Asymptotically free theory with scale invariant thermodynamics

Abstract

A recently developed variational resummation technique, incorporating renormalization group properties consistently, has been shown to solve the scale dependence problem that plagues the evaluation of thermodynamical quantities, e.g., within the framework of approximations such as in the hard-thermal-loop resummed perturbation theory. This method is used in the present work to evaluate thermodynamical quantities within the two-dimensional nonlinear sigma model, which, apart from providing a technically simpler testing ground, shares some common features with YangMills theories, like asymptotic freedom, trace anomaly and the nonperturbative generation of a mass gap. The present application confirms that nonperturbative results can be readily generated solely by considering the lowest-order (quasi-particle) contribution to the thermodynamic effective potential, when this quantity is required to be renormalization group invariant. We also show that when the next-to-leading correction from the method is accounted for, the results indicate convergence, apart from optimally preserving, within the approximations here considered, the sought-after scale invariance.

Renormalization group improved pressure for cold and dense QCD

“…Scale variations in the range M = µ − 4µ also show that the method reduces the scale uncertainties (although moderately at two-loop order) as compared to pQCD, which is important as far as EoS suitable to describe neutron stars are concerned. The scale uncertainty improvement from RGOPT thus appears less spectacular than for other models explored at two-loop orders at T = 0, µ = 0 compared with standard perturbation and HTLpt [35][36][37]. But this is merely due to the fact that standard pQCD at T = 0, µ = 0 has less severe remnant scale dependence issues (as already noted in Ref.…”

“…a generic result also for other theories [32,[34][35][36][37]. Moreover, the same value of a is taken also when considering higher orders of the δ-expansion, keeping the simple interpolating form of Eq.…”

“…More details and applications of the method can be found in Refs. [29,32,[34][35][36][37]. The GN model is described by the Lagrangian density for a fermion field with N components given by [30]…”

“…The method has also been used to derive an accurate value of the quark condensate [34]. More recently, it has been applied to the scalar λφ 4 theory [35,36], as well as to the non-linear sigma model (NLSM) [37], producing results that show its compatibility with control parameters such as the temperature. The present paper is the first RGOPT application to (cold) in-medium QCD, for a non-zero chemical potential, so that one can analyze how the method performs in the regime of finite baryonic densities.…”

Interplay between Approximation Theory and Renormalization Group

“…The renormalization scale is often chosen as µ = 2πT to avoid the logarithmic terms ln(µ/2πT ) coming from remnant scale dependence. This method was used for considering the O(N)-symmetric ϕ 4 theory, a three-color Nambu-Jona-Lasinio model, and quantum chromodynamics [138][139][140][141][142].…”