Lattice study of vacuum polarization function and determination of strong coupling constant

TL;DR

This paper uses lattice QCD with overlap fermions to compute vacuum polarization functions, matching them with perturbative and OPE expansions to determine the strong coupling constant and four-quark condensates.

Contribution

It presents a novel lattice calculation of vacuum polarization functions using overlap fermions to extract the strong coupling constant and condensates.

Findings

Determined $eta$-function and $ar{ ext{MS}}$ coupling constant at specific scales.

Extracted four-quark condensates from vector and axial-vector channel differences.

Provided systematic and statistical error estimates for the coupling constant.

Abstract

We calculate the vacuum polarization functions on the lattice using the overlap fermion formulation.By matching the lattice data at large momentum scales with the perturbative expansion supplemented by Operator Product Expansion (OPE), we extract the strong coupling constant $\alpha_s(\mu)$ in two-flavor QCD as $\Lambda^{(2)}_{\overline{MS}}$ = $0.234(9)(^{+16}_{- 0})$ GeV, where the errors are statistical and systematic, respectively. In addition, from the analysis of the difference between the vector and axial-vector channels, we obtain some of the four-quark condensates.