Quantum and Thermal Fluctuations of Cherenkov Radiation from HQET

Abstract

Charged particles travelling faster than the speed of light in the medium in which they propagate emit Cherenkov radiation. The formula for the spectrum of this radiation as a function of frequency, known as the Frank-Tamm formula, first derived almost 90 years ago, follows purely from classical electromagnetism. In this work, we demonstrate how this result also follows from a short quantum field theory calculation, which in addition to it contains all of the cumulants of thermal and quantum fluctuations around the classical radiation spectrum at leading order in the inverse of the particle's mass. All of these results follow from the particle's momentum change probability, which we calculate for weakly coupled gauge theories using the tools of Heavy Quark Effective theory.

Figures (1)

• Figure 1: Plots of $P(\Delta k_\|,v = 2c_m)$ for the hard cutoffs $\omega_\mathrm{IR} = 0.2, \omega_\mathrm{UV} = 1$. The distributions at different normalised times $\tilde{t} = t \frac{g^2 C_2}{4 \pi^2}$ are plotted in different colours. All the distributions have a component proportional to $\delta(k_\|)$ (\ref{['eq:delta']}), these have been explicitly drawn for the $T = 0$ distributions as arrows --- for the $T = 1$ and $T \to \infty$ distributions however they are not shown as their norms are very small. The asymptotic ($t \to \infty$) distributions for $T = 1$ and $T \to \infty$ are shown in dashed gray line, and the bounded part ($P_\mathrm{bounded}(\Delta k_\|)$) of the distribution have been rescaled such that $P_\mathrm{bounded}(0) = 1$.