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Flavor, transverse momentum, and azimuthal dependence of charged pion multiplicities in semi-inclusive deep-inelastic scattering with 10.6 GeV electrons

P. Bosted ¹, H. Bhatt², S. Jia³, W. Armstrong⁴, D. Dutta², R. Ent⁵, D. Gaskell⁵, E. Kinney⁶, H. Mkrtchyan⁷ et al. (Hall C SIDIS Collaboration)

H. Mkrtchyan⁷, S. Ali⁸, R. Ambrose⁹, D. Androic¹⁰, C. Ayerbe Gayoso², A. Bandari¹, V. Berdnikov⁸, D. Bhetuwal², D. Biswas¹¹, M. Boer³, E. Brash¹², A. Camsonne⁵, M. Cardona³, J. P. Chen⁵, J. Chen¹, M. Chen¹³, E. M. Christy¹¹, S. Covrig⁵, S. Danagoulian¹⁴, M. Diefenthaler⁵, B. Duran³, C. Elliot¹⁵, H. Fenker⁵, E. Fuchey¹⁶, J. O. Hansen⁵, F. Hauenstein¹⁷, T. Horn⁸, G. M. Huber⁹, M. K. Jones⁵, M. L. Kabir², A. Karki², B. Karki¹⁸, S. J. D. Kay^9,19, C. Keppel⁵, V. Kumar⁹, N. Lashley-Colthirst¹¹, W. B. Li^1,2, D. Mack⁵, S. Malace⁵, P. Markowitz²⁰, M. McCaughan⁵, E. McClellan⁵, D. Meekins⁵, R. Michaels⁵, A. Mkrtchyan⁷, C. Morean^15,5, G. Niculescu²¹, I. Niculescu²¹, B. Pandey^11,22, S. Park²³, E. Pooser⁵, B. Sawatzky⁵, G. R. Smith⁵, H. Szumila-Vance^5,20, A. S. Tadepalli⁵, V. Tadevosyan⁷, R. Trotta⁸, H. Voskanyan⁷, S. A. Wood⁵, Z. Ye^4,24, C. Yero²⁰, and X. Zheng¹³ (Hall C SIDIS Collaboration)

¹The College of William & Mary, Williamsburg, Virginia 23185, USA
²Mississippi State University, Mississippi State, Mississippi 39762, USA
³Temple University, Philadelphia, Pennsylvania 19122, USA
⁴Argonne National Laboratory, Lemont, Illinois 60439, USA
⁵Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA
⁶University of Colorado Boulder, Boulder, Colorado 80309, USA
⁷A.I. Alikhanyan National Science Laboratory, Yerevan Physics Institute, Yerevan 0036, Armenia
⁸Catholic University of America, Washington, DC 20064, USA
⁹University of Regina, Regina, Saskatchewan S4S 0A2, Canada
¹⁰University of Zagreb, Zagreb, Croatia
¹¹Hampton University, Hampton, Virginia 23669, USA
¹²Christopher Newport University, Newport News, Virginia 23606, USA
¹³University of Virginia, Charlottesville, Virginia 22903, USA
¹⁴North Carolina A & T State University, Greensboro, North Carolina 27411, USA
¹⁵University of Tennessee, Knoxville, Tennessee 37996, USA
¹⁶University of Connecticut, Storrs, Connecticut 06269, USA
¹⁷Old Dominion University, Norfolk, Virginia 23529, USA
¹⁸Ohio University, Athens, Ohio 45701, USA
¹⁹University of York, Heslington, York YO10 5DD, United Kingdom
²⁰Florida International University, University Park, Florida 33199, USA
²¹James Madison University, Harrisonburg, Virginia 22807, USA
²²Virginia Military Institute, Lexington, Virginia 24450, USA
²³Stony Brook University, Stony Brook, New York 11794, USA
²⁴Tsinghua University, Beijing 100084, China

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Phys. Rev. C 113, 035205 – Published 19 March, 2026

DOI: https://doi.org/10.1103/xh6f-6fhy

Abstract

Measurements of semi-inclusive deep-inelastic scattering multiplicities for $π^{+}$ and $π^{-}$ from proton and deuteron targets are reported on a grid of hadron kinematic variables $z, P_{T}$ , and $ϕ^{*}$ for leptonic kinematic variables in the range $0.3 < x < 0.6$ and $3 < Q^{2} < 5 {GeV}^{2}$ . Data were acquired in 2018 and 2019 at Jefferson Lab Hall C with a 10.6 GeV electron beam impinging on 10-cm-long liquid hydrogen and deuterium targets. Scattered electrons and charged pions were detected in the High Momentum Spectrometer and Super High Momentum Spectrometer, respectively. The multiplicities were fitted for each bin in $(x, Q^{2}, z, P_{t})$ to extract the $ϕ^{*}$ —independent $M_{0}$ and the azimuthal modulations $〈 cos (ϕ^{*}) 〉$ and $〈 cos (2 ϕ^{*}) 〉$ . The $P_{t}$ dependence of the $M_{0}$ results was found to be remarkably consistent for the four cases studied: $e p \to e π^{+} X, e p \to e π^{-} X, e d \to e π^{+} X, e d \to e π^{-} X$ over the range $0 GeV < P_{t} < 0.4 GeV$ , as were the multiplicities evaluated near $ϕ^{*} = 180^{\circ}$ over the extended range $0 GeV < P_{t} < 0.7 GeV$ . The Gaussian widths of the $P_{t}$ dependence exhibit a quadratic increase with $z$ . The $cos (ϕ^{*})$ modulations were found to be consistent with zero for $π^{+}$ , in agreement with previous world data, while the $π^{-}$ moments were, in many cases, significantly greater than zero. The $cos (2 ϕ^{*})$ modulations were found to be consistent with zero. The higher statistical precision of this dataset of about 20 000 individual multiplicity values, compared with previously published data, should allow improved determinations of quark transverse momentum distributions and higher twist contributions.

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Phys. Rev. C 113, 035205– Published 19 March, 2026

Vol. 113, Iss. 3 — March 2026

Received 7 October 2025
Revised 29 December 2025
Accepted 20 February 2026

DOI: https://doi.org/10.1103/xh6f-6fhy

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP³.

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Flavor, transverse momentum, and azimuthal dependence of charged pion multiplicities in semi-inclusive deep-inelastic scattering with 10.6 GeV electrons

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