RI/MOM renormalization of the parton quasidistribution functions in lattice regularization

Abstract

We analyze the lattice spacing dependence for the pion unpolarized matrix element of a quark bilinear operator with a Wilson link (parton quasidistribution functions operator, quasi-PDFs) in the rest frame, using 13 lattice spacings ranging from 0.032 to 0.121 fm. We compare results for three different fermion actions with or without good chiral symmetry on dynamical gauge ensembles from three collaborations. This investigation is motivated by the fact that the gauge link generates a 1=a divergence, the cancellation of which in many ratios can be numerically tricky. Indeed, our results show that this cancellation deteriorates with decreasing lattice spacing, and that the RI/MOM method leaves a linearly divergent residue for quasi-PDFs. We also show that in the Landau gauge the interaction between the Wilson link and the external state results in a linear divergence which depends on the discretized fermion action.

Pion and Kaon Distribution Amplitudes from Lattice QCD

“…Using LaMET, several calculations of the x-dependence of meson DAs have been carried out [32][33][34]. However, a recent analysis [35] showed that the nonperturbative renormalization of the quasi-light-front (quasi-LF) correlation in LaMET could be highly nontrivial, especially when off-shell quark matrix elements are used. In such a case, even after renormalization there may still be residual linear divergences rendering the continuum extrapolation problematic.…”

“…On the lattice, the numerical subtraction of linear divergences is extremely delicate. In particular, such divergences may not be fully removed if the RI/MOM renormalization scheme is used [35]. Here we adopt the self renormalization proposed in Ref.…”

Renormalization of transverse-momentum-dependent parton distribution on the lattice

“…Although there have been some preliminary lattice studies of the Collins-Soper evolution kernel and the intrinsic soft function [14][15][16][17][18][19], an important piece of information is still missing in realizing the lattice calculation of TMDPDFs, that is, a systematic study of the nonperturbative renormalization of quasi-TMDPDF operators. This is highly non-trivial, given that both the regularization-independent momentum subtraction (RI/MOM) [20] and the Wilson line/loop renormalization fail to cancel the power UV divergences in the case of straight-line quasi-PDF operators [21]. It is the purpose of this work to perform such a systematic analysis and to find a viable nonperturbative renormalization approach for the quasi-TMDPDFs, as the hybrid scheme [22] with self-renormalization in the case of quasi-PDFs [23].…”

“…Since the UV divergence shall be independent of the hadron state, as shown in the quasi-PDF case [21,23], in the following we will concentrate on the pion matrix element hπ (b, z, L) ≡ π|O γt (b, z, L)|π of the quasi-TMDPDF operator O γt (b, z, L) as an illustrative example, which can be extracted from the following ratio…”

“…where ∆m is the mass gap between the pion and its first excited state which is aournd 1 GeV. 1-step HYP smearing is applied on the staple-shaped link to enhance the signal to noise ratio (SNR), and our previous studies [21,23] on the quasi-PDF operator suggest that such a smearing will not change the renormalization behavior of the results. The source/sink setup and also the ground state matrix element extraction are similar to that in Refs.…”