Pion gravitational form factors in the QCD instanton vacuum. I

Journal Article · 18 September 2024 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.110.054021 · OSTI ID:2447005

Liu, Wei-Yang ; Shuryak, Edward; Weiss, Christian ; Zahed, Ismail

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 EMT, the spin-0 (trace) and spin-2 (traceless rank-2 tensor) 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. Published by the American Physical Society 2024

• Sponsoring Organization: USDOE Office of Nuclear Energy (NE)
• Grant/Contract Number: SC0023646; AC05-06OR23177
• OSTI ID: 2447005
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 5 Vol. 110; ISSN PRVDAQ; ISSN 2470-0010
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English