Cottingham formula and the pion electromagnetic mass difference at finite temperature

TL;DR

This paper extends the Cottingham formula to finite temperature using imaginary time formalism, enabling the study of thermal effects on hadron electromagnetic mass differences, exemplified by the pion mass difference near deconfinement.

Contribution

The authors generalize the Cottingham formula to finite temperature, providing a new tool to analyze thermal effects on hadron mass differences.

Findings

Reproduces known behavior of pion mass difference at low T

Identifies deviations from low T behavior near deconfinement temperature

Provides a framework for studying thermal effects in hadronic processes

Abstract

We generalize the Cottingham formula at finite (T\neq 0) temperature by using the imaginary time formalism. The Cottingham formula gives the theoretical framework to compute the electromagnetic mass differences of the hadrons using a dispersion relation approach. It can be also used in other contexts, such as non leptonic weak decays, and its generalization to finite temperature might be useful in evaluating thermal effects in these processes. As an application we compute the \pi^+-\pi^0 mass difference at T\neq 0; at small T we reproduce the behaviour found by other authors: \delta m^2(T)= \delta m^2(0)+\mathcal{O}(\alpha T^2), while for moderate T, near the deconfinement temperature, we observe deviations from this behaviour.