Speaker
Description
Counting hadronic states and QCD thermodynamics in a finite box are intimately
related. At small temperatures hadronic states are expected to saturate the partition
function, so, accepting the Particle Data Group (PDG) table [1] as the reference for
hadronic states, all the states listed by the PDG should also be counted as genuine
contributions to the QCD partition function and, hence, blindly included in the Hadron
Resonance Gas (HRG).
However, Dashen and Kane [2] pointed out the possibility that not all hadron states
should be counted on a hadronic scale as they become fluctuations in a mass-spectrum
coarse grained sense. Hence, the proliferation of new XYZ states and their inclusion
in the PDG poses the natural question whether or not these states have some degree of
redundancy in order to build the hadron spectrum [3, 4].
In this work, we analyze if the renowned X(3872), a weakly bound state right
below the DD ̄ ∗
threshold, should effectively enter a hadronic representation of the QCD
partition function. This can be decided by analyzing the DD ̄ ∗
scattering phase-shifts
in the JPC = 1++ channel and their contribution to the level density in the continuum
from which the abundance in a hot medium can be determined. For that purpose we
use a recent coupled-channels calculation [5] which includes the effect of nearby DD ̄ ∗
threshold on the dynamics of the bare cc ̄ spectrum.
We show that in a purely molecular picture the bound state contribution cancels the
continuum providing a vanishing ocupation number density at finite temperature and
the X(3872) does not count below the Quark-Gluon Plasma crossover happening at
T ∼ 150MeV. In contrast, for a non vanishing cc ̄ content the cancellation does not occur
due to the onset of the X(3940) which effectively counts as an elementary particle for
temperatures above T & 250MeV. Thus, a blind inclusion of the X(3872) in the Hadron
Resonance Gas is not justified.
References
[1] Particle Data Group, C. Patrignani et al., Chin. Phys. C40 (2016) 100001.
[2] R.F. Dashen and G.L. Kane, Phys. Rev. D11 (1975) 136.
[3] E. Ruiz Arriola, L.L. Salcedo and E. Megias, Acta Phys. Polon. B45 (2014) 2407.
[4] E. Ruiz Arriola, L.L. Salcedo and E. Megias, Acta Phys. Polon. Supp. 8 (2015)
439.
[5] P.G. Ortega et al., Phys. Rev. D81 (2010) 054023.
