Abstract
We calculate the cross-sections for the radiative formation of bound states by dark matter whose interactions are described in the non-relativistic regime by a Yukawa potential. These cross-sections are important for cosmological and phenomenological studies of dark matter with long-range interactions, residing in a hidden sector, as well as for TeV-scale WIMP dark matter. We provide the leading-order contributions to the cross-sections for the dominant capture processes occurring via emission of a vector or a scalar boson. We offer a detailed inspection of their features, including their velocity dependence within and outside the Coulomb regime, and their resonance structure. For pairs of annihilating particles, we compare bound-state formation with annihilation.
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References
K. Petraki, M. Postma and M. Wiechers, Dark-matter bound states from Feynman diagrams, JHEP 06 (2015) 128 [arXiv:1505.00109] [INSPIRE].
H. An, M.B. Wise and Y. Zhang, Effects of bound states on dark matter annihilation, Phys. Rev. D 93 (2016) 115020 [arXiv:1604.01776] [INSPIRE].
H. An, M.B. Wise and Y. Zhang, Strong CMB constraint on P-wave annihilating dark matter, arXiv:1606.02305 [INSPIRE].
P. Asadi, M. Baumgart, P.J. Fitzpatrick, E. Krupczak and T.R. Slatyer, Capture and decay of electroweak WIMPonium, JCAP 02 (2017) 005 [arXiv:1610.07617] [INSPIRE].
A. Sommerfeld, Über die Beugung und Bremsung der Elektronen (in German), Ann. Phys. 403 (1931) 257.
P. Hoyer, Bound states — from QED to QCD, arXiv:1402.5005 [INSPIRE].
B. von Harling and K. Petraki, Bound-state formation for thermal relic dark matter and unitarity, JCAP 12 (2014) 033 [arXiv:1407.7874] [INSPIRE].
I. Baldes and K. Petraki, Asymmetric thermal-relic dark matter: Sommerfeld-enhanced freeze-out, annihilation signals and unitarity bounds, arXiv:1703.00478 [INSPIRE].
K.M. Belotsky, E.A. Esipova and A.A. Kirillov, On the classical description of the recombination of dark matter particles with a Coulomb-like interaction, Phys. Lett. B 761 (2016) 81 [arXiv:1506.03094] [INSPIRE].
K. Petraki and R.R. Volkas, Review of asymmetric dark matter, Int. J. Mod. Phys. A 28 (2013) 1330028 [arXiv:1305.4939] [INSPIRE].
F.-Y. Cyr-Racine and K. Sigurdson, Cosmology of atomic dark matter, Phys. Rev. D 87 (2013) 103515 [arXiv:1209.5752] [INSPIRE].
L. Pearce, K. Petraki and A. Kusenko, Signals from dark atom formation in halos, Phys. Rev. D 91 (2015) 083532 [arXiv:1502.01755] [INSPIRE].
L. Pearce and A. Kusenko, Indirect detection of self-interacting asymmetric dark matter, Phys. Rev. D 87 (2013) 123531 [arXiv:1303.7294] [INSPIRE].
J.M. Cline, Y. Farzan, Z. Liu, G.D. Moore and W. Xue, 3.5 keV X-rays as the “21 cm line” of dark atoms and a link to light sterile neutrinos, Phys. Rev. D 89 (2014) 121302 [arXiv:1404.3729] [INSPIRE].
J.J. Sakurai, Modern quantum mechanics, (1985).
M. Pospelov and A. Ritz, Astrophysical signatures of secluded dark matter, Phys. Lett. B 671 (2009) 391 [arXiv:0810.1502] [INSPIRE].
C. Kouvaris, K. Langæble and N.G. Nielsen, The spectrum of darkonium in the sun, JCAP 10 (2016) 012 [arXiv:1607.00374] [INSPIRE].
M. Cirelli, P. Panci, K. Petraki, F. Sala and M. Taoso, Dark matter’s secret liaisons: phenomenology of a dark U(1) sector with bound states, arXiv:1612.07295 [INSPIRE].
K. Griest and M. Kamionkowski, Unitarity limits on the mass and radius of dark matter particles, Phys. Rev. Lett. 64 (1990) 615 [INSPIRE].
X. Kong and F. Ravndal, Proton proton scattering lengths from effective field theory, Phys. Lett. B 450 (1999) 320 [Erratum ibid. B 458 (1999) 565] [nucl-th/9811076] [INSPIRE].
X. Kong and F. Ravndal, Proton proton fusion in leading order of effective field theory, Nucl. Phys. A 656 (1999) 421 [nucl-th/9902064] [INSPIRE].
K. Blum, R. Sato and T.R. Slatyer, Self-consistent calculation of the Sommerfeld enhancement, JCAP 06 (2016) 021 [arXiv:1603.01383] [INSPIRE].
M. Cirelli, N. Fornengo and A. Strumia, Minimal dark matter, Nucl. Phys. B 753 (2006) 178 [hep-ph/0512090] [INSPIRE].
M. Cirelli, A. Strumia and M. Tamburini, Cosmology and astrophysics of minimal dark matter, Nucl. Phys. B 787 (2007) 152 [arXiv:0706.4071] [INSPIRE].
M. Cirelli and A. Strumia, Minimal dark matter: model and results, New J. Phys. 11 (2009) 105005 [arXiv:0903.3381] [INSPIRE].
A. Hryczuk, R. Iengo and P. Ullio, Relic densities including Sommerfeld enhancements in the MSSM, JHEP 03 (2011) 069 [arXiv:1010.2172] [INSPIRE].
A. Hryczuk, I. Cholis, R. Iengo, M. Tavakoli and P. Ullio, Indirect detection analysis: wino dark matter case study, JCAP 07 (2014) 031 [arXiv:1401.6212] [INSPIRE].
M. Beneke, C. Hellmann and P. Ruiz-Femenia, Heavy neutralino relic abundance with Sommerfeld enhancements — a study of pMSSM scenarios, JHEP 03 (2015) 162 [arXiv:1411.6930] [INSPIRE].
M. Cirelli, F. Sala and M. Taoso, Wino-like minimal dark matter and future colliders, JHEP 10 (2014) 033 [Erratum ibid. 01 (2015) 041] [arXiv:1407.7058] [INSPIRE].
J. Ellis, F. Luo and K.A. Olive, Gluino coannihilation revisited, JHEP 09 (2015) 127 [arXiv:1503.07142] [INSPIRE].
S. Kim and M. Laine, Rapid thermal co-annihilation through bound states in QCD, JHEP 07 (2016) 143 [arXiv:1602.08105] [INSPIRE].
S. Kim and M. Laine, On thermal corrections to near-threshold annihilation, JCAP 01 (2017) 013 [arXiv:1609.00474] [INSPIRE].
J.D. March-Russell and S.M. West, WIMPonium and boost factors for indirect dark matter detection, Phys. Lett. B 676 (2009) 133 [arXiv:0812.0559] [INSPIRE].
B. Holdom, Two U(1)’s and ϵ charge shifts, Phys. Lett. B 166 (1986) 196 [INSPIRE].
R. Foot and X.-G. He, Comment on ZZ′ mixing in extended gauge theories, Phys. Lett. B 267 (1991) 509 [INSPIRE].
B. Körs and P. Nath, A Stückelberg extension of the Standard Model, Phys. Lett. B 586 (2004) 366 [hep-ph/0402047] [INSPIRE].
D. Feldman, B. Körs and P. Nath, Extra-weakly interacting dark matter, Phys. Rev. D 75 (2007) 023503 [hep-ph/0610133] [INSPIRE].
M. Pospelov, A. Ritz and M.B. Voloshin, Secluded WIMP dark matter, Phys. Lett. B 662 (2008) 53 [arXiv:0711.4866] [INSPIRE].
P. Fayet, U-boson production in e + e − annihilations, ψ and Y decays and light dark matter, Phys. Rev. D 75 (2007) 115017 [hep-ph/0702176] [INSPIRE].
M. Goodsell, J. Jaeckel, J. Redondo and A. Ringwald, Naturally light hidden photons in LARGE volume string compactifications, JHEP 11 (2009) 027 [arXiv:0909.0515] [INSPIRE].
P. Fayet, The light U-boson as the mediator of a new force, coupled to a combination of Q, B, L and dark matter, Eur. Phys. J. C 77 (2017) 53 [arXiv:1611.05357] [INSPIRE].
D.N. Spergel and P.J. Steinhardt, Observational evidence for selfinteracting cold dark matter, Phys. Rev. Lett. 84 (2000) 3760 [astro-ph/9909386] [INSPIRE].
J.L. Feng, M. Kaplinghat, H. Tu and H.-B. Yu, Hidden charged dark matter, JCAP 07 (2009) 004 [arXiv:0905.3039] [INSPIRE].
A. Loeb and N. Weiner, Cores in dwarf galaxies from dark matter with a Yukawa potential, Phys. Rev. Lett. 106 (2011) 171302 [arXiv:1011.6374] [INSPIRE].
N. Arkani-Hamed, D.P. Finkbeiner, T.R. Slatyer and N. Weiner, A theory of dark matter, Phys. Rev. D 79 (2009) 015014 [arXiv:0810.0713] [INSPIRE].
I. Cholis, D.P. Finkbeiner, L. Goodenough and N. Weiner, The PAMELA positron excess from annihilations into a light boson, JCAP 12 (2009) 007 [arXiv:0810.5344] [INSPIRE].
M. Abdullah, A. DiFranzo, A. Rajaraman, T.M.P. Tait, P. Tanedo and A.M. Wijangco, Hidden on-shell mediators for the galactic center γ-ray excess, Phys. Rev. D 90 (2014) 035004 [arXiv:1404.6528] [INSPIRE].
A. Berlin, P. Gratia, D. Hooper and S.D. McDermott, Hidden sector dark matter models for the galactic center gamma-ray excess, Phys. Rev. D 90 (2014) 015032 [arXiv:1405.5204] [INSPIRE].
K.K. Boddy, J.L. Feng, M. Kaplinghat, Y. Shadmi and T.M.P. Tait, Strongly interacting dark matter: self-interactions and keV lines, Phys. Rev. D 90 (2014) 095016 [arXiv:1408.6532] [INSPIRE].
W. Detmold, M. McCullough and A. Pochinsky, Dark nuclei I: cosmology and indirect detection, Phys. Rev. D 90 (2014) 115013 [arXiv:1406.2276] [INSPIRE].
K. Petraki, L. Pearce and A. Kusenko, Self-interacting asymmetric dark matter coupled to a light massive dark photon, JCAP 07 (2014) 039 [arXiv:1403.1077] [INSPIRE].
A. Kusenko and P.J. Steinhardt, Q ball candidates for selfinteracting dark matter, Phys. Rev. Lett. 87 (2001) 141301 [astro-ph/0106008] [INSPIRE].
J.L. Feng, H. Tu and H.-B. Yu, Thermal relics in hidden sectors, JCAP 10 (2008) 043 [arXiv:0808.2318] [INSPIRE].
R. Foot and Z.K. Silagadze, Thin disk of co-rotating dwarfs: a fingerprint of dissipative (mirror) dark matter?, Phys. Dark Univ. 2 (2013) 163 [arXiv:1306.1305] [INSPIRE].
J. Fan, A. Katz, L. Randall and M. Reece, Dark-disk universe, Phys. Rev. Lett. 110 (2013) 211302 [arXiv:1303.3271] [INSPIRE].
R. Foot, Tully-Fisher relation, galactic rotation curves and dissipative mirror dark matter, JCAP 12 (2014) 047 [arXiv:1307.1755] [INSPIRE].
R. Foot, A dark matter scaling relation from mirror dark matter, Phys. Dark Univ. 5-6 (2014) 236 [arXiv:1303.1727] [INSPIRE].
R. Foot and S. Vagnozzi, Dissipative hidden sector dark matter, Phys. Rev. D 91 (2015) 023512 [arXiv:1409.7174] [INSPIRE].
R. Foot and S. Vagnozzi, Diurnal modulation signal from dissipative hidden sector dark matter, Phys. Lett. B 748 (2015) 61 [arXiv:1412.0762] [INSPIRE].
R. Foot, Dissipative dark matter and the rotation curves of dwarf galaxies, JCAP 07 (2016) 011 [arXiv:1506.01451] [INSPIRE].
K.K. Boddy, M. Kaplinghat, A. Kwa and A.H.G. Peter, Hidden sector hydrogen as dark matter: small-scale structure formation predictions and the importance of hyperfine interactions, Phys. Rev. D 94 (2016) 123017 [arXiv:1609.03592] [INSPIRE].
R. Laha and E. Braaten, Direct detection of dark matter in universal bound states, Phys. Rev. D 89 (2014) 103510 [arXiv:1311.6386] [INSPIRE].
R. Laha, Directional detection of dark matter in universal bound states, Phys. Rev. D 92 (2015) 083509 [arXiv:1505.02772] [INSPIRE].
A. Butcher, R. Kirk, J. Monroe and S.M. West, Can tonne-scale direct detection experiments discover nuclear dark matter?, arXiv:1610.01840 [INSPIRE].
W. Shepherd, T.M.P. Tait and G. Zaharijas, Bound states of weakly interacting dark matter, Phys. Rev. D 79 (2009) 055022 [arXiv:0901.2125] [INSPIRE].
H. An, B. Echenard, M. Pospelov and Y. Zhang, Probing the dark sector with dark matter bound states, Phys. Rev. Lett. 116 (2016) 151801 [arXiv:1510.05020] [INSPIRE].
X.-J. Bi, Z. Kang, P. Ko, J. Li and T. Li, ADMonium: asymmetric dark matter bound state, Phys. Rev. D 95 (2017) 043540 [arXiv:1602.08816] [INSPIRE].
F. Nozzoli, A balance for dark matter bound states, Astropart. Phys. 91 (2017) 22 [arXiv:1608.00405] [INSPIRE].
A.I. Akhiezer and N.P. Merenkov, The theory of lepton bound-state production, J. Phys. B 29 (1996) 2135.
J. de Vries, U.-G. Meißner, E. Epelbaum and N. Kaiser, Parity violation in proton-proton scattering from chiral effective field theory, Eur. Phys. J. A 49 (2013) 149 [arXiv:1309.4711] [INSPIRE].
J. de Vries, N. Li, U.-G. Meißner, A. Nogga, E. Epelbaum and N. Kaiser, Parity violation in neutron capture on the proton: determining the weak pion-nucleon coupling, Phys. Lett. B 747 (2015) 299 [arXiv:1501.01832] [INSPIRE].
W. Glöckle, The quantum mechanical few-body problem, Springer, Germany, (1983).
E. Epelbaum, W. Glöckle and U.-G. Meißner, The two-nucleon system at next-to-next-to-next-to-leading order, Nucl. Phys. A 747 (2005) 362 [nucl-th/0405048] [INSPIRE].
E. Anderson et al., LAPACK users’ guide, third ed., Society for Industrial and Applied Mathematics, Philadelphia PA U.S.A., (1999).
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Petraki, K., Postma, M. & de Vries, J. Radiative bound-state-formation cross-sections for dark matter interacting via a Yukawa potential. J. High Energ. Phys. 2017, 77 (2017). https://doi.org/10.1007/JHEP04(2017)077
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DOI: https://doi.org/10.1007/JHEP04(2017)077