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Related Experiment Video

Updated: Dec 29, 2025

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
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A Sommerfeld toolbox for colored dark sectors.

Sonia El Hedri1, Anna Kaminska1, Maikel de Vries1

  • 1PRISMA Cluster of Excellence and Mainz Institute for Theoretical Physics, Johannes Gutenberg University, 55099 Mainz, Germany.

The European Physical Journal. C, Particles and Fields
|February 4, 2020
PubMed
Summary
This summary is machine-generated.

We developed formulas for Sommerfeld corrections in dark matter annihilation, crucial for accurate relic density calculations. Our work includes all orders of partial wave expansion and arbitrary particle spin for strongly interacting particles.

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Area of Science:

  • Particle Physics
  • Cosmology
  • Dark Matter Physics

Background:

  • Accurate computation of dark matter relic density requires precise understanding of annihilation processes.
  • Sommerfeld corrections are significant for massive colored particles coannihilating with partners through strong interactions.
  • Previous calculations were limited in their treatment of partial wave expansion and particle spin effects.

Purpose of the Study:

  • To present analytical formulas for Sommerfeld corrections to the annihilation of massive colored particles.
  • To compute the Sommerfeld effect for all orders in the partial wave expansion, including arbitrary particle spin.
  • To generalize these results beyond Quantum Chromodynamics (QCD) to arbitrary SU(N) gauge groups.

Main Methods:

  • Developed analytical formulas for Sommerfeld corrections considering the strong interaction between massive colored particles.
  • Incorporated all orders of the partial wave expansion and accounted for particle spin effects on the two-particle wave function symmetry.
  • Extended calculations to arbitrary SU(N) gauge groups, relevant for dark glueball models.

Main Results:

  • Formulas are provided for Sommerfeld corrections for particles in triplet, sextet, and octet color representations with arbitrary spin.
  • Including Sommerfeld corrections on the next-to-leading order partial wave modifies the total annihilation cross section by 10-20% for typical freeze-out velocities.
  • Generalization to arbitrary SU(N) gauge groups is achieved, broadening the applicability of the results.

Conclusions:

  • The presented analytical formulas enable precise calculations of Sommerfeld corrections for dark matter relic density.
  • The inclusion of higher-order partial waves and arbitrary spin significantly impacts annihilation cross sections.
  • This work provides a valuable tool, including a Mathematica notebook, for studying strongly interacting dark matter candidates.