Abstract
Dark Z/dark photon (Z ′) is one candidate of dark force carrier, which helps to interpret the properties of dark matter (DM). Other than conventional studies of DM including direct detection, indirect detection and collider simulation, in this work we take flavor physics as a complementary approach to investigate the features of dark matter. We give an exact calculation of the new type of penguin diagram induced by Z ′ which further modifies the well-known X, Y, Z functions in penguin-box expansion. The measurement of rare decays B → K (*) μ + μ − and B s → μ + μ − at LHC, together with direct CP violation ε ′ /ε in K → ππ as well as K L → μ + μ −, are used to determine the parameter space. The size of coupling constant, however, is found to be \( \mathcal{O}(1) \) which is much weaker than the known constraints.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Planck collaboration, P.A.R. Ade et al., Planck 2013 results. I. Overview of products and scientific results, Astron. Astrophys. 571 (2014) A1 [arXiv:1303.5062] [INSPIRE].
B. Holdom, Two U(1)’s and ϵ charge shifts, Phys. Lett. B 166 (1986) 196 [INSPIRE].
P. Fayet, Light spin 1/2 or spin 0 dark matter particles, Phys. Rev. D 70 (2004) 023514 [hep-ph/0403226] [INSPIRE].
D.P. Finkbeiner and N. Weiner, Exciting dark matter and the INTEGRAL/SPI 511 keV signal, Phys. Rev. D 76 (2007) 083519 [astro-ph/0702587] [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].
S. Andreas, M.D. Goodsell and A. Ringwald, Dark matter and dark forces from a supersymmetric hidden sector, Phys. Rev. D 87 (2013) 025007 [arXiv:1109.2869] [INSPIRE].
J.-W. Cui, H.-J. He, L.-C. Lu and F.-R. Yin, Spontaneous mirror parity violation, common origin of matter and dark matter and the LHC signatures, Phys. Rev. D 85 (2012) 096003 [arXiv:1110.6893] [INSPIRE].
D. Fargion, M. Khlopov and C.A. Stephan, Cold dark matter by heavy double charged leptons?, Class. Quant. Grav. 23 (2006) 7305 [astro-ph/0511789] [INSPIRE].
M.Y. Khlopov and C.A. Stephan, Composite dark matter with invisible light from almost-commutative geometry, astro-ph/0603187 [INSPIRE].
J.M. Cline, Z. Liu and W. Xue, Millicharged atomic dark matter, Phys. Rev. D 85 (2012) 101302 [arXiv:1201.4858] [INSPIRE].
F.-Y. Cyr-Racine and K. Sigurdson, Cosmology of atomic dark matter, Phys. Rev. D 87 (2013) 103515 [arXiv:1209.5752] [INSPIRE].
S. Andreas, M.D. Goodsell and A. Ringwald, Hidden photons in connection to dark matter, AIP Conf. Proc. 1563 (2013) 114 [arXiv:1306.1168] [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].
K.-W. Ng, H. Tu and T.-C. Yuan, Dark photons as fractional cosmic neutrino masquerader, JCAP 09 (2014) 035 [arXiv:1406.1993] [INSPIRE].
H. Davoudiasl, H.-S. Lee and W.J. Marciano, ‘Dark’ Z implications for parity violation, rare meson decays and Higgs physics, Phys. Rev. D 85 (2012) 115019 [arXiv:1203.2947] [INSPIRE].
PAMELA collaboration, O. Adriani et al., An anomalous positron abundance in cosmic rays with energies 1.5–100 GeV, Nature 458 (2009) 607 [arXiv:0810.4995] [INSPIRE].
D. Kazanas, R.N. Mohapatra, S. Nussinov, V.L. Teplitz and Y. Zhang, Supernova bounds on the dark photon using its electromagnetic decay, Nucl. Phys. B 890 (2014) 17 [arXiv:1410.0221] [INSPIRE].
R. Foot and S. Vagnozzi, Dissipative hidden sector dark matter, Phys. Rev. D 91 (2015) 023512 [arXiv:1409.7174] [INSPIRE].
H. An, M. Pospelov, J. Pradler and A. Ritz, Direct detection constraints on dark photon dark matter, arXiv:1412.8378 [INSPIRE].
BaBar collaboration, J.P. Lees et al., Search for a dark photon in e + e − collisions at BaBar, Phys. Rev. Lett. 113 (2014) 201801 [arXiv:1406.2980] [INSPIRE].
O. Moreno, The heavy photon search experiment at Jefferson Lab, arXiv:1310.2060 [INSPIRE].
PHENIX collaboration, A. Adare et al., Search for dark photons from neutral meson decays in p + p and d + Au collisions at \( \sqrt{s_{NN}}=200 \) GeV, Phys. Rev. C 91 (2015) 031901 [arXiv:1409.0851] [INSPIRE].
W.-S. Hou, M. Kohda and F. Xu, Measuring the fourth generation b → s quadrangle at the LHC, Phys. Rev. D 84 (2011) 094027 [arXiv:1107.2343] [INSPIRE].
LHCb collaboration, Differential branching fraction and angular analysis of the decay B 0 → K *0 μ + μ −, JHEP 08 (2013) 131 [arXiv:1304.6325] [INSPIRE].
S.D. Aristizabal, F. Staub and A. Vicente, Shedding light on the b → s anomalies with a dark sector, arXiv:1503.06077 [INSPIRE].
H. Ruegg and M. Ruiz-Altaba, The Stueckelberg field, Int. J. Mod. Phys. A 19 (2004) 3265 [hep-th/0304245] [INSPIRE].
W.-Z. Feng, G. Shiu, P. Soler and F. Ye, Building a Stückelberg portal, JHEP 05 (2014) 065 [arXiv:1401.5890] [INSPIRE].
A.J. Buras, Weak Hamiltonian, CP-violation and rare decays, hep-ph/9806471 [INSPIRE].
CMS and LHCb collaborations, Observation of the rare B 0 s → μ + μ − decay from the combined analysis of CMS and LHCb data, Nature 522 (2015) 68 [arXiv:1411.4413] [INSPIRE].
W.-S. Hou, M. Kohda and F. Xu, Implication of possible observation of enhanced B 0 d → μ + μ − decay, Phys. Rev. D 87 (2013) 094005 [arXiv:1302.1471] [INSPIRE].
K. De Bruyn et al., Branching ratio measurements of B s decays, Phys. Rev. D 86 (2012) 014027 [arXiv:1204.1735] [INSPIRE].
K. De Bruyn et al., Probing new physics via the B 0 s → μ + μ − effective lifetime, Phys. Rev. Lett. 109 (2012) 041801 [arXiv:1204.1737] [INSPIRE].
A.J. Buras, R. Fleischer, J. Girrbach and R. Knegjens, Probing new physics with the B s → μ + μ − time-dependent rate, JHEP 07 (2013) 077 [arXiv:1303.3820] [INSPIRE].
CMS and LHCb collaborations, Combination of results on the rare decays B 0(s) → μ + μ − from the CMS and LHCb experiments, CMS-PAS-BPH-13-007, LHCb-CONF-2013-012 (2014).
Heavy Flavor Averaging Group collaboration, Y. Amhis et al., Averages of b-hadron, c-hadron and τ-lepton properties as of early 2012, arXiv:1207.1158 [INSPIRE].
A.J. Buras, F. De Fazio and J. Girrbach, 331 models facing new b → sμ + μ − data, JHEP 02 (2014) 112 [arXiv:1311.6729] [INSPIRE].
W. Altmannshofer, P. Paradisi and D.M. Straub, Model-independent constraints on new physics in b → s transitions, JHEP 04 (2012) 008 [arXiv:1111.1257] [INSPIRE].
D.M. Straub, Constraints on new physics from rare (semi-)leptonic B decays, arXiv:1305.5704 [INSPIRE].
G. Isidori and R. Unterdorfer, On the short distance constraints from K L,S → μ + μ −, JHEP 01 (2004) 009 [hep-ph/0311084] [INSPIRE].
A.J. Buras et al., Patterns of flavour violation in the presence of a fourth generation of quarks and leptons, JHEP 09 (2010) 106 [arXiv:1002.2126] [INSPIRE].
M. Gorbahn and U. Haisch, Charm-quark contribution to K L → μ + μ − at next-to-next-to-leading order, Phys. Rev. Lett. 97 (2006) 122002 [hep-ph/0605203] [INSPIRE].
A.J. Buras and J. Girrbach, Towards the identification of new physics through quark flavour violating processes, Rept. Prog. Phys. 77 (2014) 086201 [arXiv:1306.3775] [INSPIRE].
G. Buchalla, A.J. Buras and M.K. Harlander, Penguin box expansion: flavor changing neutral current processes and a heavy top quark, Nucl. Phys. B 349 (1991) 1 [INSPIRE].
A.J. Buras, F. De Fazio and J. Girrbach, ΔI = 1/2 rule, ε ′ /ε and \( K\to \pi \nu \overline{\nu} \) in Z ′(Z) and G ′ models with FCNC quark couplings, Eur. Phys. J. C 74 (2014) 2950 [arXiv:1404.3824] [INSPIRE].
V. Cirigliano, A. Pich, G. Ecker and H. Neufeld, Isospin violation in ϵ ′, Phys. Rev. Lett. 91 (2003) 162001 [hep-ph/0307030] [INSPIRE].
Particle Data Group collaboration, K.A. Olive et al., Review of particle physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
T. Blum et al., Lattice determination of the K → (ππ) I = 2 decay amplitude A 2, Phys. Rev. D 86 (2012) 074513 [arXiv:1206.5142] [INSPIRE].
G. ’t Hooft and M.J.G. Veltman, Scalar one loop integrals, Nucl. Phys. B 153 (1979) 365 [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1504.07415
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Xu, F. Dark Z implication for flavor physics. J. High Energ. Phys. 2015, 170 (2015). https://doi.org/10.1007/JHEP06(2015)170
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2015)170