Light-front wavefunctions of mesons by design

Abstract

We develop a mechanism to build the light-front wavefunctions (LFWFs) of meson bound states on a small-sized basis function representation. Unlike in a standard Hamiltonian formalism, the Hamiltonian in this method is implicit, and the information of the system is carried directly by the functional form and adjustable parameters of the LFWFs. In this work, we model the LFWFs for four charmonium states, ${\eta }_c$, $J/\psi$, ${\psi }^{\prime }$, and $\psi (3770)$ as superpositions of orthonormal basis functions. We choose the basis functions as eigenfunctions of an effective Hamiltonian, which has a longitudinal confining potential in addition to the transverse confining potential from light-front holographic QCD. We determine the basis function parameters and superposition coefficients by employing both guidance from the nonrelativistic description of the meson states and the experimental measurements of the meson decay widths. With the obtained wavefunctions, we study the features of those meson states, including charge radii and parton distribution functions. We use the $J/\psi$ LFWF to calculate the meson production in diffractive deep inelastic scattering and ultra-peripheral heavy-ion collisions, and the ${\eta }_c$ LFWF to calculate its diphoton transition form factor. Both results show good agreement with experiments. The obtained LFWFs have simple-functional forms and can be readily used to predict additional experimental observables.

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Cited by in corpus (10)

• The valence quark, sea, and gluon content of the pion from the parton distribution functions and the electromagnetic form factor
• Mixing effects on 1S and 2S state heavy mesons in the light-front quark model
• Two-photon transitions of charmonia on the light front
• Pseudoscalar meson decay constants and distribution amplitudes up to twist-4 in the light-front quark model
• Self-consistent $M1$ radiative transitions of excited $B_c$ and heavy quarkonia with different polarizations in the light-front quark model
• Stress out of charmonia
• Spectroscopy of excited quarkonium states in the light-front quark model
• Valence quark distribution of light $\rho$ and heavy $J/\psi$ vector mesons in light-cone quark model
• Anisotropic flow and the valence quark skeleton of hadrons
• Prospects for observing the ${\eta }_t$ $\to$ $W^{+}{W}^{-}$ decay at the HL-LHC