How sharp is the chiral crossover phenomenon for realistic meson masses?

Abstract

The mass dependence of the chiral phase transition is studied in the linear $SU(3)\times SU(3)$ sigma-model to leading order in a $1/N_f$-expansion, $N_f$ denoting the number of flavours. For realistic meson masses we find a smooth crossover between $T\sim181.5$ to 192.6~[MeV]. The crossover looks more rapid in the light quark condensate than in thermodynamic quantities like the energy and entropy densities. The change in the light quark condensate in this temperature interval is $\sim$~50\% of the zero-temperature condensate value, while the entropy density increases by ($5.5\pm0.8)\cdot10^{-3}$~[GeV$^3$]. Since the numerical error is particularly large in this region, we cannot rule out a finite latent heat smaller than 0.2~[GeV/fm$^3$]. The chiral transition is washed out for an average pseudoscalar meson octet mass of 203~[MeV]. This gives an upper bound on the first-order transition region in the meson mass parameter space. The corresponding ratio of critical to realistic light current quark masses $m^{crit}_{u,d}/m_{u,d}$ is estimated as $0.26\pm0.08$. This result is by an order of magnitude larger than the corresponding mean-field value. Therefore theComment: LaTeX, HD--TVP--94--16, Please contact authors via email for figure

Application of the heat-kernel method to the constituent quark model at finite temperature

“…Previously [10] we did not allow such temperature dependent terms in calculations of the order of the phase transition. Especially a third order term would add to the determinant term in Flavour-SU(3) from instantons which is nine times larger at T c [11]. …”

ηandη′mesons in the Dyson-Schwinger approach at finite temperature

“…This is in contrast to the chiral-limit f 0 π (T ), where f 0 π (T ≥ T Ch ) = 0 precludes its usage in WV relation for T ≥ T Ch (e.g., Ref. [59] or the studies [27,58,60] employing chiral Lagrangians).…”

Hadron resonance mass spectrum and lattice QCD thermodynamics

“…chiral perturbation theory [10] and effective chiral models [11,12]. The strength of these approaches is that they incorporate the correct symmetries of the QCD Lagrangian and thus have a chance to predict the universal properties, e.g.…”