Abstract

Bound-state formation can have a large impact on the dynamics of dark matter freeze-out in the early Universe, in particular for colored coannihilators. We present a general formalism to include an arbitrary number of excited bound states in terms of an effective annihilation cross section, taking bound-state formation, decay and transitions into account, and derive analytic approximations in the limiting cases of no or efficient transitions. Furthermore, we provide explicit expressions for radiative bound-state formation rates for states with arbitrary principal and angular quantum numbers $n,\ell$ for a mediator in the fundamental representation of $SU(3)_c$, as well as electromagnetic transition rates among them in the Coulomb approximation. We then assess the impact of bound states within a model with Majorana dark matter and a colored scalar $t$-channel mediator. We consider the regime of coannihilation as well as conversion-driven freeze-out (or coscattering), where the relic abundance is set by the freeze-out of conversion processes. We find that the region in parameter space where the latter occurs is considerably enhanced into the multi-TeV regime. For conversion-driven freeze-out, dark matter is very weakly coupled, evading direct and indirect detection constraints but leading to prominent signatures of long-lived particles that provide great prospects to be probed by dedicated searches at the upcoming LHC runs.

Highlights

  • Thermal freeze-out of dark matter has proved to be a successful framework for explaining the measured dark matter abundance in the Universe

  • We extend the study of bound-state effects in several aspects: (i) First, we revisit the formulation of the underlying Boltzmann equations in the presence of excited bound states and derive a general framework for incorporating their effects in terms of an effective annihilation cross section of the coannihilator

  • We revisited the computation of the relic density in the presence of bound-state effects during dark matter freeze-out

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Summary

INTRODUCTION

The boundary between the coannihilation and conversion-driven freeze-out region marks a significant change in the phenomenology within the parameter space of a given model While the former is characterized by sizeable couplings that give rise to observable signals in conventional dark matter searches, the latter is largely immune to constraints from (in)direct detection but predicts long-lived particles with typical lifetimes of the order of millimeters to meters to be searched for at the LHC. While it has been shown that bound-state formation effects provide sizeable corrections to the effective annihilation cross section for a coannihilation scenario with a colored mediator [26,31,32], it has widely been overlooked that their effects become considerably more relevant for scenarios with small dark matter couplings such as conversion-driven freeze-out. Appendixes A and B contain further details of the computation of bound-state formation cross sections and discuss next-to-leading-order (NLO) QCD effects, respectively

MODEL AND CONVERSION-DRIVEN FREEZE-OUT
INCLUDING BOUND STATES
Single bound state
Multiple bound states
No transition limit
Efficient transition limit
Ionization equilibrium
Ionization and recombination
Transitions
Effective cross section
VIABLE PARAMETER SPACE
Boundary between coannihilation and conversion-driven regime
CONCLUSION
NLO corrections to bound-state formation
Findings
NLO corrections to bound-state decay
Full Text
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