Abstract
A future Electron-Ion Collider will enable the gluon contributions to the gravitational form factors of the proton to be constrained experimentally for the first time. Here, the first calculation of these form factors from lattice Quantum Chromodynamics is presented. The calculations use a larger-than-physical value of the light quark mass corresponding to $m_\pi \sim 450$ MeV. All three form factors, which encode the momentum-dependence of the lowest moment of the spin independent gluon generalised parton distributions and are related to different components of the energy-momentum tensor, are resolved. In particular, the gluon $D$-term form factor, related to the pressure distribution inside the nucleon, is determined for the first time. The gluon contributions to the two gravitational form factors of the pion are also determined, and are compared to existing lattice determinations of the quark contributions to the gravitational form factors and to phenomenology.
Highlights
A defining challenge for hadronic physics research is to achieve a quantitative understanding of the structure of the proton and other hadrons in terms of their fundamental quark and gluon constituents
Performing first measurements of these quantities is a key goal of the planned electron-ion collider (EIC) [28,29], and theory constraints on the gluon Generalized parton distributions (GPDs) will provide important information as the physics case for an EIC is refined
The focus of this work is on the lowest moments of the spin-independent gluon GPDs, which are related to the nucleon matrix element of the gluon contribution to the energy-momentum tensor
Summary
A defining challenge for hadronic physics research is to achieve a quantitative understanding of the structure of the proton and other hadrons in terms of their fundamental quark and gluon constituents. Performing first measurements of these quantities is a key goal of the planned electron-ion collider (EIC) [28,29], and theory constraints on the gluon GPDs will provide important information as the physics case for an EIC is refined This manuscript presents the first LQCD determination of the complete set of gluon gravitational form factors (GFFs) of the nucleon, which are defined as the lowest moments of the spin-independent gluon GPDs. The calculations are undertaken with a larger-than-physical value of the light quark mass that corresponds to a pion mass mπ ∼ 450 MeV. V highlights the conclusions that can be drawn from this study
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