Dark matter bound-state formation at higher order: a non-equilibrium quantum field theory approach
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Springer
Received: March Revised: June Accepted: July Published: September
16, 23, 28, 11,
2020 2020 2020 2020
Dark matter bound-state formation at higher order: a non-equilibrium quantum field theory approach
a
Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan b Mathematisches Institut, Bunsenstr. 3–5, 37073 G¨ ottingen, Germany c Physik Department T70, Technische Universit¨ at M¨ unchen, James-Franck-Straße, 85748 Garching, Germany d Deutsches Elektronen-Synchrotron (DESY), Notkestraße 85, Hamburg, D-22607 Germany
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: The formation of meta-stable dark matter bound states in coannihilating scenarios could efficiently occur through the scattering with a variety of Standard Model bath particles, where light bosons during the electroweak cross over or even massless photons and gluons are exchanged in the t-channel. The amplitudes for those higher-order processes, however, are divergent in the collinear direction of the in- and out-going bath particles if the mediator is massless. To address the issue of collinear divergences, we derive the boundstate formation collision term in the framework of non-equilibrium quantum field theory. The main result is an expression for a more general cross section, which allows to compute higher-order bound-state formation processes inside the primordial plasma background in a comprehensive manner. Based on this result, we show that next-to-leading order contributions, including the bath-particle scattering, are i) collinear finite and ii) generically dominate over the on-shell emission for temperatures larger than the absolute value of the binding energy. Based on a simplified model, we demonstrate that the impact of these new effects on the thermal relic abundance is significant enough to make it worthwhile to study more realistic coannihilation scenarios. Keywords: Beyond Standard Model, Cosmology of Theories beyond the SM, Thermal Field Theory ArXiv ePrint: 2002.07145
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)086
JHEP09(2020)086
Tobias Binder,a Burkhard Blobel,b Julia Harzc and Kyohei Mukaidad
Contents 1 Introduction
1
2 Generalized bound-state formation cross section
4
3 Recovering on-shell emission at the leading order
9 10 12 16 17 19
5 Impact on thermal relic abundance
20
6 Discussion
24
7 Summary and conclusion
26
A Computation of double commutator
28
B Retarded self-energy for massless fermions
30
C Next-to-leading order contributions in more detail C.1 Contour integration for vacuum part C.2 Scale dependence of the vacuum part C.3 Contour integration for the finite temperature part C.4 Individual contributions of the finite temperature part
32 32 33 34 35
1
Introduction
One of the leading dark matter (DM) candidates are Weakly Interacting Massive Particles (WIMPs) [1–3], which can account for all the present DM energy fraction [4] through t
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