arXiv subjects

Jian-Hui Zhang

Publications and source records attributed to Jian-Hui Zhang.

At least 55 records · Page 3Linked to original sources

arXiv2021

A Hybrid Renormalization Scheme for Quasi Light-Front Correlations in Large-Momentum Effective Theory

In large-momentum effective theory (LaMET), calculating parton physics starts from calculating coordinate-space-$z$ correlation functions $\tilde h(z, a,P^z)$ in a hadron of momentum $P^z$ in lattice QCD. Such correlation functions involve both linear and logarithmic divergences in lattice spacing $a$, and thus need to be properly renormalized. We introduce a hybrid renormalization procedure to match these lattice correlations to those in the continuum $\overline{\rm MS}$ scheme, without introducing extra non-perturbative effects at large $z$. We analyze the effect of ${\cal O}(Λ_{\rm QCD})$ ambiguity in the Wilson line self-energy subtraction involved in this hybrid scheme. To obtain the momentum-space distributions, we recommend to extrapolate the lattice data to the asymptotic $z$-region using the generic properties of the coordinate space correlations at moderate and large $P^z$, respectively.

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arXiv2020

Complete Matching for Quasi-distribution Functions in Large Momentum Effective Theory

We complete the procedure of extracting parton distribution functions (PDFs) using large momentum effective theory (LaMET) at leading power accuracy in the hadron momentum. We derive a general factorization formula for the quasi PDFs in the presence of mixing, and give the corresponding hard matching kernel at $\mathcal O(α_s)$, both for the unpolarized and for the polarized quark and gluon quasi-PDFs. Our calculation is performed in a regularization-independent momentum subtraction scheme. The results allow us to match the nonperturbatively renormalized quasi-PDFs to normal PDFs in the presence of mixing, and therefore can be used to extract flavor-singlet quark PDFs as well as gluon PDFs from lattice simulations.

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arXiv2020

Parton distributions and lattice QCD calculations: toward 3D structure

The strong force which binds hadrons is described by the theory of Quantum Chromodynamics (QCD). Determining the character and manifestations of QCD is one of the most important and challenging outstanding issues necessary for a comprehensive understanding of the structure of hadrons. Within the context of the QCD parton picture, the Parton Distribution Functions (PDFs) have been remarkably successful in describing a wide variety of processes. However, these PDFs have generally been confined to the description of collinear partons within the hadron. New experiments and facilities provide the opportunity to additionally explore the transverse structure of hadrons which is described by Generalized Parton Distributions (GPDs) and Transverse Momentum Dependent Parton Distribution Functions (TMD PDFs). In our previous review, we compared and contrasted the two main approaches used to determine the collinear PDFs: the first based on perturbative QCD factorization theorems, and the second based on lattice QCD calculations. In the present report, we provide an update of recent progress on the collinear PDFs, and also expand the scope to encompass the generalized PDFs (GPDs and TMD PDFs). We review the current state of the various calculations, and consider what new data might be available in the near future. We also examine how a shared effort can foster dialog between the PDF and Lattice QCD communities, and yield improvements for these generalized PDFs.

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arXiv2020

Pion generalized parton distribution from lattice QCD

We present the first lattice calculation of the valence-quark generalized parton distribution (GPD) of the pion using the large-momentum effective theory (LaMET) approach. We focus on the zero-skewness limit, where the GPD has a probability-density interpretation in the longitudinal Bjorken $x$ and the transverse impact-parameter distributions. Our calculation is done using clover valence fermions on an ensemble of gauge configurations with $2+1+1$ flavors (degenerate up/down, strange and charm) of highly improved staggered quarks (HISQ) with lattice spacing $a \approx 0.12$ fm, box size $L \approx 3$ fm and pion mass $m_π\approx 310$ MeV. The parton distribution function and the form factor are reproduced as special limits of the GPD as expected. Due to the large errors, this exploratory study does not show a clear preference among different model assumptions about the kinematic dependence of the GPD. To discriminate between these assumptions, future studies using higher-statistics data will be crucial.

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arXiv2019

Unpolarized isovector quark distribution function from Lattice QCD: A systematic analysis of renormalization and matching

We present a detailed Lattice QCD study of the unpolarized isovector quark Parton Distribution Function (PDF) using large-momentum effective theory framework. We choose a quasi-PDF defined by a spatial correlator which is free from mixing with other operators of the same dimension. In the lattice simulation, we use a Gaussian-momentum-smeared source at $M_π=356$ MeV and $P_z \in \{1.8,2.3\}$ GeV. To control the systematics associated with the excited states, we explore {five different source-sink separations}. The nonperturbative renormalization is conducted in a regularization-independent momentum subtraction scheme, and the matching between the renormalized quasi-PDF and $\bar{\rm MS}$ PDF is calculated based on perturbative QCD up to one-loop order. Systematic errors due to renormalization and perturbative matching are also analyzed in detail. Our results for lightcone PDF are in reasonable agreement with the latest phenomenological analysis.

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arXiv2019

Matching Quasi Generalized Parton Distributions in the RI/MOM scheme

Within the framework of large momentum effective theory (LaMET), genenaralized parton distributions (GPDs) can be extracted from lattice calculations of quasi-GPDs through a perturbative matching relation, up to power corrections that are suppressed by the hadron momentum. In this paper, we focus on isovector quark GPDs, including the unpolarized, longitudinally and transversely polarized cases, and present the one-loop matching that connects the quasi-GPDs renormalized in a regularization-independent momentum subtraction (RI/MOM) scheme to the GPDs in MS scheme. We find that the matching coefficient is independent of the momentum transfer squared. As a consequence, the matching for the quasi-GPD with zero skewness is the same as that for the quasi-PDF. Our results provide a crucial input for the determination of quark GPDs from lattice QCD using LaMET.

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arXiv2019

First direct lattice-QCD calculation of the $x$-dependence of the pion parton distribution function

We present the first direct lattice-QCD calculation of the Bjorken-$x$ dependence of the valence quark distribution of the pion. Using large-momentum effective theory (LaMET), we calculate the boosted pion state with long Wilson link operators. After implementing the one-loop matching and meson mass corrections, our result at $m_π\approx 310$ MeV is in agreement with those extracted from experimental data as well as from Dyson-Schwinger equation in small $x$ region, but a sizeable discrepancy in the large $x$ region. This discrepancy provides a nice opportunity to systematically study and disentangle the artifacts in the LaMET approach, which will eventually help to discern various existing analyses in the literature.

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arXiv2019

Symmetry Properties of Nonlocal Quark Bilinear Operators on a Lattice

Using symmetry properties, we determine the mixing pattern of a class of nonlocal quark bilinear operators containing a straight Wilson line along a spatial direction. We confirm the previous study that mixing among the lowest dimensional operators, which have mass dimension equals three, can occur if chiral symmetry is broken in the lattice action. For higher dimensional operators, we find that the dimension three operators will always mix with dimension four operators even if chiral symmetry is preserved. Also, the number of dimension four operators involved in the mixing is large hence it is impractical to remove the mixing by the improvement procedure. Our result is important to determining the Bjorken-$x$ dependence parton distribution functions using the quasi-distribution method on a Euclidean lattice. The requirement of using large hadron momentum in this approach makes the control of errors from dimension four operators even more important.

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arXiv2019

Transverse Momentum Dependent Quasi-Parton-Distributions

We investigate the transverse momentum dependent parton distributions (TMDs) in the quasi-parton-distribution framework. The long standing hurdle of the so-called pinch pole singularity from the space-like gauge links in the TMD definitions can be resolved by the finite length of the gauge link along the hadron moving direction. In addition, with the soft factor subtraction, the quasi-TMD is free of linear divergence. We further demonstrate that the energy evolution equation of the quasi-TMD a.k.a. the Collins-Soper evolution, only depends on the hadron momentum. This leads to a clear matching between the quasi-TMD and the standard TMDs.

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arXiv2019

Gaussian-weighted Parton Quasi-distribution

We propose a revised definition of quasi-distributions within the framework of large-momentum effective theory (LaMET) that improves convergence towards the large-momentum limit. Since the definition of quasi-distributions is not unique, each choice goes along with a specific matching function, we can use this freedom to optimize convergence towards the large-momentum limit. As an illustration, we study quasi-distributions with a Gaussian weighting factor that naturally suppresses long-range correlations, which are plagued by artifacts. This choice has the advantage that the matching functions can be trivially obtained from the known ones. We apply the Gaussian weighting to the previously published results for the nonperturbatively renormalized unpolarized quark distribution, and find that the unphysical oscillatory behavior is significantly reduced.

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arXiv2019

Accessing gluon parton distributions in large momentum effective theory

Gluon parton distribution functions (PDFs) in the proton can be calculated directly on Euclidean lattices using large momentum effective theory (LaMET). To realize this goal, one has to find renormalized gluon quasi-PDFs in which power divergences and operator mixing are thoroughly understood. For the unpolarized distribution, we identify four independent quasi-PDF correlators that can be multiplicatively renormalized on the lattice. Similarly, the helicity distribution can be derived from three independent multiplicatively renormalizable quasi-PDFs. We provide a LaMET factorization formula for these renormalized quasi-PDFs from which one can extract the gluon PDFs.

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arXiv2019

Proton Isovector Helicity Distribution on the Lattice at Physical Pion Mass

We present a state-of-the-art calculation of the isovector quark helicity Bjorken-$x$ distribution in the proton using lattice-QCD ensembles at the physical pion mass. We compute quasi-distributions at proton momenta $P_z \in \{2.2, 2.6, 3.0\}$~GeV on the lattice, and match them systematically to the physical parton distribution using large-momentum effective theory (LaMET). We reach an unprecedented precision through high statistics in simulations, large-momentum proton matrix elements, and control of excited-state contamination. The resulting distribution with combined statistical and systematic errors is in agreement with the latest phenomenological analysis of the spin-dependent experimental data; in particular, $Δ\bar{u}(x)>Δ\bar{d}(x)$.

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arXiv2018

Pion distribution amplitude from Euclidean correlation functions: Exploring universality and higher-twist effects

Building upon our recent study arXiv:1709.04325, we investigate the feasibility of calculating the pion distribution amplitude from suitably chosen Euclidean correlation functions at large momentum. We demonstrate in this work the advantage of analyzing several correlation functions simultaneously and extracting the pion distribution amplitude from a global fit. This approach also allows us to study higher-twist corrections, which are a major source of systematic error. Our result for the higher-twist parameter $δ^π_2$ is in good agreement with estimates from QCD sum rules. Another novel element is the use of all-to-all propagators, calculated using stochastic estimators, which enables an additional volume average of the correlation functions, thereby reducing statistical errors.

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arXiv2018

Nucleon Transversity Distribution at the Physical Pion Mass from Lattice QCD

We report a state-of-the-art lattice calculation of the isovector quark transversity distribution of the proton at the physical pion mass. Within the framework of large-momentum effective theory (LaMET), we compute the transversity quasi-distributions using clover valence fermions on 2+1+1-flavor (up/down, strange, charm) HISQ-lattice configurations with boosted proton momenta as large as 3.0~GeV. The relevant lattice matrix elements are nonperturbatively renormalized in regularization-independent momentum-subtraction (RI/MOM) scheme and systematically matched to the physical transversity distribution. With high statistics, large proton momenta and meticulous control of excited-state contamination, we provide the best theoretical prediction for the large-$x$ isovector quark transversity distribution, with better precision than the most recent global analyses of experimental data. Our result also shows that the sea quark asymmetry in the proton transversity distribution is consistent with zero, which has been assumed in all current global analyses.

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arXiv2018

Lattice Calculation of Parton Distribution Function from LaMET at Physical Pion Mass with Large Nucleon Momentum

We present a lattice-QCD calculation of the unpolarized isovector parton distribution function (PDF) using ensembles at the physical pion mass with large proton boost momenta $P_z \in \{2.2,2.6,3.0\}$~GeV within the framework of large-momentum effective theory (LaMET). In contrast to our previous physical-pion PDF result, we increase the statistics significantly, double the boost momentum, increase the investment in excited-state contamination systematics, and switch to $γ_t$ operator to avoid mixing with scalar matrix elements. We use four source-sink separations in our analysis to control the systematics associated with excited-state contamination. The one-loop LaMET matching corresponding to the new operator is calculated and applied to our lattice data. We detail the systematics that affect PDF calculations, providing guidelines to improve the precision of future lattice PDF calculations. We find our final parton distribution to be in reasonable agreement with the PDF provided by the latest phenomenological analysis.

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arXiv2018

Parton distribution functions from reduced Ioffe-time distributions

We show that the correct way to extract parton distribution functions from the reduced Ioffe-time distribution (RITD), a ratio of the Ioffe-time distribution for a moving hadron and a hadron at rest, is through a factorization formula. This factorization exists because, at small distances, forming the ratio does not change the infrared behavior of the numerator, which is factorizable. We illustrate the effect of such a factorization by applying it to results in the literature.

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arXiv2018

Pion distribution amplitude from Euclidean correlation functions

Following the proposal in [1], we study the feasibility to calculate the pion distribution amplitude (DA) from suitably chosen Euclidean correlation functions at large momentum. In our lattice study we employ the novel momentum smearing technique [2,3]. This approach is complementary to the calculations of the lowest moments of the DA using the Wilson operator product expansion and avoids mixing with lower dimensional local operators on the lattice. The theoretical status of this method is similar to that of quasi-distributions [4], which has recently been applied to the same problem in [5]. The similarities and differences between these two techniques are highlighted.

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arXiv2018

Kaon Distribution Amplitude from Lattice QCD and the Flavor SU(3) Symmetry

We present the first lattice-QCD calculation of the kaon distribution amplitude using the large-momentum effective theory (LaMET) approach. The momentum-smearing technique has been implemented to improve signals at large meson momenta. We subtract the power divergence due to Wilson line to high precision using multiple lattice spacings. The kaon structure clearly shows an asymmetry of the distribution amplitude around $x=1/2$, a clear sign of its skewness. We also study the leading SU(3) flavor symmetry breaking relations for the pion, kaon and eta meson distribution amplitudes, and the results are consistent with the prediction from chiral perturbation theory.

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