Behaviour of the topological susceptibility in two colour QCD across the finite density transition

Abstract

The behaviour of the topological susceptibility χ in QCD with two colours and 8 flavours of quarks is studied at nonzero temperature on the lattice across the finite density transition. It is shown that the signal of χ drops abruptly at a critical chemical potential µ c , much as it happens at the finite temperature and zero density transition. The Polyakov loop and the chiral condensate undergo their transitions at the same critical value µ c . At a value µ s of the chemical potential, called saturation point, which in our case satisfies µ s > µ c , Pauli blocking supervenes and consequently the theory becomes quenched.

Effects of the regularization on the restoration of chiral and axial symmetries

“…2, we plot the topological susceptibility, and we see that it decreases but does not vanish when regularization II is used; the effect of regularization I, approximately at the same temperature, a result that has already been found in [15,22]; the new finding is that the critical temperature with the new regularization is now T c ≃ 177…”

“…Several lattice calculations (see [21] and references therein) indicate a sharp decrease of the topological susceptibility with temperature at zero density, and, more recently [22], it was shown that, at a fixed T and by varying the chemical potential µ, a critical µ is found, where the quark condensate and the topological susceptibility drop and the Polyakov loop raises; its derivatives vary sharply.…”

Can we study quark matter in the quenched approximation?

“…This scenario was subsequently confirmed by simulations with staggered lattice fermions [5,9]. More recent simulations have found evidence for a second transition at larger µ to a deconfined phase, as evidenced by a non-vanishing Polyakov loop [11] and by a fall in the topological susceptibility [12]. In this regime thermodynamic quantities scale according to the expectations of free field theory (also referred to as "Stefan-Boltzmann" (SB) scaling), namely n q ∝ µ 3 , and energy density ε ∝ µ 4 [11].…”

“…We have chosen β = 9.0 sufficiently close to the continuum limit for the DR formalism to be trustworthy, and start with a point with T = 2T c according to (12); from Table 1 this corresponds to κ = 0.3620027, λ = 0.0020531. For this parameter set, we have explored system volumes 8 3 × L t , with L t = 16, 32, 64 and 128.…”

“…1 we report some sample lattice parameter sets obtained by calculating x and y according to Eqs. (12) and fixing the ratio T /T c ; then we have calculated κ and λ using Eqs. (13).…”