Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Finite Temperature NLO Corrections in Relativistic Scatterings: Implications for Dark Matter Freeze-In

Sampriti Roy, Pritam Sen, Satyanarayan Mukhopadhyay

Abstract

We study the next-to-leading order (NLO) virtual and thermal corrections to relativistic $2 \rightarrow 2$ scattering processes involving scalar particles in the early Universe thermal plasma. Taking the example of freeze-in production of scalar dark matter pairs through these scatterings, we evaluate the impact of the NLO corrections to the annihilation rate and the dark matter yield. We find that including only thermal mass corrections to a leading order interaction rate can overestimate the reduction in these rates, and the full NLO corrections can modify the DM abundance predictions by $\mathcal{O}(30\%)$. It is also observed that while the virtual NLO effects are larger, the finite temperature NLO corrections to the matrix elements in the relativistic regime can modify the DM abundance by $\mathcal{O}(10\%)$, in comparison to the virtual NLO corrections.

Finite Temperature NLO Corrections in Relativistic Scatterings: Implications for Dark Matter Freeze-In

Abstract

We study the next-to-leading order (NLO) virtual and thermal corrections to relativistic scattering processes involving scalar particles in the early Universe thermal plasma. Taking the example of freeze-in production of scalar dark matter pairs through these scatterings, we evaluate the impact of the NLO corrections to the annihilation rate and the dark matter yield. We find that including only thermal mass corrections to a leading order interaction rate can overestimate the reduction in these rates, and the full NLO corrections can modify the DM abundance predictions by . It is also observed that while the virtual NLO effects are larger, the finite temperature NLO corrections to the matrix elements in the relativistic regime can modify the DM abundance by , in comparison to the virtual NLO corrections.

Paper Structure

This paper contains 6 sections, 20 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Scalar dark matter freeze-in from scattering
  3. DM freeze-in from scattering: virtual and thermal NLO corrections
  4. Analytical approximation for the thermal NLO matrix element
  5. Numerical results: NLO corrections to relativistic freeze-in
  6. Summary

Figures (3)

  • Figure 1: Feynman diagrams representing the virtual and thermal NLO corrections to the matrix elements for the freeze-in process $\phi \phi \rightarrow \chi \chi$, with the momentum labels $p=p_1+p_2, ~p_t=p_1-p_3$ and $p_u=p_1-p_4$.
  • Figure 2: (Left) The thermally averaged annihilation rate ${\langle \sigma v \rangle}_{\phi \phi \rightarrow \chi \chi}(x)$ for the freeze-in process as a function of $x=m_\chi^{(0)}/T$, (i) at LO, (ii) at LO including thermal mass effects, (iii) at NLO including only the vacuum NLO matrix elements and thermal mass, and (iv) at NLO including both the vacuum and thermal NLO matrix elements and mass corrections. (Right) The ratio of different annihilation rates with ${\langle \sigma v \rangle}_{\rm LO}^{m^{(0)}}$.
  • Figure 3: (Left) Ratio of the reaction rates $\Delta \langle \sigma v \rangle_{\rm NLO}^{\rm T}/{\Delta \langle \sigma v \rangle_{\rm NLO}^{\rm V}}$ as defined in Eq. \ref{['Eq:ratio']}, as a function of $x=m_\chi^{(0)}/T$. This ratio is representative of the thermal NLO corrections to the reaction matrix elements, see text for details. (Right) Dark matter yield $Y_{\rm DM}=n_\chi/s$, as a function of $x$, in all the four different computational setups considered.