Abstract
In this work, we complete our CT18qed study with the neutron’s photon parton distribution function (PDF), which is essential for the nucleus scattering phenomenology. Two methods, CT18lux and CT18qed, based on the LUXqed formalism and the DGLAP evolution, respectively, to determine the neutron’s photon PDF have been presented. Various low-Q2 non-perturbative variations have been carefully examined, which are treated as additional uncertainties on top of those induced by quark and gluon PDFs. The impacts of the momentum sum rule as well as isospin symmetry violation have been explored and turned out to be negligible. A detailed comparison with other neutron’s photon PDF sets has been performed, which shows a great improvement in the precision and a reasonable uncertainty estimation. Finally, two phenomenological implications are demonstrated with photon-initiated processes: neutrino-nucleus W-boson production, which is important for the near-future TeV–PeV neutrino observations, and the axion-like particle production at a high-energy muon beam-dump experiment.
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K. Kovařík, P.M. Nadolsky and D.E. Soper, Hadronic structure in high-energy collisions, Rev. Mod. Phys. 92 (2020) 045003 [arXiv:1905.06957] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, PTEP 2022 (2022) 083C01 [INSPIRE].
Z. Ye, J. Arrington, R.J. Hill and G. Lee, Proton and Neutron Electromagnetic Form Factors and Uncertainties, Phys. Lett. B 777 (2018) 8 [arXiv:1707.09063] [INSPIRE].
E. Fermi, On the Theory of the impact between atoms and electrically charged particles, Z. Phys. 29 (1924) 315 [INSPIRE].
C.F. von Weizsacker, Radiation emitted in collisions of very fast electrons, Z. Phys. 88 (1934) 612 [INSPIRE].
E.J. Williams, Nature of the high-energy particles of penetrating radiation and status of ionization and radiation formulae, Phys. Rev. 45 (1934) 729 [INSPIRE].
V.M. Budnev, I.F. Ginzburg, G.V. Meledin and V.G. Serbo, The Two photon particle production mechanism. Physical problems. Applications. Equivalent photon approximation, Phys. Rept. 15 (1975) 181 [INSPIRE].
C. Schmidt, J. Pumplin, D. Stump and C.P. Yuan, CT14QED parton distribution functions from isolated photon production in deep inelastic scattering, Phys. Rev. D 93 (2016) 114015 [arXiv:1509.02905] [INSPIRE].
Y.L. Dokshitzer, Calculation of the Structure Functions for Deep Inelastic Scattering and e+e− Annihilation by Perturbation Theory in Quantum Chromodynamics, Sov. Phys. JETP 46 (1977) 641 [INSPIRE].
V.N. Gribov and L.N. Lipatov, Deep inelastic e p scattering in perturbation theory, Sov. J. Nucl. Phys. 15 (1972) 438 [INSPIRE].
L. Lipatov, The parton model and perturbation theory, Sov. J. Nucl. Phys. 20 (1975) 94.
G. Altarelli and G. Parisi, Asymptotic Freedom in Parton Language, Nucl. Phys. B 126 (1977) 298 [INSPIRE].
A.D. Martin, R.G. Roberts, W.J. Stirling and R.S. Thorne, Parton distributions incorporating QED contributions, Eur. Phys. J. C 39 (2005) 155 [hep-ph/0411040] [INSPIRE].
NNPDF collaboration, Parton distributions with QED corrections, Nucl. Phys. B 877 (2013) 290 [arXiv:1308.0598] [INSPIRE].
ZEUS collaboration, Measurement of isolated photon production in deep inelastic ep scattering, Phys. Lett. B 687 (2010) 16 [arXiv:0909.4223] [INSPIRE].
H. Anlauf et al., KRONOS: A Monte Carlo event generator for higher order electromagnetic radiative corrections to deep inelastic scattering at HERA, Comput. Phys. Commun. 70 (1992) 97 [INSPIRE].
J. Blumlein, G. Levman and H. Spiesberger, On the measurement of the proton structure at small Q2, J. Phys. G 19 (1993) 1695 [INSPIRE].
A. Mukherjee and C. Pisano, Manifestly covariant analysis of the QED Compton process in ep → eγp and ep → eγX, Eur. Phys. J. C 30 (2003) 477 [hep-ph/0306275] [INSPIRE].
A. Manohar, P. Nason, G.P. Salam and G. Zanderighi, How bright is the proton? A precise determination of the photon parton distribution function, Phys. Rev. Lett. 117 (2016) 242002 [arXiv:1607.04266] [INSPIRE].
A.V. Manohar, P. Nason, G.P. Salam and G. Zanderighi, The Photon Content of the Proton, JHEP 12 (2017) 046 [arXiv:1708.01256] [INSPIRE].
CTEQ-TEA collaboration, Photon PDF within the CT18 global analysis, Phys. Rev. D 105 (2022) 054006 [arXiv:2106.10299] [INSPIRE].
L.A. Harland-Lang, A.D. Martin, R. Nathvani and R.S. Thorne, Ad Lucem: QED Parton Distribution Functions in the MMHT Framework, Eur. Phys. J. C 79 (2019) 811 [arXiv:1907.02750] [INSPIRE].
T. Cridge, L.A. Harland-Lang, A.D. Martin and R.S. Thorne, QED parton distribution functions in the MSHT20 fit, Eur. Phys. J. C 82 (2022) 90 [arXiv:2111.05357] [INSPIRE].
NNPDF collaboration, Illuminating the photon content of the proton within a global PDF analysis, SciPost Phys. 5 (2018) 008 [arXiv:1712.07053] [INSPIRE].
S. Amoroso et al., Snowmass 2021 Whitepaper: Proton Structure at the Precision Frontier, Acta Phys. Polon. B 53 (2022) 12 [arXiv:2203.13923] [INSPIRE].
A.D. Martin and M.G. Ryskin, The photon PDF of the proton, Eur. Phys. J. C 74 (2014) 3040 [arXiv:1406.2118] [INSPIRE].
L.A. Harland-Lang, V.A. Khoze and M.G. Ryskin, The photon PDF in events with rapidity gaps, Eur. Phys. J. C 76 (2016) 255 [arXiv:1601.03772] [INSPIRE].
L.A. Harland-Lang, V.A. Khoze and M.G. Ryskin, Photon-initiated processes at high mass, Phys. Rev. D 94 (2016) 074008 [arXiv:1607.04635] [INSPIRE].
HERMES collaboration, Inclusive Measurements of Inelastic Electron and Positron Scattering from Unpolarized Hydrogen and Deuterium Targets, JHEP 05 (2011) 126 [arXiv:1103.5704] [INSPIRE].
H. Abramowicz, E.M. Levin, A. Levy and U. Maor, A Parametrization of σT(γ*p) above the resonance region Q2 ≥ 0, Phys. Lett. B 269 (1991) 465 [INSPIRE].
H. Abramowicz and A. Levy, The ALLM parameterization of σtot(γ * p): An Update, hep-ph/9712415 [INSPIRE].
CLAS collaboration, A Kinematically complete measurement of the proton structure function F(2) in the resonance region and evaluation of its moments, Phys. Rev. D 67 (2003) 092001 [hep-ph/0301204] [INSPIRE].
M.E. Christy and P.E. Bosted, Empirical fit to precision inclusive electron-proton cross-sections in the resonance region, Phys. Rev. C 81 (2010) 055213 [arXiv:0712.3731] [INSPIRE].
P.E. Bosted and M.E. Christy, Empirical fit to inelastic electron-deuteron and electron-neutron resonance region transverse cross-sections, Phys. Rev. C 77 (2008) 065206 [arXiv:0711.0159] [INSPIRE].
M.E. Christy, N. Kalantarians, J. Either and W. Melnitchouk, to be published.
S. Galster et al., Elastic electron-deuteron scattering and the electric neutron form factor at four-momentum transfers 5fm−2 < q2 < 14fm−2, Nucl. Phys. B 32 (1971) 221 [INSPIRE].
G. Ricco, S. Simula and M. Battaglieri, Power corrections in the longitudinal and transverse structure functions of proton and deuteron, Nucl. Phys. B 555 (1999) 306 [hep-ph/9901360] [INSPIRE].
J.J. Kelly, Simple parametrization of nucleon form factors, Phys. Rev. C 70 (2004) 068202 [INSPIRE].
E143 collaboration, Measurements of R = σ(L) / σ(T) for 0.03 < × < 0.1 and fit to world data, Phys. Lett. B 452 (1999) 194 [hep-ex/9808028] [INSPIRE].
L.W. Whitlow et al., A Precise extraction of R = sigma-L / sigma-T from a global analysis of the SLAC deep inelastic e p and e d scattering cross-sections, Phys. Lett. B 250 (1990) 193 [INSPIRE].
E140X collaboration, Precision measurement of R = sigma-L / sigma-T on hydrogen, deuterium and beryllium targets in deep inelastic electron scattering, Z. Phys. C 70 (1996) 387 [INSPIRE].
New Muon collaboration, Measurements of R(d) - R(p) and R (Ca) - R(C) in deep inelastic muon scattering, Phys. Lett. B 294 (1992) 120 [INSPIRE].
New Muon collaboration, The Q**2 dependence of the structure function ratio F2 Sn / F2 C and the difference R Sn - R C in deep inelastic muon scattering, Nucl. Phys. B 481 (1996) 23 [INSPIRE].
New Muon collaboration, Accurate measurement of F2(d) / F2(p) and Rd − Rp, Nucl. Phys. B 487 (1997) 3 [hep-ex/9611022] [INSPIRE].
M. Guzzi, P.M. Nadolsky, H.-L. Lai and C.-P. Yuan, General-Mass Treatment for Deep Inelastic Scattering at Two-Loop Accuracy, Phys. Rev. D 86 (2012) 053005 [arXiv:1108.5112] [INSPIRE].
K.G. Wilson, Nonlagrangian models of current algebra, Phys. Rev. 179 (1969) 1499 [INSPIRE].
T.-P. Cheng and L.-F. Li, Gauge Theory of Elementary Particle Physics, Oxford University Press, Oxford, U.K. (1984).
D.J. Gross and S.B. Treiman, Light cone structure of current commutators in the gluon quark model, Phys. Rev. D 4 (1971) 1059 [INSPIRE].
A. Accardi et al., Constraints on large-x parton distributions from new weak boson production and deep-inelastic scattering data, Phys. Rev. D 93 (2016) 114017 [arXiv:1602.03154] [INSPIRE].
I. Abt et al., Study of HERA ep data at low Q2 and low xBj and the need for higher-twist corrections to standard perturbative QCD fits, Phys. Rev. D 94 (2016) 034032 [arXiv:1604.02299] [INSPIRE].
J.L. Miramontes and J. Sanchez Guillen, Understanding higher twist: operator approach to power corrections, Z. Phys. C 41 (1988) 247 [INSPIRE].
H. Georgi and H.D. Politzer, Freedom at Moderate Energies: Masses in Color Dynamics, Phys. Rev. D 14 (1976) 1829 [INSPIRE].
O. Nachtmann, Positivity constraints for anomalous dimensions, Nucl. Phys. B 63 (1973) 237 [INSPIRE].
I. Schienbein et al., A Review of Target Mass Corrections, J. Phys. G 35 (2008) 053101 [arXiv:0709.1775] [INSPIRE].
M. Goharipour and S. Rostami, Implementation of target mass corrections and higher-twist effects in the xFitter framework, Phys. Rev. D 101 (2020) 074015 [arXiv:2004.03403] [INSPIRE].
T.-J. Hou et al., New CTEQ global analysis of quantum chromodynamics with high-precision data from the LHC, Phys. Rev. D 103 (2021) 014013 [arXiv:1912.10053] [INSPIRE].
B. Zhou and J.F. Beacom, W-boson and trident production in TeV–PeV neutrino observatories, Phys. Rev. D 101 (2020) 036010 [arXiv:1910.10720] [INSPIRE].
M. Ackermann et al., High-energy and ultra-high-energy neutrinos: a Snowmass white paper, JHEAp 36 (2022) 55 [arXiv:2203.08096] [INSPIRE].
IceCube collaboration, A combined maximum-likelihood analysis of the high-energy astrophysical neutrino flux measured with IceCube, Astrophys. J. 809 (2015) 98 [arXiv:1507.03991] [INSPIRE].
KM3Net collaboration, Letter of intent for KM3NeT 2.0, J. Phys. G 43 (2016) 084001 [arXiv:1601.07459] [INSPIRE].
BAIKAL collaboration, The prototyping/early construction phase of the BAIKAL-GVD project, Nucl. Instrum. Meth. A 742 (2014) 82 [arXiv:1308.1833] [INSPIRE].
IceCube-Gen2 collaboration, The IceCube-Gen2 High Energy Array, PoS ICRC2015 (2016) 1146 [INSPIRE].
P-ONE collaboration, The Pacific Ocean Neutrino Experiment, Nature Astron. 4 (2020) 913 [arXiv:2005.09493] [INSPIRE].
Z.P. Ye et al., Proposal for a neutrino telescope in South China Sea, arXiv:2207.04519 [INSPIRE].
FASER collaboration, First Direct Observation of Collider Neutrinos with FASER at the LHC, Phys. Rev. Lett. 131 (2023) 031801 [arXiv:2303.14185] [INSPIRE].
B. Zhou and J.F. Beacom, Neutrino-nucleus cross sections for W-boson and trident production, Phys. Rev. D 101 (2020) 036011 [arXiv:1910.08090] [INSPIRE].
R.D. Peccei and H.R. Quinn, CP Conservation in the Presence of Instantons, Phys. Rev. Lett. 38 (1977) 1440 [INSPIRE].
S. Weinberg, A New Light Boson?, Phys. Rev. Lett. 40 (1978) 223 [INSPIRE].
F. Wilczek, Problem of Strong P and T Invariance in the Presence of Instantons, Phys. Rev. Lett. 40 (1978) 279 [INSPIRE].
J.E. Kim and G. Carosi, Axions and the Strong CP Problem, Rev. Mod. Phys. 82 (2010) 557 [Erratum ibid. 91 (2019) 049902] [arXiv:0807.3125] [INSPIRE].
L. Di Luzio, M. Giannotti, E. Nardi and L. Visinelli, The landscape of QCD axion models, Phys. Rept. 870 (2020) 1 [arXiv:2003.01100] [INSPIRE].
D.J.E. Marsh, Axion Cosmology, Phys. Rept. 643 (2016) 1 [arXiv:1510.07633] [INSPIRE].
K. Choi, S.H. Im and C. Sub Shin, Recent Progress in the Physics of Axions and Axion-Like Particles, Ann. Rev. Nucl. Part. Sci. 71 (2021) 225 [arXiv:2012.05029] [INSPIRE].
C. Cesarotti, S. Homiller, R.K. Mishra and M. Reece, Probing New Gauge Forces with a High-Energy Muon Beam Dump, Phys. Rev. Lett. 130 (2023) 071803 [arXiv:2202.12302] [INSPIRE].
D. Acosta and W. Li, A muon–ion collider at BNL: The future QCD frontier and path to a new energy frontier of μ+μ− colliders, Nucl. Instrum. Meth. A 1027 (2022) 166334 [arXiv:2107.02073] [INSPIRE].
J.P. Delahaye et al., Muon Colliders, arXiv:1901.06150 [INSPIRE].
Muon Collider collaboration, The physics case of a 3 TeV muon collider stage, arXiv:2203.07261 [INSPIRE].
J. Alwall et al., The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations, JHEP 07 (2014) 079 [arXiv:1405.0301] [INSPIRE].
C. Degrande et al., UFO - The Universal FeynRules Output, Comput. Phys. Commun. 183 (2012) 1201 [arXiv:1108.2040] [INSPIRE].
I. Brivio et al., ALPs Effective Field Theory and Collider Signatures, Eur. Phys. J. C 77 (2017) 572 [arXiv:1701.05379] [INSPIRE].
A. Alloul et al., FeynRules 2.0 - A complete toolbox for tree-level phenomenology, Comput. Phys. Commun. 185 (2014) 2250 [arXiv:1310.1921] [INSPIRE].
S. Frixione, M.L. Mangano, P. Nason and G. Ridolfi, Improving the Weizsacker-Williams approximation in electron - proton collisions, Phys. Lett. B 319 (1993) 339 [hep-ph/9310350] [INSPIRE].
Y. Liu and B. Yan, Searching for the axion-like particle at the EIC, Chin. Phys. C 47 (2023) 043113 [arXiv:2112.02477] [INSPIRE].
A. Buckley et al., LHAPDF6: parton density access in the LHC precision era, Eur. Phys. J. C 75 (2015) 132 [arXiv:1412.7420] [INSPIRE].
D. Stump et al., Uncertainties of predictions from parton distribution functions. 1. The Lagrange multiplier method, Phys. Rev. D 65 (2001) 014012 [hep-ph/0101051] [INSPIRE].
J. Pumplin et al., Uncertainties of predictions from parton distribution functions. 2. The Hessian method, Phys. Rev. D 65 (2001) 014013 [hep-ph/0101032] [INSPIRE].
N. Armesto, Nuclear shadowing, J. Phys. G 32 (2006) R367 [hep-ph/0604108] [INSPIRE].
B.Z. Kopeliovich, J.G. Morfin and I. Schmidt, Nuclear Shadowing in Electro-Weak Interactions, Prog. Part. Nucl. Phys. 68 (2013) 314 [arXiv:1208.6541] [INSPIRE].
European Muon collaboration, A Measurement of the ratio of the nucleon structure function in copper and deuterium, Z. Phys. C 57 (1993) 211 [INSPIRE].
Acknowledgments
We thank Thomas Cridge for the help with the clarification of MSHT20qed results, and our CTEQ-TEA colleagues for useful discussions. The work of KX was supported by the U.S. Department of Energy under grant No. DE-SC0007914, the U.S. National Science Foundation under Grants No. PHY-2112829, No. PHY-2013791, and No. PHY-2310497, and also in part by the PITT PACC. The work of BZ was supported by the Simons Foundation. The work of TJH was supported by Argonne National Laboratory, operated by UChicago Argonne, LLC, for the U.S. Department of Energy under Contract No. DE-AC02-06CH11357. The work of KX was performed partly at the Aspen Center for Physics, which is supported by the U.S. National Science Foundation under Grant No. PHY-1607611 and No. PHY-2210452. This work used resources of high-performance computing clusters from SMU M2/M3, MSU HPCC, as well as Pitt CRC.
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The CTEQ-TEA collaboration., Xie, K., Zhou, B. et al. The photon content of the neutron. J. High Energ. Phys. 2024, 22 (2024). https://doi.org/10.1007/JHEP04(2024)022
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DOI: https://doi.org/10.1007/JHEP04(2024)022