Universal formula for the flavor non-singlet axial-vector current from the gradient flow

Abstract

By employing the gradient/Wilson flow, we derive a universal formula that expresses a correctly normalized flavor non-singlet axial-vector current of quarks. The formula is universal in the sense that it holds independently of regularization and especially holds with lattice regularization. It is also confirmed that, in the lowest non-trivial order of perturbation theory, the triangle diagram containing the formula and two flavor non-singlet vector currents possesses non-local structure that is compatible with the triangle anomaly.

11 pages, 7 figures. In previous versions, a coefficient in Eq. (1.4) was wrong and this mistake propagated to subsequent equations, Eqs. (1.6) and (3.14). We would like to thank Robert Harlander for pointing this out to us

Cited by in corpus (13)

• Exploring Nf=2+1 QCD thermodynamics from the gradient flow
• Smeared quasidistributions in perturbation theory
• Small flow-time representation of fermion bilinear operators
• Four quark operators for kaon bag parameter with gradient flow
• Short flow-time coefficients of CP-violating operators
• Möbius domain-wall fermions on gradient-flowed dynamical HISQ ensembles
• Using Wilson flow to study the SU(3) deconfinement transition
• Background field method in the gradient flow
• 4D $\mathcal{N}=1$ SYM supercurrent in terms of the gradient flow
• Supersymmetric gradient flow in the Wess-Zumino model
• Short-flow-time expansion of quark bilinears through next-to-next-to-leading order QCD
• Gradient flow representation of the four-dimensional $\mathcal{N}=2$ super Yang--Mills supercurrent
• Axial $U(1)$ anomaly in a gravitational field via the gradient flow