Relativistic composite-particle theory of the gravitational form factors of pion: quantitative results

Abstract

We use a version of the instant-form relativistic quantum mechanics of composite systems to obtain the gravitational form factors of the pion in a common approach to its electroweak and gravitational properties. In the preceding work [arXiv:2010.11640] we formulated the mathematical background, presented the principal scheme of calculation and testified the obtained qualitative results to satisfy the general constraints given by the principles of the theory of hadron structure. In the present work we give the detailed calculation of the gravitational form factors in large range of momentum transfer, their static limits and the slopes at zero value, the mean-square mass and mechanical radii of the pion. Now we take into account the qravitational structure of the constituent quarks. We show that the results are almost insensitive to the type of the model two-quark wave function in a close analogy to the case of the pion electromagnetic form factor. We present a correct calculation of the form factor $D$ and corresponding matrix element of the energy-momentum tensor, going beyond the scope of the modified impulse approximation. Most of the parameters that we use for the calculation had been fixed even earlier in our works on the pion electromagnetic form factors. The only free parameter is the $D$-term of the constituent quark, which we fix by fitting the result for the slope at zero of the normalized to pion $D$-term form factor $D$ of pion, to a choosen experimental value.

13 pages, 3 figures (5 panels), RevTex 4-2. V3: considerable changes in presentaton, results unchanged. Version accepted by PRD

References in corpus (12)

• Electron-Ion Collider in China
• The mass radius of the proton
• Dispersive evaluation of the D-term form factor in deeply virtual Compton scattering
• Nucleon mass radii and distribution: Holographic QCD, Lattice QCD and GlueX data
• First-time measurement of Timelike Compton Scattering
• The gravitational form factor D(t) of the electron
• 2D energy-momentum tensor distributions of nucleon in a large-$N_c$ quark model from ultra-relativistic to non-relativistic limit
• A bound on the nucleon Druck-term from chiral EFT in curved space-time and mechanical stability conditions
• The Three-loop MHV Octagon from $\bar{Q}$ equations
• Proton and deuteron mass radii from near-threshold $\varphi$-meson photoproduction
• Quark spin-orbit correlations in the pion meson in light-cone quark model
• K0 and K+ meson electromagnetic form factors: a nonperturbative relativistic quark model versus experimental, perturbative and lattice Quantum-Chromodynamics results

Cited by in corpus (7)

• Gravitational form factors of pion from top-down holographic QCD
• Dominance of gluonic scale anomaly in confining pressure inside nucleon and D-term
• Pion gravitational form factors at large momentum transfer in the instant-form relativistic impulse approximation approach
• Gravitational form factors of pions, kaons and nucleons from dispersion relations
• A step towards estimation of the neutral-hadron size: the gravitational mass radius of pi0 meson in a relativistic theory of composite particles
• Scale-anomaly-induced binding pressure in hadrons
• Scalar-glueball-mediated scale-anomaly dominance of the confining pressure of the pion in holographic QCD