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Li Y, Xia SC, Alexandrou C, Cichy K, Constantinou M, Feng X, Hadjiyiannakou K, Jansen K, Liu C, Scapellato A, Steffens F, Tarello J. Lattice QCD Study of Transverse-Momentum Dependent Soft Function. PHYSICAL REVIEW LETTERS 2022; 128:062002. [PMID: 35213201 DOI: 10.1103/physrevlett.128.062002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2021] [Revised: 11/22/2021] [Accepted: 01/24/2022] [Indexed: 06/14/2023]
Abstract
In this work, we perform a lattice QCD study of the intrinsic, rapidity-independent soft function within the framework of large momentum effective theory. The computation is carried out using a gauge ensemble of N_{f}=2+1+1 clover-improved twisted mass fermion. After applying an appropriate renormalization procedure and the removal of significant higher-twist contamination, we obtain the intrinsic soft function that is comparable to the one-loop perturbative result at large external momentum. The determination of the nonperturbative soft function from first principles is crucial to sharpen our understanding of the processes with small transverse momentum such as the Drell-Yan production and the semi-inclusive deep inelastic scattering. Additionally, we calculate the Collins-Soper evolution kernel using the quasi-transverse-momentum-dependent wave function as input.
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Affiliation(s)
- Yuan Li
- School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China
| | - Shi-Cheng Xia
- School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China
| | - Constantia Alexandrou
- Department of Physics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus
- Computation-based Science and Technology Research Center, The Cyprus Institute, 20 Kavafi Str., Nicosia 2121, Cyprus
| | - Krzysztof Cichy
- Faculty of Physics, Adam Mickiewicz University, ul. Uniwersytetu Poznańskiego 2, 61-614 Poznań, Poland
| | - Martha Constantinou
- Temple University, 1925 N. 12th Street, Philadelphia, Pennsylvania 19122-1801, USA
| | - Xu Feng
- School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- Center for High Energy Physics, Peking University, Beijing 100871, China
| | - Kyriakos Hadjiyiannakou
- Computation-based Science and Technology Research Center, The Cyprus Institute, 20 Kavafi Str., Nicosia 2121, Cyprus
| | - Karl Jansen
- NIC, DESY, Platanenallee 6, D-15738 Zeuthen, Germany
| | - Chuan Liu
- School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- Center for High Energy Physics, Peking University, Beijing 100871, China
| | - Aurora Scapellato
- Temple University, 1925 N. 12th Street, Philadelphia, Pennsylvania 19122-1801, USA
| | - Fernanda Steffens
- Institut für Strahlen- und Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, Nussallee 14-16, 53115 Bonn, Germany
| | - Jacopo Tarello
- Computation-based Science and Technology Research Center, The Cyprus Institute, 20 Kavafi Str., Nicosia 2121, Cyprus
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Cichy K. Overview of lattice calculations of the x-dependence of PDFs, GPDs and TMDs. EPJ WEB OF CONFERENCES 2022. [DOI: 10.1051/epjconf/202225801005] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
For a long time, lattice QCD was unable to address the x-dependence of partonic distributions, direct access to which is impossible in Euclidean spacetime. Recent years have brought a breakthrough for such calculations when it was realized that partonic light-cone correlations can be accessed through spatial correlations computable on the lattice. Appropriately devised observables can be factorized into physical PDFs via a perturbative procedure called matching, analogous to the standard factorization of experimental cross sections. In this short review, aimed at a broader high-energy and nuclear physics community, we discuss the recent highlights of this research program. Key concepts are outlined, followed by a case study illustrating the typical stage of current lattice extractions and by a brief review of the most recent explorations. We finalize with a number of messages for the prospects of lattice determinations of partonic structure.
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Bhattacharya S, Cichy K, Constantinou M, Metz A, Scapellato A, Steffens F. Parton distribution functions beyond leading twist from lattice QCD: The
hL(x)
case. Int J Clin Exp Med 2021. [DOI: 10.1103/physrevd.104.114510] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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5
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Zhang R, Lin HW, Yoon B. Probing nucleon strange and charm distributions with lattice QCD. Int J Clin Exp Med 2021. [DOI: 10.1103/physrevd.104.094511] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Lin HW. Nucleon Tomography and Generalized Parton Distribution at Physical Pion Mass from Lattice QCD. PHYSICAL REVIEW LETTERS 2021; 127:182001. [PMID: 34767417 DOI: 10.1103/physrevlett.127.182001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2021] [Accepted: 09/28/2021] [Indexed: 06/13/2023]
Abstract
We present the first lattice calculation of the nucleon isovector unpolarized generalized parton distribution at the physical pion mass using a lattice ensemble with 2+1+1 flavors of highly improved staggered quarks generated by the MILC Collaboration, with lattice spacing a≈0.09 fm and volume 64^{3}×96. We use momentum-smeared sources to improve the signal at nucleon boost momentum P_{z}≈2.2 GeV and report results at nonzero momentum transfers in [0.2,1.0] GeV^{2}. Nonperturbative renormalization in a regularization-independent momentum-subtraction scheme is used to obtain the quasidistribution before matching to the light-cone generalized parton distributions. The three-dimensional distributions H(x,Q^{2}) and E(x,Q^{2}) at ξ=0 are presented, along with the three-dimensional nucleon tomography and impact parameter-dependent distribution for selected Bjorken x at μ=3 GeV in a modified minimal subtraction scheme.
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Affiliation(s)
- Huey-Wen Lin
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
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Karthik N, Sufian RS. Bayesian-Wilson coefficients in lattice QCD computations of valence PDFs and GPDs. Int J Clin Exp Med 2021. [DOI: 10.1103/physrevd.104.074506] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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9
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Alexandrou C, Constantinou M, Hadjiyiannakou K, Jansen K, Manigrasso F. Flavor Decomposition for the Proton Helicity Parton Distribution Functions. PHYSICAL REVIEW LETTERS 2021; 126:102003. [PMID: 33784129 DOI: 10.1103/physrevlett.126.102003] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2020] [Revised: 11/06/2020] [Accepted: 02/12/2021] [Indexed: 06/12/2023]
Abstract
We present, for the first time, an ab initio calculation of the individual up, down, and strange quark helicity parton distribution functions for the proton. The calculation is performed within the twisted mass clover-improved fermion formulation of lattice QCD. The analysis is performed using one ensemble of dynamical up, down, strange, and charm quarks with a pion mass of 260 MeV. The lattice matrix elements are nonperturbatively renormalized and the final results are presented in the MS[over ¯] scheme at a scale of 2 GeV. We give results for Δu^{+}(x), Δd^{+}(x) Δu^{-}(x), Δd^{-}(x), including disconnected quark loop contributions, as well as for Δs^{+}(x) and Δs^{-}(x). For the latter we achieve unprecedented precision compared to the phenomenological estimates.
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Affiliation(s)
- Constantia Alexandrou
- Department of Physics, University of Cyprus, P.O. Box 20537, Nicosia 1678, Cyprus
- Computation-based Science and Technology Research Center, The Cyprus Institute, 20 Kavafi Street, Nicosia 2121, Cyprus
| | - Martha Constantinou
- Department of Physics, Temple University, 1925 N. 12th Street, Philadelphia, Pennsylvania 19122-1801, USA
| | - Kyriakos Hadjiyiannakou
- Department of Physics, University of Cyprus, P.O. Box 20537, Nicosia 1678, Cyprus
- Computation-based Science and Technology Research Center, The Cyprus Institute, 20 Kavafi Street, Nicosia 2121, Cyprus
| | - Karl Jansen
- NIC, DESY, Platanenallee 6, D-15738 Zeuthen, Germany
| | - Floriano Manigrasso
- Department of Physics, University of Cyprus, P.O. Box 20537, Nicosia 1678, Cyprus
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
- Dipartimento di Fisica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica 1, 00133 Rome, Italy
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Constantinou M. The x-dependence of hadronic parton distributions: A review on the progress of lattice QCD. THE EUROPEAN PHYSICAL JOURNAL. A, HADRONS AND NUCLEI 2021; 57:77. [PMID: 33654456 PMCID: PMC7905977 DOI: 10.1140/epja/s10050-021-00353-7] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/14/2020] [Accepted: 01/13/2021] [Indexed: 06/12/2023]
Abstract
In this article, we review recent lattice calculations on the x-dependence of parton distributions, with the latter providing information on hadron structure. These calculations are based on matrix elements of boosted hadrons coupled to non-local operators and can be related to the standard, light-cone distribution functions via an appropriate factorization formalism. There is significant progress in several directions, including calculations of flavor-singlet parton distribution functions (PDFs), first calculations of generalized parton distributions (GPDs), as well as the implementation of some of the approaches for the transverse-momentum-dependent PDFs (TMD PDFs). This new direction of lattice calculations is particularly interesting for phenomenological fits on experimental data sets, as the lattice results can help improve the constraints on the distribution functions.
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11
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Bhat M, Cichy K, Constantinou M, Scapellato A. Flavor nonsinglet parton distribution functions from lattice QCD at physical quark masses via the pseudodistribution approach. Int J Clin Exp Med 2021. [DOI: 10.1103/physrevd.103.034510] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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12
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Li ZY, Ma YQ, Qiu JW. Extraction of Next-to-Next-to-Leading-Order Parton Distribution Functions from Lattice QCD Calculations. PHYSICAL REVIEW LETTERS 2021; 126:072001. [PMID: 33666473 DOI: 10.1103/physrevlett.126.072001] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2020] [Revised: 10/05/2020] [Accepted: 11/29/2020] [Indexed: 06/12/2023]
Abstract
We present for the first time complete next-to-next-to-leading-order coefficient functions to match flavor nonsinglet quark correlation functions in position space, which are calculable in lattice QCD, to parton distribution functions (PDFs). Using PDFs extracted from experimental data and our calculated matching coefficients, we predict valence-quark correlation functions that can be confronted by lattice QCD calculations. The uncertainty of our predictions is greatly reduced with higher order matching coefficients. By performing Fourier transformation, we also obtain matching coefficients for corresponding quasi-PDFs and pseudo-PDFs. Our method of calculations can be readily generalized to evaluate the matching coefficients for sea-quark and gluon correlation functions, making the program to extract partonic structure of hadrons from lattice QCD calculations comparable with and complementary to that from experimental measurements.
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Affiliation(s)
- Zheng-Yang Li
- School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China
| | - Yan-Qing Ma
- School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China
- Center for High Energy physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Jian-Wei Qiu
- Theory Center, Jefferson Lab, 12000 Jefferson Avenue, Newport News, Virginia 23606, USA
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Chen LB, Wang W, Zhu R. Next-to-Next-to-Leading Order Calculation of Quasiparton Distribution Functions. PHYSICAL REVIEW LETTERS 2021; 126:072002. [PMID: 33666478 DOI: 10.1103/physrevlett.126.072002] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2020] [Revised: 01/18/2021] [Accepted: 01/22/2021] [Indexed: 06/12/2023]
Abstract
We present the next-to-next-to-leading order (NNLO) calculation of quark quasiparton distribution functions (PDFs) in the large momentum effective theory. The nontrivial factorization at this order is established explicitly and the full analytic matching coefficients between the quasidistribution and the light-cone distribution are derived. We demonstrate that the NNLO numerical contributions can improve the behavior of the extracted PDFs sizably. With the unprecedented precision study of nucleon tomography at the planned electron-ion collider, high precision lattice QCD simulations with our NNLO results implemented will enable to test the QCD theory and more precise results on the PDFs of nucleons will be obtained.
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Affiliation(s)
- Long-Bin Chen
- School of Physics and Materials Science, Guangzhou University, Guangzhou 510006, China
| | - Wei Wang
- INPAC, Shanghai Key Laboratory for Particle Physics and Cosmology, Key Laboratory for Particle Astrophysics and Cosmology (MOE), School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Ruilin Zhu
- Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing, Jiangsu 210023, China
- Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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Alexandrou C, Bacchio S, Cloët I, Constantinou M, Hadjiyiannakou K, Koutsou G, Lauer C. Mellin moments
⟨x⟩
and
⟨x2⟩
for the pion and kaon from lattice QCD. Int J Clin Exp Med 2021. [DOI: 10.1103/physrevd.103.014508] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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15
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Bringewatt J, Sato N, Melnitchouk W, Qiu JW, Steffens F, Constantinou M. Confronting lattice parton distributions with global QCD analysis. Int J Clin Exp Med 2021. [DOI: 10.1103/physrevd.103.016003] [Citation(s) in RCA: 25] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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16
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Alexandrou C, Cichy K, Constantinou M, Hadjiyiannakou K, Jansen K, Scapellato A, Steffens F. Unpolarized and Helicity Generalized Parton Distributions of the Proton within Lattice QCD. PHYSICAL REVIEW LETTERS 2020; 125:262001. [PMID: 33449769 DOI: 10.1103/physrevlett.125.262001] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2020] [Accepted: 11/18/2020] [Indexed: 06/12/2023]
Abstract
We present the first calculation of the x dependence of the proton generalized parton distributions (GPDs) within lattice QCD. Results are obtained for the isovector unpolarized and helicity GPDs. We compute the appropriate matrix elements of fast-moving protons coupled to nonlocal operators containing a Wilson line. We present results for proton momenta 0.83,1.25,1.67 GeV, and momentum transfer squared 0.69,1.38 GeV^{2}. These combinations include cases with zero and nonzero skewness. The calculation is performed using one ensemble of two degenerate mass light quarks, a strange quark, and a charm quark of maximally twisted mass fermions with a clover term. The lattice results are matched to the light-cone GPDs using one-loop perturbation theory within the framework of large momentum effective theory. The final GPDs are given in the MS[over ¯] scheme at a scale of 2 GeV.
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Affiliation(s)
- Constantia Alexandrou
- Department of Physics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus
- Computation-based Science and Technology Research Center, The Cyprus Institute, 20 Kavafi Street, Nicosia 2121, Cyprus
| | - Krzysztof Cichy
- Faculty of Physics, Adam Mickiewicz University, Uniwersytetu Poznańskiego 2, 61-614 Poznań, Poland
| | - Martha Constantinou
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122-1801, USA
| | | | - Karl Jansen
- NIC, DESY, Platanenallee 6, D-15738 Zeuthen, Germany
| | - Aurora Scapellato
- Faculty of Physics, Adam Mickiewicz University, Uniwersytetu Poznańskiego 2, 61-614 Poznań, Poland
| | - Fernanda Steffens
- Institut für Strahlen- und Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, Nussallee 14-16, 53115 Bonn, Germany
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Joó B, Karpie J, Orginos K, Radyushkin AV, Richards DG, Zafeiropoulos S. Parton Distribution Functions from Ioffe Time Pseudodistributions from Lattice Calculations: Approaching the Physical Point. PHYSICAL REVIEW LETTERS 2020; 125:232003. [PMID: 33337179 DOI: 10.1103/physrevlett.125.232003] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2020] [Revised: 07/27/2020] [Accepted: 09/09/2020] [Indexed: 06/12/2023]
Abstract
We present results for the unpolarized parton distribution function of the nucleon computed in lattice QCD at the physical pion mass. This is the first study of its kind employing the method of Ioffe time pseudodistributions. Beyond the reconstruction of the Bjorken-x dependence, we also extract the lowest moments of the distribution function using the small Ioffe time expansion of the Ioffe time pseudodistribution. We compare our findings with the pertinent phenomenological determinations.
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Affiliation(s)
- Bálint Joó
- Oak Ridge Leadership Facility, Oak Ridge National Laboratory, One Bethel Valley Road, Oak Ridge, Tennessee 37831, USA
- Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA
| | - Joseph Karpie
- Physics Department, Columbia University, New York City, New York 10027, USA
| | - Kostas Orginos
- Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA
- Physics Department, College of William and Mary, Williamsburg, Virginia 23187, USA
| | - Anatoly V Radyushkin
- Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA
- Physics Department, Old Dominion University, Norfolk, Virginia 23529, USA
| | - David G Richards
- Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA
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18
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Liu KF. Parton degrees of freedom in PDFs from the hadronic tensor and large momentum effective theory. Int J Clin Exp Med 2020. [DOI: 10.1103/physrevd.102.074502] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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19
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Abstract
Highlights from recent computations in lattice QCD involving baryons are presented. Calcula tions of the proton mass and spin decompositions are discussed, a percent level determination of the nucleon axial coupling is described, and determinations of the proton and neutron electromagnetic form factors and light-cone parton distribution functions are outlined. Recent results applying the so-called Luscher method to meson-baryon systems are presented. Key points emphasized are that much better precision with disconnected diagrams is being achieved, incorporating multi-hadron operators is now feasible, and more and more studies are being done with physical quark masses.
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Deur A, Brodsky SJ, de Téramond GF. The spin structure of the nucleon. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2019; 82:076201. [PMID: 30818290 DOI: 10.1088/1361-6633/ab0b8f] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We review the present understanding of the spin structure of protons and neutrons, the fundamental building blocks of nuclei collectively known as nucleons. The field of nucleon spin provides a critical window for testing Quantum Chromodynamics (QCD), the gauge theory of the strong interactions, since it involves fundamental aspects of hadron structure which can be probed in detail in experiments, particularly deep inelastic lepton scattering on polarized targets. QCD was initially probed in high energy deep inelastic lepton scattering with unpolarized beams and targets. With time, interest shifted from testing perturbative QCD to illuminating the nucleon structure itself. In fact, the spin degrees of freedom of hadrons provide an essential and detailed verification of both perturbative and nonperturbative QCD dynamics. Nucleon spin was initially thought of coming mostly from the spin of its quark constituents, based on intuition from the parton model. However, the first experiments showed that this expectation was incorrect. It is now clear that nucleon physics is much more complex, involving quark orbital angular momenta as well as gluonic and sea quark contributions. Thus, the nucleon spin structure remains a most active aspect of QCD research, involving important advances such as the developments of generalized parton distributions (GPD) and transverse momentum distributions (TMD). Elastic and inelastic lepton-proton scattering, as well as photoabsorption experiments provide various ways to investigate non-perturbative QCD. Fundamental sum rules-such as the Bjorken sum rule for polarized photoabsorption on polarized nucleons-are also in the non-perturbative domain. This realization triggered a vigorous program to link the low energy effective hadronic description of the strong interactions to fundamental quarks and gluon degrees of freedom of QCD. This has also led to advances in lattice gauge theory simulations of QCD and to the development of holographic QCD ideas based on the AdS/CFT or gauge/gravity correspondence, a novel approach providing a well-founded semiclassical approximation to QCD. Any QCD-based model of the nucleon's spin and dynamics must also successfully account for the observed spectroscopy of hadrons. Analytic calculations of the hadron spectrum, a long sought goal of QCD research, have now being realized using light-front holography and superconformal quantum mechanics, a formalism consistent with the results from nucleon spin studies. We begin this review with a phenomenological description of nucleon structure in general and of its spin structure in particular, aimed to engage non-specialist readers. Next, we discuss the nucleon spin structure at high energy, including topics such as Dirac's front form and light-front quantization which provide a frame-independent, relativistic description of hadron structure and dynamics, the derivation of spin sum rules, and a direct connection to the QCD Lagrangian. We then discuss experimental and theoretical advances in the nonperturbative domain-in particular the development of light-front holographic QCD and superconformal quantum mechanics, their predictions for the spin content of nucleons, the computation of PDFs and of hadron masses.
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Affiliation(s)
- Alexandre Deur
- Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, United States of America
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21
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Liu YS, Wang W, Xu J, Zhang QA, Zhao S, Zhao Y. Matching the meson quasidistribution amplitude in the RI/MOM scheme. Int J Clin Exp Med 2019. [DOI: 10.1103/physrevd.99.094036] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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22
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Zhang JH, Ji X, Schäfer A, Wang W, Zhao S. Accessing Gluon Parton Distributions in Large Momentum Effective Theory. PHYSICAL REVIEW LETTERS 2019; 122:142001. [PMID: 31050468 DOI: 10.1103/physrevlett.122.142001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2018] [Revised: 01/13/2019] [Indexed: 06/09/2023]
Abstract
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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Affiliation(s)
- Jian-Hui Zhang
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Xiangdong Ji
- Tsung-Dao Lee Institute, and School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
- Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Andreas Schäfer
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Wei Wang
- SKLPPC, MOE KLPPC, School of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dongchuan RD, Shanghai, 200240, China
| | - Shuai Zhao
- SKLPPC, MOE KLPPC, School of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dongchuan RD, Shanghai, 200240, China
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Geesaman DF, Reimer PE. The sea of quarks and antiquarks in the nucleon. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2019; 82:046301. [PMID: 30736022 DOI: 10.1088/1361-6633/ab05a7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The quark and gluon structure of the proton has been under intense experimental and theoretical investigation for five decades. Even for the distributions of the well-studied valence quarks, challenges such as the value of the down quark to up quark ratio at high fractional momenta remain. Much of the sea of quark-antiquark pairs emerges from the splitting of gluons and is well described by perturbative evolution in quantum chromodynamics. However, experiments confirm that there is a non-perturbative component to the sea that is not well understood and hitherto has been difficult to calculate with ab initio non-perturbative methods. This non-perturbative structure shows up, perhaps most directly, in the flavor dependence of the sea antiquark distributions. While some of the general trends can be reproduced by models, there are features of the data that do not seem to be well described. This article discusses the experimental situation, the status of calculations and models, and the directions where these studies will progress in the near future.
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Affiliation(s)
- D F Geesaman
- Argonne Associate of Global Empire, LLC, Argonne National Laboratory, Argonne, IL 60439, United States of America
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24
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Li ZY, Ma YQ, Qiu JW. Multiplicative Renormalizability of Operators defining Quasiparton Distributions. PHYSICAL REVIEW LETTERS 2019; 122:062002. [PMID: 30822040 DOI: 10.1103/physrevlett.122.062002] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2018] [Indexed: 06/09/2023]
Abstract
Extracting parton distribution functions (PDFs) from lattice QCD calculation of quasi-PDFs has been actively pursued in recent years. We extend our proof of the multiplicative renormalizability of the quasiquark operators of Ishikawa et al. [Phys Rev. D 96, 094019 (2017)] to quasigluon operators, and demonstrated that quasigluon operators could be multiplicatively renormalized to all orders in perturbation theory, without mixing with other operators. We find that using a gauge-invariant UV regulator is essential for achieving this proof. With the multiplicative renormalizability of both quasiquark and quasigluon operators, and QCD collinear factorization of hadronic matrix elements of there operators into PDFs, extracting PDFs from lattice QCD calculated hadronic matrix elements of quasiparton operators could have a solid theoretical foundation.
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Affiliation(s)
- Zheng-Yang Li
- School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China
| | - Yan-Qing Ma
- School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China
- Center for High Energy physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Jian-Wei Qiu
- Theory Center, Jefferson Lab, 12000 Jefferson Avenue, Newport News, Virginia 23606, USA
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Lin HW, Chen JW, Ji X, Jin L, Li R, Liu YS, Yang YB, Zhang JH, Zhao Y. Proton Isovector Helicity Distribution on the Lattice at Physical Pion Mass. PHYSICAL REVIEW LETTERS 2018; 121:242003. [PMID: 30608734 DOI: 10.1103/physrevlett.121.242003] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2018] [Indexed: 06/09/2023]
Abstract
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 quasidistributions at proton momenta P_{z}∈{2.2,2.6,3.0} GeV on the lattice and match them systematically to the physical parton distribution using the large-momentum effective theory. 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, Δu[over ¯](x)>Δd[over ¯](x).
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Affiliation(s)
- Huey-Wen Lin
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
- Department of Computational Mathematics, Michigan State University, East Lansing, Michigan 48824, USA
| | - Jiunn-Wei Chen
- Department of Physics, Center for Theoretical Physics, and Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 106, Taiwan
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Xiangdong Ji
- Tsung-Dao Lee Institute and School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
- Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Luchang Jin
- Physics Department, University of Connecticut, Storrs, Connecticut 06269-3046, USA
- RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - Ruizi Li
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
| | - Yu-Sheng Liu
- Tsung-Dao Lee Institute, Shanghai Jiao-Tong University, Shanghai 200240, China
| | - Yi-Bo Yang
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
- Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Jian-Hui Zhang
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Yong Zhao
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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