Abstract
The gravitational form factors for a hadron, the form factors for the hadron matrix element of the QCD energy-momentum tensor, not only describe the coupling of the hadron with a graviton, but also serve as unique quantities for describing the shape inside the hadron reflecting dynamics of quarks and gluons, such as the internal shear forces acting on the quarks/gluons and their pressure distributions. We consider the quark contribution to the gravitational form factors for a (pseudo)scalar hadron, and derive and clarify the relations satisfied by them as direct consequences of the symmetries and the equations of motion in QCD, and connections to the generalized parton distributions. Our results reveal the connections between the gravitational form factors and the higher-twist quark-gluon correlation effects inside the hadrons.
Highlights
The gravitational form factors of hadrons have received considerable attention recently [1,2,3,4]
It has been demonstrated [19] that the behaviors of the gravitational form factors for the pion could be extracted through the determination of the generalized distribution amplitudes (GDAs) [8,20,21,22] using the Belle data on γÃγ → π0π0
It is remarkable that the formulas in (47) provide the exact relations between the three independent gravitational form factors arising in (6) and the second moment of the three generalized parton distributions (GPDs) which form a complete set of GPDs associated with the nonlocal quark-antiquark vector operator
Summary
The gravitational form factors of hadrons have received considerable attention recently [1,2,3,4]. Their empirical information was considered to be severely restricted because the pion target for measuring its GPDs is unavailable It has been demonstrated [19] that the behaviors of the gravitational form factors for the pion could be extracted through the determination of the generalized distribution amplitudes (GDAs) [8,20,21,22] using the Belle data on γÃγ → π0π0. We discuss the relations which hold for the gravitational form factors for a spin-0 particle such as a pion We clarify how those relations are derived as direct consequences of constraints (symmetries and equations of motion) in QCD, applied to the gauge-invariant operator corresponding to the quark contribution for the energy-momentum tensor. Results are immediately extended to the corresponding relations for the gravitational form factors of the nucleon
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