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Chiral Cherenkov radiation in the presence of a time-dependent chiral chemical potential

Kirill Tuchin

TL;DR

This work analyzes how a time-dependent chiral chemical potential $b_0(t)$ modifies chiral Cherenkov radiation from a fast fermion. By formulating the photon production rate in the ultra-relativistic limit and solving for the photon amplitude under two analytic models of $b_0(t)$, the authors obtain exact and adiabatic results that reveal resonance structures: model (i) can produce one or two resonances depending on the signs of the asymptotic $b_0$ values, while model (ii) yields no resonances and equal polarization spectra. The adiabatic approximation is shown to reproduce exact results in appropriate limits, indicating a robust and potentially universal spectral pattern governed by the time dependence of $b_0(t)$. The findings have implications for the quark-gluon plasma in heavy-ion collisions and broader contexts like Weyl semimetals or cosmic-field settings where transient chirality affects radiation and energy loss.

Abstract

The photon production process $f\to f+γ$ in the presence of a time-dependent chiral chemical potential $μ_5$ is studied. The validity of the adiabatic approximation is demonstrated in the ultra-relativistic limit. Analytical expressions for the photon spectrum are derived for two models of the chiral magnetic conductivity $b_0\propto μ_5$: (i) $b_0(t)= A_1+B_1\tanh(t/τ)$ and (ii) $b_0(t)= A_2(t/τ)/(1+t^2/τ^2)$. It is known that for constant $b_0$, photon emission may exhibit a resonance for one photon polarization depending on the sign of $b_0$. It is shown that in model (i), up to two resonances may occur, depending on the sign of the asymptotic values $b_0(\infty)$ and $b_0(-\infty)$. No resonances are observed in model (ii). Numerical calculations are performed using parameters relevant to quark-gluon plasma, and the universality of the results is discussed.

Chiral Cherenkov radiation in the presence of a time-dependent chiral chemical potential

TL;DR

This work analyzes how a time-dependent chiral chemical potential modifies chiral Cherenkov radiation from a fast fermion. By formulating the photon production rate in the ultra-relativistic limit and solving for the photon amplitude under two analytic models of , the authors obtain exact and adiabatic results that reveal resonance structures: model (i) can produce one or two resonances depending on the signs of the asymptotic values, while model (ii) yields no resonances and equal polarization spectra. The adiabatic approximation is shown to reproduce exact results in appropriate limits, indicating a robust and potentially universal spectral pattern governed by the time dependence of . The findings have implications for the quark-gluon plasma in heavy-ion collisions and broader contexts like Weyl semimetals or cosmic-field settings where transient chirality affects radiation and energy loss.

Abstract

The photon production process in the presence of a time-dependent chiral chemical potential is studied. The validity of the adiabatic approximation is demonstrated in the ultra-relativistic limit. Analytical expressions for the photon spectrum are derived for two models of the chiral magnetic conductivity : (i) and (ii) . It is known that for constant , photon emission may exhibit a resonance for one photon polarization depending on the sign of . It is shown that in model (i), up to two resonances may occur, depending on the sign of the asymptotic values and . No resonances are observed in model (ii). Numerical calculations are performed using parameters relevant to quark-gluon plasma, and the universality of the results is discussed.

Paper Structure

This paper contains 10 sections, 5 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Photon radiation probability
  3. Photon spectrum at constant $b_0$
  4. Adiabatic approximation
  5. Photon spectrum for $b_0(t)=A_1+ B_1\tanh\frac{t}{\tau}$
  6. Exact solution for $a(t)$
  7. Adiabatic approximation
  8. Sudden transition
  9. Photon spectrum for $b(t)= A_2(t/\tau)/(1+t^2/\tau^2)$
  10. Summary

Figures (5)

  • Figure 1: The photon spectrum for a constant $b_0=10$ MeV. The incident fermion energy $E=20$ GeV, mass $m=0.3$ GeV and unit charge. The Lorentzian parameter $\epsilon=1$ MeV. Only the right-handed photons $\lambda=1$ are emitted.
  • Figure 2: The photon spectrum for $b_0(t)=A_1+ B_1\tanh\frac{t}{\tau}$ with $A_1=B_1=10$ MeV and $\tau=25$ GeV$^{-1}\approx$ 5 fm/c. The incident fermion energy $E=20$ GeV, mass $m=0.3$ GeV, and unit charge.
  • Figure 3: The photon spectrum for $b_0(t)=A_1+ B_1\tanh\frac{t}{\tau}$ with $A_1=-B_1=-10$ MeV (left), $A_1=0$, $B_1=10$ MeV (right) and $\tau=25$ GeV$^{-1}\approx$ 5 fm/c. The incident fermion energy $E=20$ GeV, mass $m=0.3$ GeV, and unit charge. The turquoise color indicates that the spectrum is independent of the photon's polarization.
  • Figure 4: The photon spectrum for $b_0(t)=A_1+ B_1\tanh\frac{t}{\tau}$ with $A_1=15$ MeV, $B_1=5$ MeV $\tau=25$ GeV$^{-1}\approx$ 5 fm/c. The incident fermion energy $E=20$ GeV, mass $m=0.3$ GeV, and unit charge.
  • Figure 5: The photon spectrum for $b_0(t)= A(t/\tau)/(1+t^2/\tau^2)$ with $A_2=10$ MeV and $\tau=25$ GeV$^{-1}\approx$ 5 fm/c. The incident fermion energy $E=20$ GeV, mass $m=0.3$ GeV, and unit charge. The spectrum does not depend on the photon's polarization, which is reflected in turquoise color, and does not exhibit any resonances.