Abstract
We study a class of six-dimensional models based on positive curvature surfaces (spherical 2-orbifolds) as extra-spaces. Using the Newman-Penrose formalism, we discuss the particle spectrum in this class of models. The fermion spectrum problem, which has been addressed with flux compactifications in the past, can be avoided using localised fermions. In this framework, we find that there are four types of geometry compatible with the existence of a stable dark matter candidate and we study the simplest case in detail. Using the complementarity between collider resonance searches and relic density constraints, we show that this class of models is under tension, unless the model lies in a funnel region characterised by a resonant Higgs s-channel in the dark matter annihilation.
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References
G. Nordstrom, On the possibility of unifying the electromagnetic and the gravitational fields, Phys. Z. 15 (1914) 504 [physics/0702221] [INSPIRE].
T. Kaluza, On the problem of unity in physics, Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.) 1921 (1921) 966 [INSPIRE].
O. Klein, Quantum theory and five-dimensional theory of relativity (in German and English), Z. Phys. 37 (1926) 895 [INSPIRE].
G. Servant and T.M.P. Tait, Is the lightest Kaluza-Klein particle a viable dark matter candidate?, Nucl. Phys. B 650 (2003) 391 [hep-ph/0206071] [INSPIRE].
I. Antoniadis, A possible new dimension at a few TeV, Phys. Lett. B 246 (1990) 377 [INSPIRE].
I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos and G.R. Dvali, New dimensions at a millimeter to a Fermi and superstrings at a TeV, Phys. Lett. B 436 (1998) 257 [hep-ph/9804398] [INSPIRE].
T. Appelquist, H.-C. Cheng and B.A. Dobrescu, Bounds on universal extra dimensions, Phys. Rev. D 64 (2001) 035002 [hep-ph/0012100] [INSPIRE].
L. Randall and R. Sundrum, An alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064] [INSPIRE].
K. Agashe, A. Falkowski, I. Low and G. Servant, KK parity in warped extra dimension, JHEP 04 (2008) 027 [arXiv:0712.2455] [INSPIRE].
A. Ahmed, B. Grzadkowski, J.F. Gunion and Y. Jiang, Higgs dark matter from a warped extra dimension — the truncated-inert-doublet model, JHEP 10 (2015) 033 [arXiv:1504.03706] [INSPIRE].
G. Cacciapaglia, A. Deandrea and J. Llodra-Perez, A dark matter candidate from Lorentz invariance in 6D, JHEP 03 (2010) 083 [arXiv:0907.4993] [INSPIRE].
B.A. Dobrescu and E. Poppitz, Number of fermion generations derived from anomaly cancellation, Phys. Rev. Lett. 87 (2001) 031801 [hep-ph/0102010] [INSPIRE].
N. Maru, T. Nomura, J. Sato and M. Yamanaka, The universal extra dimensional model with S 2 /Z 2 extra-space, Nucl. Phys. B 830 (2010) 414 [arXiv:0904.1909] [INSPIRE].
H. Dohi and K.-Y. Oda, Universal extra dimensions on real projective plane, Phys. Lett. B 692 (2010) 114 [arXiv:1004.3722] [INSPIRE].
S. Randjbar-Daemi, A. Salam and J.A. Strathdee, Spontaneous compactification in six-dimensional Einstein-Maxwell theory, Nucl. Phys. B 214 (1983) 491 [INSPIRE].
J.M. Frère, M.V. Libanov, E.Y. Nugaev and S.V. Troitsky, Fermions in the vortex background on a sphere, JHEP 06 (2003) 009 [hep-ph/0304117] [INSPIRE].
J.M. Frère, M. Libanov, S. Mollet and S. Troitsky, Neutrino hierarchy and fermion spectrum from a single family in six dimensions: realistic predictions, JHEP 08 (2013) 078 [arXiv:1305.4320] [INSPIRE].
J.-M. Frère, M. Libanov, S. Mollet and S. Troitsky, Flavour changing Z ′ signals in a 6D inspired model, arXiv:1505.08017 [INSPIRE].
P.T. Winslow, K. Sigurdson and J.N. Ng, Multi-state dark matter from spherical extra dimensions, Phys. Rev. D 82 (2010) 023512 [arXiv:1005.3013] [INSPIRE].
R. Flurry, Symmetry groups: theory and chemical applications, Prentice-Hall, U.S.A. (1980).
M. Rausch de Traubenberg, Clifford algebras in physics, in 7th International Conference on Clifford Algebras and their Applications in Mathematical Physics, Toulouse France May 19-29 2005 [hep-th/0506011] [INSPIRE].
B.A. Dobrescu and E. Ponton, Chiral compactification on a square, JHEP 03 (2004) 071 [hep-th/0401032] [INSPIRE].
A. Lichnerowicz, Champs spinoriels et propagateurs en relativité générale (in French), Bull. Soc. Math. France 92 (1964) 11.
J.H. Conway and D.H. Huson, The orbifold notation for two-dimensional groups, Struct. Chem. 13 (2002) 247.
J.H. Conway, H. Burgiel and C. Goodman-Strauss, The symmetries of things, A.K. Peters Ltd., Wellesley MA U.S.A. (2008).
S.M. Carroll and M.M. Guica, Sidestepping the cosmological constant with football shaped extra dimensions, hep-th/0302067 [INSPIRE].
A.A. Geraci, S.J. Smullin, D.M. Weld, J. Chiaverini and A. Kapitulnik, Improved constraints on non-Newtonian forces at 10 microns, Phys. Rev. D 78 (2008) 022002 [arXiv:0802.2350] [INSPIRE].
I.M. Gelfand, R.A. Minlos and Z.J. Shapiro, Representations of the rotation group and of the Lorentz group, and their applications, MacMillan, U.K. (1963).
E.T. Newman and R. Penrose, Note on the Bondi-Metzner-Sachs group, J. Math. Phys. 7 (1966) 863 [INSPIRE].
R. Penrose and W. Rindler, Spinors and space-time, vol. 1, Cambridge University Press, Cambridge U.K. (1984).
G.T. del Castillo, Spin-weighted spherical harmonics and their applications, Rev. Mex. Fıs. 53 (2007) 125.
H. Dohi, T. Kakuda, K. Nishiwaki, K.-Y. Oda and N. Okuda, Notes on sphere-based universal extra dimensions, Afr. Rev. Phys. 9 (2014) 0069 [arXiv:1406.1954] [INSPIRE].
R. Camporesi and A. Higuchi, On the eigen functions of the Dirac operator on spheres and real hyperbolic spaces, J. Geom. Phys. 20 (1996) 1 [gr-qc/9505009] [INSPIRE].
A.A. Abrikosov, Jr., Dirac operator on the Riemann sphere, hep-th/0212134 [INSPIRE].
L. Nilse, Classification of 1D and 2D orbifolds, hep-ph/0601015 [INSPIRE].
H.-C. Cheng, K.T. Matchev and M. Schmaltz, Radiative corrections to Kaluza-Klein masses, Phys. Rev. D 66 (2002) 036005 [hep-ph/0204342] [INSPIRE].
G. Cacciapaglia, A. Deandrea and J. Llodra-Perez, The universal real projective plane: LHC phenomenology at one loop, JHEP 10 (2011) 146 [arXiv:1104.3800] [INSPIRE].
L. Da Rold, Radiative corrections in 5D and 6D expanding in winding modes, Phys. Rev. D 69 (2004) 105015 [hep-th/0311063] [INSPIRE].
G. Cacciapaglia and B. Kubik, Even tiers and resonances on the real projective plane, JHEP 02 (2013) 052 [arXiv:1209.6556] [INSPIRE].
ATLAS collaboration, Search for high-mass dilepton resonances in pp collisions at \( \sqrt{s}=8 \) TeV with the ATLAS detector, Phys. Rev. D 90 (2014) 052005 [arXiv:1405.4123] [INSPIRE].
CMS collaboration, Search for physics beyond the standard model in dilepton mass spectra in proton-proton collisions at \( \sqrt{s}=8 \) TeV, JHEP 04 (2015) 025 [arXiv:1412.6302] [INSPIRE].
A. Alloul, N.D. Christensen, C. Degrande, C. Duhr and B. Fuks, FeynRules 2.0 — a complete toolbox for tree-level phenomenology, Comput. Phys. Commun. 185 (2014) 2250 [arXiv:1310.1921] [INSPIRE].
J. Alwall et al., The automated computation of tree-level and next-to-leading order differential cross sections and their matching to parton shower simulations, JHEP 07 (2014) 079 [arXiv:1405.0301] [INSPIRE].
T. Sjöstrand, S. Mrenna and P.Z. Skands, PYTHIA 6.4 physics and manual, JHEP 05 (2006) 026 [hep-ph/0603175] [INSPIRE].
DELPHES 3 collaboration, J. de Favereau et al., DELPHES 3, a modular framework for fast simulation of a generic collider experiment, JHEP 02 (2014) 057 [arXiv:1307.6346] [INSPIRE].
S. Ovyn, X. Rouby and V. Lemaitre, DELPHES, a framework for fast simulation of a generic collider experiment, arXiv:0903.2225 [INSPIRE].
B. Dumont et al., Toward a public analysis database for LHC new physics searches using MadAnalysis 5, Eur. Phys. J. C 75 (2015) 56 [arXiv:1407.3278] [INSPIRE].
E. Conte, B. Fuks and G. Serret, MadAnalysis 5, A User-Friendly Framework for Collider Phenomenology, Comput. Phys. Commun. 184 (2013) 222 [arXiv:1206.1599] [INSPIRE].
E. Conte, B. Dumont, B. Fuks and C. Wymant, Designing and recasting LHC analyses with MadAnalysis 5, Eur. Phys. J. C 74 (2014) 3103 [arXiv:1405.3982] [INSPIRE].
S. Nussinov, Technocosmology: could a technibaryon excess provide a ‘natural’ missing mass candidate?, Phys. Lett. B 165 (1985) 55 [INSPIRE].
K. Petraki and R.R. Volkas, Review of asymmetric dark matter, Int. J. Mod. Phys. A 28 (2013) 1330028 [arXiv:1305.4939] [INSPIRE].
K.M. Zurek, Asymmetric dark matter: theories, signatures and constraints, Phys. Rept. 537 (2014) 91 [arXiv:1308.0338] [INSPIRE].
K. Griest and D. Seckel, Three exceptions in the calculation of relic abundances, Phys. Rev. D 43 (1991) 3191 [INSPIRE].
A. Arbey, G. Cacciapaglia, A. Deandrea and B. Kubik, Dark matter in a twisted bottle, JHEP 01 (2013) 147 [arXiv:1210.0384] [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].
Wolfram Resarch Inc., Mathematica 8, U.S.A. (2010).
K. Kong and K.T. Matchev, Precise calculation of the relic density of Kaluza-Klein dark matter in universal extra dimensions, JHEP 01 (2006) 038 [hep-ph/0509119] [INSPIRE].
Planck collaboration, P.A.R. Ade et al., Planck 2015 results. XIII. Cosmological parameters, arXiv:1502.01589 [INSPIRE].
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Cacciapaglia, G., Deandrea, A. & Deutschmann, N. Dark matter and localised fermions from spherical orbifolds?. J. High Energ. Phys. 2016, 83 (2016). https://doi.org/10.1007/JHEP04(2016)083
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DOI: https://doi.org/10.1007/JHEP04(2016)083