β function and equation of state for QCD with two flavors of quarks

Abstract

We measure the pressure and energy density of two avor QCD in a wide range of quark masses and temperatures. The pressure is obtained from an integral over the average plaquette or . We measure the QCD function, including the anomalous dimension of the quark mass, in new Monte Carlo simulations and from results in the literature. We use it to nd the interaction measure, " 0 3p, yielding non-perturbative values for both the energy density " and the pressure p.12.38.Gc, 11.15.Ha

Color confinement and dual superconductivity in full QCD

“…In particular we have chosen, in the transition region, to vary the temperature, T = 1/ (N t a(β, m q )), moving in the (β, m q ) plane while keeping a fixed value of m π /m ρ . To do this and to extract the physical scale we have used fits to the m ρ and m π masses published in [10]. We present here results obtained at m π /m ρ 0.505: in this case, at N t = 4, the β corresponding to the transition is approximately β c ∼ 5.35 [11].…”

Reviewing the problem of the U(1) axial symmetry and the chiral transition in QCD

“…From lattice determinations of the chiral order parameter qq one knows that the SU(L) ⊗ SU(L) chiral phase transition temperature T ch , defined as the temperature at which the chiral condensate qq goes to zero (in the chiral limit sup(m i ) → 0), is nearly equal to the deconfining temperature T c (see, e.g., Ref. [2]). But this is not the whole story: QCD possesses not only an approximate SU(L) ⊗ SU(L) chiral symmetry, for L light quark flavours, but also a U(1) axial symmetry (at least at the classical level) [3,4].…”

“…(Clearly, if both chiral symmetries are restored, then all π, η ′ , σ and δ correlators should become the same.) In practice, one can construct, for each meson channel f , the corresponding chiral susceptibility 2) and then define two order parameters: χ SU (2)⊗SU (2) ≡ χ σ − χ π , and χ U (1) ≡ χ δ − χ π . If an order parameter is non-zero in the chiral limit, then the corresponding symmetry is broken.…”

Equation of state from lattice QCD

“…The first results were obtained with staggered fermions. Calculations were performed by the MILC collaboration [ 4,5] and by Karsch, Laermann and Peikert from Bielefeld [ 6]. The first calculation with Wilson fermions was done by the CP-PACS collaboration [ 7].…”