Pion gravitational form factors in the QCD instanton vacuum I

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.

18 pages, 6 figures

References in corpus (7)

• Pion Generalized Parton Distributions with covariant and Light-front constituent quark models
• Gravitational and higher-order form factors of the pion in chiral quark models
• Trace anomaly form factors from lattice QCD
• Stress inside the pion in holographic light-front QCD
• Hadronic structure on the light-front VIII. Light scalar and vector mesons
• Pion gravitational form factors in the QCD instanton vacuum II
• Hadronic structure on the light-front VII. Pions and kaons and their partonic distributions

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• Tomography of the Rho meson in the QCD Instanton Vacuum: Transverse Momentum Dependent Parton Distribution Functions
• Scale-anomaly-induced binding pressure in hadrons
• Scalar-glueball-mediated scale-anomaly dominance of the confining pressure of the pion in holographic QCD
• Tomography of Pions and Kaons in the QCD Vacuum: Transverse Momentum Dependent Parton Distribution Functions
• Pion generalized parton distributions at zero skewness