Electroweak corrections in a pseudo Nambu-Goldstone Dark Matter model revisited
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Received: September 3, 2020 Accepted: October 25, 2020 Published: December 4, 2020
Electroweak corrections in a pseudo Nambu-Goldstone Dark Matter model revisited
a
Institute for Theoretical Physics, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany b Institute for Nuclear Physics, Karlsruhe Institute of Technology, 76344 Karlsruhe, Germany c Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edifício C8 1749-016 Lisboa, Portugal d ISEL — Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa, 1959-007 Lisboa, Portugal
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: Having so far only indirect evidence for the existence of Dark Matter a plethora of experiments aims at direct detection of Dark Matter through the scattering of Dark Matter particles off atomic nuclei. For the correct interpretation and identification of the underlying nature of the Dark Matter constituents higher-order corrections to the cross section of Dark Matter-nucleon scattering are important, in particular in models where the tree-level cross section is negligibly small. In this work we revisit the electroweak corrections to the dark matter-nucleon scattering cross section in a model with a pseudo Nambu-Goldstone boson as the Dark Matter candidate. Two calculations that already exist in the literature, apply different approaches resulting in different final results for the cross section in some regions of the parameter space leading us to redo the calculation and analyse the two approaches to clarify the situation. We furthermore update the experimental constraints and examine the regions of the parameter space where the cross section is above the neutrino floor but which can only be probed in the far future. Keywords: Beyond Standard Model, Higgs Physics ArXiv ePrint: 2008.12985
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP12(2020)034
JHEP12(2020)034
Seraina Glaus,a,b Margarete Mühlleitner,a Jonas Müller,a Shruti Patel,a,b Tizian Römera and Rui Santosc,d
Contents 1
2 The model
2
3 Renormalisation of the PNGDM 3.1 Gauge sector 3.2 Scalar sector 3.3 Quark sector 3.4 Renormalisation of the mixing angle 3.5 Renormalisation of the singlet VEV vs
4 4 5 7 7 8
4 Spin-independent cross section in the PNGDM 4.1 SI cross section at tree level 4.2 EW corrections to the SI cross section 4.2.1 Mediator corrections 4.2.2 Upper vertex (upV) corrections 4.2.3 Lower vertex (loV) corrections 4.2.4 Box diagrams 4.2.5 General mapping to the Wilson coefficients 4.2.6 Gluon contributions
8 10 10 11 12 13 14 16 17
5 Numerical results 5.1 Numerical set-up and parameters 5.2 Results and discussion
19 19 21
6 Conclusions
26
1
Introduction
Ever since Dark Matter (DM) became an inevitable ingredient in model building, all kind of proposals integrating DM candidates into phenomenologically viable models have
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