Off-forward gluonic structure of vector mesons

Abstract

The spin-independent and transversity generalized form factors (GFFs) of the ϕ meson are studied using lattice QCD calculations with light quark masses corresponding to a pion mass m π ∼ 450ð5Þ MeV. One transversity and three spin-independent GFFs related to the lowest moments of leading-twist spinindependent and transversity gluon distributions are obtained at six nonzero values of the momentum transfer up to 1.2 GeV 2 . These quantities are compared with the analogous spin-independent quark GFFs and the electromagnetic form factors determined on the same lattice ensemble. The results show quantitative distinction between the spatial distribution of transversely polarized gluons, unpolarized gluons, and quarks and point the way towards further investigations of the gluon structure of nucleons and nuclei.

First lattice QCD study of the gluonic structure of light nuclei

“…This number can be compared with the unrenormalized result for the gluon momentum fraction in the deuteron, subject to these caveats and under the assumption that the multiplicative renormalization of the two operators is similar. At m π ∼ 806 MeV, the bare result is hxi ðdÞ g ¼ b ðdÞ 2 ¼ 0.51ð5Þ, giving a ratio of the transversity to spin-independent gluon structure quantities that is approximately an order of magnitude smaller than seen in previous studies of the ϕ meson [44,45] at m π ∼ 450 MeV (again, subject to assumptions about renormalization effects cancelling in this ratio). This scaling is consistent with expectations from large-N c , which predicts an additional suppression of 1=N 2 c of the transversity operator relative to the spin-independent operator in the deuteron [64][65][66][67][68] as compared to the ratio in a typical compact spin-1 hadron such as the ϕ meson.…”

“…The value indicates a suppression of this quantity relative to the momentum fraction that is a factor of 5-10 more severe than observed in LQCD calculations of the same distributions in a ϕ meson [44,45], as predicted by large-N c [64][65][66][67][68]. Future calculations of this quantity at lighter values of the pion mass will allow this result to be extrapolated to the physical point and will provide important information guiding design requirements for experiments at Jefferson Lab [28] and the EIC that seek to perform first measurements of non-nucleonic gluons in nuclei.…”

“…There have been studies of the pion [39] and nucleon [40,41] gluon momentum fractions and the gluon contributions to the nucleon mass and spin [41][42][43], as well as the generalized form factors corresponding to the momentum fraction and first moment of the transversity distribution of the ϕ meson [44,45]. In this work, these studies are extended to light nuclei for the first time.…”

Polynomiality sum rules for generalized parton distributions of spin-1 targets

“…As GFFs appear in the decomposition of local operators, they can be calculated on the lattice [14][15][16][17][18][19]. From the computation of these local matrix elements, after performing an inverse Mellin transform, the GPDs or collinear parton distribution functions (in the case of forward matrix elements) can in principle be recovered.…”

“…A complete picture of polynomiality for spin-1 targets is desirable due to an emerging interest in the partonic structure of particular spin-1 targets, and hard exclusive reactions involving such targets. Generalized parton distributions of the deuteron [26][27][28][29][30][31][32][33][34][35], rho meson [36][37][38][39], phi meson [19], and photon [40][41][42] have been the subjects of theoretical studies. Deeply virtual Compton scattering from the deuteron has been performed at HERMES [43,44], and is a topic of interest at Jefferson Lab [45,46], as well as the proposed Electron Ion Collider [47].…”