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Parton distribution functions of ground state mesons composed of c or b quarks

Qian Wu (吴迁)1,*, Zhu-Fang Cui (崔著钫)1,†, and Jorge Segovia2,‡

  • *Contact author: qwu@nju.edu.cn
  • †Contact author: phycui@nju.edu.cn
  • ‡Contact author: jsegovia@upo.es
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Phys. Rev. D 111, 116023 – Published 26 June, 2025

DOI: https://doi.org/10.1103/9mkx-cn8b

Abstract

The valence quark parton distribution functions (PDFs) of all ground state heavy mesons composed of b or c quarks, are discussed; namely, the pseudoscalar ηc(1S), ηb(1S), and Bc, together with the corresponding vector ones, J/ψ, ϒ(1S), and Bc*. We use a quantum chromodynamics (QCD)-inspired constituent quark model, which has been applied with success to conventional heavy mesons, so that one advantage here is that all parameters have already been fixed by previous studies. The wave functions of the heavy mesons in the rest frame are obtained by solving the Schrödinger equation, then boosted to its light-front, based on Susskind’s Lorentz transformation. The PDFs at the hadron scale, are then obtained by integrating out the transverse momenta of the modulus square of the light-front wave function. Our study shows how the valence quark distributions differ between pseudoscalar and vector mesons, as well as among charmonia, bottomonia and bottom-charmed mesons. Comparisons with other theoretical calculations demonstrate that the PDFs obtained herein are in general narrower but align well with the expected patterns. Moreover, each PDF’s pointwise behavior is squeezed with respect to the scale-free partonlike PDF.

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Phys. Rev. D 111, 116023– Published 26 June, 2025
  • Received 16 March 2025
  • Accepted 3 June 2025
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