Abstract
It is well known that the annihilation of Majorana dark matter into fermions is helicity suppressed. Here, we point out that the underlying mechanism is a subtle combination of two distinct effects, and we present a comprehensive analysis of how the suppression can be partially or fully lifted by the internal bremsstrahlung of an additional boson in the final state. As a concrete illustration, we compute analytically the full amplitudes and annihilation rates of supersymmetric neutralinos to final states that contain any combination of two standard model fermions, plus one electroweak gauge boson or one of the five physical Higgs bosons that appear in the minimal supersymmetric standard model. We classify the various ways in which these three-body rates can be large compared to the two-body rates, identifying cases that have not been pointed out before. In our analysis, we put special emphasis on how to avoid the double counting of identical kinematic situations that appear for two-body and three-body final states, in particular on how to correctly treat differential rates and the spectrum of the resulting stable particles that is relevant for indirect dark matter searches. We find that both the total annihilation rates and the yields can be significantly enhanced when taking into account the corrections computed here, in particular for models with somewhat small annihilation rates at tree-level which otherwise would not be testable with indirect dark matter searches. Even more importantly, however, we find that the resulting annihilation spectra of positrons, neutrinos, gamma-rays and antiprotons differ in general substantially from the model-independent spectra that are commonly adopted, for these final states, when constraining particle dark matter with indirect detection experiments.
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References
Planck collaboration, P.A.R. Ade et al., Planck 2015 results XIII. Cosmological parameters, Astron. Astrophys. 594 (2016) A13 [arXiv:1502.01589] [INSPIRE].
G. Bertone, Particle dark matter: observations, models and searches, Cambridge University Press, Cambridge U.K., (2010).
B.W. Lee and S. Weinberg, Cosmological lower bound on heavy neutrino masses, Phys. Rev. Lett. 39 (1977) 165 [INSPIRE].
P. Gondolo and G. Gelmini, Cosmic abundances of stable particles: improved analysis, Nucl. Phys. B 360 (1991) 145 [INSPIRE].
LUX collaboration, D.S. Akerib et al., Improved limits on scattering of weakly interacting massive particles from reanalysis of 2013 LUX data, Phys. Rev. Lett. 116 (2016) 161301 [arXiv:1512.03506] [INSPIRE].
PandaX-II collaboration, A. Tan et al., Dark matter results from first 98.7 days of data from the PandaX-II experiment, Phys. Rev. Lett. 117 (2016) 121303 [arXiv:1607.07400] [INSPIRE].
ATLAS collaboration, Dark matter interpretations of ATLAS searches for the electroweak production of supersymmetric particles in \( \sqrt{s}=8 \) TeV proton-proton collisions, JHEP 09 (2016)175 [arXiv:1608.00872] [INSPIRE].
CMS collaboration, Phenomenological MSSM interpretation of CMS searches in pp collisions at \( \sqrt{s}=7 \) and 8 TeV, JHEP 10 (2016) 129 [arXiv:1606.03577] [INSPIRE].
Fermi-LAT collaboration, M. Ackermann et al., Searching for dark matter annihilation from milky way dwarf spheroidal galaxies with six years of Fermi Large Area Telescope data, Phys. Rev. Lett. 115 (2015) 231301 [arXiv:1503.02641] [INSPIRE].
L. Bergstrom, T. Bringmann, I. Cholis, D. Hooper and C. Weniger, New limits on dark matter annihilation from AMS cosmic ray positron data, Phys. Rev. Lett. 111 (2013) 171101 [arXiv:1306.3983] [INSPIRE].
L. Bergstrom, Radiative processes in dark matter photino annihilation, Phys. Lett. B 225 (1989) 372 [INSPIRE].
R. Flores, K.A. Olive and S. Rudaz, Radiative processes in LSP annihilation, Phys. Lett. B 232 (1989) 377 [INSPIRE].
T. Bringmann, L. Bergstrom and J. Edsjö, New gamma-ray contributions to supersymmetric dark matter annihilation, JHEP 01 (2008) 049 [arXiv:0710.3169] [INSPIRE].
L. Bergstrom, T. Bringmann and J. Edsjö, New positron spectral features from supersymmetric dark matter — a way to explain the PAMELA data?, Phys. Rev. D 78 (2008) 103520 [arXiv:0808.3725] [INSPIRE].
M. Kachelriess, P.D. Serpico and M.A. Solberg, On the role of electroweak bremsstrahlung for indirect dark matter signatures, Phys. Rev. D 80 (2009) 123533 [arXiv:0911.0001] [INSPIRE].
P. Ciafaloni, D. Comelli, A. Riotto, F. Sala, A. Strumia and A. Urbano, Weak corrections are relevant for dark matter indirect detection, JCAP 03 (2011) 019 [arXiv:1009.0224] [INSPIRE].
M. Cirelli et al., PPPC 4 DM ID: a Poor Particle Physicist Cookbook for Dark Matter Indirect Detection, JCAP 03 (2011) 051 [Erratum ibid. 10 (2012) E01] [arXiv:1012.4515] [INSPIRE].
T. Bringmann and F. Calore, Significant enhancement of neutralino dark matter annihilation from electroweak bremsstrahlung, Phys. Rev. Lett. 112 (2014) 071301 [arXiv:1308.1089] [INSPIRE].
H. Goldberg, Constraint on the photino mass from cosmology, Phys. Rev. Lett. 50 (1983) 1419 [Erratum ibid. 103 (2009) 099905] [INSPIRE].
F. Luo and T. You, Enhancement of Majorana dark matter annihilation through Higgs bremsstrahlung, JCAP 12 (2013) 024 [arXiv:1310.5129] [INSPIRE].
T. Toma, Internal bremsstrahlung signature of real scalar dark matter and consistency with thermal relic density, Phys. Rev. Lett. 111 (2013) 091301 [arXiv:1307.6181] [INSPIRE].
F. Giacchino, L. Lopez-Honorez and M.H.G. Tytgat, Scalar dark matter models with significant internal bremsstrahlung, JCAP 10 (2013) 025 [arXiv:1307.6480] [INSPIRE].
A. Ibarra, T. Toma, M. Totzauer and S. Wild, Sharp gamma-ray spectral features from scalar dark matter annihilations, Phys. Rev. D 90 (2014) 043526 [arXiv:1405.6917] [INSPIRE].
F. Giacchino, L. Lopez-Honorez and M.H.G. Tytgat, Bremsstrahlung and gamma-ray lines in 3 scenarios of dark matter annihilation, JCAP 08 (2014) 046 [arXiv:1405.6921] [INSPIRE].
F. Giacchino, A. Ibarra, L. Lopez Honorez, M.H.G. Tytgat and S. Wild, Signatures from scalar dark matter with a vector-like quark mediator, JCAP 02 (2016) 002 [arXiv:1511.04452] [INSPIRE].
G. Bambhaniya, J. Kumar, D. Marfatia, A.C. Nayak and G. Tomar, Vector dark matter annihilation with internal bremsstrahlung, Phys. Lett. B 766 (2017) 177 [arXiv:1609.05369] [INSPIRE].
N.F. Bell, Y. Cai, J.B. Dent, R.K. Leane and T.J. Weiler, Enhancing dark matter annihilation rates with dark bremsstrahlung, Phys. Rev. D 96 (2017) 023011 [arXiv:1705.01105] [INSPIRE].
G. Jungman, M. Kamionkowski and K. Griest, Supersymmetric dark matter, Phys. Rept. 267 (1996) 195 [hep-ph/9506380] [INSPIRE].
T. Bringmann, A.J. Galea and P. Walia, Leading QCD corrections for indirect dark matter searches: a fresh look, Phys. Rev. D 93 (2016) 043529 [arXiv:1510.02473] [INSPIRE].
P. Ciafaloni, M. Cirelli, D. Comelli, A. De Simone, A. Riotto and A. Urbano, On the importance of electroweak corrections for Majorana dark matter indirect detection, JCAP 06 (2011) 018 [arXiv:1104.2996] [INSPIRE].
N.F. Bell, J.B. Dent, A.J. Galea, T.D. Jacques, L.M. Krauss and T.J. Weiler, W/Z bremsstrahlung as the dominant annihilation channel for dark matter, revisited, Phys. Lett. B 706 (2011) 6 [arXiv:1104.3823] [INSPIRE].
N.F. Bell, J.B. Dent, T.D. Jacques and T.J. Weiler, Dark matter annihilation signatures from electroweak bremsstrahlung, Phys. Rev. D 84 (2011) 103517 [arXiv:1101.3357] [INSPIRE].
M. Garny, A. Ibarra and S. Vogl, Antiproton constraints on dark matter annihilations from internal electroweak bremsstrahlung, JCAP 07 (2011) 028 [arXiv:1105.5367] [INSPIRE].
K. Shudo and T. Nihei, Electroweak bremsstrahlung in binolike dark matter annihilations, Phys. Rev. D 88 (2013) 055019 [arXiv:1306.5901] [INSPIRE].
L.A. Cavasonza, M. Krämer and M. Pellen, Electroweak fragmentation functions for dark matter annihilation, JCAP 02 (2015) 021 [arXiv:1409.8226] [INSPIRE].
M. Garny, A. Ibarra and S. Vogl, Dark matter annihilations into two light fermions and one gauge boson: general analysis and antiproton constraints, JCAP 04 (2012) 033 [arXiv:1112.5155] [INSPIRE].
P. Ciafaloni, D. Comelli, A. De Simone, A. Riotto and A. Urbano, Electroweak bremsstrahlung for wino-like dark matter annihilations, JCAP 06 (2012) 016 [arXiv:1202.0692] [INSPIRE].
J. Kumar, J. Liao and D. Marfatia, Dark matter annihilation with s-channel internal Higgsstrahlung, Phys. Lett. B 759 (2016) 277 [arXiv:1605.00611] [INSPIRE].
P. Gondolo, J. Edsjö, P. Ullio, L. Bergstrom, M. Schelke and E.A. Baltz, DarkSUSY: computing supersymmetric dark matter properties numerically, JCAP 07 (2004) 008 [astro-ph/0406204] [INSPIRE].
T. Bringmann, J. Edsjö, P. Gondolo, P. Ullio and L. Bergstrom, DarkSUSY 6.0: an advanced tool to compute dark matter properties numerically, in preparation, (2017).
J. Kumar and D. Marfatia, Matrix element analyses of dark matter scattering and annihilation, Phys. Rev. D 88 (2013) 014035 [arXiv:1305.1611] [INSPIRE].
C. Becchi, A. Rouet and R. Stora, Renormalization of the Abelian Higgs-Kibble model, Commun. Math. Phys. 42 (1975) 127 [INSPIRE].
C. Becchi, A. Rouet and R. Stora, Renormalization of gauge theories, Annals Phys. 98 (1976) 287 [INSPIRE].
K. Fujikawa, B.W. Lee and A.I. Sanda, Generalized renormalizable gauge formulation of spontaneously broken gauge theories, Phys. Rev. D 6 (1972) 2923 [INSPIRE].
J. Edsjö, Aspects of neutrino detection of neutralino dark matter, Ph.D. thesis, Uppsala U., Uppsala Sweden, (1997) [hep-ph/9704384] [INSPIRE].
X.-L. Chen and M. Kamionkowski, Three body annihilation of neutralinos below two-body thresholds, JHEP 07 (1998) 001 [hep-ph/9805383] [INSPIRE].
C.E. Yaguna, Large contributions to dark matter annihilation from three-body final states, Phys. Rev. D 81 (2010) 075024 [arXiv:1003.2730] [INSPIRE].
G. Bélanger, F. Boudjema, A. Pukhov and A. Semenov, MicrOMEGAs 3 : a program for calculating dark matter observables, Comput. Phys. Commun. 185 (2014) 960 [arXiv:1305.0237] [INSPIRE].
Particle Data Group collaboration, K.A. Olive et al., Review of particle physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
C.F. Uhlemann and N. Kauer, Narrow-width approximation accuracy, Nucl. Phys. B 814 (2009) 195 [arXiv:0807.4112] [INSPIRE].
J. Chakrabortty, A. Kundu and T. Srivastava, Novel method to deal with off-shell particles in cascade decays, Phys. Rev. D 93 (2016) 053005 [arXiv:1601.02375] [INSPIRE].
J. Chakrabortty, A. Kundu, R. Maji and T. Srivastava, Cut and compute: quick cascades with multiple amplitudes, arXiv:1703.07174 [INSPIRE].
F. Bloch and A. Nordsieck, Note on the radiation field of the electron, Phys. Rev. 52 (1937) 54 [INSPIRE].
T. Kinoshita, Mass singularities of Feynman amplitudes, J. Math. Phys. 3 (1962) 650 [INSPIRE].
M. Bauer, T. Cohen, R.J. Hill and M.P. Solon, Soft collinear effective theory for heavy WIMP annihilation, JHEP 01 (2015) 099 [arXiv:1409.7392] [INSPIRE].
G. Ovanesyan, T.R. Slatyer and I.W. Stewart, Heavy dark matter annihilation from effective field theory, Phys. Rev. Lett. 114 (2015) 211302 [arXiv:1409.8294] [INSPIRE].
M. Baumgart, I.Z. Rothstein and V. Vaidya, Calculating the annihilation rate of weakly interacting massive particles, Phys. Rev. Lett. 114 (2015) 211301 [arXiv:1409.4415] [INSPIRE].
J. Hisano, S. Matsumoto and M.M. Nojiri, Explosive dark matter annihilation, Phys. Rev. Lett. 92 (2004) 031303 [hep-ph/0307216] [INSPIRE].
M. Beneke, C. Hellmann and P. Ruiz-Femenia, Non-relativistic pair annihilation of nearly mass degenerate neutralinos and charginos III. Computation of the Sommerfeld enhancements, JHEP 05 (2015) 115 [arXiv:1411.6924] [INSPIRE].
M. Beneke, A. Bharucha, A. Hryczuk, S. Recksiegel and P. Ruiz-Femenia, The last refuge of mixed wino-Higgsino dark matter, JHEP 01 (2017) 002 [arXiv:1611.00804] [INSPIRE].
T. Sjöstrand, S. Mrenna and P.Z. Skands, A brief introduction to PYTHIA 8.1, Comput. Phys. Commun. 178 (2008) 852 [arXiv:0710.3820] [INSPIRE].
M. Asano, T. Bringmann, G. Sigl and M. Vollmann, 130 GeV gamma-ray line and generic dark matter model building constraints from continuum gamma rays, radio and antiproton data, Phys. Rev. D 87 (2013) 103509 [arXiv:1211.6739] [INSPIRE].
F. Feroz, M.P. Hobson and M. Bridges, MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics, Mon. Not. Roy. Astron. Soc. 398 (2009) 1601 [arXiv:0809.3437] [INSPIRE].
J. Edsjö and P. Gondolo, Neutralino relic density including coannihilations, Phys. Rev. D 56 (1997) 1879 [hep-ph/9704361] [INSPIRE].
J. Edsjö, M. Schelke, P. Ullio and P. Gondolo, Accurate relic densities with neutralino, chargino and sfermion coannihilations in mSUGRA, JCAP 04 (2003) 001 [hep-ph/0301106] [INSPIRE].
ATLAS and CMS collaborations, Combined measurement of the Higgs boson mass in pp collisions at \( \sqrt{s}=7 \) and 8 TeV with the ATLAS and CMS experiments, Phys. Rev. Lett. 114 (2015) 191803 [arXiv:1503.07589] [INSPIRE].
CMS collaboration, Searches for supersymmetry using the M T2 variable in hadronic events produced in pp collisions at 8 TeV, JHEP 05 (2015) 078 [arXiv:1502.04358] [INSPIRE].
CMS collaboration, Exclusion limits on gluino and top-squark pair production in natural SUSY scenarios with inclusive razor and exclusive single-lepton searches at 8 TeV, CMS-PAS-SUS-14-011, CERN, Geneva Switzerland, (2014).
CMS collaboration, Search for top squarks decaying to a charm quark and a neutralino in events with a jet and missing transverse momentum, CMS-PAS-SUS-13-009, CERN, Geneva Switzerland, (2013).
CMS collaboration, Search for top-squark pair production in the single-lepton final state in pp collisions at \( \sqrt{s}=8 \) TeV, Eur. Phys. J. C 73 (2013) 2677 [arXiv:1308.1586] [INSPIRE].
CMS collaboration, Search for top squarks in multijet events with large missing momentum in proton-proton collisions at 8 TeV, CMS-PAS-SUS-13-015, CERN, Geneva Switzerland, (2013).
CMS collaboration, Search for top-squark pairs decaying into Higgs or Z bosons in pp collisions at \( \sqrt{s}=8 \) TeV, Phys. Lett. B 736 (2014) 371 [arXiv:1405.3886] [INSPIRE].
CMS collaboration, Search for supersymmetry in pp collisions at \( \sqrt{s}=8 \) TeV in events with three leptons and at least one b-tagged jet, CMS-PAS-SUS-13-008, CERN, Geneva Switzerland, (2013).
ATLAS collaboration, Search for pair-produced third-generation squarks decaying via charm quarks or in compressed supersymmetric scenarios in pp collisions at \( \sqrt{s}=8 \) TeV with the ATLAS detector, Phys. Rev. D 90 (2014) 052008 [arXiv:1407.0608] [INSPIRE].
ATLAS collaboration, Search for direct third-generation squark pair production in final states with missing transverse momentum and two b-jets in \( \sqrt{s}=8 \) TeV pp collisions with the ATLAS detector, JHEP 10 (2013) 189 [arXiv:1308.2631] [INSPIRE].
ATLAS collaboration, Search for direct production of charginos, neutralinos and sleptons in final states with two leptons and missing transverse momentum in pp collisions at \( \sqrt{s}=8 \) TeV with the ATLAS detector, JHEP 05 (2014) 071 [arXiv:1403.5294] [INSPIRE].
ATLAS collaboration, Search for the direct production of charginos, neutralinos and staus in final states with at least two hadronically decaying taus and missing transverse momentum in pp collisions at \( \sqrt{s}=8 \) TeV with the ATLAS detector, JHEP 10 (2014) 096 [arXiv:1407.0350] [INSPIRE].
LUX collaboration, D.S. Akerib et al., First results from the LUX dark matter experiment at the Sanford Underground Research Facility, Phys. Rev. Lett. 112 (2014) 091303 [arXiv:1310.8214] [INSPIRE].
GAMBIT collaboration, P. Athron et al., A global fit of the MSSM with GAMBIT, arXiv:1705.07917 [INSPIRE].
H. Liu, T.R. Slatyer and J. Zavala, Contributions to cosmic reionization from dark matter annihilation and decay, Phys. Rev. D 94 (2016) 063507 [arXiv:1604.02457] [INSPIRE].
AMS collaboration, L. Accardo et al., High statistics measurement of the positron fraction in primary cosmic rays of 0.5–500 GeV with the Alpha Magnetic Spectrometer on the International Space Station, Phys. Rev. Lett. 113 (2014) 121101 [INSPIRE].
K. Fukushima, Y. Gao, J. Kumar and D. Marfatia, Bremsstrahlung signatures of dark matter annihilation in the sun, Phys. Rev. D 86 (2012) 076014 [arXiv:1208.1010] [INSPIRE].
A. Ibarra, M. Totzauer and S. Wild, High-energy neutrino signals from the sun in dark matter scenarios with internal bremsstrahlung, JCAP 12 (2013) 043 [arXiv:1311.1418] [INSPIRE].
A. Ibarra, M. Totzauer and S. Wild, Higher order dark matter annihilations in the sun and implications for IceCube, JCAP 04 (2014) 012 [arXiv:1402.4375] [INSPIRE].
N.F. Bell, A.J. Brennan and T.D. Jacques, Neutrino signals from electroweak bremsstrahlung in solar WIMP annihilation, JCAP 10 (2012) 045 [arXiv:1206.2977] [INSPIRE].
A. De Simone, A. Monin, A. Thamm and A. Urbano, On the effective operators for dark matter annihilations, JCAP 02 (2013) 039 [arXiv:1301.1486] [INSPIRE].
F. Calore, Unveiling dark matter through gamma rays: spectral features, spatial signatures and astrophysical backgrounds, Ph.D. thesis, Hamburg U., Hamburg Germany, (2013).
T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260] [INSPIRE].
J. Edsjö and P. Gondolo, Neutralino relic density including coannihilations, Phys. Rev. D 56 (1997) 1879 [hep-ph/9704361] [INSPIRE].
T. Hahn, FormCalc 6, PoS(ACAT08)121 [arXiv:0901.1528] [INSPIRE].
M. Jacob and G.C. Wick, On the general theory of collisions for particles with spin, Annals Phys. 7 (1959) 404 [Annals Phys. 281 (2000) 774] [INSPIRE].
P. Ciafaloni, M. Cirelli, D. Comelli, A. De Simone, A. Riotto and A. Urbano, Initial state radiation in Majorana dark matter annihilations, JCAP 10 (2011) 034 [arXiv:1107.4453] [INSPIRE].
A. Belyaev, N.D. Christensen and A. Pukhov, CalcHEP 3.4 for collider physics within and beyond the Standard Model, Comput. Phys. Commun. 184 (2013) 1729 [arXiv:1207.6082] [INSPIRE].
B.C. Allanach, SOFTSUSY: a program for calculating supersymmetric spectra, Comput. Phys. Commun. 143 (2002) 305 [hep-ph/0104145] [INSPIRE].
P. Gondolo, J. Edsjö, P. Ullio, L. Bergstrom, M. Schelke and E.A. Baltz, DarkSUSY: computing supersymmetric dark matter properties numerically, JCAP 07 (2004) 008 [astro-ph/0406204] [INSPIRE].
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Bringmann, T., Calore, F., Galea, A. et al. Electroweak and Higgs boson internal bremsstrahlung. General considerations for Majorana dark matter annihilation and application to MSSM neutralinos. J. High Energ. Phys. 2017, 41 (2017). https://doi.org/10.1007/JHEP09(2017)041
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DOI: https://doi.org/10.1007/JHEP09(2017)041