Abstract
I present a numerical study of the crossover between the low temperature chirally broken phase and the high temperature chirally restored phase in $SU(N_c)$ gauge theory with $N_c=3-5$ colors and $N_f=2$ degenerate fermion flavors. Fermion masses span a range of intermediate values (represented by the squared ratio of pseudoscalar to vector meson masses $(m_{PS}/m_V)^2\sim 0.25$ to 0.63). Observables include the temperature dependent chiral condensate and screening masses. At each fermion mass these quantities show nearly identical temperature dependence across $N_c$.
Highlights
AND MOTIVATIONThe limit of QCD when the number of colors Nc is taken large has a long history as a source of insight about Nc 1⁄4 3 QCD itself [1,2,3]
To what extent are these predictions true? Checking them requires a lattice simulation, and there is a small literature of lattice calculations away from Nc 1⁄4 3 to provide such tests. (See Refs. [4,5,6] for a selection of reviews.)
There is no evidence in any of the simulations reported here for anything other than a smooth crossover. (This makes the identification of a particular crossover temperature problematic.) As to the other scenarios, my results indicate that the temperature dependence of observables computed at common values of the fermion mass show essentially identical behavior, including inflection points at finite temperature, which is nearly independent of Nc
Summary
The limit of QCD when the number of colors Nc is taken large has a long history as a source of insight about Nc 1⁄4 3 QCD itself [1,2,3]. Sigma models contain one dimensional parameter, the vacuum expectation value of the scalar field, and all derived dimensionful quantities (the pseudoscalar decay constant, and the crossover temperature Tc itself) are proportional to it It is well known frompffipffiffirffiffieffi vious large Nc spectroscopy comparisons that fPS ∝ Ncp. Tffiffihffiffiffiuffi s the naive prediction of the second scenario is Tc ∝ Nc [13]. (This makes the identification of a particular crossover temperature problematic.) As to the other scenarios, my results indicate that the temperature dependence of observables computed at common values of the fermion mass show essentially identical behavior, including inflection points at finite temperature, which is nearly independent of Nc. And there is no evidence in any of the simulations reported here for anything other than a smooth crossover.
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