Small flow-time representation of fermion bilinear operators

Abstract

Fermion bilinear operators of mass dimension~$3$, such as the axial-vector and vector currents, the pseudo-scalar and scalar densities, whose normalizations are fixed by Ward--Takahashi (WT) relations, are related to small flow-time behavior of composite operators of fermion fields evolved by Lüscher's flow equation. The representations can be useful in lattice numerical simulations, as recently demonstrated by the WHOT QCD collaboration for the chiral condensation of the $N_f=2+1$ quantum chromodynamics (QCD) at finite temperature.

arXiv comment15 pages, 4 figures. In previous versions, the coefficient in Eq. (2.7) was wrong and this mistake propagated to subsequent equations, Eqs. (2.9), (2.15), (2.17), (2.30), (2.31), (2.33), (2.35), (3.3), (3.7), (3.11), (3.13), and (4.2). We would like to thank Robert Harlander for pointing this out to us

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Cited by in corpus (21)

• Quasi parton distributions and the gradient flow
• Topological susceptibility in finite temperature (2+1)-flavor QCD using gradient flow
• Exploring Nf=2+1 QCD thermodynamics from the gradient flow
• Smeared quasidistributions in perturbation theory
• Four quark operators for kaon bag parameter with gradient flow
• Short flow-time coefficients of CP-violating operators
• 4D $\mathcal{N}=1$ SYM supercurrent in terms of the gradient flow
• One-loop matching of $CP$-odd four-quark operators to the gradient-flow scheme
• 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
• Equation of state in (2+1)-flavor QCD at physical point with improved Wilson fermion action using gradient flow
• Equation of state in (2+1)-flavor QCD with gradient flow
• Gradient Flow: Perturbative and Non-Perturbative Renormalization
• Nonperturbative Renormalization of the Quark Chromoelectric Dipole Moment with the Gradient Flow:Power Divergences
• Axial $U(1)$ anomaly in a gravitational field via the gradient flow
• Temperature dependence of topological susceptibility using gradient flow
• On the chiral anomaly and the Yang-Mills gradient flow
• Conserved vector current in QCD-like theories and the gradient flow
• 4D $\mathcal{N}=1$ SYM supercurrent on the lattice in terms of the gradient flow
• One-loop matching of the LEFT to the QCD gradient flow