Cumulants of the QCD topological charge distribution

Feng-Kun Guo,Ulf-G Meißner

doi:10.1016/j.physletb.2015.07.076

Feng-Kun Guo, Ulf-G Meißner

Open Access

https://doi.org/10.1016/j.physletb.2015.07.076

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Abstract

The distribution of the QCD topological charge can be described by cumulants, with the lowest one being the topological susceptibility. The vacuum energy density in a θ-vacuum is the generating function for these cumulants. In this paper, we derive the vacuum energy density in SU(2) chiral perturbation theory up to next-to-leading order keeping different up and down quark masses, which can be used to calculate any cumulant of the topological charge distribution. We also give the expression for the case of SU(N) with degenerate quark masses. In this case, all cumulants depend on the same linear combination of low-energy constants and chiral logarithm, and thus there are sum rules between the N-flavor quark condensate and the cumulants free of next-to-leading order corrections.

Highlights

Because of the axial U(1) anomaly, there exists a θ-term in quantum chromodynamics (QCD) which is a topological term
The renormalized low-energy constants (LECs) l3r and high-energy constants (HECs) hr1 are scale dependent [20] and this scale dependence cancels that in the chiral logarithm resulting in a scale-independent vacuum energy density in a θ-vacuum
We have derived the expressions for the vacuum energy density in a θ-vacuum in SU(2) chiral perturbation theory (CHPT) up to next-to-leading order (NLO) keeping different up and down quark masses as well as in SU(N ) CHPT with degenerate quark masses

Summary

Introduction

Because of the axial U(1) anomaly, there exists a θ-term in quantum chromodynamics (QCD) which is a topological term. The expression for the vacuum energy density can be used to calculate any cumulant of the distribution of the QCD topological charge defined in Eq (4) [28] that lattice simulations of these topological quantities with degenerate quarks are very interesting to pin down the N -flavor quark condensate Both the topological susceptibility and the fourth cumulant depend on several low-energy constants (LECs) in the NLO chiral Lagrangian, in addition to the quark condensate, the authors found an interesting linear combination, χt + N 2c4/4 with N the number of flavors, independent of any LEC.

Leading order

Next-to-leading order

Summary