Abstract
The charged lepton flavour violating (LFV) radiative decays, μ → e + γ, τ → μ + γ and τ → e + γ are investigated in a class of supersymmetric A 4 models with three heavy right-handed (RH) Majorana neutrinos, in which the lepton (neutrino) mixing is predicted to leading order (LO) to be tri-bimaximal. The light neutrino masses are generated via the type I see-saw mechanism. The analysis is done within the framework of the minimal supergravity (mSUGRA) scenario, which provides flavour universal boundary conditions at the scale of grand unification M X ≈ 2 × 1016 GeV. Detailed predictions for the rates of the three LFV decays are obtained in two explicit realisations of the A4 models due to Altarelli and Feruglio and Altarelli and Meloni, respectively.
Similar content being viewed by others
References
T. Schwetz, M.A. Tortola and J.W.F. Valle, Three-flavour neutrino oscillation update, New J. Phys. 10 (2008) 113011 [arXiv:0808.2016] [SPIRES].
P.F. Harrison, D.H. Perkins and W.G. Scott, Tri-bimaximal mixing and the neutrino oscillation data, Phys. Lett. B 530 (2002) 167 [hep-ph/0202074] [SPIRES].
P.F. Harrison and W.G. Scott, Symmetries and generalisations of tri-bimaximal neutrino mixing, Phys. Lett. B 535 (2002) 163 [hep-ph/0203209] [SPIRES].
Z.-Z. Xing, Nearly tri-bimaximal neutrino mixing and CP-violation, Phys. Lett. B 533 (2002) 85 [hep-ph/0204049] [SPIRES].
P.F. Harrison and W.G. Scott, μ-τ reflection symmetry in lepton mixing and neutrino oscillations, Phys. Lett. B 547 (2002) 219 [hep-ph/0210197] [SPIRES].
P.F. Harrison and W.G. Scott, Permutation symmetry, tri-bimaximal neutrino mixing and the S 3 group characters, Phys. Lett. B 557 (2003) 76 [hep-ph/0302025] [SPIRES].
P.F. Harrison and W.G. Scott, Status of tri-/bi-maximal neutrino mixing, hep-ph/0402006 [SPIRES].
P.F. Harrison and W.G. Scott, The simplest neutrino mass matrix, Phys. Lett. B 594 (2004) 324 [hep-ph/0403278] [SPIRES].
S.M. Bilenky, J. Hosek and S.T. Petcov, On oscillations of neutrinos with Dirac and Majorana masses, Phys. Lett. B 94 (1980) 495 [SPIRES].
S.M. Bilenky, S. Pascoli and S.T. Petcov, Majorana neutrinos, neutrino mass spectrum, CP-violation and neutrinoless double beta-decay. I: the three-neutrino mixing case, Phys. Rev. D 64 (2001) 053010 [hep-ph/0102265] [SPIRES].
S.T. Petcov, Towards complete neutrino mixing matrix and CP-violation, Nucl. Phys. (Proc. Suppl.) 143 (2005) 159 [hep-ph/0412410] [SPIRES].
E. Ma and G. Rajasekaran, Softly broken A 4 symmetry for nearly degenerate neutrino masses, Phys. Rev. D 64 (2001) 113012 [hep-ph/0106291] [SPIRES].
K.S. Babu, E. Ma and J.W.F. Valle, Underlying A 4 symmetry for the neutrino mass matrix and the quark mixing matrix, Phys. Lett. B 552 (2003) 207 [hep-ph/0206292] [SPIRES].
M. Hirsch, J.C. Romao, S. Skadhauge, J.W.F. Valle and A. Villanova del Moral, Degenerate neutrinos from a supersymmetric A 4 model, hep-ph/0312244 [SPIRES].
M. Hirsch, J.C. Romao, S. Skadhauge, J.W.F. Valle and A. Villanova del Moral, Phenomenological tests of supersymmetric A 4 family symmetry model of neutrino mass, Phys. Rev. D 69 (2004) 093006 [hep-ph/0312265] [SPIRES].
S.-L. Chen, M. Frigerio and E. Ma, Hybrid seesaw neutrino masses with A 4 family symmetry, Nucl. Phys. B 724 (2005) 423 [hep-ph/0504181] [SPIRES].
K.S. Babu and X.-G. He, Model of geometric neutrino mixing, hep-ph/0507217 [SPIRES].
X.-G. He, Y.-Y. Keum and R.R. Volkas, A 4 flavour symmetry breaking scheme for understanding quark and neutrino mixing angles, JHEP 04 (2006) 039 [hep-ph/0601001] [SPIRES].
S.F. King and M. Malinsky, A 4 family symmetry and quark-lepton unification, Phys. Lett. B 645 (2007) 351 [hep-ph/0610250] [SPIRES].
F. Bazzocchi, S. Kaneko and S. Morisi, A SUSY A 4 model for fermion masses and mixings, JHEP 03 (2008) 063 [arXiv:0707.3032] [SPIRES].
G. Altarelli, F. Feruglio and C. Hagedorn, A SUSY SU(5) grand unified model of tri-bimaximal mixing from A 4, JHEP 03 (2008) 052 [arXiv:0802.0090] [SPIRES].
Y. Lin, Tri-bimaximal neutrino mixing from A 4 and θ13 ∼ θ C , Nucl. Phys. B 824 (2010) 95 [arXiv:0905.3534] [SPIRES].
G. Altarelli and F. Feruglio, Tri-bimaximal neutrino mixing from discrete symmetry in extra dimensions, Nucl. Phys. B 720 (2005) 64 [hep-ph/0504165] [SPIRES].
G. Altarelli and F. Feruglio, Tri-bimaximal neutrino mixing, A 4 and the modular symmetry, Nucl. Phys. B 741 (2006) 215 [hep-ph/0512103] [SPIRES].
G. Altarelli and D. Meloni, A simplest A 4 model for tri-bimaximal neutrino mixing, J. Phys. G 36 (2009) 085005 [arXiv:0905.0620] [SPIRES].
C.S. Lam, Determining horizontal symmetry from neutrino mixing, Phys. Rev. Lett. 101 (2008) 121602 [arXiv:0804.2622] [SPIRES].
C.S. Lam, The unique horizontal symmetry of leptons, Phys. Rev. D 78 (2008) 073015 [arXiv:0809.1185] [SPIRES].
F. Bazzocchi, L. Merlo and S. Morisi, Fermion masses and mixings in a S4-based model, Nucl. Phys. B 816 (2009) 204 [arXiv:0901.2086] [SPIRES].
C.S. Lam, A bottom-up analysis of horizontal symmetry, arXiv:0907.2206 [SPIRES].
H. Ishimori, Y. Shimizu and M. Tanimoto, S4 flavor symmetry of quarks and leptons in SU(5) GUT, Prog. Theor. Phys. 121 (2009) 769 [arXiv:0812.5031] [SPIRES].
C. Hagedorn, E. Molinaro and S.T. Petcov, Majorana phases and leptogenesis in see-saw models with A 4 symmetry, JHEP 09 (2009) 115 [arXiv:0908.0240] [SPIRES].
S.T. Petcov, Theoretical prospects of neutrinoless double beta decay, Phys. Scripta T 121 (2005) 94 [hep-ph/0504166] [SPIRES].
S. Pascoli and S.T. Petcov, Majorana neutrinos, neutrino mass spectrum and the |〈m〉| ∼ 10−3 eV frontier in neutrinoless double beta decay, Phys. Rev. D 77 (2008) 113003 [arXiv:0711.4993] [SPIRES].
C. Aalseth et al., Neutrinoless double beta decay and direct searches for neutrino mass, hep-ph/0412300 [SPIRES].
E. Bertuzzo, P. Di Bari, F. Feruglio and E. Nardi, Flavor symmetries, leptogenesis and the absolute neutrino mass scale, JHEP 11 (2009) 036 [arXiv:0908.0161] [SPIRES].
E.E. Jenkins and A.V. Manohar, Tribimaximal mixing, leptogenesis and θ13, Phys. Lett. B 668 (2008) 210 [arXiv:0807.4176] [SPIRES].
B. Adhikary and A. Ghosal, Nonzero U e3 , CP-violation and leptogenesis in a see-saw type softly broken A 4 symmetric model, Phys. Rev. D 78 (2008) 073007 [arXiv:0803.3582] [SPIRES].
G.C. Branco, R. Gonzalez Felipe, M.N. Rebelo and H. Serodio, Resonant leptogenesis and tribimaximal leptonic mixing with A 4 symmetry, Phys. Rev. D 79 (2009) 093008 [arXiv:0904.3076] [SPIRES].
D. Aristizabal Sierra, F. Bazzocchi, I. de Medeiros Varzielas, L. Merlo and S. Morisi, Tri-bimaximal lepton mixing and leptogenesis, Nucl. Phys. B 827 (2010) 34 [arXiv:0908.0907] [SPIRES].
WMAP collaboration, J. Dunkley et al., Five-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: likelihoods and parameters from the WMAP data, Astrophys. J. Suppl. 180 (2009) 306 [arXiv:0803.0586] [SPIRES].
F. Feruglio, C. Hagedorn, Y. Lin and L. Merlo, Lepton flavour violation in models with A 4 flavour symmetry, Nucl. Phys. B 809 (2009) 218 [arXiv:0807.3160] [SPIRES].
F. Feruglio, C. Hagedorn, Y. Lin and L. Merlo, Theory of the neutrino mass, arXiv:0808.0812 [SPIRES].
S.T. Petcov, The processes μ → eγ, μ → eeē, ν΄→ νγ in the Weinberg-Salam model with neutrino mixing, Sov. J. Nucl. Phys. 25 (1977) 340 [Yad. Fiz. 25 (1977) 641] [Erratum ibid. 25 (698) 1977] [Erratum ibid. 25 (1977) 1336] [SPIRES].
S.M. Bilenky, S.T. Petcov and B. Pontecorvo, Lepton mixing, μ → e + γ decay and neutrino oscillations, Phys. Lett. B 67 (1977) 309 [SPIRES].
T.P. Cheng and L.-F. Li, μ → eγ in theories with Dirac and Majorana neutrino mass terms, Phys. Rev. Lett. 45 (1980) 1908 [SPIRES].
M. Raidal et al., Flavour physics of leptons and dipole moments, Eur. Phys. J. C 57 (2008) 13 [arXiv:0801.1826] [SPIRES].
S.M. Bilenky and S.T. Petcov, Massive neutrinos and neutrino oscillations, Rev. Mod. Phys. 59 (1987) 671 [Erratum ibid. 60 (1988) 575] [Erratum ibid. 61 (1989) 169] [SPIRES].
F. Feruglio, C. Hagedorn and L. Merlo, Vacuum alignment in SUSY A 4 models, arXiv:0910.4058 [SPIRES].
F. Borzumati and A. Masiero, Large muon and electron number violations in supergravity theories, Phys. Rev. Lett. 57 (1986) 961 [SPIRES].
J. Hisano, T. Moroi, K. Tobe, M. Yamaguchi and T. Yanagida, Lepton flavor violation in the supersymmetric standard model with seesaw induced neutrino masses, Phys. Lett. B 357 (1995) 579 [hep-ph/9501407] [SPIRES].
J. Hisano and D. Nomura, Solar and atmospheric neutrino oscillations and lepton flavor violation in supersymmetric models with the right-handed neutrinos, Phys. Rev. D 59 (1999) 116005 [hep-ph/9810479] [SPIRES].
S.T. Petcov, S. Profumo, Y. Takanishi and C.E. Yaguna, Charged lepton flavor violating decays: leading logarithmic approximation versus full RG results, Nucl. Phys. B 676 (2004) 453 [hep-ph/0306195] [SPIRES].
S.T. Petcov, W. Rodejohann, T. Shindou and Y. Takanishi, The see-saw mechanism, neutrino Yukawa couplings, LFV decays ℓ i → ℓj + γ and leptogenesis, Nucl. Phys. B 739 (2006) 208 [hep-ph/0510404] [SPIRES].
V. Barger, D. Marfatia, A. Mustafayev and A. Soleimani, SUSY dark matter and lepton flavor violation, Phys. Rev. D 80 (2009) 076004 [arXiv:0908.0941] [SPIRES].
Z.-Z. Xing, H. Zhang and S. Zhou, Updated values of running quark and lepton masses, Phys. Rev. D 77 (2008) 113016 [arXiv:0712.1419] [SPIRES].
ALEPH collaboration, S. Schael et al., Search for neutral MSSM Higgs bosons at LEP, Eur. Phys. J. C 47 (2006) 547 [hep-ex/0602042] [SPIRES].
Particle Data Group collaboration, C. Amsler et al., Review of particle physics, Phys. Lett. B 667 (2008) 1 [SPIRES].
P.H. Chankowski and Z. Pluciennik, Renormalization group equations for seesaw neutrino masses, Phys. Lett. B 316 (1993) 312 [hep-ph/9306333] [SPIRES].
K.S. Babu, C.N. Leung and J.T. Pantaleone, Renormalization of the neutrino mass operator, Phys. Lett. B 319 (1993) 191 [hep-ph/9309223] [SPIRES].
S. Antusch, M. Drees, J. Kersten, M. Lindner and M. Ratz, Neutrino mass operator renormalization revisited, Phys. Lett. B 519 (2001) 238 [hep-ph/0108005] [SPIRES].
S. Antusch, M. Drees, J. Kersten, M. Lindner and M. Ratz, Neutrino mass operator renormalization in two Higgs doublet models and the MSSM, Phys. Lett. B 525 (2002) 130 [hep-ph/0110366] [SPIRES].
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] [SPIRES].
S.T. Petcov, T. Shindou and Y. Takanishi, Majorana CP-violating phases, RG running of neutrino mixing parameters and charged lepton flavour violating decays, Nucl. Phys. B 738 (2006) 219 [hep-ph/0508243] [SPIRES].
H. Baer, C. Balázs, A. Belyaev, T. Krupovnickas and X. Tata, Updated reach of the CERN LHC and constraints from relic density, b → sγ and a(μ) in the mSUGRA model, JHEP 06 (2003) 054 [hep-ph/0304303] [SPIRES].
J.R. Ellis, K.A. Olive, Y. Santoso and V.C. Spanos, Supersymmetric dark matter in light of WMAP, Phys. Lett. B 565 (2003) 176 [hep-ph/0303043] [SPIRES].
H. Baer and A.D. Box, Fine-tuning favors mixed axion/axino cold dark matter over neutralinos in the minimal supergravity model, arXiv:0910.0333 [SPIRES].
F.E. Paige, S.D. Protopopescu, H. Baer and X. Tata, ISAJET 7.69: a Monte Carlo event generator for pp, \( \overline p p \) and e + e − reactions, hep-ph/0312045 [SPIRES].
V. Barger, D. Marfatia and A. Mustafayev, Neutrino sector impacts SUSY dark matter, Phys. Lett. B 665 (2008) 242 [arXiv:0804.3601] [SPIRES].
MEGA collaboration, M.L. Brooks et al., New limit for the family-number non-conserving decay μ+ → e ±γ, Phys. Rev. Lett. 83 (1999) 1521 [hep-ex/9905013] [SPIRES].
A. Maki, Status of the MEG experiment, AIP Conf. Proc. 981 (2008) 363 [SPIRES].
BABAR collaboration, B. Aubert et al., Searches for lepton flavor violation in the decays τ → eγ and τ → μγ, arXiv:0908.2381 [SPIRES].
M. Bona et al., SuperB: a high-luminosity asymmetric e + e − super flavor factory. Conceptual design report, arXiv:0709.0451 [SPIRES].
SuperKEKB Physics Working Group collaboration, A.G. Akeroyd et al., Physics at super B factory, hep-ex/0406071 [SPIRES].
GERDA collaboration, A.A. Smolnikov, Status of the GERDA experiment aimed to search for neutrinoless double beta decay of 76Ge, arXiv:0812.4194 [SPIRES].
CUORE collaboration, A. Giuliani, From Cuoricino to CUORE: investigating the inverted hierarchy region of neutrino mass, J. Phys. Conf. Ser. 120 (2008) 052051 [SPIRES].
G.L. Fogli et al., Observables sensitive to absolute neutrino masses (Addendum), Phys. Rev. D 78 (2008) 033010 [arXiv:0805.2517] [SPIRES].
M. Tegmark, Cosmological neutrino bounds for non-cosmologists, Phys. Scripta T 121 (2005) 153 [hep-ph/0503257] [SPIRES].
S. Hannestad, H. Tu and Y.Y.Y. Wong, Measuring neutrino masses and dark energy with weak lensing tomography, JCAP 06 (2006) 025 [astro-ph/0603019] [SPIRES].
J. Lesgourgues, L. Perotto, S. Pastor and M. Piat, Probing neutrino masses with CMB lensing extraction, Phys. Rev. D 73 (2006) 045021 [astro-ph/0511735] [SPIRES].
PRIME Working Group collaboration, Y. Mori et al., An experimental search for μ− → e − conversion process at an ultimate sensitivity of the order of 10−18 with PRISM, LOI-25, J-PARC, Japan (2006).
Mu2e collaboration, E.C. Dukes et al., Proposal to search for μ−N → e −N with a single event sensitivity below 10−16, FERMILAB-PROPOSAL-0973 [SPIRES].
SINDRUM collaboration, U. Bellgardt et al., Search for the decay μ+ → e + e + e −, Nucl. Phys. B 299 (1988) 1 [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hagedorn, C., Molinaro, E. & Petcov, S.T. Charged lepton flavour violating radiative decays ℓ i → ℓ j + γ in see-saw models with A 4 symmetry. J. High Energ. Phys. 2010, 47 (2010). https://doi.org/10.1007/JHEP02(2010)047
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2010)047