$ B_c B_c J/\psi $ Vertex Form Factor at Finite Temperature in the Framework of QCD Sum Rules Approach

TL;DR

This study calculates the temperature-dependent strong form factor of the $B_c B_c J/\psi$ vertex using QCD sum rules, revealing its stability up to 100 MeV and a sharp decrease after 160 MeV, with results aligning well with vacuum calculations.

Contribution

It introduces a finite temperature QCD sum rules approach to evaluate the $B_c B_c J/\psi$ vertex form factor, including thermal operators and Wilson expansion effects.

Findings

Form factor remains stable up to 100 MeV

Slight increase in form factor after 100 MeV

Sharp decrease after 160 MeV

Abstract

The strong form factor of the $B_{c} B_{c}J/\Psi$ vertex is calculated in the framework of the QCD sum rules method at finite temperature. Taking into account additional operators appearing at finite temperature, thermal Wilson expansion is obtained and QCD sum rules are derived. While increasing temperature, the strong form factor remains unchanged up to $T\simeq100~MeV$ but slightly increases after this point. After $T\simeq160~MeV$, the form factor suddenly decreases up to $T\simeq170~MeV$. The obtained result of the coupling constant by fitting the form factor at $Q^2=-m^2_{offshell}$ at $T=0$ is in a very good agreement with the QCD sum rules calculations at vacuum. Our prediction can be checked in the future experiments.