One-photon decay of the tetraquark state $X(3872) \to \gamma + J/\psi$ in a relativistic constituent quark model with infrared confinement

TL;DR

This paper models the X(3872) as a tetraquark and calculates its one-photon decay to J/psi using a relativistic quark model with infrared confinement, aligning results with experimental data.

Contribution

It introduces a gauge-invariant method to compute the X(3872) decay within a relativistic, confined quark framework, extending previous models.

Findings

Decay width consistent with experimental data

Calculated helicity and multipole amplitudes

Proved gauge invariance of the transition matrix

Abstract

We further explore the consequences of treating the X(3872) meson as a tetraquark bound state by analyzing its one-photon decay X => \gamma + J/psi in the framework of our approach developed in previous papers which incorporates quark confinement in an effective way. To introduce electromagnetism we gauge a nonlocal effective Lagrangian describing the interaction of the X(3872) meson with its four constituent quarks by using the P-exponential path-independent formalism. We calculate the matrix element of the transition X => \gamma+ J/psi and prove its gauge invariance. We evaluate the X=> \gamma + J/psi decay width and the longitudinal/transverse composition of the J/psi in this decay. For a reasonable value of the size parameter of the X(3872) meson we find consistency with the available experimental data. We also calculate the helicity and multipole amplitudes of the process, and describe how they can be obtained from the covariant transition amplitude by covariant projection.