LaMET 2021 Online

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Martha Constantinou (Temple University), Xiangdong Ji, Huey-Wen Lin, Peter Petreczky (BNL), David Richards (Jefferson Lab), Andreas Schaefer (Regensburg University), Yi-Bo Yang (CAS), Yong Zhao (Brookhaven National Laboratory)
Description

The 2021 Meeting on Lattice Parton Physics from Large-Momentum Effective Theory (LaMET 2021) will be held online by Center for Nuclear Femtography (CNF) at SURA in Washington DC. The meeting will take place from Dec. 7-9, 2021. Registration is open now at https://indico.cern.ch/event/1082505/, and abstracts can be submitted for presentation. The deadline for abstract submission is 12:00 AM EST, Nov. 15, 2021.

Large-momentum effective theory (LaMET) is based on the field theoretical realization of Feynman parton model in which PDFs are momentum distributions of quarks and gluons in an infinite momentum hadron state. One can start from the momentum distributions in a hadron with finite but large momentum, which can be calculated in Euclidean approaches such as lattice QCD, and then expand the results systematically. The leading term is the PDFs after proper field-theoretical matching and running. Over the past years, LaMET has enabled much progress in the lattice QCD calculation of PDFs as well as GPDs and TMDs. The lattice data for LaMET calculations can also be analyzed in coordinate-space factorization approaches to get moments of PDFs or $x$-distributions through phenomenological parametrizations.  

Due to the current situation with Covid-19, LaMET 2021 will be held using Zoom video conferencing and a Slack working space for participants to interact with each other. Zoom and Slack will be open to registered participants only. To accommodate participants around the world, talks will start 9:00am and end at 12:05pm in US EST. We will first consider talks on newly published works, and priority will be given to postdocs and advanced students.

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Click here to join Slack (from LaMET 2020)

If you have any question, please contact with Dr. Yong Zhao (yong.zhao@anl.gov).

Previous workshops in this series:

CNF (SURA) and CFNS (Stony Brook U), virtual Meeting, September 7-11, 2020

Brookhaven National Laboratory, NY. April 17-19, 2019

College Park, MD. April 6-8, 2018

Beijing, China. July 14-16, 2017

Shanghai, China. December 17-18, 2016

College Park, MD. March 30 - April 2, 2014

Shanghai, China. November 2-4, 2012

Registration
Registration for LaMET 2021
Participants
  • Alexey Vladimirov
  • Andreas Metz
  • Anthony Grebe
  • Aurora Scapellato
  • Carl Carlson
  • Chang Yang
  • Chen Chen
  • Chien-yu Chou
  • Chris Monahan
  • Colin Egerer
  • David Richards
  • Fei Huang
  • Fei Yao
  • Feng Yuan
  • Fernanda Steffens
  • Frank Winter
  • Gen Wang
  • Guy de Teramond
  • Heng-Tong Ding
  • Huey-Wen Lin
  • Ian Cloet
  • ismail zahed
  • Jack Dodson
  • Jack Holligan
  • Jia-Yue ZHANG
  • Jianhui Zhang
  • Jinchen He
  • Jiunn-Wei Chen
  • Johannes Michel
  • Joseph Delmar
  • Joseph Karpie
  • Jun Hua
  • Jun Zeng
  • Keh-Fei Liu
  • Krzysztof Cichy
  • Lisa Walter
  • Liuming Liu
  • Luchang Jin
  • Markus Ebert
  • Martha Constantinou
  • Matthias Burkardt
  • Maximilian Schlemmer
  • Min-Huan Chu
  • Nikhil Karthik
  • Patrick Barry
  • peng sun
  • Peter Petreczky
  • Piotr Korcyl
  • Qi Shi
  • Qi-An Zhang
  • Raza Sufian
  • Robert Edwards
  • Robert Perry
  • Ruilin Zhu
  • Salvatore Cali
  • santanu mondal
  • Savvas Zafeiropoulos
  • Sebastian Lahrtz
  • Shohini Bhattacharya
  • Shuai Zhao
  • Simonetta Liuti
  • Stan Brodsky
  • Swagato Mukherjee
  • Tobias Sizmann
  • Vladimir Braun
  • Wayne Morris
  • Wei Wang
  • Wei-Yang Liu
  • Xiang Gao
  • Xiangdong Ji
  • Xiaonu Xiong
  • Xu Cao
  • Xuanbo Tong
  • Yao Ji
  • Yi Chen
  • Yi-Bo Yang
  • Yong Zhao
  • Yu-Jie Zhang
  • Yushan Su
  • Zhifu Deng
  • Zhiquan Sun
  • Zhuoyi Pang
  • 宽 张
  • 志鹏 邢
Contact Dr. Yong Zhao
    • Welcome
      Convener: Xiangdong Ji
    • Session I
      Convener: Martha Constantinou (Temple University)
      • 1
        Lattice QCD Determination of the Bjorken-$x$ Dependence of PDFs at Next-to-next-to-leading Order

        In this talk, we present a direct calculation of the $x$-dependence of pion valence PDF with the large-momentum effective theory approach. In this calculation we adopt the most up-to-date theoretical developments on the systematic corrections, which include the hybrid renormalization scheme that rigorously renormalizes the lattice matrix elements at both short and long distances, as well as the two-loop matching kernel that allows for direct calculation of the $x$-dependence of the PDF without any model assumption. Therefore, we are able to make predictions for the PDF at $x\in [x_{\rm min}, x_{\rm max}]$ where the systematic uncertainties are under control, which is a firm step towards precision-controlled calculation.

        Speaker: Yong Zhao
      • 2
        Valence parton distribution of pion from lattice QCD at physical point

        We present the first lattice calculation of pion valence parton distribution using matching formula at NNLO level. We use the Wilson-Clover fermion on three 2+1 flavor HISQ ensembles of lattice spacings a = 0.04, 0.06 and 0.076 fm, with two pion mass including the physical one. Two unitary Domain-Wall calculations at physical point are also presented. This allows us to control the continuum limit, quark mass effects as well as the chiral symmetry. Our analysis use ratio-based schemes to renormalize the equal-time bilocal quark-bilinear matrix elements. We extract first few moments model independently and reconstruct the x-dependent PDF.

        Speaker: Xiang Gao (BNL&CCNU)
      • 3
        Review on Linear Divergence

        Large-momentum effective theory provides a way to extract the parton physics from lattice data based on first-principle calculation. 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. We will give a review on different renormalization methods to deal with linear divergences, including RI/MOM and ratio scheme. In these renormalization methods, people divide the bare hadron matrix element by another matrix element. Then we will talk about the self-renormalization method proposed recently, including a detailed numerical test on the linear divergence factors in the previous methods. Our test shows that the linear divergence can be eliminated in the ratio scheme. Moreover, we find a large non-perturbative effect in the RI/MOM and
        ratio scheme, suggesting favor of the hybrid renormalization procedure proposed recently. Finally, we will talk about the hybrid renormalization method.

        Speaker: Yushan Su (University of Maryland)
      • 4
        Topics in LaMET

        I would like to talk about some unrelated topics in LaMET, including the renormalon effect, applying Chiral Perturbation Theory to quasi-PDFs, and the matching kernels for the hybrid renormalization and self-renormalization.

        Speaker: Jiunn-Wei Chen
    • 09:55
      Break and Discussion
    • Session II
      Convener: Peter Petreczky (BNL)
      • 5
        The continuum and leading twist limits of pseudo-PDFs

        The continuum limit is a fundamental step when using a lattice regulator and necessary for any high precision calculation using lattice QCD. The matrix elements used in determining a PDF have two dimensionful parameters, compared to the 0 or 1 of most lattice calculations, which significantly complicates the continuum limit extrapolation. In this presentation, I will describe a method which will allow for a continuum limit extrapolation from any ensemble without having to fix any of the parameters. It also can be extended to other systematic errors such as removing higher twist effects. I will demonstrate this method on a set of ensembles with $m_\pi = 440$ MeV and lattice spacings $a = 0.048, 0.065,$ and $0.075$ fm.

        Speaker: Joseph Karpie
      • 6
        Towards High-Precision Nucleon Parton Distributions via Distillation

        We apply the Distillation spatial smearing program to the extraction of the
        unpolarized isovector valence PDF of the nucleon using the pseudo-distribution formalism. The improved volume sampling and control of excited-states afforded by distillation leads to a dramatically improved determination of the requisite Ioffe-time Pseudo-distribution (pITD).
        The valence PDF is extracted by analyzing both the matched Ioffe-time Distribution (ITD), as well as a direct matching of the pITD to the PDF. The latter method of extraction is facilitated by a novel expansion of the pITD in a set of Jacobi polynomials using the NLO coordinate space matching kernel. Generalizing this expansion, we are able to introduce nuisance parameters to quantify and remove higher-twist and discretization effects present in the pITD signal - the most notable among these being a short-distance tension of the pITD with the expected DGLAP evolution of the unpolarized pseudo-PDF. Observance and correction of this discrepancy underscores the utility of distillation in such structure studies. Prospects for other collinear distributions is also discussed.

        Speaker: Colin Egerer (Jefferson Lab)
      • 7
        Lattice Calculation of the Second Moment of the Pion Light-Cone Distribution Amplitude

        The pion light-cone distribution amplitude (LCDA) carries information about the momentum distribution of its quarks, which is an important input to various experiments. We present a proof-of-concept lattice calculation of the second Mellin moment of the pion LCDA as the first numerical implementation of the heavy-quark operator product expansion (HOPE) method. The resulting value for the second Mellin moment, determined in quenched QCD at a pion mass of $m_\pi = 550$ MeV at a factorization scale of 2 GeV, is $\langle \xi^2 \rangle = 0.210 \pm 0.013$ (stat.) $\pm 0.034$ (sys.). This result is compatible with those from previous determinations of this quantity.

        Speaker: Anthony Grebe
      • 8
        Investigation of the fourth moment of the pion light-cone distribution amplitude

        The light-cone distribution amplitude (LCDA) is a key object of interest in a range of high-energy, exclusive processes in QCD. In this talk, we describe the application of the heavy quark operator product expansion (HOPE) method to a preliminary study of the fourth Mellin moment of the pion LCDA. This constitutes the first study of the fourth moment from lattice QCD. We present an exploratory investigation at a pion mass of 560 MeV in the quenched approximation.

        Speaker: Robert Perry (National Yang Ming Chiao Tung University)
      • 9
        Global QCD Analysis of Pion Parton Distributions Including Lattice QCD Data

        For the first time, we perform a fit of pion parton distribution functions (PDFs) to reduced pseudo Ioffe time distributions and current-current correlator "good lattice cross sections" generated from lattice QCD simultaneously with experimental data. We make use of the factorization formulas convoluting the matching coefficients with the valence quark distribution to fit to real components of the lattice QCD data. We discuss the impacts of each of the lattice QCD datasets on the central values and uncertainties of the various JAM PDF sets, as well as quantify the systematic effects associated with the lattice.

        Speaker: Patrick Barry
    • Discussion: Additional Discussion
    • Session I
      Convener: Huey-Wen Lin
      • 10
        Pion and kaon distribution amplitudes and SU(3) flavor breaking effect from lattice QCD

        We present the state-of-the-art lattice QCD calculation of the light-cone distribution amplitudes (DAs) of pion and kaon using large-momentum effective theory. The calculation is done at three lattice spacings $a\approx\{0.06,0.09,0.12\}$~fm and physical pion and kaon masses, with the meson momenta $P_z = \{1.29,1.72,2.15\}$ GeV. The result is non-perturbatively renormalized in a recently proposed hybrid scheme, and extrapolated to the continuum as well as the infinite momentum limit. We find {a significant deviation of the pion and kaon DAs from the asymptotic form, and make a prediction for the $SU(3)$ flavor breaking effect in the kaon DA.

        Speaker: Jinchen He
      • 11
        Distribution amplitudes of K* and φ from lattice QCD with large momentum effective theory

        We present the first lattice QCD calculation of the distribution amplitudes of longitudinally and transversely polarized vector mesons K∗ and φ using large momentum effective theory. We use the clover fermion action on three ensembles with 2+1+1 flavors of highly improved staggered quarks (HISQ) action, generated by MILC collaboration, at physical pion mass and {0.06, 0.09, 0.12} fm lattice spacings, and choose three different hadron momenta Pz = {1.29,1.72,2.15} GeV. The resulting lattice matrix elements are nonperturbatively renormalized in a hybrid scheme proposed recently. An extrapolation to the continuum and infinite momentum limit is carried out. We find that while the longitudinal distribution amplitudes tend to be close to the asymptotic form, the transverse ones deviate rather significantly from the asymptotic form. Our final results provide crucial ab initio theory inputs for analyzing pertinent exclusive processes.

        Speaker: Jun Hua
      • 12
        The transversity parton distribution function of the nucleon using the pseudo-distribution approach

        I will present some recent results from the HadStruc collaboration on the extraction of transversity PDF of the proton by using fits to NLO leading-twist OPE. I will explain how the systematic errors are taken care of, and then present the x-dependence of the transversity PDF and its comparison with recent JAM global fit results.

        Speaker: Nikhil Karthik
      • 13
        Updated Result on Nucleon Transversity Parton Distribution Function from Lattice QCD

        In this talk, I present some updated results on nucleon transversity parton distribution function (PDF) from lattice QCD using large-momentum effective theory. The calculation is done with three lattice spacings, 0.086, 0.064 and 0.049 fm. The bare matrix elements are nonperturbatively renormalized in a recently proposed hybrid scheme. Also a continuum extrapolation is performed. Our results show agreement with recent global analyses within errors.

        Speaker: Fei Yao
    • 10:05
      Break and Discussion
    • Session II
      Convener: David Richards (Jefferson Lab)
      • 14
        Polarized gluon pseudodistributions at short distances

        We present the results that are necessary in the ongoing lattice calculations of the polarized gluon parton distribution functions within the pseudo-PDF approach. We give a classification of possible two-gluon correlator functions and identify those that contain the invariant amplitude determining the polarized gluon PDF in the light-cone $z^2 \to 0$ limit. One-loop calculations have been performed in the coordinate representation and in an explicitly gauge-invariant form. We introduce the reduced Ioffe-time distribution (ITD), which requires a special construction in this case, and obtain the matching relation between the reduced ITD and its light-cone analog that is necessary for conversion of lattice data into the light-cone PDF.

        Speaker: Wayne Morris
      • 15
        Gluon Parton Distribution of the Pion and Nucleon from Lattice QCD

        We present the $x$-dependent nucleon and pion gluon distribution from lattice QCD using the pseudo-PDF approach, on lattice ensembles with $2+1+1$ flavors of highly improved staggered quarks (HISQ), generated by MILC Collaboration. We use clover fermions for the valence action and momentum smearing to achieve pion boost momentum up to 2.56~GeV on three lattice spacings $a\approx 0.9, 0.12$ and 0.15~fm and three pion masses $M_{\pi}\approx 220$, 310 and 690~MeV.
        We compare our pion and preliminary nucleon gluon results with the determination by global fits.

        Speaker: Zhouyou Fan
      • 16
        Gluon distributions of the nucleon from lattice QCD

        We present lattice QCD calculation of unpolarized and polarized gluon Ioffe-time distributions using the pseudo-PDFs approach. We construct the nucleon interpolation fields using the distillation technique and smear the gauge fields using gradient flow. We calculate flow time-independent reduced Ioffe-time pseudo-distribution and from that, determine the unpolarized gluon PDF in the $\overline{\rm MS}$ scheme at $\mu = 2$ GeV. We also present progress towards determining gluon helicity distribution from lattice QCD calculation.

        Speaker: Raza Sufian
      • 17
        One-loop structure of parton distribution for the gluon condensate and "zero modes"

        We present the results for the one-loop corrections to the "gluon condensate" twist-4 PDF F(x), in particular, we give expression for the $gg$-part of its evolution kernel. To enforce strict compliance with the gauge invariance requirements, we have used on-shell states for external gluons and have obtained identical results both in Feynman and light-cone gauges. No "zero mode" terms were found for $F(x)$. However, a $q^2 \delta (x)$ term was found for the $\xi=0$ GPD $F(x,q^2)$ at nonzero momentum transfer $q$. These results do not agree with the original attempt of one-loop calculations of $F(x)$ for gluon states, which sets alarm warning for calculations and the lattice renormalization procedures that use matrix elements with virtual external gluons.

        Speaker: Shuai Zhao (Old Dominion University/Jefferson Lab)
    • Discussion: Additional Discussion
    • Session I
      Convener: Yi-Bo Yang (CAS)
      • 18
        Light-Front Wave Functions From LaMET

        Light-front wave functions play a fundamental role in the light-front quantization approach to QCD and hadron structure. However, a naive implementation of the light-front quantization suffers from various subtleties including the well-known zero-mode problem such as the associated rapidity divergences as well as breaking of spatial rotational symmetry. In the talk, I will show that the light-front quantization should be viewed as an effective theory in which small $k^+$ modes have been effectively ``integrated out'', with an infinite number of renormalization constants. Instead of solving light-front quantized field theories directly, we make the large momentum expansion of the equal-time Euclidean correlation functions in instant quantization as an effective way to systematically calculate light-front correlations, including the light-front wave function amplitudes. This large-momentum effective theory accomplishes an effective light-front quantization through lattice QCD calculations. We demonstrate our approach using an example of a pseudo-scalar meson wave function.

        Speaker: Yizhuang Liu (Jagiellonian University)
      • 19
        Collins-Soper kernel from transverse momentum-dependent wave functions in LaMET

        In this work we present the transversity $b_{\perp}$-dependence Collins-Soper kernel extracted from pion transverse momentum dependent wave functions in the framework of large momentum effective theory from lattice QCD. We use clover fermion action with $2 + 1 + 1$ flavors of highly improved staggered quarks (HISQ), generated by MILC Collaboration. A single ensemble is used, with lattice spacing $a=0.12$fm and volume as $L^3\times T=48^3\times64$. The results are presented based on pion mass $M_{\pi}=670$MeV, and three hadron momenta as $P^z = 2\pi/L\times\{8, 10, 12\} = \{1.72, 2.15, 2.58\}$GeV. The result of Collins-Soper kernel is determined of joint fit through momentum pairs.

        Speaker: Min-Huan Chu (Shanghai Jiao Tong University)
      • 20
        Lattice QCD calculation of the Collins-Soper kernel from quasi TMDPDFs

        I will present a LQCD calculation of the nonperturbative Collins-Soper kernel, which describes the rapidity evolution of quark transverse-momentum-dependent parton distribution functions. The kernel is extracted at transverse momentum scales in the range 400 MeV < qT < 1.7 GeV in a calculation with dynamical fermions and quark masses corresponding to a larger-than-physical pion mass of 538 MeV. It is found that different approaches to extract the Collins-Soper kernel from the same underlying lattice QCD matrix elements yield significantly different results and uncertainty estimates, revealing that power corrections, such as those associated with higher-twist effects, and perturbative matching between quasi and light-cone beam functions, cannot be neglected.

        Speaker: Michael Wagman
      • 21
        Renormalize quasi TMD-PDF on lattice

        Non-local operator has linear divergence on lattice. RI/MOM scheme cannot eliminate the linear divergence in quasi-PDF operator, especially for the clover valence quark. Using RI/MOM scheme will undermine the credibility of our results.
        We try to use the square root of Wilson loop to renormalize bare matrix element of TMD-PDF. When calculating TMD-PDF in the rest frame, we found renormalized matrix elements on different lattice spacings are separated, especially for the finer lattice. But if we change the scale from fm to a(lattice spacing), the curves of different lattice spacings are consistent, which indicates that the linear divergence has been eliminated and only the log(z/a) and log(b/a) are left. In fact, perturbation theory tells us that Wilson loop is not able to cancel out all the log divergences, even in the one-loop level.
        We are trying to remove those log divergences and renormalize quasi TMD-PDF.

        Speaker: Kuan Zhang (Institute of Theoretical Physics,Chinese Academy of Sciences)
    • 10:05
      Break
    • Session II
      Convener: Andreas Schaefer (Regensburg University)
      • 22
        Disentangling Long and Short Distances in Momentum-Space TMDs

        The extraction of nonperturbative TMD physics is made challenging by prescriptions that shield the Landau pole, which entangle long- and short-distance contributions in momentum space. The use of different prescriptions then makes the comparison of fit results for underlying nonperturbative contributions meaningless on their own. We propose a model-independent method to restrict momentum-space observables to the perturbative domain. This method is based on a set of integral functionals that act linearly on terms in the conventional position-space operator product expansion (OPE). Artifacts from the truncation of the integral can be systematically pushed to higher powers in $\Lambda_{\rm QCD}/k_T$. We demonstrate that this method can be used to compute the cumulative integral of TMDPDFs over $k_T$ in terms of collinear PDFs, accounting for both radiative corrections and evolution effects. This gives a systematic way of correcting the naive picture where the TMDPDF integrates to a collinear PDF, and we find that for the unpolarized distribution the corrections are a percent-level effect. We also show that, when supplemented with experimental data and improved perturbative inputs, these functionals will enable model-independent limits to be put on the nonperturbative OPE contributions in the Collins-Soper kernel and intrinsic TMD distributions.

        Speaker: Zhiquan Sun
      • 23
        x-dependence of transversity GPDs on the lattice

        In this talk we present results for isovector transversity generalized parton distributions (GPDs) of the proton obtained within lattice QCD. We employ the quasi-distribution formalism, which relies on computations of nonlocal matrix elements of boosted hadron states. Large momentum effective theory (LaMET) is then used to match quasi- to light-cone GPDs.
        Results are obtained on an $N_f=2+1+1$ ensemble of maximally twisted mass fermions, with pion mass $M_\pi=260$ MeV and lattice spacing $a\simeq 0.093$ fm. The proton is boosted up to 1.67 GeV. Using this setup we disentangle the four transversity GPDs that exist for the proton ($H_T$, $E_T$, $\tilde{H}_T$, $\tilde{E}_T$) and extract the $x$-dependence of the GPDs at zero and nonzero skewness.

        Speaker: Aurora Scapellato
      • 24
        First Lattice QCD Study of Proton Twist-3 GPDs

        Calculating the x-dependence of PDFs and GPDs from lattice QCD has become feasible in the last few years due to novel approaches. In the work presented, we employ the quasi-distributions method, which relies on matrix elements of non-local operators, matched to the light-cone distributions using Large Momentum Effective Theory (LaMET). We focus on results for the first-ever lattice QCD calculation of twist-3 GPDs. The calculation is performed using one ensemble of two degenerate light, a strange and a charm quark (Nf =2+1+1) of maximally twisted mass fermions with a clover term leading to a pion mass of 260 MeV.

        Speaker: Jack Dodson
      • 25
        QCD factorization for twist-3 quasi and pseudo-distributions

        In this talk, I will discuss our recent studies of the twist-3 nucleon parton distribution functions suitable for lattice simulations. The corresponding factorized expressions are derived in terms of the twist-two and twist-three collinear distributions to one-loop accuracy. We present the one-loop matching coefficient functions both in position space, as the factorization theorem for Ioffe-time distributions, and in momentum space, for quasi- and pseudo-distributions.

        Speaker: Yao Ji
    • Discussion: Additional Discussion