Pion gravitational form factors in the QCD instanton vacuum I

TL;DR

This paper investigates pion gravitational form factors within the QCD instanton vacuum model, revealing how gluonic and quark contributions shape the form factors and comparing results with lattice QCD data.

Contribution

It introduces a detailed calculation of pion EMT form factors in the instanton liquid model, including gluonic contributions and evolution to higher scales, with comparisons to lattice results.

Findings

Gluonic trace anomaly contributes half the pion mass.

Form factors are governed by glueball and scalar meson exchanges.

Results align well with recent lattice QCD calculations.

Abstract

The pion form factors of the QCD energy-momentum tensor (EMT) are studied in the instanton liquid model (ILM) of the QCD vacuum. In this approach the breaking of conformal symmetry is encoded in the form of stronger-than-Poisson fluctuations in the number of instantons. For the trace of the EMT, it is shown that the gluonic trace anomaly term contributes half the pion mass, with the other half coming from the quark-mass-dependent sigma term. The $Q^2$ dependence of the form factors is governed by glueball and scalar meson exchanges. For the traceless EMT, the spin-0 and 2 form factors are computed at next-to-leading order in the instanton density using effective quark operators. Relations between the gluon and quark contributions to the EMT form factors are derived. The form factors are also expressed in terms of the pion light-front wave functions in the ILM. The results at the low resolution scale of the inverse instanton size are evolved to higher scales using the renormalization group equation. The ILM results compare well with those of recent lattice QCD calculations.