pseudoscalars were present in the K_{s}^{0}K_{s}^{0}π^{0} mass spectrum[36].

The K_{s}^{0}K_{s}^{0}π^{0} mass spectrum, obtained from π^{−}p → K_{S}^{0}K_{S}^{0}π^{0}n at 21.4 GeV/c incident momentum at Brookhaven showed a complex structure . A selection on the momentum transfer t > 0.2GeV/c was applied to enhance the pseudoscalar component around 1.45 GeV/c^{2}. Both the best fit of the K_{s}^{0}K_{s}^{0}π^{0} mass spectrum (see fig.13) and the amplitude analysis indicated that two pseudoscalars could be present, one decaying to a_{0}(980)π, with mass M_{1} = 1412.8 ± 5.4 MeV/c^{2} and width Γ_{1} = 19.0 ± 7.0 MeV/c^{2}, and another one decaying to and \overline{K}^{∗}K + c.c., with mass M_{2} = 1475.0 ± 3.8 MeV/c^{2} and width Γ_{2} = 50.6 ± 12.7 MeV/c^{2}[36]. Even if the statistics severely limited the significance of the two pseudoscalars a single resonance fit led to a poor χ^{2} and an abnormally large resonance width. As the author themselves noted, the two pseudoscalar solution fitted much better with the other experimental results.

It must be noted that the K_{s}^{0}K_{s}^{0}π^{0}system is a pure C = +1 eigen-state. Therefore these data fixed, in a direct way, the η(1440) state(s) C-parity.

About twenty years later, another Brookhaven experiment studied, with high statistics the π^{−}p → K_{S}^{0}K^{±}π^{∓}n reaction with 18 GeV incident beam. About 20000 K_{S}^{0}K^{±}π^{∓} events, with momentum transfer |t| < 0.1GeV/c^{2}, were selected for the partial wave analysis. The partial wave analysis was performed binning the K_{S}^{0}K^{±}π^{∓} mass using 20 MeV/c^{2} intervals. Independent fits were performed at each bin. Different wave sets were used to describe the data above and below the K^{∗}\overline{K} threshold. The analysis indicated the simultaneous presence of the f_{1}(1420) axial vector and of two pseudoscalar states, corresponding to the η(1405) and the η(1475) (using the PDG-04 notation). Masses, widths and decay modes are reported in table 3.

The significance for the η(1475) was checked by comparing the fits with and without this state. Without the η(1475) the fit deteriorates (χ^{2}/d.o.f. increases from 1.07 to 1.38) and the η(1405) mass increases to 300 MeV/c^{2}. It must be noted that a small K^{∗}\overline{K} + c.c. was found in the η(1405) decay mode. Its fraction with respect to the a_{0}(980)π mode was

\frac{BR(η(1405)→K^{∗}\overline{K}+c.c.)}{BR(η(1405)→a_{0}π)} = 0.084 ± 0.024_{stat} The relative weight, in the K^{∗}\overline{K} + c.c. decay mode, of the η(1405) and the η(1475)

was also measured:

\frac{BR(η(1405)→K^{∗}\overline{K})}{BR(η(1475)→K^{∗}\overline{K})} = 0.16 ± 0.04_{stat}

Several peripheral hadroproduction experiments studied the ηππ final state. The f_{1}(1420) decay proceeds through \overline{K}^{∗}K + c.c.; this point has been verified by many experiments. The ηππ final state presents the advantage of enabling the study of the η(1440) pseudoscalar contribution , without the interference of the f_{1}(1420). Moreover, since the higher mass pseudoscalar, the η(1475) quoted above, appears to decay through \overline{K}^{∗}K + c.c. only, it does not contribute to the ηππ final state. For these reasons ηππ is the ideal environment to study the η(1440) lower mass component, the η(1405).

The π^{−}p → ηπ^{+}π^{−}n reaction with an incident beam momentum of 8.06 GeV/c was studied at KEK with the purpose of searching the η(1440) in the ηππ final state. The η(1440) signal was very well identified. A shoulder in the 1.4 GeV/c^{2} mass region was already visible in the ηππ mass spectrum. It became particularly evident selecting the a_{0}(980)π region in the ηπ effective mass, 0.95 < M_{ηπ} < 1.01 GeV/c^{2}, (see fig.15).

The η(1440) was then unambiguously identified in the partial wave analysis in the 0^{−} → a_{0}(980)π wave, both in the intensity distribution (see fig.16) and in the phase motion plot (see fig.17). The fitted mass and width were: M = 1420 ± 5 MeV/c^{2}and width Γ = 31 ± 7 MeV/c^{2}.

In the mass region around 1.3 GeV/c^{2} the f_{1}(1285) and the η(1285) were also identified (see figures 16,17). No signal of an axial vector in the 1.4 ÷ 1.5 GeV/c^{2} mass region was

Amplitude  decay  \begin{matrix}Mass \\ (MeV/c^{2}) \end{matrix}  \begin{matrix}Width \\ (MeV/c^{2}) \end{matrix}
1^{++}  \overline{K}^{∗}K + c.c.  1428 ± 4 ± 2 38 ± 9 ± 6
0^{−+}  a_{0}(980)π − \overline{K}^{∗}K + c.c 1416 ± 4 ± 2 98 ± 18 ± 3
0^{−+}  \overline{K}^{∗}K + c.c.  1485 ± 8 ± 5 98 ± 18 ± 3

Table 3: π^{−}p → K_{S}^{0}K^{±}π^{∓}n, at 18 GeV E852 experiment[51], resonance parameters and decay modes Figure 14: π^{−}p → K_{S}^{0}K^{±}π^{∓}n data from π^{−} at 18 GeV E852 experiment[51], π^{−}p → K_{S}^{0}K^{±}π^{∓}n, at 18 GeV E852 experiment[51], results of mass-independent fits (points) and mass-dependent fits (lines) for (a) 0^{−+} [a_{0}(980)π] S0^{+} intensity, (b) 1^{++} [K^{∗}(892)] S0^{+} intensity; and (c) phase difference between (a) and (b), (d) 0^{−+} [K^{∗}(892)] P 0^{+} intensity,

(e) 1^{++} [K^{∗}(892)] S0^{+} intensity, and (f) phase difference between (d) and (e).

Figure 15: π^{−}p → ηπ^{+}π^{−}n data from π^{−} at 8.06 GeV/c at KEK[40], (a) raw mass spectrum for the ηππ system, (b) mass spectrum for the ηππ above 1.1 GeV with a δ cut [0.95 GeV < M(ηπ) < 1.01 GeV].

found, in agreement with the \overline{K}^{∗}K + c.c. decay mode of the f_{1}(1420). The identification of a pseudoscalar η(1440) signal in the ηππ final state from peripheral hadroproduction was further confirmed at KEK [41], Protvino[74] and Brookhaven[75].

This state is now associated to the η(1405), whose dominant decay modes are a_{0}(980)π or direct ηππ and K\overline{K}π[12]. The η(1405) is the lower mass component of the η(1440) in the previous notation [11].

In summary, central and peripheral hadroproduction provided an enormous amount of experimental results. Despite the sometime controversial nature of the provided information, the following points can be taken.

• central production identified unambiguously the f_{1}(1420), with \overline{K}^{∗}K + c.c. as decay mode. None of the η(1440) pseudoscalars was observed in this production mechanism

• peripheral hadroproduction in ηππ identified quite well the η(1405), the lower mass component of the η(1440), with dominant a_{0}(980)π decay mode

• peripheral hadroproduction in K\overline{K}π represents the greatest number of experimental data and also the most controversial. Limitations due to the statistics (in the case of the older experiments) and even more, the fast increasing phase space background and the contributions for many partial waves to be disentangled, made the analysis task extremely complex. It took more than two decades to establish that, both the two pseudoscalars, η(1405), η(1475), and the axial vector f_{1}(1420), are produced (and observed), in the K\overline{K}π final state, from peripheral hadroproduction[51].

Figure 16: π^{−}p → ηπ^{+}π^{−}n data from π^{−} at 8.06 GeV/c at KEK[40], intensity distributions of the labeled partial waves. Intensities are plotted by summing up in every 20-MeV bin. The solid lines are the Breit-Wigner fit.

Figure 17: π^{−}p → ηπ^{+}π^{−}n data from π^{−} at 8.06 GeV/c at KEK[40], phase variations of the labeled partial waves. (a-c) Effective-mass region around 1.28 GeV. (d),(e) Effectivemass region around 1.42 GeV. The solid lines are the Breit-Wigner fit.

3.3 Two-photon collision

Two-photon collision has the peculiar characteristics of acting as a spin filter. Because of the Yang theorem[76] two real photons cannot couple to a spin 1 resonance. The process takes the form e^{+}e^{−} → e^{+}e^{−}γ^{∗}γ^{∗} → e^{+}e^{−}R, where R is the resonance produced. In order to produce a spin 1 resonance the two photons need to be virtual. A highly virtual photon is characterized by a large q^{2}(where q is the photon four-momentum) and will be associated to a e^{±} scattered at sufficiently large angle to allow detection. Experimentally, the detection of the associated e^{±} (tagging) implies that the photon will be highly virtual. In that case J = 1 resonances can be produced. In conclusion tagged data can contain spin 1 resonances while these are not allowed in the ”untagged” data sample.

Moreover, being SU(3) singlets, glueballs do not carry charge, therefore they do not couple directly to photons. Therefore glueballs are expected not to be produced in γγ collision.

Several experiments studied the K\overline{K}π final state in γγ collision with the MarkII[77], the TASSO[78], the TPC/2γ [30], the MARKIII[32] and the CELLO[79] detectors.

All of them agreed in observing a signal, at a mass of 1420 MeV/c^{2}, in the tagged data sample, where spin 1 and spin 0 states are allowed, and no signal in the untagged data sample, where spin 1 objects are forbidden.

This allowed to conclude that the observed state was a spin one object, associated to f_{1}(1420), and enforced the hypothesis that the ι(1440) was a glueball candidate.

The γγ data in the ηππ final state[31, 33, 80] confirmed the suppression of the ι(1440) production in γγ collision .

Many years later, the L3 experiment at LEP, studied the K\overline{K}π and ηππ final states from γγ collision[50]. In the untagged data sample they observed a signal, decaying \overline{K}^{∗}K + c.c., consistent with the η(1475), in the K\overline{K}π channel, while no signal, around the η(1405) mass, was observed in ηππ. The Γ_{γγ} width observed for the η(1475) was consistent with the expectations for a 2^{1}S_{0} s\overline{s} state[6].

This result provided indirect, but very important and clear evidence for the existence of two pseudoscalars in the η(1440). In addition it provided further indication of a large gluonic content for the η(1405).

3.4 Antiproton-proton annihilation

Antiproton-proton annihilation at rest is considered an environment where glueball production can be specially favoured. Through the annihilation process quarks, antiquarks and gluons, originating from the two \overline{q}q pairs are present. Under these conditions there is a chance to give rise to gluonic states.

Antiproton-proton annihilation at rest has necessarily limited accessible phase space but, on the other hand, presents the enormous advantage of involving only S and P waves. Higher angular momentum states do not contribute because of the negligible overlap of the proton and antiproton wave functions for l > 1. This leads to much simplified analysis conditions because it constraints the initial state and, as a consequence, the accessible final states. Moreover the relative S and P wave fraction is a function of the target density. This mechanism, is related to the antiproton capture process. An antiproton brought at rest in a hydrogen target forms a \overline{p}p atom (protonium) in a highly excited state. The protonium undergoes a cascade process until it reaches a low n level. The annihilation occurs when the transition width from one level to the lower one is smaller than the \overline{p}−p wave functions overlap. This occurs (see above) on the P level. In an ideal case of an isolated atom all annihilations should occur from P-states. In practice chemical effects as Auger and Stark induced transitions determine a mixing among the S and P states changing the level populations and in another way the annihilation probability. These effects depend on the number of collisions of the protonium atom with the surrounding medium, hence on the target density. In liquid hydrogen this effect is maximum and it is such that the annihilation occurs dominantly form S-states. This effect is known as Day-Snow-Sucher mechanism[81]. As the density decreases, and the number of collisions reduces, the annihilation from P-states becomes more important.

In summary, using a liquid hydrogen target, one selects mainly S wave annihilation, introducing a further constraint on the final states and, as a consequence, on the analysis.

The accessible phase space, limited to two times the proton mass, has another interesting implication. In the process \overline{p}p → η(1440)ππ the η(1440) recoils almost at rest because of the limited available energy. It is therefore natural to expect a relative angular momentum L between the η(1440) and the dipion system equal to 0. Since the ππ system invariant mass is less than 500 MeV/c^{2}, contributions for higher waves is unlikely in this case also and its relative angular momentum l should also be 0. This aspect has been experimentally verified on the η(1440) − ππ, and ππ angular distributions (see refs. [34, 44, 82]). The assumption L = l = 0 implies that the production of η(1440), which has also spin 0, should occur from the ^{1}S_{0} initial state. For f_{1}(1420) the available initial state is ^{3}P_{1}.

In summary \overline{p}p annihilation at rest presents as a powerful tool for the study of the E/ι case, since in liquid hydrogen the axial vector is suppressed and the pseudoscalar states can be studied in a cleaner environment. Moreover since the η(1440)ππ system can come from the ^{1}S_{0} initial state only, the analysis is further simplified. By decreasing the target density and studying annihilation in gas the η(1440) contribution decreases and the f_{1}(1420) should be observed.

After these considerations it is not surprising if the first observation of the E meson, in \overline{p}p → K_{s}^{0}K^{±}π^{∓}π^{+}π^{−}, more than forty years ago[14], was so clean despite the reduced statistics. Also the spin parity analysis, performed on the same data a few years later[15], could be done, notwithstanding the poor statistics, thanks to the high quality of the data and to the simplified analysis conditions in \overline{p}p at rest. The analysis enabled identifying the E as a pseudoscalar decaying 50% to \overline{K}^{∗}K + c.c. and 50% to a_{0}(980)π. At that time the a_{0}(980) was not yet known but it was observed that the (\overline{K}K) system resonated around 1 GeV/c^{2}. The E(1420) was discovered. Its mass and width parameters were: M = 1425 ± 7 MeV/c^{2} and width Γ = 80 ± 10 MeV/c^{2}.

However for several years the E(1420) was still considered an unclear object[63]. Its spin assignment was questioned, by several other experiments, in π^{−}p interaction and \overline{p}p annihilation at 0.7 and 0.76 GeV/c^{2}[64, 65, 66, 67, 16]. All these experiments showed an enhancement corresponding to the E(1420) but their analysis indicated the state was an axial vector. Finally this led to the identification of the E(1420) as a 1^{++} state[10] (see Sect. 3.2).

Despite the excellent conditions, in \overline{p}p annihilation at rest, to study the E(1420) nature, it took more than 20 years, since the first measurement, before other data were taken. The main reason was the absence of suitable antiproton beams. The advent of the Low Energy Antiproton Ring (LEAR) at CERN made a quantum leap possible. First the Asterix experiment studied the E(1420) production in \overline{p}p annihilation at rest with a gaseous target at NTP[34]. Here we follow the authors[34] notations who used the original name as in bubble chamber data[15]. The studied final state was (K^{0})_{miss}K^{±}π^{∓}π^{+}π^{−}. The statistics was limited and the background important (37%) because of the missing kaon. A spin parity analysis was therefore not possible, even if a clear enhancement at mass M = 1413 ± 8 MeV/c^{2} and width Γ = 62 ± 16 MeV/c^{2} was observed. The authors measured the branching ratio B(E → K_{L}^{0}K^{±}π^{∓}) and from its scaling from liquid hydrogen, they inferred it was a 0^{−+} state. The argument was that the branching ratio was about a factor two lower with respect to the bubble chamber data[15], in agreement with the estimated decrease of the ^{1}S_{0} annihilation fraction going from liquid hydrogen to gaseous hydrogen at NTP. Taking the assumptions above, i.e. that a 0^{−+} E(ππ) should be produced from ^{1}S_{0} states only, the obtained results were considered a proof of the pseudoscalar nature of the E(1420).

The Asterix results[34] were limited by the statistics and the poor selectivity on the final state but they opened a promising path to study the E/ι case.

Two second generation LEAR experiments, Crystal Barrel and Obelix, later performed, a detailed study of the E/ι production from \overline{p}p annihilation at rest, the first one in ηππ and the second one in K\overline{K}π final states.

The Crystal Barrel experiment studied the ηπ^{+}π^{−} and the ηπ^{0}π^{0} decay modes of the η(1440) in liquid hydrogen[39, 85] and also in gaseous hydrogen at 12 bar[85]. The η(1440) signal was observed (see fig.18) and the spin parity analysis established it was a pseudoscalar state decaying partially through a_{0}(980)π and partially through direct η(ππ)_{S} (where (ππ)_{S} indicates an S-wave dipion). Its mass and width parameters were: M = 1409±8 MeV/c^{2} and width Γ = 86±10 MeV/c^{2}[39]. These mass and width values are in agreement with the other results in ηππ from J/Ψ decay[42, 43] and hadroproduction[40, 41, 74, 75] (see Sect. 3.1,3.2).

Therefore, with the contribution of \overline{p}p annihilation at rest[39], the ηππ data present a fairly consistent picture for the low mass component of the η(1440)(see Sect. 4 below).

The Obelix experiment studied the process \overline{p}p → (E/ι → K\overline{K}π)ππ using different target densities. As discussed above, the power of this method has been shown by the Asterix experiment[34]. With Obelix the use of different target densities became a tool to perform a detailed study of the E/ι pseudoscalar and axial vector components[86].

Annihilation from S-states dominates in liquid hydrogen. Since, in the \overline{p}p → (E/ι → K\overline{K}π)ππ process, a 1^{++} state can be produced from ^{3}P_{1} states only, the f_{1}(1420) produc-Figure 18: \overline{p}p → π^{+}π^{−}π^{0}π^{0}η data at rest in liquid hydrogen, Crystal Barrel experiment[39], ηπ^{0}π^{0} (a) and ηπ^{+}π^{−} (b) invariant mass distributions after removal of the π^{0}ηω and π^{0}ηη

tion is suppressed in liquid hydrogen. This environment is therefore the best one to study the pseudoscalar component. Obelix first studied the same channel as Asterix, namely the final state (K^{0})_{miss}K^{±}π^{∓}π^{+}π^{−} [44]. The statistics was about ten times higher and allowed to report evidence for two pseudoscalar states, with masses M_{1} = 1416±2 MeV/c^{2}, M_{2} = 1460 ± 10 MeV/c^{2} and widths Γ_{1} = 50 ± 4 MeV/c^{2}, Γ_{2} = 105 ± 15 MeV/c^{2}. The first resonance was found to decay dominantly to K\overline{K}π and partially to a_{0}(980)π. The higher mass resonance was found to decay through \overline{K}^{∗}K + c.c.. The presence of two pseudoscalars was definitely required by the fit, however the result suffered from several limitations:

• the channel with a missing kaon, was characterized by a sizeable background (as in the Asterix case)

• the evidence for the second resonance was affected by the \overline{K}^{∗}K threshold and by the limited phase space.

The \overline{K}^{∗}K system has a threshold located at 1390 MeV/c^{2} and its width has a strong energy dependence (see. fig.19). This effect can artefact the second resonance, either because of direct K^{∗}(890) production or because the lower mass resonance has a \overline{K}^{∗}K+c.c. decay mode that is distorted by the \overline{K}^{∗}K threshold. The problem has been known for years and is common to all the results concerning the second pseudoscalar resonance.

A second data set was taken by Obelix, in liquid hydrogen, in the channel K_{S}^{0}K^{±}π^{∓}π^{+}π^{−}[45]. This time all particles were identified, the vertex definition improved, the was background negligible and the statistics much higher. The improvement in the data quality is apparent in fig.20 . In the new data set the K^{∗}(890) bands are much cleaner and more visible. The K\overline{K}π invariant mass distribution (fig.21) is very clean and resembles closely that of the first bubble chamber experiment[14], but the statistics is an order of magnitude higher and the asymmetric peak, as in the MarkIII case[37], suggests a complex structure.

A much refined analysis, with respect to ref.[44], based on a Flattè form allowing energy dependent partial widths was employed. This approach allowed to take into account the effect of the \overline{K}^{∗}K threshold and its fast rising width. The analysis confirmed the existence of two pseudoscalars one decaying dominantly to K\overline{K}π and the other through \overline{K}^{∗}K + c.c.[45]. The hypothesis that the second resonance could be an artefact due to the \overline{K}^{∗}K threshold and its energy dependent width was ruled out. This point was further confirmed from the study of the \overline{p}p → (E/ι → K^{+}K^{−}π^{0})π^{+}π^{−} process[47]. Here fig.22 clearly shows the K^{∗}(890) signal in the charged K^{±}π^{0} invariant mass while the signal is absent in the neutral K^{±}π^{∓} combination. This provides a strong indication that all the K^{∗}(890) production originates from the E/ι, namely the η(1475) or the f_{1}(1425) and is absent or negligible in direct production. Therefore direct K^{∗}(890) production cannot be responsible for artefacting the η(1475).

The analysis of ref. [45] provided two solutions, equivalent from the fit point of view. In both solutions two pseudoscalars were required. In the first solution the masses and widths of the two pseudoscalars are as follows: M_{1} = 1405 ± 5MeV/c^{2}, Γ_{1} = 50 ± 4 MeV/c^{2}, M_{2} = 1500 ± 10 MeV/c^{2}, Γ_{2} = 100 ± 20 MeV/c^{2}. The lower mass pseudoscalar decays dominantly to K\overline{K}π and the higher mass one to \overline{K}^{∗}K + c.c..

In the second solution the parameters of the first resonance stay unchanged while the second resonance has a higher and undetermined mass and width: M_{2} = 1700 ÷ 1800 MeV/c^{2}, Γ_{2} = 100 ÷ 400 MeV/c^{2}. Moreover, with this solution, the low mass pseudoscalar has a sizeable \overline{K}^{∗}K + c.c. decay mode, at the same level as the direct K\overline{K}π decay component, while the higher mass pseudoscalar takes a sizeable K\overline{K}π decay mode. One could not discriminate, between the two solutions, on the basis of the fit results, but the first solution was retained and the second solution discarded since the mass and width of the second pseudoscalar and the decay modes of both two pseudoscalars were in total disagreement with the available results, both from \overline{p}p at rest and from the other production mechanisms.

In conclusion the analysis of ref.[45] provided definite evidence for the presence of two pseudoscalars, in the 1.4 ÷ 1.5 GeV/c^{2} mass region with parameters in substantial agreement with the J/Ψ MARKIII data[37], the hadroproduction data of ref.[36, 51] and the previous Obelix \overline{p}p results[44].

The Obelix experiment collected data also using a hydrogen gas target. In this case P-states annihilation is present roughly at the same level as S-states annihilation. The (K^{0})_{miss}K^{±}π^{∓}π^{+}π^{−} [46] and the K^{+}K^{−}π^{+}π^{−}π^{0}[47] final states were studied. Evidence for the f_{1}(1425) produced from P-states annihilation was reported. The presence of the two η(1440) pseudoscalars was also confirmed, even if the sensitivity to the pseudoscalars states was not as good as in the liquid hydrogen data since the analysis was more complex because of the additional contributing initial and final states.

A further study of the dependence of the η(1440) production from the initial \overline{p}p states, using three different target densities was also performed[48]. It showed a clear correlation between the η(1440) production rate and the annihilation fraction from ^{1}S_{0} \overline{p}p state.

Figure 19: Partial widths as function of M_{K\overline{K}π} (normalized at M_{K\overline{K}π} = 1405 MeV/c^{2}) from ref.[45]

4 Towards a coherent framework

It is not easy (to some extent impossible) to find a perfect agreement among so many experimental results, spanning a period of four decades. Albeit difficult, there are sufficient elements to aim at a coherent picture where at least most of the data can be accommodated in a consistent way. The f_{1}(1425) state has been considered established a long time ago [10]. It has been observed in all production mechanisms: J/Ψ decay, peripheral and central hadro-production, \overline{p}p annihilation at rest and γγ collision.

It decays to \overline{K}^{∗}K + c.c. and it is therefore not observed in the ηππ final state.

The ηππ final state is the best environment to study the low mass pseudoscalar, namely the η(1405), because both the f_{1}(1425) and the η(1475) are absent. As apparent from table 4 the ηππ data represent quite a coherent data set. The η(1405) is observed, in the ηππ final state, in J/Ψ decay, peripheral hadro-production and \overline{p}p annihilation at rest. It is not observed in γγ collision and this has been one of the arguments for being a gluonium candidate. The reported mass and width parameters are in good agreement, the absence of the f_{1}(1425) and the η(1475) make this data set the best one to determine the η(1405) mass parameters.

Concerning the decay modes both the a_{0}(980)π and direct η(ππ)_{S} decays (where (ππ)_{S} indicates an S-wave dipion) have been observed. It must be noted that, in the cases where the η(ππ)_{S} decay is not quoted, this decay hypothesis was simply not tested in the analysis.

The K\overline{K}π final state is definitely more rich and complex. Potentially all the three states are present and the task of identifying and disentangling them is difficult. However looking at table 5 it is possible to remark that, the combined data, coming from the different production mechanisms, allow extracting a coherent picture.

The low statistics experiments normally identify either only one of the two pseudoscalars, or the axial vector, according to the production mechanism. Table 6 reviews Figure 20: \overline{p}p → K^{0}K^{±}π^{∓}π^{+}π^{−}[45], 6 prong folded Dalitz plot (a), 4 prong folded Dalitz plot (b)

Figure 21: \overline{p}p → K^{0}K^{±}π^{∓}π^{+}π^{−}[45], K\overline{K}π invariant mass and double charge combination (a), K\overline{K}π invariant mass without combinatorial background (b)

Figure 22: \overline{p}p → K^{+}K^{−}π^{+}π^{−}π^{0}[47], charged (a) and neutral (b) Kπ invariant mass spectra for the full and reduced (without η and ω) data samples.

these results for the η(1440). Looking at the table it is possible to verify that these results refer either to low statistics data, or to earlier results updated by the same experiments, as in the case of E769 [36], DM2 [42, 38] and E852 (MPS) [23, 24, 25, 51] (see also table 5).

However if one retains the high statistics experiments only, one can observe a consistent picture where two pseudoscalars: the η(1405) and the η(1475), and one axial vector: the f_{1}(1425) are identified.

The mass and width parameters are also in good agreement.

The η(1405) has the following dominant decay modes: a_{0}(980)π and direct ηππ or K\overline{K}π. The η(1475) decays dominantly through \overline{K}^{∗}K + c.c..

The DM2 experiment only, reports opposite decay modes for the η(1405) and the η(1475). It must be noted that, in their article [38], the DM2 collaboration presented an alternative solution, where the lower mass pseudoscalar decays to a_{0}(980)π and the higher mass pseudoscalar decays to \overline{K}^{∗}K + c.c.. This solution was not retained because it gave poorer fit with respect to the other one.

The quantitative results for the branching ratios are not in good agreement. Several elements can play a role in these differences: the presence of both the \overline{K}K threshold at the a_{0}(980) mass and the \overline{K}^{∗}K threshold at 1390 MeV certainly make the K\overline{K}π channel more complicate to analyze and can affect, in different ways, the results from different production mechanisms.

The most relevant results, from high statistics experiments, are listed below, according to the production mechanism.

• Central hadroproduction experiments do not observe any of the two pseudoscalar states. A possible, small, pseudoscalar contribution was considered in one of the earlier WA76 analysis[29] but it was later excluded [69, 70, 71, 72, 73] Only the f_{1}(1425) axial vector is observed, this is therefore the best environment to establish its parameters.

• Antiproton-proton annihilation at rest in liquid hydrogen provides the reverse situation. Here the f_{1}(1425) production is suppressed, it is therefore possible to perform a better study of the η(1405) and the η(1475) pseudoscalars[44, 45]. By moving from liquid to gaseous hydrogen target both the pseudoscalars and the axial vector have been observed but the η(1405) and the η(1475) measurement became less precise [46, 47].

• J/Ψ radiative decay data from MarkIII[37] and DM2[38] report the observation of two pseudoscalars and an axial vector but DM2 results disagree on the decay modes: according to the MARKIII analysis the lower mass pseudoscalar decay dominantly to a_{0}(980)π, while the higher mass pseudoscalar decays through \overline{K}^{∗}K+c.c.. However the DM2 analysis provided also a second solution with a better agreement with the MARKIII results.

• Peripheral hadroproduction is one of the most difficult cases, because of the overlapping contribution of several waves. Nevertheless two Brookhaven experiments, E769 in 1989[36] and E852 in 2001[51], were capable of disentangling the different contributions and of identifying two pseudoscalars and an axial vector.

• in γγ collision, the L3 experiment[50], observed only one state, compatible with the η(1475), while no signal was observed in the ηππ final state (see table 4).

The f_{1}(1425) existence has been established a long time ago. The existence of two pseudoscalar states has been questioned for many years. From the list above it appears that the existence of the η(1405) and the η(1475), their mass and width parameters and their main decay modes are consistently supported by six experiments, in four different production mechanisms (with the exception of DM2 for the decay modes).

In addition, all the experiments that studied the ηππ final state, provide indirect support to this picture (see 4) since they consistently observed one state, with the mass and with parameters in agreement with the η(1405), whose decay modes are compatible with the observation in the ηππ final state. None of the ηππ experiments observes a signal of the η(1475), in agreement with the K\overline{K}π experiments, that report a \overline{K}^{∗}K + c.c.decay mode for this state.

5 Conclusions

In summary we can consider established, in place of η(1440), two pseudoscalar resonances: η(1405), decaying dominantly through a_{0}(980)π or direct ηππ/K\overline{K}π and η(1475), decaying dominantly through \overline{K}^{∗}K + c.c..

Assuming the η(1295) the first radial excitation of the η, one of these two pseudoscalars could be the η′ first radial excitation. This state should be mainly s\overline{s}, assuming ideal mixing, as suggested by the η(1295) and the π(1300) mass degeneracy. The η(1475), with its \overline{K}^{∗}K + c.c. coupling is therefore the natural choice. This assignment is further confirmed by the fact that also its width matches the expected width for the radially excited s\overline{s} state [6, 90, 87].

The nature of the η(1405) still remains an open question. Since the discovery of a pseudoscalar state in this mass region the glueball hypothesis was claimed [17, 18, 19, 20]. If we consider the gluonium signatures discussed in the introduction, we can see that the η(1405) fulfils most of the requirements.

A) The existence of the η(1475) makes the η(1405) an ”extra” state, i.e. it does not fit within the corresponding J^{P C} nonet.

B) The results of the γγ collision experiments have shown the η(1405) coupling to photons is suppressed.

C) The sizeable direct ηππ/K\overline{K}π coupling represent another hint of a large gluonium content.

D) The outstanding production in a gluon rich mechanism, as J/Ψ radiative decay, completes the features for a gluonium candidate.

For a long time now, the combined information from γγ collision and J/Ψ radiative decay data, has been employed as an indication of a state gluonium nature. The concept of stickiness (S_{R}) developed by Chanowitz[20], related, for a resonance R, the resonance’ s width in J/Ψ radiative decay to its γγ coupling:

S_{R} = \frac{Γ(J/Ψ→γR)X_{LIP S}(R→γγ)}{Γ(R→γγ)X_{LIP S}(J/Ψ→γR)}

(where LIPS denotes the Lorentz-invariant phase space).

This formula, applied to the η(1440), returned a stickiness value more than ten times higher than the η(547).

This procedure has been by extended and quantified by Close, Farrar and Li [90] who made an estimate of the gluonium content of isosinglet mesons using their radiative quarkonium production rates. This approach is based on the relationship proposed by Cakir and Farrar [91] and leads to calculate the branching fraction to gluon of a resonance R: B(R → gg), from its branching fraction in radiative quarkonium decay. B(R → gg) is expected to be 0.1÷0.2 for a q\overline{q} state and 1 for a glueball.

According to this procedure the η(1405) branching fraction to gluon is 0.9 ± 0.2 [90]. The η(547), η′(958) and η(1405), gluonium-quarkonium mixing framework has been

studied by different authors [90, 92, 93, 94, 95, 96], who compared their models with the data obtained from J/Ψ decay into vector and pseudoscalar mesons and the data on pseudoscalar and vector meson two-photon decays. All of them agree in assigning a dominant gluonium component to the η(1405).

One of the most recent studies, by Li, Ma and Yu[96], indicated the η(1405), is mainly a glueball state, with about 78% glueball component[96].

However, despite all these elements, indicating a strong gluon content for the η(1405), the glueball interpretation is disfavored by lattice calculations, which predict, for the pseudoscalar glueball, a mass above 2 GeV[88, 89].

For this reason alternative hypotheses have been suggested. The η(1405) properties are consistent with predictions for a gluino-gluino bound state [91, 97, 98]. Within this framework the 0^{++} glueball would be in a supermultiplet with the pseudoscalar gluinogluino and the spin 1/2 gluino-gluino bound states.

In addition, it must be considered that, other models, based on gluonic fluxtubes[99], predict a mass, for the pseudoscalar glueball, almost degenerate with that of the 0^{++} glueball and compatible with the η(1405) mass.

Despite the difficulties, that still persist, in understanding the nature of the η(1405), we can now, after forty years, thanks to the cumulative effort of so many experiments, draw a consistent experimental picture for the E/ι case. It is amazing to observe how the study of the E/ι has followed the steps of the experimental progress in light quark spectroscopy. Its story, spanning a period of over 40 years, has developed in parallel with the experimental techniques, from the bubble chambers to the LEP era, and represents a sort of paradigm of the experimental effort in light quark spectroscopy.

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Production mechanism Experiment

\begin{matrix}Mass \\ (MeV/c^{2}) \end{matrix}

\begin{matrix}Width \\ (MeV/c^{2}) \end{matrix}

Decay modes

π^{−}p[40]  BENKEI  1420 ± 5  31 ± 7  a_{0}(980)π
π^{−}p[41]  BENKEI  1388 ± 4  31 ± 7  a_{0}(980)
π^{−}p[74]  GAMS  1424 ± 6  85 ± 18  a_{0}(980)
π^{−}p[75]  MPS  1404 ± 6  80 ± 21  a_{0}(980)
J/Ψ rad.[42]  DM2  1398 ± 6  53 ± 11  a_{0}(980)π
J/Ψ rad.[43]  MARKIII  1400 ± 6  47 ± 13  a_{0}(980)
\overline{p}p at rest[39] CRYSTAL BARREL 1409 ± 3  86 ± 10  a_{0}(980) & ηππ

Table 4: Summary of results on the η(1405) pseudoscalar in the ηππ final state Production mechanism Experiment State

\begin{matrix}Mass \\ (MeV/c^{2}) \end{matrix} \begin{matrix}Width \\ (MeV/c^{2}) \end{matrix}

Dominant decay mode

π^{−}p[36]  E769  \begin{matrix}η(1405) \\ η(1475) \end{matrix}  \begin{matrix}1413 ± 5 \\ 1475 ± 4 \end{matrix}  \begin{matrix}19 ± 7 \\ 51 ± 13 \end{matrix}  \begin{matrix}a_{0}(980)π \\ \overline{K}^{∗}K + c.c. \end{matrix}
π^{−}p[51]  E852 (MPS) \begin{matrix}η(1405) \\ η(1475) \end{matrix}  \begin{matrix}1416 ± 4 ± 2 \\ 1485 ± 8 ± 5 \end{matrix}  \begin{matrix}42 ± 10 ± 9 \\ 98 ± 18 ± 3 \end{matrix}  \begin{matrix}a_{0}(980)π \\ \overline{K}^{∗}K + c.c. \end{matrix}
J/Ψ rad.[37] MARKIII  \begin{matrix}η(1405) \\ η(1475) \end{matrix}  \begin{matrix}1416_{−8−5}^{+8+7} \\ 1490_{−8−16}^{+14+3} \end{matrix}  \begin{matrix}54_{−21−24}^{+37+13} \\ 91_{−31−38}^{+67+15} \end{matrix}  \begin{matrix}a_{0}(980)π \\ \overline{K}^{∗}K + c.c. \end{matrix}
J/Ψ rad.[38]  DM2  \begin{matrix}η(1405) \\ η(1475) \end{matrix}  \begin{matrix}1421 ± 14 \\ 1459 ± 5 \end{matrix}  \begin{matrix}63 ± 18 \\ 75 ± 9 \end{matrix}  \begin{matrix}\overline{K}^{∗}K + c.c. \\ a_{0}(980)π \end{matrix}
\overline{p}p at rest[44]  Obelix  \begin{matrix}η(1405) \\ η(1475) \end{matrix}  \begin{matrix}1416 ± 2 \\ 1460 ± 10 \end{matrix}  \begin{matrix}50 ± 4 \\ 105 ± 15 \end{matrix}  \begin{matrix}a_{0}(980)π \\ \overline{K}^{∗}K + c.c. \end{matrix}
\overline{p}p at rest[46]  Obelix  \begin{matrix}η(1405) \\ η(1475) \end{matrix}  \begin{matrix}1407 ± 5 \\ 1464 ± 10 \end{matrix}  \begin{matrix}48 ± 5 \\ 105 ± 15 \end{matrix}  \begin{matrix}a_{0}(980)π \\ \overline{K}^{∗}K + c.c. \end{matrix}
\overline{p}p at rest[45]  Obelix  \begin{matrix}η(1405) \\ η(1475) \end{matrix}  \begin{matrix}1405 ± 5 \\ 1500 ± 10 \end{matrix}  \begin{matrix}50 ± 4 \\ 100 ± 20 \end{matrix}  \begin{matrix}K\overline{K}π direct \\ \overline{K}^{∗}K + c.c. \end{matrix}
\overline{p}p at rest[47]  Obelix  \begin{matrix}η(1405) \\ η(1475) \end{matrix}  \begin{matrix}1413 ± 4 \\ 1460 ± 19 \end{matrix}  \begin{matrix}51 ± 6 \\ 120 ± 19 \end{matrix}  \begin{matrix}a_{0}(980)π \\ \overline{K}^{∗}K + c.c. \end{matrix}

Table 5: Summary of results on the η(1405) and the η(1475) pseudoscalars in the K\overline{K}π final state.

Production mechanism Experiment State

\begin{matrix}Mass \\ (MeV/c^{2}) \end{matrix} \begin{matrix}Width \\ (MeV/c^{2}) \end{matrix}

Decay modes

π^{−}p[23]  MPS  η(1440) 1421 ± 2  60 ± 10  a_{0}(980)
π^{−}p[25]  MPS  η(1440) 1424 ± 3  60 ± 10  a_{0}(980)π
π^{−}p[24]  MPS  η(1440) 1419 ± 1  66 ± 2  a_{0}(980)
π^{−}p[36]  E769  η(1440) 1453 ± 7  100 ± 11 a_{0}(980)π & \overline{K}^{∗}K + c.c.
J/Ψ rad.[7]  Mark II  η(1440) 1440_{−15}^{+10}  50_{−20}^{+30}  a_{0}(980)π & \overline{K}^{∗}K + c.c.
J/Ψ rad.[8]  Crystal Ball  η(1440) 1416_{−15}^{+20}  55_{−30}^{+20}  \overline{K}^{∗}K + c.c.& a_{0}(980)π
J/Ψ rad.[42]  DM2  η(1440) \begin{matrix}1445 ± 8 \\ 1433 ± 8 \end{matrix}  \begin{matrix}93 ± 14 \\ 105 ± 10 \end{matrix} \overline{K}^{∗}K + c.c.& a_{0}(980)π
J/Ψ rad.[49]  BES  η(1440) 1421 ± 14  63 ± 18  \overline{K}^{∗}K + c.c.& a_{0}(980)π

\overline{p}p at rest[15]

CERN-

Coll. de France.  η(1440) 1425 ± 7  80 ± 10  a_{0}(980)π & \overline{K}^{∗}K + c.c.
\overline{p}p at rest[34]  Asterix  η(1440) 1413 ± 8  62 ± 16  a_{0}(980)π

Table 6: Summary of results on the η(1440) pseudoscalar in the K\overline{K}π final state. The label η(1440) indicates that these experiments identified only one pseudoscalar state. DM2 provided two solutions with different masses and widths