Abstract
We show how approximate Minimal Flavour Violation (MFV) can emerge from an SU(5) Supersymmetric Grand Unified Theory (SUSY GUT) supplemented by an S 4 × U(1) family symmetry, which provides a good description of all quark and lepton (including neutrino) masses, mixings and CP violation. Assuming a SUSY breaking mechanism which respects the family symmetry, we calculate in full explicit detail the low energy mass insertion parameters in the super-CKM basis, including the effects of canonical normalisation and renormalisation group running. We find that the very simple family symmetry S 4 ×U(1) is sufficient to approximately reproduce the effects of low energy MFV.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.F. King, Neutrino mass models, Rept. Prog. Phys. 67 (2004) 107 [hep-ph/0310204] [INSPIRE].
G. Altarelli and F. Feruglio, Discrete Flavor Symmetries and Models of Neutrino Mixing, Rev. Mod. Phys. 82 (2010) 2701 [arXiv:1002.0211] [INSPIRE].
S.F. King and C. Luhn, Neutrino Mass and Mixing with Discrete Symmetry, Rept. Prog. Phys. 76 (2013) 056201 [arXiv:1301.1340] [INSPIRE].
S.F. King, A. Merle, S. Morisi, Y. Shimizu and M. Tanimoto, Neutrino Mass and Mixing: from Theory to Experiment, New J. Phys. 16 (2014) 045018 [arXiv:1402.4271] [INSPIRE].
S.F. King, Models of Neutrino Mass, Mixing and CP-violation, J. Phys. G 42 (2015) 123001 [arXiv:1510.02091] [INSPIRE].
R.S. Chivukula and H. Georgi, Composite Technicolor Standard Model, Phys. Lett. B 188 (1987) 99 [INSPIRE].
L.J. Hall and L. Randall, Weak scale effective supersymmetry, Phys. Rev. Lett. 65 (1990) 2939 [INSPIRE].
A.J. Buras, P. Gambino, M. Gorbahn, S. Jager and L. Silvestrini, Universal unitarity triangle and physics beyond the standard model, Phys. Lett. B 500 (2001) 161 [hep-ph/0007085] [INSPIRE].
G. D’Ambrosio, G.F. Giudice, G. Isidori and A. Strumia, Minimal flavor violation: An Effective field theory approach, Nucl. Phys. B 645 (2002) 155 [hep-ph/0207036] [INSPIRE].
V. Cirigliano, B. Grinstein, G. Isidori and M.B. Wise, Minimal flavor violation in the lepton sector, Nucl. Phys. B 728 (2005) 121 [hep-ph/0507001] [INSPIRE].
C. Bobeth, T. Ewerth, F. Krüger and J. Urban, Enhancement of \( B\left({\overline{B}}_d\to {\mu}^{+}{\mu}^{-}\right)/B\left({\overline{B}}_s\to {\mu}^{+}{\mu}^{-}\right) \) in the MSSM with minimal flavor violation and large tan beta, Phys. Rev. D 66 (2002) 074021 [hep-ph/0204225] [INSPIRE].
B. Grinstein, M. Redi and G. Villadoro, Low Scale Flavor Gauge Symmetries, JHEP 11 (2010) 067 [arXiv:1009.2049] [INSPIRE].
D. Guadagnoli, R.N. Mohapatra and I. Sung, Gauged Flavor Group with Left-Right Symmetry, JHEP 04 (2011) 093 [arXiv:1103.4170] [INSPIRE].
R.T. D’Agnolo and D.M. Straub, Gauged flavour symmetry for the light generations, JHEP 05 (2012) 034 [arXiv:1202.4759] [INSPIRE].
G. Krnjaic and D. Stolarski, Gauging the Way to MFV, JHEP 04 (2013) 064 [arXiv:1212.4860] [INSPIRE].
R. Franceschini and R.N. Mohapatra, New Patterns of Natural R-Parity Violation with Supersymmetric Gauged Flavor, JHEP 04 (2013) 098 [arXiv:1301.3637] [INSPIRE].
D.J.H. Chung, L.L. Everett, G.L. Kane, S.F. King, J.D. Lykken and L.-T. Wang, The soft supersymmetry breaking Lagrangian: theory and applications, Phys. Rept. 407 (2005) 1 [hep-ph/0312378] [INSPIRE].
H. Georgi and S.L. Glashow, Unity of All Elementary Particle Forces, Phys. Rev. Lett. 32 (1974) 438 [INSPIRE].
J.C. Pati and A. Salam, Unified Lepton-Hadron Symmetry and a Gauge Theory of the Basic Interactions, Phys. Rev. D 8 (1973) 1240 [INSPIRE].
J.C. Pati and A. Salam, Lepton Number as the Fourth Color, Phys. Rev. D 10 (1974) 275 [Erratum ibid. D 11 (1975) 703] [INSPIRE].
T. Feldmann, See-Saw Masses for Quarks and Leptons in SU(5), JHEP 04 (2011) 043 [arXiv:1010.2116] [INSPIRE].
T. Feldmann, F. Hartmann, W. Kilian and C. Luhn, Combining Pati-Salam and Flavour Symmetries, JHEP 10 (2015) 160 [arXiv:1506.00782] [INSPIRE].
R. Barbieri and F. Senia, Minimal flavour violation and SU(5)-unification, Eur. Phys. J. C 75 (2015) 602 [arXiv:1506.09201] [INSPIRE].
G.G. Ross and O. Vives, Yukawa structure, flavor and CP-violation in supergravity, Phys. Rev. D 67 (2003) 095013 [hep-ph/0211279] [INSPIRE].
G.G. Ross, L. Velasco-Sevilla and O. Vives, Spontaneous CP-violation and nonAbelian family symmetry in SUSY, Nucl. Phys. B 692 (2004) 50 [hep-ph/0401064] [INSPIRE].
S. Antusch, S.F. King and M. Malinsky, Solving the SUSY Flavour and CP Problems with SU(3) Family Symmetry, JHEP 06 (2008) 068 [arXiv:0708.1282] [INSPIRE].
S. Antusch, S.F. King, M. Malinsky and G.G. Ross, Solving the SUSY Flavour and CP Problems with Non-Abelian Family Symmetry and Supergravity, Phys. Lett. B 670 (2009) 383 [arXiv:0807.5047] [INSPIRE].
W. Altmannshofer, A.J. Buras, S. Gori, P. Paradisi and D.M. Straub, Anatomy and Phenomenology of FCNC and CPV Effects in SUSY Theories, Nucl. Phys. B 830 (2010) 17 [arXiv:0909.1333] [INSPIRE].
A.J. Buras and J. Girrbach, BSM models facing the recent LHCb data: A First look, Acta Phys. Polon. B 43 (2012) 1427 [arXiv:1204.5064] [INSPIRE].
D.M. Straub, Overview of Constraints on New Physics in Rare B Decays, arXiv:1205.6094 [INSPIRE].
S.F. King and I.N.R. Peddie, Canonical normalization and Yukawa matrices, Phys. Lett. B 586 (2004) 83 [hep-ph/0312237] [INSPIRE].
S.F. King, I.N.R. Peddie, G.G. Ross, L. Velasco-Sevilla and O. Vives, Kähler corrections and softly broken family symmetries, JHEP 07 (2005) 049 [hep-ph/0407012] [INSPIRE].
P. Minkowski, μ → eγ at a Rate of One Out of 109 Muon Decays?, Phys. Lett. B 67 (1977) 421 [INSPIRE].
M. Gell-Mann, P. Ramond and R. Slansky, Complex Spinors and Unified Theories, Conf. Proc. C 790927 (1979) 315 [arXiv:1306.4669] [INSPIRE].
T. Yanagida, Horizontal Symmetry And Masses Of Neutrinos, Conf. Proc. C 7902131 (1979) 95.
R.N. Mohapatra and G. Senjanović, Neutrino Mass and Spontaneous Parity Violation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].
Y. Yamada, SUSY and GUT threshold effects in SUSY SU(5) models, Z. Phys. C 60 (1993) 83 [INSPIRE].
S. Antusch and M. Spinrath, Quark and lepton masses at the GUT scale including SUSY threshold corrections, Phys. Rev. D 78 (2008) 075020 [arXiv:0804.0717] [INSPIRE].
C. Hagedorn, S.F. King and C. Luhn, A SUSY GUT of Flavour with S 4 × SU(5) to NLO, JHEP 06 (2010) 048 [arXiv:1003.4249] [INSPIRE].
C. Hagedorn, S.F. King and C. Luhn, SUSY S 4 × SU(5) revisited, Phys. Lett. B 717 (2012) 207 [arXiv:1205.3114] [INSPIRE].
S.P. Martin, A Supersymmetry primer, hep-ph/9709356 [INSPIRE].
Y. Shirman, Introduction to Supersymmetry and Supersymmetry Breaking, arXiv:0907.0039 [INSPIRE].
G. Altarelli and F. Feruglio, Tri-bimaximal neutrino mixing from discrete symmetry in extra dimensions, Nucl. Phys. B 720 (2005) 64 [hep-ph/0504165] [INSPIRE].
G. Altarelli and F. Feruglio, Tri-bimaximal neutrino mixing, A 4 and the modular symmetry, Nucl. Phys. B 741 (2006) 215 [hep-ph/0512103] [INSPIRE].
L. Wolfenstein, Parametrization of the Kobayashi-Maskawa Matrix, Phys. Rev. Lett. 51 (1983) 1945 [INSPIRE].
G.-J. Ding, S.F. King, C. Luhn and A.J. Stuart, Spontaneous CP-violation from vacuum alignment in S 4 models of leptons, JHEP 05 (2013) 084 [arXiv:1303.6180] [INSPIRE].
F. Feruglio, C. Hagedorn and R. Ziegler, A realistic pattern of lepton mixing and masses from S 4 and CP, Eur. Phys. J. C 74 (2014) 2753 [arXiv:1303.7178] [INSPIRE].
C. Luhn, Trimaximal TM 1 neutrino mixing in S 4 with spontaneous CP-violation, Nucl. Phys. B 875 (2013) 80 [arXiv:1306.2358] [INSPIRE].
R. Gatto, G. Sartori and M. Tonin, Weak Selfmasses, Cabibbo Angle and Broken SU(2) × SU(2), Phys. Lett. B 28 (1968) 128 [INSPIRE].
H. Georgi and C. Jarlskog, A New Lepton-Quark Mass Relation in a Unified Theory, Phys. Lett. B 86 (1979) 297 [INSPIRE].
X.-G. He and A. Zee, Minimal modification to the tri-bimaximal neutrino mixing, Phys. Lett. B 645 (2007) 427 [hep-ph/0607163] [INSPIRE].
W. Grimus and L. Lavoura, A model for trimaximal lepton mixing, JHEP 09 (2008) 106 [arXiv:0809.0226] [INSPIRE].
C.H. Albright, A. Dueck and W. Rodejohann, Possible Alternatives to Tri-bimaximal Mixing, Eur. Phys. J. C 70 (2010) 1099 [arXiv:1004.2798] [INSPIRE].
H. Ishimori, Y. Shimizu, M. Tanimoto and A. Watanabe, Neutrino masses and mixing from S 4 flavor twisting, Phys. Rev. D 83 (2011) 033004 [arXiv:1010.3805] [INSPIRE].
Y. Shimizu, M. Tanimoto and A. Watanabe, Breaking Tri-bimaximal Mixing and Large θ 13, Prog. Theor. Phys. 126 (2011) 81 [arXiv:1105.2929] [INSPIRE].
E. Ma and D. Wegman, Nonzero θ 13 for neutrino mixing in the context of A 4 symmetry, Phys. Rev. Lett. 107 (2011) 061803 [arXiv:1106.4269] [INSPIRE].
X.-G. He and A. Zee, Minimal Modification to Tri-bimaximal Mixing, Phys. Rev. D 84 (2011) 053004 [arXiv:1106.4359] [INSPIRE].
S.F. King and C. Luhn, Trimaximal neutrino mixing from vacuum alignment in A4 and S4 models, JHEP 09 (2011) 042 [arXiv:1107.5332] [INSPIRE].
I.K. Cooper, S.F. King and C. Luhn, A4 × SU(5) SUSY GUT of Flavour with Trimaximal Neutrino Mixing, JHEP 06 (2012) 130 [arXiv:1203.1324] [INSPIRE].
S.F. King, C. Luhn and A.J. Stuart, A Grand Δ(96) × SU(5) Flavour Model, Nucl. Phys. B 867 (2013) 203 [arXiv:1207.5741] [INSPIRE].
C. Luhn, K.M. Parattu and A. Wingerter, A Minimal Model of Neutrino Flavor, JHEP 12 (2012) 096 [arXiv:1210.1197] [INSPIRE].
F. Feruglio, C. Hagedorn and L. Merlo, Vacuum Alignment in SUSY A4 Models, JHEP 03 (2010) 084 [arXiv:0910.4058] [INSPIRE].
S. Antusch, J. Kersten, M. Lindner and M. Ratz, Running neutrino masses, mixings and CP phases: Analytical results and phenomenological consequences, Nucl. Phys. B 674 (2003) 401 [hep-ph/0305273] [INSPIRE].
S. Antusch, J. Kersten, M. Lindner, M. Ratz and M.A. Schmidt, Running neutrino mass parameters in see-saw scenarios, JHEP 03 (2005) 024 [hep-ph/0501272] [INSPIRE].
C. Jarlskog, Commutator of the Quark Mass Matrices in the Standard Electroweak Model and a Measure of Maximal CP-violation, Phys. Rev. Lett. 55 (1985) 1039 [INSPIRE].
F. Gabbiani, E. Gabrielli, A. Masiero and L. Silvestrini, A Complete analysis of FCNC and CP constraints in general SUSY extensions of the standard model, Nucl. Phys. B 477 (1996) 321 [hep-ph/9604387] [INSPIRE].
M. Misiak, S. Pokorski and J. Rosiek, Supersymmetry and FCNC effects, Adv. Ser. Direct. High Energy Phys. 15 (1998) 795 [hep-ph/9703442] [INSPIRE].
M. Dimou, S.F. King and C. Luhn, Phenomenological Implications of an S 4 × SU(5) SUSY GUT of Flavour, arXiv:1512.09063 [INSPIRE].
F. Feruglio, C. Hagedorn and R. Ziegler, Lepton Mixing Parameters from Discrete and CP Symmetries, JHEP 07 (2013) 027 [arXiv:1211.5560] [INSPIRE].
M. Holthausen, M. Lindner and M.A. Schmidt, CP and Discrete Flavour Symmetries, JHEP 04 (2013) 122 [arXiv:1211.6953] [INSPIRE].
W. Grimus and M.N. Rebelo, Automorphisms in gauge theories and the definition of CP and P, Phys. Rept. 281 (1997) 239 [hep-ph/9506272] [INSPIRE].
M.-C. Chen, M. Fallbacher, K.T. Mahanthappa, M. Ratz and A. Trautner, CP Violation from Finite Groups, Nucl. Phys. B 883 (2014) 267 [arXiv:1402.0507] [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: 1511.07886
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
Dimou, M., King, S.F. & Luhn, C. Approaching Minimal Flavour Violation from an SU(5) × S 4 × U(1) SUSY GUT. J. High Energ. Phys. 2016, 118 (2016). https://doi.org/10.1007/JHEP02(2016)118
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2016)118