Speaker
Description
Gravitational form factors are related to a particular moment of the GPDs, and are relevant to EIC physics. Gravitational form factors are defined as the hadron matrix elements of the energy-momentum tensor (EMT). In QCD, the gauge-invariant part of the EMT is expressed as a sum of the several composite operators built from quark and gluon fields. Although the total EMT is finite and is not renormalized due to energy-momentum conservation, the individual components represented by the gauge-invariant composite operators are UV divergent and are renormalized; as a result, their physical interpretations are not straightforward due to their sophisticated renormalization mixing and the associated trace anomalies. Even within the MSbar scheme in the dimensional regularization, different choices of the composite-operator basis for renormalization lead to different prescriptions for treating the renormalization mixing, and these prescriptions appear to give inequivalent results, creating a source of confusion among the researchers. We clarify the relations between those inequivalent results and discuss the consequences for the renormalized quark and gluon contributions to the EMT as well as to its trace. On this basis, we derive the EMT in terms of the renormalized composite operators at the three-loop level in the MSbar scheme. We also make contact with the four-loop extension by Ahmed, Chen, and Czakon [JHEP 01 (2023) 077], and with the two-loop results based on the gradient-flow formalism by Harlander, Kluth, and Lange [Eur. Phys. J. C 78 (2018) 944], which provide important cross-checks of our three-loop results.
As applications of our three-loop renormalized EMT, we discuss quantitative evaluations of the proton properties, taking into account the empirical information of a few relevant non-perturbative parameters: we present a quantitative evaluation of the forward values of the twist-four gravitational form factors \bar{C}_q and \bar{C}_g, which have been argued to be related to the quark and gluon contributions to the internal pressure. We also discuss the proton mass decomposition by reorganizing the terms appearing in our three-loop EMT. We further present the corresponding results for the pion, which exhibit quite different behaviors from those of the proton.
This presentation is based on our papers, 2511.18310, JHEP03 (2023) 013, JHEP01 (2019) 120, JHEP12 (2018) 008, and on our work in progress.