Abstract
We perform a perturbative QCD analysis of the gluonic gravitational form factors (GFFs) of the proton and pion at large momentum transfer. We derive the explicit factorization formula of the GFFs in terms of the distribution amplitudes of hadrons. At the leading power, we find that the gluon GFFs Ag and Cg scale as Agπ(t)=Cgπ(t)∼1/(−t) for pion, Agp(t)∼1/(−t)2 and Cgp(t)∼ln2(−t/Λ2)/(−t)3 for proton, respectively, where t is the momentum transfer and Λ a non-perturbative scale to regulate the endpoint singularity in Cgp calculation. Our results provide a unique perspective of the momentum dependence of the GFFs and will help to improve our understanding of the internal pressure distributions of hadrons.
Highlights
The gravitational form factors (GFFs) are the fundamental ingredients to probe the internal structure of hadrons
The GFFs can be constrained from the generalized parton distributions (GPD) [5, 6, 21,22,23] which are measured in the hard exclusive processes like deeply virtual Compton scattering [5, 6, 24,25,26] and deeply virtual meson production [27,28,29]
The factorization formalism for the GFFs follows that developed in the literature for the hard exclusive processes at large momentum transfer and the final results depend on the gauge invariant distribution amplitudes of hadrons [55,56,57,58,59,60]
Summary
We perform a perturbative QCD analysis of the gluonic gravitational form factors (GFFs) of the proton and pion at large momentum transfer. We derive the explicit factorization formula of the GFFs in terms of the distribution amplitudes of hadrons. We find that Aπg (t) = Cgπ(t) ∼ 1/(−t) for pion, Apg(t) ∼ 1/(−t) and Cgp(t) ∼ ln2(−t/Λ2)/(−t) for proton, respectively, where t is the momentum transfer and Λ a non-perturbative scale to regulate the endpoint singularity in Cgp calculation. Our results provide a unique perspective of the momentum dependence of the GFFs and will help to improve our understanding of the internal pressure distributions of hadrons
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