Remark on in-medium masses of hadrons with one heavy quark

TL;DR

This paper derives a temperature-dependent formula for the in-medium masses of hadrons with a single heavy quark, based on the bag model, highlighting differences from light hadron behavior.

Contribution

It introduces a simple scaling formula for heavy hadron masses in a heat bath, derived from dimensional analysis within the bag model framework.

Findings

Mass splitting between pseudoscalar and vector mesons varies with temperature.

The formula differs from that of light hadrons, indicating unique in-medium effects for heavy quark hadrons.

The MIT bag model exemplifies the derived scenario.

Abstract

In this short note we derive a formula which describes the dependence of the mass of a hadron which contains a single heavy quark on the temperature of the heat bath. It takes a simple scaling form with the exponent which is different than in the case of the light hadrons. The derivation is based on dimensional arguments within the framework of the bag model paradigm. The simple realization of this scenario is presented for the MIT bag model. The mass splitting between pseudoscalar and vector mesons ($D, D^\ast$ or $B, B^\ast$) as a function of temeperature is presented.