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Yao F, Walter L, Chen JW, Hua J, Ji X, Jin L, Lahrtz S, Ma L, Mohanta P, Schäfer A, Shu HT, Su Y, Sun P, Xiong X, Yang YB, Zhang JH. Nucleon Transversity Distribution in the Continuum and Physical Mass Limit from Lattice QCD. PHYSICAL REVIEW LETTERS 2023; 131:261901. [PMID: 38215369 DOI: 10.1103/physrevlett.131.261901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2022] [Revised: 10/17/2023] [Accepted: 11/17/2023] [Indexed: 01/14/2024]
Abstract
We report a state-of-the-art lattice QCD calculation of the isovector quark transversity distribution of the proton in the continuum and physical mass limit using large-momentum effective theory. The calculation is done at four lattice spacings a={0.098,0.085,0.064,0.049} fm and various pion masses ranging between 220 and 350 MeV, with proton momenta up to 2.8 GeV. The result is nonperturbatively renormalized in the hybrid scheme with self-renormalization, which treats the infrared physics at large correlation distance properly, and extrapolated to the continuum, physical mass, and infinite momentum limit. We also compare with recent global analyses for the nucleon isovector quark transversity distribution.
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Affiliation(s)
- Fei Yao
- Center of Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Lisa Walter
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Jiunn-Wei Chen
- Department of Physics, Center for Theoretical Physics, and Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 10617, Taiwan
- Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan
| | - Jun Hua
- Guangdong Provincial Key Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal University, Guangzhou 510006, China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Southern Nuclear Science Computing Center, South China Normal University, Guangzhou 510006, China
| | - Xiangdong Ji
- 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
| | - Sebastian Lahrtz
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Lingquan Ma
- Center of Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Protick Mohanta
- Center of Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing 100875, China
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Odisha 752050, India
| | - Andreas Schäfer
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Hai-Tao Shu
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Yushan Su
- Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Peng Sun
- Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, Gansu Province 730000, China
- Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing, Jiangsu 210023, China
| | - Xiaonu Xiong
- School of Physics, Central South University, Changsha 418003, China
| | - Yi-Bo Yang
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS, Hangzhou 310024, China
- International Centre for Theoretical Physics Asia-Pacific, Beijing/Hangzhou, China
- University of Chinese Academy of Sciences, School of Physical Sciences, Beijing 100049, China
| | - Jian-Hui Zhang
- Center of Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing 100875, China
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen 518172, China
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2
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He F, Ji CR, Melnitchouk W, Thomas A, Wang P. Generalized parton distributions of sea quarks in the proton from nonlocal chiral effective theory. Int J Clin Exp Med 2022. [DOI: 10.1103/physrevd.106.054006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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3
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Gao X, Hanlon AD, Mukherjee S, Petreczky P, Scior P, Syritsyn S, Zhao Y. Lattice QCD Determination of the Bjorken-x Dependence of Parton Distribution Functions at Next-to-Next-to-Leading Order. PHYSICAL REVIEW LETTERS 2022; 128:142003. [PMID: 35476471 DOI: 10.1103/physrevlett.128.142003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2021] [Revised: 02/04/2022] [Accepted: 03/10/2022] [Indexed: 06/14/2023]
Abstract
We report the first lattice QCD calculation of pion valence quark distribution with next-to-next-to-leading order perturbative matching correction, which is done using two fine lattices with spacings a=0.04 and 0.06 fm and valence pion mass m_{π}=300 MeV, at boost momentum as large as 2.42 GeV. As a crucial step to control the systematics, we renormalize the pion valence quasidistribution in the recently proposed hybrid scheme, which features a Wilson-line mass subtraction at large distances in coordinate space, and develop a procedure to match it to the MS[over ¯] scheme. We demonstrate that the renormalization and the perturbative matching in Bjorken-x space yield a reliable determination of the valence quark distribution for 0.03≲x≲0.80 with 5%-20% uncertainties.
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Affiliation(s)
- Xiang Gao
- Key Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China
| | - Andrew D Hanlon
- Physics Department, Brookhaven National Laboratory, Building 510A, Upton, New York 11973, USA
| | - Swagato Mukherjee
- Physics Department, Brookhaven National Laboratory, Building 510A, Upton, New York 11973, USA
| | - Peter Petreczky
- Physics Department, Brookhaven National Laboratory, Building 510A, Upton, New York 11973, USA
| | - Philipp Scior
- Physics Department, Brookhaven National Laboratory, Building 510A, Upton, New York 11973, USA
| | - Sergey Syritsyn
- RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973, USA
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11790, USA
| | - Yong Zhao
- Physics Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
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4
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Detmold W, Grebe AV, Kanamori I, Lin CJD, Mondal S, Perry RJ, Zhao Y. Parton physics from a heavy-quark operator product expansion: Lattice QCD calculation of the second moment of the pion distribution amplitude. Int J Clin Exp Med 2022. [DOI: 10.1103/physrevd.105.034506] [Citation(s) in RCA: 6] [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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5
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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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6
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Gao X, Karthik N, Mukherjee S, Petreczky P, Syritsyn S, Zhao Y. Pion form factor and charge radius from lattice QCD at the physical point. Int J Clin Exp Med 2021. [DOI: 10.1103/physrevd.104.114515] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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7
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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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8
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Alexandrou C, Bacchio S, Bergner G, Finkenrath J, Gasbarro A, Hadjiyiannakou K, Jansen K, Kostrzewa B, Ottnad K, Petschlies M, Pittler F, Steffens F, Urbach C, Wenger U. Quark and Gluon Momentum Fractions in the Pion from N_{f}=2+1+1 Lattice QCD. PHYSICAL REVIEW LETTERS 2021; 127:252001. [PMID: 35029455 DOI: 10.1103/physrevlett.127.252001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2021] [Accepted: 11/03/2021] [Indexed: 06/14/2023]
Abstract
We perform the first full decomposition of the pion momentum into its gluon and quark contributions. We employ an ensemble generated by the Extended Twisted Mass Collaboration with N_{f}=2+1+1 Wilson twisted mass clover fermions at maximal twist tuned to reproduce the physical pion mass. We present our results in the MS[over ¯] scheme at 2 GeV. We find ⟨x⟩_{u+d}=0.601(28), ⟨x⟩_{s}=0.059(13), ⟨x⟩_{c}=0.019(05), and ⟨x⟩_{g}=0.52(11) for the separate contributions, respectively, whose sum saturates the momentum sum rule.
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Affiliation(s)
- Constantia Alexandrou
- Department of Physics, University of Cyprus, Nicosia 2109, Cyprus
- Computation-based Science and Technology Research Center, The Cyprus Institute, Nicosia 2121, Cyprus
| | - Simone Bacchio
- Computation-based Science and Technology Research Center, The Cyprus Institute, Nicosia 2121, Cyprus
| | - Georg Bergner
- Institute of Theoretical Physics, Friedrich Schiller University Jena, Jena 07743, Germany
| | - Jacob Finkenrath
- Computation-based Science and Technology Research Center, The Cyprus Institute, Nicosia 2121, Cyprus
| | - Andrew Gasbarro
- Albert Einstein Center, Institute for Theoretical Physics, University of Bern, Bern CH-3012, Switzerland
| | - Kyriakos Hadjiyiannakou
- Department of Physics, University of Cyprus, Nicosia 2109, Cyprus
- Computation-based Science and Technology Research Center, The Cyprus Institute, Nicosia 2121, Cyprus
| | | | - Bartosz Kostrzewa
- High Performance Computing and Analytics Lab, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn 53115, Germany
| | - Konstantin Ottnad
- PRISMA+ Cluster of Excellence and Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, Mainz 55099, Germany
| | - Marcus Petschlies
- Helmholtz-Institut für Strahlen- und Kernphysik, University of Bonn, Bonn 53115, Germany
- Bethe Center for Theoretical Physics, University of Bonn, Bonn 53115, Germany
| | - Ferenc Pittler
- Computation-based Science and Technology Research Center, The Cyprus Institute, Nicosia 2121, Cyprus
| | - Fernanda Steffens
- Helmholtz-Institut für Strahlen- und Kernphysik, University of Bonn, Bonn 53115, Germany
- Bethe Center for Theoretical Physics, University of Bonn, Bonn 53115, Germany
| | - Carsten Urbach
- Helmholtz-Institut für Strahlen- und Kernphysik, University of Bonn, Bonn 53115, Germany
- Bethe Center for Theoretical Physics, University of Bonn, Bonn 53115, Germany
| | - Urs Wenger
- Albert Einstein Center, Institute for Theoretical Physics, University of Bern, Bern CH-3012, Switzerland
- Department of Theoretical Physics, CERN, Geneva CH-1211, Switzerland
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9
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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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10
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11
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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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12
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Hua J, Chu MH, Sun P, Wang W, Xu J, Yang YB, Zhang JH, Zhang QA. Distribution Amplitudes of K^{*} and ϕ at the Physical Pion Mass from Lattice QCD. PHYSICAL REVIEW LETTERS 2021; 127:062002. [PMID: 34420340 DOI: 10.1103/physrevlett.127.062002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2020] [Accepted: 07/07/2021] [Indexed: 06/13/2023]
Abstract
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 action, generated by the MIMD Lattice Computation Collaboration, at physical pion mass and {0.06,0.09,0.12} fm lattice spacings and choose three different hadron momenta P_{z}={1.29,1.72,2.15} GeV. The resulting lattice matrix elements are nonperturbatively renormalized in a recently proposed hybrid scheme. 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.
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Affiliation(s)
- Jun Hua
- 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
| | - Min-Huan Chu
- 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
- Shanghai Key Laboratory for Particle Physics and Cosmology, Key Laboratory for Particle Astrophysics and Cosmology (MOE), Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Peng Sun
- Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing, Jiangsu 210023, 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
| | - Ji Xu
- 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
- School of Physics and Microelectronics, Zhengzhou University, Zhengzhou, Henan 450001, China
| | - Yi-Bo Yang
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS, Hangzhou 310024, China
- International Centre for Theoretical Physics Asia-Pacific, Beijing/Hangzhou, China
| | - Jian-Hui Zhang
- Center of Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Qi-An Zhang
- Shanghai Key Laboratory for Particle Physics and Cosmology, Key Laboratory for Particle Astrophysics and Cosmology (MOE), Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China
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13
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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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14
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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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15
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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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16
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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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17
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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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18
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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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19
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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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20
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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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21
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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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22
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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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23
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Mondal C, Xu S, Lan J, Zhao X, Li Y, Chakrabarti D, Vary JP. Proton structure from a light-front Hamiltonian. Int J Clin Exp Med 2020. [DOI: 10.1103/physrevd.102.016008] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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24
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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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25
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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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26
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Lin HW. Parton Distribution Functions and Lattice QCD. EPJ WEB OF CONFERENCES 2019. [DOI: 10.1051/epjconf/201920601003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Recently, there have been rapid developments in lattice-QCD calculations of proton structure, especially in the parton distribution functions (PDFs). We overcame a longstanding obstacle and for the first time in lattice-QCD are able to directly calculate the Bjorken-x dependence of the quark, helicity and transversity distributions. The PDFs are obtained using the large-momentum effective field theory (LaMET) framework where the full Bjorken-x dependence of finite-momentum PDFs, called “quasi-PDFs”, can be calculated on the lattice. The quasi-PDF nucleon matrix elements are renormalized non-perturbatively in RI/MOM-scheme. Following a nonperturbative renormalization of the parton quasi-distribution in a regularization-independent momentum-subtraction scheme, we establish its matching to the
$ \overline {{\rm{MS}}} $
PDF and calculate the non-singlet matching coefficient at next-to-leading order in perturbation theory. In this proceeding, I will show the progress that has been made in recent years, highlighting the latest state-of-the art PDF calculations at the physical pion mass. Future impacts on the large-x global PDF fits are also discussed.
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27
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Alexandrou C, Cichy K, Constantinou M, Jansen K, Scapellato A, Steffens F. Light-Cone Parton Distribution Functions from Lattice QCD. PHYSICAL REVIEW LETTERS 2018; 121:112001. [PMID: 30265095 DOI: 10.1103/physrevlett.121.112001] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2018] [Indexed: 06/08/2023]
Abstract
We extract parton distribution functions (PDFs) of the nucleon from lattice QCD using an ensemble of gauge field configurations simulated with light quark masses fixed to their physical values. Theoretical and algorithmic improvements that allow such a calculation include momentum smearing to reach large nucleon boosts with reduced statistical errors, nonperturbative renormalization, target mass corrections, and a novel modified matching of lattice QCD results to connect to what is extracted from experimental measurements. We give results on the unpolarized and helicity PDFs in the modified minimal subtraction scheme at a scale of 2 GeV and reproduce the main features of the experimentally determined quantities, showing an overlap for a range of Bjorken-x values. This first direct nonperturbative evaluation opens a most promising path to compute PDFs in an ab initio way on the lattice and provides a framework for investigating also a wider class of similar quantities, which require the evaluation of hadronic matrix elements of nonlocal operators.
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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, Umultowska 85, 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
- Department of Physics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus
- University of Wuppertal, Gaußstrasse 20, 42119 Wuppertal, Germany
| | - Fernanda Steffens
- Institut für Strahlen- und Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, Nussallee 14-16, 53115 Bonn, Germany
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28
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de Téramond GF, Liu T, Sufian RS, Dosch HG, Brodsky SJ, Deur A. Universality of Generalized Parton Distributions in Light-Front Holographic QCD. PHYSICAL REVIEW LETTERS 2018; 120:182001. [PMID: 29775340 DOI: 10.1103/physrevlett.120.182001] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2018] [Revised: 03/14/2018] [Indexed: 06/08/2023]
Abstract
The structure of generalized parton distributions is determined from light-front holographic QCD up to a universal reparametrization function w(x) which incorporates Regge behavior at small x and inclusive counting rules at x→1. A simple ansatz for w(x) that fulfills these physics constraints with a single-parameter results in precise descriptions of both the nucleon and the pion quark distribution functions in comparison with global fits. The analytic structure of the amplitudes leads to a connection with the Veneziano model and hence to a nontrivial connection with Regge theory and the hadron spectrum.
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Affiliation(s)
| | - Tianbo Liu
- Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA
- Department of Physics, Duke University, Durham, North Carolina 27708, USA
| | - Raza Sabbir Sufian
- Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA
| | - Hans Günter Dosch
- Institut für Theoretische Physik der Universität, D-69120 Heidelberg, Germany
| | - Stanley J Brodsky
- SLAC National Accelerator Laboratory, Stanford University, Stanford, California 94309, USA
| | - Alexandre Deur
- Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA
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