Self-Renormalization of Quasi-Light-Front Correlators on the Lattice

Abstract

In applying large-momentum effective theory, renormalization of the Euclidean correlators in lattice regularization is a challenge due to linear divergences in the self-energy of Wilson lines. Based on lattice QCD matrix elements of the quasi-PDF operator at lattice spacing a= 0.03 fm ∼ 0.12 fm with clover and overlap valence quarks on staggered and domain-wall sea, we design a strategy to disentangle the divergent renormalization factors from finite physics matrix elements, which can be matched to a continuum scheme at short distance such as dimensional regularization and minimal subtraction. Our results indicate that the renormalization factors are universal in the hadron state matrix elements. Moreover, the physical matrix elements appear independent of the valence fermion formulations. These conclusions remain valid even with HYP smearing which reduces the statistical errors albeit reducing control of the renormalization procedure. Moreover, we find a large non-perturbative effect in the popular RI/MOM and ratio renormalization scheme, suggesting favor of the hybrid renormalization procedure proposed recently.

Quantum algorithms for transport coefficients in gauge theories

“…Despite these issues, efforts have been undertaken to extract nonperturbative inputs [29] -e.g. parton distrubtion functions (PDFs) [33][34][35][36][37][38], phase diagrams [39][40][41][42], transport coefficients [43][44][45][46][47][48] -for the models from lattice QCD, albeit with large uncertainties.…”

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

“…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]. Indeed, our study shows that the square root of Wilson loop combined with short distance hadron matrix elements is able to eliminate all UV divergences of the quasi-TMDPDF operator and thus ensures a well-defined continuum limit, while the RI/MOM scheme fails in a way similar to that in the quasi-PDF case.…”

“…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.…”

“…The source/sink setup and also the ground state matrix element extraction are similar to that in Refs. [21,23].…”