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\title{$\Lambda^0$ Polarization in exclusive and inclusive p-Nucleus reactions}

\author{J. F\'elix\address{Instituto de F\'{\i}sica, Universidad de Guanajuato. Lomas del
Bosque 103, Frac. Lomas del Campestre, Le\'{o}n GTO. 37150, M\'{e}xico. felix@fisica.ugto.mx}%
        \thanks{Thanks to the BNL e766 and FNAL e690 collaborations (http://www-e690.fnal.gov).
        This research was supported in part by CONACYT, M\'{e}xico, under grant No.
        2002-C01-39941, CONCYTEG 06-16-K117-99, Apoyo a la investigaci\'{o}n cient\'{\i}fica UGTO 2006,
        and PROMEP-2005.}}


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\runtitle{$\Lambda^0$ Polarization in exclusive and inclusive
p-Nucleus reactions} \runauthor{J. F\'elix}

\begin{document}

\begin{abstract}
Among all properties of baryons, the polarization they acquire when
created from unpolarized p-Nucleus collisions is the most recent
discovered one; so far, the origin of baryon polarization remains
unexplained in spite of the experimental evidences accumulated in
the past thirty years. Up to these days, $\Lambda^0$ is the most
studied baryon for polarization, because it is very easy to produce
at the energies of the principal high energy physics accelerators of
the world. This paper is a review of the experimental information
accumulated on the polarization of $\Lambda^0$ in unpolarized
exclusive and inclusive p-Nucleus collisions as function of $x_F$,
$P_T$, and diffractive mass of the $\Lambda^0K^+$ system in the past
thirty years. \vspace{1pc}
\end{abstract}

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\section{INTRODUCTION}

It is an experimental evidence that baryons in general are created
polarized, when they are produced from unpolarized {\it
particle-Nucleus} collisions. For instance $\Xi$, $\Sigma$,
$\Lambda^0$, etc., are produced polarized in exclusive as well as in
inclusive reactions at different energies\cite{1,2,3}. In the same
experimental circumstances, it appears that $\Omega^-$\cite{1}(K.B.
Luk et al) and ${\overline\Lambda^0}$\cite{1} \cite{500}(K. Heller
et al) do not appear polarized. However, it appears that
${\overline\Lambda^0}$ is created polarized in $K^-p$
reactions\cite{600}. The origin of baryon polarization is not known
up to these days.\

From the above mentioned baryons, $\Lambda^0$ is the most studied
one for polarization, because it is very easy to produce and analyze
for polarization. In many experiments $\Lambda^0$'s from unpolarized
$pp$ inclusive and exclusive collisions, at different energies, are
produced polarized\cite{2}. This polarization depends on $x_F$,
$P_T$, and $\Lambda^0K^+$ invariant mass\cite{3}.\

Based on the above experimental evidences, some authors have
proposed many theoretical ideas -in the context of the Lund model,
parton recombination, multiple scattering of the strange quark,
gluon fusion, Regge theory, coherent scattering, low and high order
QCD calculations, valence quark effects, and quark condensates-
trying to understand $\Lambda^0$ polarization\cite{4}. See reference
\cite{5} for a review of the theoretical ideas proposed to explain
$\Lambda^0$ polarization. To date, there is no a satisfactory
explanation for baryon polarization in general.\

This paper is a summary of the experimental results on $\Lambda^0$
polarization, as function of $x_F$, $P_T$, and $M_{\Lambda^0K^+}$,
in the specific final states
\begin{equation}\label{eq:1}
pp\to p\Lambda^{0}K^{+}(\pi ^{+}\pi ^{-})^N; N=1,2,3,4,5,
\end{equation}
at $27.5~GeV$, from the BNL e766 collaboration. And in the specific
final state

\begin{equation}\label{eq:2}
pp\to p\Lambda^{0}K^{+},
\end{equation}
at $800~GeV$, from the FNAL e690 collaboration.\

FNAL e690 and BNL e766 collaborations are described in detail
elsewhere\cite{6}.\


\section{TECHNIQUE TO MEASURE $\Lambda^0$ POLARIZATION}

%For $\Lambda^0$ weakly decays into $p\pi^-$ and the angular
%distribution of the protons from $\Lambda^0$'s, in the reference
%system where $\Lambda^0$ is at rest, is very well known\cite{800},
%the measurement of $\Lambda^0$ polarization consists in determining
%the angular distribution of the proton from the $\Lambda^0$ and
%fitting it to a straight line. For an ample description of this
%technique, see reference\cite{90}.\

The polarization of $\Lambda^0$ is measured with respect to the
normal vector to the $\Lambda^0$ production plane defined as

\begin{equation}\label{eq:3}
\hat{n} \equiv \frac{\vec{P}_{beam} \times \vec{P}_{\Lambda^0}}{
\mid \vec{P}_{beam} \times \vec{P}_{\Lambda^0} \mid},
\end{equation}
where $\vec{P}_{beam}$ and $\vec{P}_{\Lambda^0}$ are the momentum
vectors of the incident beam proton and of the $\Lambda^0$,
respectively.\

The angular distribution of the proton from $\Lambda^0$, in the
$\Lambda^0$ rest frame, is described by this expression\cite{800}:

\begin{equation}\label{eq:4}
\frac{dN}{d\Omega} = N_0(1+ \alpha \mathcal{P} cos\theta),
\end{equation}

where $\alpha$ is the $\Lambda^0$ decay asymmetry parameter ($0.642
\pm 0.013$\cite{7}) and $\mathcal{P}$ is the $\Lambda^0$
polarization. The polarization is determined by a linear fit of a
function of the above form to the $cos \theta$ distribution of the
proton -after Monte Carlo detector acceptance corrections- for two
free parameters: Intercepts ($N_0$), and slope $N_0 \alpha
\mathcal{P}$. From these parameters the $\Lambda^0$ polarization and
its statistical error are measured. The systematic errors are
obtained simulating the detector acceptance and efficiency using the
Monte Carlo technique.\


\section{$\Lambda^0$ POLARIZATION AS FUNCTION OF $x_F$ AND $P_T$}

The discovery of $\Lambda^0$ polarization in inclusive $pp$
reactions showed that it depends linearly on $P_T$ and that it is
negative with respect to the $\Lambda^0$ production plane\cite{8}:
At $P_T=0.0$, $\mathcal{P}=0.0$, and it decreases as $P_T$ increases
up to close $\mathcal{P}= -0.25$ at $P_T=1.2~GeV.$ Also it was
determined in inclusive $pp$ reactions that $\Lambda^0$ polarization
depends on $x_F.$ See Reference \cite{9} for a review of the
experimental results on $\Lambda^0$ polarization.\

In the reaction $pp \to p \Lambda^0 K^+ (\pi^+ \pi^-)^2$ at
$27.5~GeV$, $\Lambda^0$ polarization in a function of $P_T$ and
$x_F$\cite{10}. Reference\cite{10} was the first report on
$\Lambda^0$ polarization in exclusive reactions at high energies.\

%Fig. 1 shows the results as function of $P_T$.
$\Lambda^0$ polarization as function of $P_T$ is given by
$\mathcal{P}=(-0.250\pm0.067)P_T+(0.063\pm0.041)$
-$\frac{\chi^2}{N_{DOF}}=1.04$, for $x_F>0.0$-; by
$\mathcal{P}=(0.147\pm0.056)P_T+(-0.007\pm0.033)$
-$\frac{\chi^2}{N_{DOF}}=1.04$, for $x_F<0.0$-; and by
$\mathcal{P}=(-0.189\pm0.042)P_T+(0.029\pm0.025)$
-$\frac{\chi^2}{N_{DOF}}=1.68$, for $x_F>0.0$ and $x_F<0.0$-
combined.\

%Fig. 2 shows the results as function of $x_F$.
The average $\Lambda^0$ polarization is roughly linear as function
of $x_F$. This is given by
$\mathcal{P}=(-0.20\pm0.06)x_F+(-0.032\pm0.018)$
-$\frac{\chi^2}{N_{DOF}}=0.247$, for $x_F>0.0$ and $x_F<0.0$
combined-. The average $\Lambda^0$ polarization changes sign at
$x_F\simeq0.0$.\

A complete analysis of $\Lambda^0$ polarization in the particular
reactions described by Eq. 1, with $N=1,2,3,4$, was performed at
high statistics, searching for $\Lambda^0$ polarization as function
of $x_F$ and $P_T$\cite{11} together. To analyze the data,
$\mathcal{P}$ is parameterized as a function of $x_F$ and $P_T$
simultaneously: $\mathcal{P} = \mathcal{P}(x_F,P_T)$. The parameters
of this function are determined using the maximum likelihood
method\cite{40} with Eq. 4 as the probability distribution for
having $dN$ protons in a solid angle $d\Omega$. For the maximum
likelihood analysis, the chosen function that represents the
simplest bilinear combination of $x_F$ and $P_T$ is as follows:

\begin{equation}\label{eq:5}
\mathcal{P}(x_F, P_T) = (-0.443\pm0.037)x_F P_T,
\end{equation}
for -$1.0 \leq x_F\leq1.0$ and $0.0\leq P_T \leq 1.8~GeV/c$-.

The conclusion from this result is as follows: The mechanism
responsible for $\Lambda^0$ polarization is independent of the
$\Lambda^0$ production mechanism, at least for the examined final
state reactions.\

Furthermore, in general, equation

\begin{equation}\label{eq:6}
\mathcal{P}(x_F, P_T) = (-a)x_F P_T,
\end{equation}

for $-1.0 \leq x_F \leq 1.0$ and $0.0 \leq P_T \leq 1.8~GeV/c$, is
valid for $\Lambda^0$ polarization from exclusive and inclusive
$p-Nucleus$ reactions\cite{100} with the proper $a$ value that
depends on the particular beam and target reaction.\

Both $\Lambda^0$ polarization from inclusive and exclusive
$p-nucleus$ reactions follow the same trend as function of $x_F$ and
$P_T$: $\mathcal{P}(x_F,P_T)=(a)x_FP_T$. This equation is valid for
$-1.0<x_F<+1.0$ and $0.0<P_T<2.0~GeV/c$ and for $nucleus=p, Be, Cu,
W$ and $Pb$. The value of $a$ depends on the target nature: For
instance it is $-(0.443\pm0.037)$, in exclusive $pp$ reactions;
$-(0.376\pm0.024)$, in inclusive $pp$ reactions; -there is no
statistical difference between $\Lambda^0$ polarization from
inclusive and exclusive reactions-. This equation is independent of
the beam energy and is the most simple bilinear form that describes
$\Lambda^0$ polarization in
$-1.0<x_F<+1.0$ and $0.0<P_T<2.0~GeV/c$ kinematical region.\\

From Eq. 2, $\Lambda^0$ polarization at $800$ GeV as function of
$x_F$ and $P_T$ is shown in Table II of the Reference\cite{3} (J.
F\'elix et al). This functionality of $\Lambda^0$ polarization in
terms of $x_F$ and $P_T$ is not observed in the reactions described
by Eq. 1. This was the first time that large $\Lambda^0$
polarization is reported at low $P_T$. At large $P_T$ -greater than
$0.6~GeV/c$- $\Lambda^0$ polarization agrees with previous reported measurements.\\

From Eq. 1, with $N=5$, the polarization of 1973 $\Lambda^0$'s from
the specific reaction $pp \to p\Lambda^0K^+(\pi^+\pi^-)^5$ created
from $27.5~GeV$ incident protons on a liquid Hydrogen target, as
function of $x_F$, $P_T$, and $M_{\Lambda^0K^+}$, is, inside
statistics, consistent with the polarization of $\Lambda^0$'s from
$pp \to p_{fast}\Lambda^0K^+$ at $800~GeV$\cite{200,201}.


\section{$\Lambda^0$ POLARIZATION AS FUNCTION OF $M_X$}

$\Lambda^0$ polarization depends on $x_F$, $P_T$ -parameters
associated with $\Lambda^0$- as well as on $M_{\Lambda^0K^+}$ -the
diffractive mass of the system $X=\Lambda^0K^+$-. In general
$\Lambda^0$ polarization depends on the diffractive mass of the
system $\{\Lambda^0K^+(\pi^+\pi^-)^N\}$, with $N=0,1,2,3,4,5$. \

From Eq. 1, for $N=2$, $\Lambda^0$ polarization depends on
$(\Lambda^0K^+)$, $(\Lambda^0K^+\pi^+\pi^-)$,
$(\Lambda^0K^+\pi^+\pi^-\pi^+\pi^-)$ diffracted mass
systems\cite{10}. This is a novel result indicating that $\Lambda^0$
polarization could be related with the polarization of some
resonances from where $\Lambda^0$'s are created. These results are
as follows:\

$\Lambda^0$ polarization is roughly linear with
$M_{(\Lambda^0K^+)}$, decreasing from zero at $M_{(\Lambda^0K^+)} =
1.63~GeV$ to $-0.16$ at $M_{(\Lambda^0K^+)} = 2.47~GeV$. The linear
fit is $\mathcal{P} =
(-0.185\pm0.068)M_{(\Lambda^0K^+)}+(0.30\pm0.14)$, with
$\chi^2/N_{dof}=0.002$. These results agree with those reported in
Reference\cite{3}(T. Henkes {\it et al}) in the reaction $pp \to
p\Lambda^0K^+$ at higher energies and for masses from $1.6$ to $2.4$
$GeV/c^2$. To boot, $\Lambda^0$ polarization is roughly linear with
$M_{(\Lambda^0K^+\pi^+\pi^-)}$, decreasing from zero at
$M_{(\Lambda^0K^+\pi^+\pi^-)}=2.75~GeV$ to $-0.16$ at
$M_{(\Lambda^0K^+\pi^+\pi^-)} = 3.75~GeV$; the linear fit is
$\mathcal{P} =
(-0.170\pm0.057)M_{(\Lambda^0K^+\pi^+\pi^-)}+(0.475\pm0.187)$, with
$\chi^2/N_{dof}=0.073$. And additionally, $\Lambda^0$ polarization
is roughly linear with $M_{(\Lambda^0K^+\pi^+\pi^-\pi^+\pi^-)}$,
decreasing from zero at
$M_{(\Lambda^0K^+\pi^+\pi^-\pi^+\pi^-)}=3.9~GeV$ to $-0.14$ at
$M_{(\Lambda^0K^+\pi^+\pi^-\pi^+\pi^-)} = 5.1~GeV$; the linear fit
is $\mathcal{P} =
(-0.154\pm0.048)M_{(\Lambda^0K^+\pi^+\pi^-\pi^+\pi^-)}+(0.63\pm0.22)$,
with $\chi^2/N_{dof}=0.55$.\

Furthermore, from Eq. 1, for $N=1, 2, 3, 4, 5 $, $\Lambda^0$
polarization depends on $M_{(\Lambda^0K^+)}$. From Eq. 2,
$\Lambda^0$ polarization also is a function of
$M_{(\Lambda^0K^+)}$.\

There is some relation between $\Lambda^0K^+$ mass distribution and
$\Lambda^0$ polarization. That relation evidences the connection
between $\Lambda^0$ polarization and $\Lambda^0K^+$ resonance
structure -where the variations in $M_{(\Lambda^0K^+)}$, from Eq. 2,
are bigger, the variations of $\Lambda^0$ polarization are bigger;
see, and compare, Fig. 6 and Fig. 4 from Reference\cite{3} (J.
F\'elix {\it et al}). Maybe both polarizations, $\Lambda^0$
polarization and $\Lambda^0K^+$ system polarization, could be
related. In this case the origin of $\Lambda^0$ polarization -and in
general of all baryons- could be due to parity conservation in
strong interactions. \

\section{CONCLUSIONS}

$\Lambda^0$ polarization is a function of $x_F$, $P_T$, and the
diffractive mass of $\Lambda^0K^+$ system. This functionality is not
unique; it seems that it depends on the production mechanism.\

For exclusive $pp \to p\Lambda^0K^+(\pi^+\pi^-)^N$, with $N=1,2,3,4$
at $27.5~GeV$, $\Lambda^0$ polarization depends on the diffractive
mass of the $\Lambda^0K^+$ system and on the diffractive mass of
$(\Lambda^0K^+(\pi^+\pi^-)^N, N=1,2,3,4)$, differing from that from
$pp \to p \Lambda^0K^+$ at $800~GeV$ and from $pp \to
p\Lambda^0K^+(\pi^+\pi^-)^5$ at $27.5~GeV$.\

The production mechanism of $\Lambda^0$ is very important and plays
a fundamental role in the $\Lambda^0$ polarization. It appears that
different production mechanisms of $\Lambda^0$ produce different
$\Lambda^0$ polarization functionality.\

It appears that $\Lambda^0$ polarization does not depend on the
$beam$ energy but on the nature -quark content- of the beam, on the
energy of the effective beam -this is, the beam that really produces
$\Lambda^0$- and on the isospin channel via $\Lambda^0$ is
produced.\

To reach a complete knowledge about $\Lambda^0$ polarization more
studies and measurements must be performed in all possible
experimental circumstances. For instance, a very important example
is the measurement of $\Lambda^0$ polarization in exclusive $pp \to
pp \Lambda^0 \overline {\Lambda}^0$ at different energies and $pp
\to p\Lambda^0K^0_s \pi^+$ at different energies.\

In spite of all the above experimental efforts, it seems that the
explanation of $\Lambda^0$ polarization is still faraway.\

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\begin{thebibliography}{9}

\bibitem{1}{J. Duryea {\it et al}, Phys. Rev. Lett. 67,
1193(1991).}~ {R. Rameika {\it et al}, Phys. Rev. {\bf D33},
3172(1986).}~{C. Wilkinson {\it et al}, Phys. Rev. Lett. 58,
855(1987).}~{B. Lundberg {\it et al}, Phys. Rev. {\bf D40},
39(1989).}~{F. Lomanno {\it et al}, Phys. Rev. Lett. 43,
1905(1979).}~{S. Erhan {\it et al}, Phys. Lett. {\bf B82},
301(1979).}~{F. Abe {\it et al}, Phys. Rev. Lett. 50,
1102(1983).}~{K. Raychaudhuri {\it et al}, Phys. Lett. {\bf B90},
319(1980).}~{K. Heller {\it et al}, Phys. Rev. Lett. 41,
607(1978).}~{F. Abe {\it et al}, J. of the Phys. S. of Japan. 52,
4107(1983).}~{P. Aahlin {\it et al}, Lettere al Nuovo Cimento 21,
236(1978).}~{A. M. Smith {\it et al}, Phys. Lett. {\bf B185},
209(1987).}~{V. Blobel {\it et al}, Nuclear Physics {\bf B122},
429(1977).}~{G. Zapalac {\it et al}, Phys. Rev. Lett. 57,
1526(1986).} ~{A. Morelos {\it et al}, Phys. Rev. Lett. 71
2172(1993).} ~{Y. W. Wah {\it et al}, Phys. Rev. Lett. 55
2551(1985).} ~{L. Deck {\it et al}, Phys. Rev. {\bf D28},
1(1983).}~{E. C. Dukes {\it et al}, Phys. Lett. {\bf B193}
135(1987).}~ {K. B. Luk {\it et al}, Phys. Rev. Lett. 70,
900(1993).}

\bibitem{2}{K. Heller {\it et al}, Phys. Lett. {\bf B68}, 480(1977).}~
{G. Bunce {\it et al}, Phys. Lett. {\bf B86}, 386(1979).}

\bibitem{3}{T. Henkes {\it et al}, Phys. Lett. B283, 155(1992).}~
{J. F\'{e}lix {\it et al}, Phys. Rev. Lett. 88, 061801-4(2002).}

\bibitem{4}{T. A. DeGrand {\it et al}, Phys. Rev. {\bf D24}, 2419(1981).}
~{B. Andersson {\it et al}, Phys. Lett. {\bf B85}, 417(1979).}~{J.
Szweed {\it et al}, Phys. Lett. {\bf B105}, 403(1981).}~{K. J. M.
Moriarty {\it et al}, Lett. Nuovo Cimento 17, 366(1976).}~{S. M.
Troshin and N. E. Tyurin, Sov. J. Nucl. Phys. 38, 4(1983).}~{J.
Soffer and N.E. T\"{o}rnqvist, Phys. Rev. Lett. 68, 907(1992).}~{Y.
Hama and T. Kodama, Phys. Rev. {\bf D48}, 3116(1993).}~{R. Barni
{\it et al}, Phys. Lett. {\bf B296}, 251(1992).}~{W. G. D.
Dharmaratna and G. R. Goldstein, Phys. Rev. {\bf D53},
1073(1996).}~{W. G. D. Dharmaratna and G. R. Goldstein, Phys. Rev.
{\bf D41}, 1731(1990).}~{S. M. Troshin and N. E. Tyurin, Phys. Rev.
{\bf D55}, 1265(1997).}~{L. Zuo-Tang and C. Boros, Phys. Rev. Lett.
79, 3608(1997).}

\bibitem{5}{J. F\'elix,  Mod. Phys. Lett. {\bf A14}, 827(1999).}

\bibitem{6}{J. Uribe {\it et al}, Phys. Rev. D49, 4373(1994).}~
{E. P. Hartouni {\it et al}, Nucl. Inst. Meth. A317, 161(1992).}~
{E. P. Hartouni {\it et al}, Phys. Rev. Lett. 72, 1322(1994).}~{E.
E. Gottschalk {\it et al}, Phys. Rev. D53, 4756(1996).}~{D. C.
Christian {\it et al}, Nucl. Instr. and Meth. A345, 62(1994).}~{B.
C. Knapp and W. Sippach, IEEE Trans. on Nucl. Sci. NS 27,
578(1980).}~{E. P. Hartouni {\it et al}, IEEE Trans. on Nucl. Sci.
NS 36, 1480(1989).}~{B. C. Knapp, Nucl. Instrum. Methods {\bf A289},
561(1980).}

\bibitem{7}{S. Eidelman {\it et al}, Phys. Lett. {\bf B592}, 1(2004).}

\bibitem{8}{G. Bunce {\it et al},  Phys. Rev. Lett. 36, 1113(1976).}

\bibitem{9}{J. F\'elix,  Mod. Phys. Lett. {\bf A12}, 363(1997).}

\bibitem{10}{J. F\'elix {\it et al},  Phys. Rev. Lett. 76, 22(1996).}

\bibitem{11}{J. F\'elix {\it et al},  Phys. Rev. Lett. 82, 5213(1999).}

\bibitem{40}{L. Montanet {\it et al}, Phys. Rev. D {\bf 50}, 1173(1994).}

\bibitem{90}{J. F\'elix, Rev. Mex. de F\'{\i}s. 45(4) 421(1999).}

\bibitem{100}{J. F\'elix,  Mod. Phys. Lett. {\bf A16}, 1741(2001).}

\bibitem{200}{J. F\'elix {\it et al}, $\Lambda^0$ Polarization in $pp \to p\Lambda^0 K^+ (\pi^+\pi^-)^5$
at 27.5 GeV. SPIN2004, proceedings. The 16$^{th}$ International Spin
Physics Symposium. Trieste, IT. 10-16 October 2004.}

\bibitem{201}{J. F\'elix {\it et al}, $\Lambda^0$ Polarization in $pp \to p\Lambda^0 K^+ (\pi^+\pi^-)^5$
at 27.5 GeV. HEPP-EPS 2005, proceedings. International Europhysics
Conference on High Energy Physics. Lisboa, Portugal July 21-27,
2005.}

\bibitem{500}{E. J. Ramberg {\it et al}, Phys. Lett. B 338, 403(1994).}

\bibitem{600}{S. A. Gourlay {\it et al},  Phys. Rev. Lett. 56, 2244(1986).}

\bibitem{800}{J. F\'elix, Ph. D. Thesis, Universidad de Guanajuato-Universidad de Massachusetts, M\'exico (1994).}

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