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

Abstract

The valence quark parton distribution functions (PDFs) of all ground state heavy mesons that composed of $b$ or $c$ quarks, are discussed; namely, the pseudoscalar ${\eta }_c(1S)$, ${\eta }_b(1S)$ and $B_c$, together with the corresponding vector ones, $J/\psi$, ${\rm Y}(1S)$ and $B_c^{\ast }$. We use a 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 point-wise behavior is squeezed with respect to the scale-free parton-like PDF.

9 pages, 7 figures, 4 table

References in corpus (14)

• Heavy quarkonium: progress, puzzles, and opportunities
• Constituent quark model study of the meson spectra
• Quark-model study of few-baryon systems
• 50 Years of Quantum Chromodynamics
• Parton Distributions in Nucleons and Nuclei
• Evidence for intrinsic charm quarks in the proton
• QCD Running Couplings and Effective Charges
• Charmed-strange Meson Spectrum: Old and New Problems
• Puzzles in hadronic transitions of heavy quarkonium with two pion emission
• Pseudo-scalar mesons: light front wave functions, GPDs and PDFs
• Towards the discovery of novel $B_c$ states: radiative and hadronic transitions
• Self-consistent $M1$ radiative transitions of excited $B_c$ and heavy quarkonia with different polarizations in the light-front quark model
• Light-front Wave Functions of Vector Mesons in an Algebraic Model
• Pion parton distribution functions with the nonrelativistic constituent quark model

Cited by in corpus (2)

• Structure of heavy quarkonia in a strong magnetic field
• The kaon off-shell generalized parton distributions and transverse momentum dependent parton distributions