Gluonic transversity from lattice QCD

Abstract

We present an exploratory study of the gluonic structure of the φ meson using lattice QCD (LQCD). This includes the first investigation of gluonic transversity via the leading moment of the twist-two double-helicity-flip gluonic structure function ∆(x, Q 2 ). This structure function only exists for targets of spin J ≥ 1 and does not mix with quark distributions at leading twist, thereby providing a particularly clean probe of gluonic degrees of freedom. We also explore the gluonic analogue of the Soffer bound which relates the helicity flip and non-flip gluonic distributions, finding it to be saturated at the level of 80%. This work sets the stage for more complex LQCD studies of gluonic structure in the nucleon and in light nuclei where ∆(x, Q 2 ) is an 'exotic glue' observable probing gluons in a nucleus not associated with individual nucleons.

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.…”

“…The results shown in later sections use operators flowed to a total time of 1 in lattice units using an integration step size of 0.01. The effects of using different levels of HYP smearing [58], as well as gradient flow, were investigated in a similar calculation of the gluonic structure of the ϕ meson [44], with consistent results found for the different smearing implementations.…”

“…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.…”

“…The construction of these operators is detailed in Refs. [44,59], and the same notation as in those works is used here. For the first representation considered, named τ (4)- (8)] that differ by lattice-spacing artefacts, all should give the same results in the continuum limit.…”