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Caucal P, Salazar F, Schenke B, Stebel T, Venugopalan R. Back-to-Back Inclusive Dijets in Deep Inelastic Scattering at Small x: Complete NLO Results and Predictions. PHYSICAL REVIEW LETTERS 2024; 132:081902. [PMID: 38457730 DOI: 10.1103/physrevlett.132.081902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2023] [Revised: 01/16/2024] [Accepted: 01/30/2024] [Indexed: 03/10/2024]
Abstract
We compute the back-to-back dijet cross section in deep inelastic scattering at small x to next-to-leading order (NLO) in the color glass condensate effective field theory. Our result can be factorized into a convolution of the Weizsäcker-Williams gluon transverse-momentum-dependent distribution function (WW gluon TMD) with a universal soft factor and an NLO coefficient function. The soft factor includes both double and single logarithms in the ratio of the relative transverse momentum P_{⊥} of the dijet pair to the dijet momentum imbalance q_{⊥}; its renormalization group (RG) evolution is resummed into the Sudakov factor. Likewise, the WW TMD obeys a nonlinear RG equation in x that is kinematically constrained to satisfy both the lifetime and rapidity ordering of the projectile. Exact analytical expressions are obtained for the NLO coefficient function of transversely and longitudinally polarized photons. Our results allow for the first quantitative separation of the dynamics of Sudakov suppression from that of gluon saturation. They can be extended to other final states and provide a framework for precision tests of novel QCD many-body dynamics at the Electron-Ion Collider.
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Affiliation(s)
- Paul Caucal
- SUBATECH UMR 6457, IMT Atlantique, Université de Nantes, IN2P3/CNRS, 4 rue Alfred Kastler, 44307 Nantes, France
| | - Farid Salazar
- Lawrence Berkeley National Laboratory, Nuclear Science Division, Berkeley, California 94720, USA
- Physics Department, University of California, Berkeley, California 94720, USA
- Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA
- Mani L. Bhaumik Institute for Theoretical Physics, University of California, Los Angeles, California 90095, USA
| | - Björn Schenke
- Physics Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - Tomasz Stebel
- Institute of Theoretical Physics, Jagiellonian University, ulica Lojasiewicza 11, 30-348 Kraków, Poland
| | - Raju Venugopalan
- Physics Department, Brookhaven National Laboratory, Upton, New York 11973, USA
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Hänninen H, Mäntysaari H, Paatelainen R, Penttala J. Proton Structure Functions at Next-to-Leading Order in the Dipole Picture with Massive Quarks. PHYSICAL REVIEW LETTERS 2023; 130:192301. [PMID: 37243632 DOI: 10.1103/physrevlett.130.192301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2022] [Revised: 02/03/2023] [Accepted: 04/18/2023] [Indexed: 05/29/2023]
Abstract
We predict heavy quark production cross sections in deep inelastic scattering at high energy by applying the color glass condensate effective theory. We demonstrate that, when the calculation is performed consistently at next-to-leading order accuracy with massive quarks, it becomes possible, for the first time in the dipole picture with perturbatively calculated center-of-mass energy evolution, to simultaneously describe both the light and heavy quark production data at small x_{Bj}. Furthermore, we show how the heavy quark cross section data provides additional strong constraints on the extracted nonperturbative initial condition for the small-x_{Bj} evolution equations.
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Affiliation(s)
- Henri Hänninen
- Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, 40014 University of Jyväskylä, Finland
- Department of Physics, University of Jyväskylä, P.O. Box 35, 40014 University of Jyväskylä, Finland
- Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, 00014 University of Helsinki, Finland
| | - Heikki Mäntysaari
- Department of Physics, University of Jyväskylä, P.O. Box 35, 40014 University of Jyväskylä, Finland
- Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, 00014 University of Helsinki, Finland
| | - Risto Paatelainen
- Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, 00014 University of Helsinki, Finland
- Department of Physics, University of Helsinki, P.O. Box 64, 00014 University of Helsinki, Finland
| | - Jani Penttala
- Department of Physics, University of Jyväskylä, P.O. Box 35, 40014 University of Jyväskylä, Finland
- Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, 00014 University of Helsinki, Finland
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3
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Liu HY, Liu XH, Shi Y, Zheng DX, Zhou J. Kinematic constraint in the BFKL evolution near threshold region. Int J Clin Exp Med 2022. [DOI: 10.1103/physrevd.106.036026] [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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4
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Beuf G, Lappi T, Paatelainen R. Massive quarks in NLO dipole factorization for DIS: Transverse photon. Int J Clin Exp Med 2022. [DOI: 10.1103/physrevd.106.034013] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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5
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Beuf G, Lappi T, Paatelainen R. Massive Quarks at One Loop in the Dipole Picture of Deep Inelastic Scattering. PHYSICAL REVIEW LETTERS 2022; 129:072001. [PMID: 36018699 DOI: 10.1103/physrevlett.129.072001] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2022] [Accepted: 07/14/2022] [Indexed: 06/15/2023]
Abstract
We calculate the light cone wave functions for a virtual photon to split into quark-antiquark states, including for the first time quark masses at one loop accuracy. These wave functions can be used to calculate cross sections for several precision probes of perturbative gluon saturation at the Electron-Ion Collider. Using these wave functions we derive, for the first time, the dipole picture deep inelastic scattering cross sections at one loop for longitudinal and transverse virtual photons including quark masses. The quark masses are renormalized in the pole mass scheme, satisfying constraints from the requirement of Lorentz invariance of the quark Dirac and Pauli form factors.
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Affiliation(s)
- G Beuf
- Theoretical Physics Division, National Centre for Nuclear Research, Pasteura 7, Warsaw 02-093, Poland
| | - T Lappi
- Department of Physics, P.O. Box 35, 40014 University of Jyväskylä, Finland
- Helsinki Institute of Physics, P.O. Box 64, 00014 University of Helsinki, Finland
| | - R Paatelainen
- Helsinki Institute of Physics, P.O. Box 64, 00014 University of Helsinki, Finland
- Department of Physics, P.O. Box 64, 00014 University of Helsinki, Finland
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Shi Y, Wang L, Wei SY, Xiao BW. Pursuing the Precision Study for Color Glass Condensate in Forward Hadron Productions. PHYSICAL REVIEW LETTERS 2022; 128:202302. [PMID: 35657879 DOI: 10.1103/physrevlett.128.202302] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2022] [Revised: 03/27/2022] [Accepted: 05/05/2022] [Indexed: 06/15/2023]
Abstract
With the tremendous accomplishments of RHIC and the LHC experiments and the advent of the future electron-ion collider on the horizon, the quest for compelling evidence of the color glass condensate (CGC) has become one of the most aspiring goals in the high energy quantum chromodynamics research. Pursuing this question requires developing the precision test of the CGC formalism. By systematically implementing the threshold resummation, we significantly improve the stability of the next-to-leading-order calculation in CGC for forward rapidity hadron productions in pp and pA collisions, especially in the high p_{T} region, and obtain reliable descriptions of all existing data measured at RHIC and the LHC across all p_{T} regions. Consequently, this technique can pave the way for the precision studies of the CGC next-to-leading-order predictions by confronting them with a large amount of precise data.
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Affiliation(s)
- Yu Shi
- Key Laboratory of Particle Physics and Particle Irradiation (MOE), Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, China
- Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China
| | - Lei Wang
- Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China
| | - Shu-Yi Wei
- Key Laboratory of Particle Physics and Particle Irradiation (MOE), Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, China
- European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*) and Fondazione Bruno Kessler, Strada delle Tabarelle 286, I-38123 Villazzano (TN), Italy
| | - Bo-Wen Xiao
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen 518172, China
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Abstract
Quantum chromodynamics (QCD) is the theory of strong interactions of quarks and gluons collectively called partons, the basic constituents of all nuclear matter. Its non-abelian character manifests in nature in the form of two remarkable properties: color confinement and asymptotic freedom. At high energies, perturbation theory can result in the growth and dominance of very gluon densities at small-x. If left uncontrolled, this growth can result in gluons eternally growing violating a number of mathematical bounds. The resolution to this problem lies by balancing gluon emissions by recombinating gluons at high energies: phenomena of gluon saturation. High energy nuclear and particle physics experiments have spent the past decades quantifying the structure of protons and nuclei in terms of their fundamental constituents confirming predicted extraordinary behavior of matter at extreme density and pressure conditions. In the process they have also measured seemingly unexpected phenomena. We will give a state of the art review of the underlying theoretical and experimental tools and measurements pertinent to gluon saturation physics. We will argue for the need of high energy electron-proton/ion colliders such as the proposed EIC (USA) and LHeC (Europe) to consolidate our knowledge of QCD knowledge in the small x kinematic domains.
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Mäntysaari H. Review of proton and nuclear shape fluctuations at high energy. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2020; 83:082201. [PMID: 32730225 DOI: 10.1088/1361-6633/aba347] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Determining the inner structure of protons and nuclei in terms of their fundamental constituents has been one of the main tasks of high energy nuclear and particle physics experiments. This quest started as a mapping of the (average) parton densities as a function of longitudinal momentum fraction and resolution scale. Recently, the field has progressed to more differential imaging, where one important development is the description of the event-by-event quantum fluctuations in the wave function of the colliding hadron. In this review, recent developments on the extraction of proton and nuclear transverse geometry with event-by-event fluctuations from collider experiments at high energy is presented. The importance of this fundamentally interesting physics in other collider experiments like in studies of the properties of the quark gluon plasma is also illustrated.
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Affiliation(s)
- Heikki Mäntysaari
- Department of Physics, University of Jyväskylä, PO Box 35, 40014 University of Jyväskylä, Finland. Helsinki Institute of Physics, P.O. Box 64, 00014 University of Helsinki, Finland
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Boussarie R, Hatta Y, Szymanowski L, Wallon S. Probing the Gluon Sivers Function with an Unpolarized Target: GTMD Distributions and the Odderons. PHYSICAL REVIEW LETTERS 2020; 124:172501. [PMID: 32412297 DOI: 10.1103/physrevlett.124.172501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2020] [Revised: 03/26/2020] [Accepted: 04/14/2020] [Indexed: 06/11/2023]
Abstract
It is commonly believed that the Sivers function has uniquely to do with processes involving a transversely polarized nucleon. In this Letter we show that this is not necessarily the case. We demonstrate that exclusive pion production in unpolarized electron-proton scattering in the forward region is a direct probe of the gluon Sivers function due to its connection to the QCD odderon.
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Affiliation(s)
- Renaud Boussarie
- Physics Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - Yoshitaka Hatta
- Physics Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - Lech Szymanowski
- National Centre for Nuclear Research (NCBJ), Pasteura 7, 02-093 Warsaw, Poland
| | - Samuel Wallon
- Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France
- Sorbonne Université, Faculté de Physique, 4 place Jussieu, 75252 Paris Cedex 05, France
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Mäntysaari H, Mueller N, Salazar F, Schenke B. Multigluon Correlations and Evidence of Saturation from Dijet Measurements at an Electron-Ion Collider. PHYSICAL REVIEW LETTERS 2020; 124:112301. [PMID: 32242674 DOI: 10.1103/physrevlett.124.112301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2019] [Revised: 02/05/2020] [Accepted: 02/05/2020] [Indexed: 06/11/2023]
Abstract
We study inclusive and diffractive dijet production in electron-proton and electron-nucleus collisions within the color glass condensate effective field theory. We compute dijet cross sections differentially in both mean dijet transverse momentum P and recoil momentum Δ, as well as the anisotropy in the relative angle between P and Δ. Our results cover a much larger kinematic range than accessible in previous computations performed in the correlation limit approximation, where it is assumed that |P|≫|Δ|. We validate this approximation in its range of applicability and quantify its failure for |P|≲|Δ|. We also predict significant target-dependent deviations from the correlation limit approximation for |P|>|Δ| and |P|≲Q_{s}, which offers a straightforward test of gluon saturation and access to multigluon distributions at a future Electron-Ion Collider.
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Affiliation(s)
- Heikki Mäntysaari
- Department of Physics, University of Jyväskylä, P.O. Box 35, 40014 University of Jyväskyä, Finland
- Helsinki Institute of Physics, P.O. Box 64, 00014 University of Helsinki, Finland
| | - Niklas Mueller
- Physics Department, Brookhaven National Laboratory, Building 510A, Upton, New York 11973, USA
| | - Farid Salazar
- Physics Department, Brookhaven National Laboratory, Building 510A, Upton, New York 11973, USA
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA
| | - Björn Schenke
- Physics Department, Brookhaven National Laboratory, Building 510A, Upton, New York 11973, USA
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12
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Boussarie R, Grabovsky A, Szymanowski L, Wallon S. Towards a complete next-to-logarithmic description of forward exclusive diffractive dijet electroproduction at HERA: Real corrections. Int J Clin Exp Med 2019. [DOI: 10.1103/physrevd.100.074020] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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13
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Gonçalves V, Machado M, Moreira B, Navarra F, Santos GSD. Color dipole predictions for the exclusive vector meson photoproduction in
pp
,
pPb
, and PbPb collisions at run 2 LHC energies. Int J Clin Exp Med 2017. [DOI: 10.1103/physrevd.96.094027] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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