Running effects on neutrino parameters and ℓ i → ℓ j γ predictions in the triplet-extended MSSM

  • F.R. JoaquimEmail author
Open Access


We investigate the renormalisation group effects induced on neutrino mass and mixing parameters in a triplet-extended minimal supersymmetric standard model where a vector-like pair of hypercharge ±1 triplet superfields is added. We first rederive the one-loop renormalisation group equation for the effective neutrino mass operator and, for the case in which this operator originates solely from the decoupling of the triplets, the corresponding equations for neutrino masses, mixing parameters and CP-violating phases. We compare our results with the ones obtained previously, and quantify the importance of the RG induced corrections to neutrino observables by means of numerical examples. In the second part of the paper, we study the correlation of the model’s predictions for the lepton flavour violating processes ℓ i → ℓ j γ with the measured neutrino mass squared differences and mixing angles. We also emphasize the rôle played by the unknown reactor neutrino mixing angle θ13 and the Dirac CP-violating phase δ. We point out that, if tan β is large, the results obtained in the commonly made approximations may deviate significantly from the ones following from solving numerically the relevant set of renormalisation group equations and using the exact one-loop formulae for the decay rates.


Rare Decays Neutrino Physics Supersymmetric Standard Model Renormalization Group 


  1. [1]
    P. Minkowski, μ → eγ at a Rate of One Out of 1-Billion Muon Decays?, Phys. Lett. B 67 (1977) 421 [SPIRES].ADSGoogle Scholar
  2. [2]
    M. Gell-Mann, P. Ramond and R. Slansky, Complex spinors and unified theories, in Supergravity, eds. P. Van Nieuwenhuizen and D. Freedman, North-Holland, Amsterdam The Neatherland (1979), pg. 315.Google Scholar
  3. [3]
    T. Yanagida, Horizontal gauge symmetry and masses of neutrinos, in Proceedings of the Baryon Number of the Universe and Unified Theoris, eds. O. Sawada and A. Sugamoto KEK, Tsukuba (1979), pg. 95.Google Scholar
  4. [4]
    S.L. Glashow, The future of elementary particle physics, NATO Adv. Study Inst. Ser. B Phys. 59 (1979) 687.Google Scholar
  5. [5]
    R.N. Mohapatra and G. Senjanovi´c, Neutrino mass and spontaneous parity nonconservation, Phys. Rev. Lett. 44 (1980) 912 [SPIRES].CrossRefADSGoogle Scholar
  6. [6]
    G. Altarelli and F. Feruglio, Theoretical models of neutrino masses and mixings, Springer Tracts Mod. Phys. 190 (2003) 169 [hep-ph/0206077] [SPIRES].Google Scholar
  7. [7]
    G. Altarelli and F. Feruglio, Models of neutrino masses and mixings, New J. Phys. 6 (2004) 106 [hep-ph/0405048] [SPIRES].CrossRefADSGoogle Scholar
  8. [8]
    R.N. Mohapatra and A.Y. Smirnov, Neutrino Mass and New Physics, Ann. Rev. Nucl. Part. Sci. 56 (2006) 569 [hep-ph/0603118] [SPIRES].CrossRefADSGoogle Scholar
  9. [9]
    M.C. Gonzalez-Garcia and M. Maltoni, Phenomenology with Massive Neutrinos, Phys. Rept. 460 (2008) 1 [arXiv:0704.1800] [SPIRES].CrossRefADSGoogle Scholar
  10. [10]
    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].CrossRefADSGoogle Scholar
  11. [11]
    P.H. Chankowski and S. Pokorski, Quantum corrections to neutrino masses and mixing angles, Int. J. Mod. Phys. A 17 (2002) 575 [hep-ph/0110249] [SPIRES].ADSGoogle Scholar
  12. [12]
    K.R.S. Balaji, A.S. Dighe, R.N. Mohapatra and M.K. Parida, Radiative magnification of neutrino mixings and a natural explanation of the neutrino anomalies, Phys. Lett. B 481 (2000) 33 [hep-ph/0002177] [SPIRES].ADSGoogle Scholar
  13. [13]
    R.N. Mohapatra, M.K. Parida and G. Rajasekaran, High scale mixing unification and large neutrino mixing angles, Phys. Rev. D 69 (2004) 053007 [hep-ph/0301234] [SPIRES].ADSGoogle Scholar
  14. [14]
    S. Antusch, J. Kersten, M. Lindner and M. Ratz, The LMA solution from bimaximal lepton mixing at the GUT scale by renormalization group running, Phys. Lett. B 544 (2002) 1 [hep-ph/0206078] [SPIRES].ADSGoogle Scholar
  15. [15]
    T. Miura, T. Shindou and E. Takasugi, The renormalization group effect to the bi-maximal mixing, Phys. Rev. D 68 (2003) 093009 [hep-ph/0308109] [SPIRES].ADSGoogle Scholar
  16. [16]
    Y. Farzan and M.E. Peskin, The contribution from neutrino Yukawa couplings to lepton electric dipole moments, Phys. Rev. D 70 (2004) 095001 [hep-ph/0405214] [SPIRES].ADSGoogle Scholar
  17. [17]
    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].CrossRefADSGoogle Scholar
  18. [18]
    J.-w. Mei, Running neutrino masses, leptonic mixing angles and CP- violating phases: From M(Z) to Lambda(GUT), Phys. Rev. D 71 (2005) 073012 [hep-ph/0502015] [SPIRES].ADSGoogle Scholar
  19. [19]
    R. Barbieri, D.V. Nanopoulos, G. Morchio and F. Strocchi, Neutrino Masses in Grand Unified Theories, Phys. Lett. B 90 (1980) 91 [SPIRES].ADSGoogle Scholar
  20. [20]
    T.P. Cheng and L.-F. Li, Neutrino Masses, Mixings and Oscillations in SU(2) × U(1) Models of Electroweak Interactions, Phys. Rev. D 22 (1980) 2860 [SPIRES].ADSGoogle Scholar
  21. [21]
    M. Magg and C. Wetterich, Neutrino mass problem and gauge hierarchy, Phys. Lett. B 94 (1980) 61 [SPIRES].ADSGoogle Scholar
  22. [22]
    J. Schechter and J.W.F. Valle, Neutrino Masses in SU(2) × U(1) Theories, Phys. Rev. D 22 (1980) 2227 [SPIRES].ADSGoogle Scholar
  23. [23]
    R.N. Mohapatra and G. Senjanović, Neutrino Masses and Mixings in Gauge Models with Spontaneous Parity Violation, Phys. Rev. D 23 (1981) 165 [SPIRES].ADSGoogle Scholar
  24. [24]
    G. Lazarides, Q. Shafi and C. Wetterich, Proton Lifetime and Fermion Masses in an SO(10) Model, Nucl. Phys. B 181 (1981) 287 [SPIRES].CrossRefADSGoogle Scholar
  25. [25]
    E. Ma and U. Sarkar, Neutrino masses and leptogenesis with heavy Higgs triplets, Phys. Rev. Lett. 80 (1998) 5716 [hep-ph/9802445] [SPIRES].CrossRefADSGoogle Scholar
  26. [26]
    W. Chao and H. Zhang, One-loop renormalization group equations of the neutrino mass matrix in the triplet seesaw model, Phys. Rev. D 75 (2007) 033003 [hep-ph/0611323] [SPIRES].ADSGoogle Scholar
  27. [27]
    M.A. Schmidt, Renormalization Group Evolution in the type-I + II seesaw model, Phys. Rev. D 76 (2007) 073010 [arXiv:0705.3841] [SPIRES].ADSGoogle Scholar
  28. [28]
    A. Rossi, Supersymmetric seesaw without singlet neutrinos: Neutrino masses and lepton-flavour violation, Phys. Rev. D 66 (2002) 075003 [hep-ph/0207006] [SPIRES].ADSGoogle Scholar
  29. [29]
    A. Rossi, Supersymmetric seesaw without singlet neutrinos: Neutrino masses and lepton-flavour violation, Phys. Rev. D 66 (2002) 075003 [hep-ph/0207006] [SPIRES].
  30. [30]
    F. Borzumati and A. Masiero, Large Muon and electron Number Violations in Supergravity Theories, Phys. Rev. Lett. 57 (1986) 961 [SPIRES].CrossRefADSGoogle Scholar
  31. [31]
    M. Raidal et al., Flavour physics of leptons and dipole moments, Eur. Phys. J. C 57 (2008) 13 [arXiv:0801.1826] [SPIRES].CrossRefADSGoogle Scholar
  32. [32]
    F.R. Joaquim and A. Rossi, Gauge and Yukawa mediated supersymmetry breaking in the triplet seesaw scenario, Phys. Rev. Lett. 97 (2006) 181801 [hep-ph/0604083] [SPIRES].CrossRefADSGoogle Scholar
  33. [33]
    F.R. Joaquim and A. Rossi, Phenomenology of the triplet seesaw mechanism with Gauge and Yukawa mediation of SUSY breaking, Nucl. Phys. B 765 (2007) 71 [hep-ph/0607298] [SPIRES].CrossRefADSGoogle Scholar
  34. [34]
    M. Hirsch, S. Kaneko and W. Porod, Supersymmetric seesaw type-II: LHC and lepton flavour violating phenomenology, Phys. Rev. D 78 (2008) 093004 [arXiv:0806.3361] [SPIRES].ADSGoogle Scholar
  35. [35]
    J.N. Esteves et al., Flavour violation at the LHC: type-I versus type-II seesaw in minimal supergravity, JHEP 05 (2009) 003 [arXiv:0903.1408] [SPIRES].CrossRefADSGoogle Scholar
  36. [36]
    L. Calibbi, M. Frigerio, S. Lavignac and A. Romanino, Flavour violation in supersymmetric SO(10) unification with a type-II seesaw mechanism, JHEP 12 (2009) 057 [arXiv:0910.0377] [SPIRES].CrossRefADSGoogle Scholar
  37. [37]
    S. Weinberg, Non-renormalization theorems in non-renormalizable theories, Phys. Rev. Lett. 80 (1998) 3702 [hep-th/9803099] [SPIRES].CrossRefADSGoogle Scholar
  38. [38]
    R. Barbieri, S. Ferrara, L. Maiani, F. Palumbo and C.A. Savoy, Quartic mass matrix and renormalization constants in supersymmetric Yang-Mills theories, Phys. Lett. B 115 (1982) 212 [SPIRES].ADSGoogle Scholar
  39. [39]
    N.K. Falck, Renormalization Group Equations for Softly Broken Supersymmetry: The Most General Case, Z. Phys. C 30 (1986) 247 [SPIRES].ADSGoogle Scholar
  40. [40]
    S.P. Martin and M.T. Vaughn, Two loop renormalization group equations for soft supersymmetry breaking couplings, Phys. Rev. D 50 (1994) 2282 [Erratum ibid. D 78 (2008) 039903] [hep-ph/9311340] [SPIRES].ADSGoogle Scholar
  41. [41]
    S. Weinberg, Baryon and Lepton Nonconserving Processes, Phys. Rev. Lett. 43 (1979) 1566 [SPIRES].CrossRefADSGoogle Scholar
  42. [42]
    J.A. Casas, J.R. Espinosa and I. Navarro, New supersymmetric source of neutrino masses and mixings, Phys. Rev. Lett. 89 (2002) 161801 [hep-ph/0206276] [SPIRES].CrossRefADSGoogle Scholar
  43. [43]
    J.A. Casas, J.R. Espinosa and I. Navarro, Large mixing angles for neutrinos from infrared fixed points, JHEP 09 (2003) 048 [hep-ph/0306243] [SPIRES].CrossRefADSGoogle Scholar
  44. [44]
    P.H. Chankowski and Z. Pluciennik, Renormalization group equations for seesaw neutrino masses, Phys. Lett. B 316 (1993) 312 [hep-ph/9306333] [SPIRES].ADSGoogle Scholar
  45. [45]
    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].ADSGoogle Scholar
  46. [46]
    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].ADSGoogle Scholar
  47. [47]
    K.S. Babu, Renormalization group analysis of the Kobayashi-Maskawa matrix, Z. Phys. C 35 (1987) 69 [SPIRES].ADSGoogle Scholar
  48. [48]
    P.H. Chankowski, W. Krolikowski and S. Pokorski, Fixed points in the evolution of neutrino mixings, Phys. Lett. B 473 (2000) 109 [hep-ph/9910231] [SPIRES].ADSGoogle Scholar
  49. [49]
    J.A. Casas, J.R. Espinosa, A. Ibarra and I. Navarro, General RG equations for physical neutrino parameters and their phenomenological implications, Nucl. Phys. B 573 (2000) 652 [hep-ph/9910420] [SPIRES].CrossRefADSGoogle Scholar
  50. [50]
    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] [SPIRES].CrossRefADSGoogle Scholar
  51. [51]
    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].CrossRefADSGoogle Scholar
  52. [52]
    BABAR collaboration, B. Aubert et al., Search for lepton flavor violation in the decay τ±e ±γ, Phys. Rev. Lett. 96 (2006) 041801 [hep-ex/0508012] [SPIRES].CrossRefADSGoogle Scholar
  53. [53]
    Belle collaboration, K. Hayasaka et al., New search for τ → μγ and τ → eγ decays at Belle, Phys. Lett. B 666 (2008) 16 [arXiv:0705.0650] [SPIRES].ADSGoogle Scholar
  54. [54]
    S. Banerjee, Searches for lepton flavor violating decays τ± → ℓ±γ, τ± → ℓ± P0 (where = e , μ and P0 = π0, η, η’) at B factories: status and combinations, Nucl. Phys. Proc. Suppl. 169 (2007) 199 [hep-ex/0702017] [SPIRES].CrossRefADSGoogle Scholar
  55. [55]
    W. Rodejohann, The see-saw mechanism: neutrino mixing, leptogenesis and lepton flavor violation, Pramana 72 (2009) 217 [arXiv:0804.3925] [SPIRES].CrossRefADSGoogle Scholar
  56. [56]
    F.R. Joaquim, Predictions for LjLi gamma in the SUSY triplet seesaw mechanism: Large tan beta effects, Nucl. Phys. Proc. Suppl. 188 (2009) 342 [SPIRES].CrossRefADSGoogle Scholar
  57. [57]
    S. Davidson, Parametrizations of the seesaw, or, can the seesaw be tested?, hep-ph/0409339 [SPIRES].
  58. [58]
    G.C. Branco et al., Minimal scenarios for leptogenesis and CP-violation, Phys. Rev. D 67 (2003) 073025 [hep-ph/0211001] [SPIRES].ADSGoogle Scholar
  59. [59]
    C. Hagedorn and W. Rodejohann, Minimal mass matrices for Dirac neutrinos, JHEP 07 (2005) 034 [hep-ph/0503143] [SPIRES].CrossRefADSGoogle Scholar
  60. [60]
    Y. Farzan and A.Y. Smirnov, Leptonic CP-violation: zero, maximal or between the two extremes, JHEP 01 (2007) 059 [hep-ph/0610337] [SPIRES].CrossRefADSGoogle Scholar
  61. [61]
    Daya-Bay collaboration, X. Guo et al., A precision measurement of the neutrino mixing angle θ13 using reactor antineutrinos at Daya Bay, hep-ex/0701029 [SPIRES].
  62. [62]
    Double CHOOZ collaboration, F. Ardellier et al., Double CHOOZ: A search for the neutrino mixing angle θ13, hep-ex/0606025 [SPIRES].
  63. [63]
    RENO collaboration, S.B. Kim, RENO: Reactor experiment for neutrino oscillation at Yonggwang, AIP Conf. Proc. 981 (2008) 205 [J. Phys. Conf. Ser. 120 (2008) 052025].CrossRefADSGoogle Scholar
  64. [64]
    J. Hisano, T. Moroi, K. Tobe and M. Yamaguchi, Lepton-Flavor Violation via Right-Handed Neutrino Yukawa Couplings in Supersymmetric Standard Model, Phys. Rev. D 53 (1996) 2442 [hep-ph/9510309] [SPIRES].ADSGoogle Scholar
  65. [65]
    Particle Data Group collaboration, C. Amsler et al., Review of particle physics, Phys. Lett. B 667 (2008) 1 [SPIRES].ADSGoogle Scholar
  66. [66]
    A. Brignole and A. Rossi, Anatomy and phenomenology of mu tau lepton flavour violation in the MSSM, Nucl. Phys. B 701 (2004) 3 [hep-ph/0404211] [SPIRES].CrossRefADSGoogle Scholar
  67. [67]
    SuperKEKB Physics Working Group collaboration, A.G. Akeroyd et al., Physics at super B factory, hep-ex/0406071 [SPIRES].
  68. [68]
    M. Bona et al., SuperB: A High-Luminosity Asymmetric e + e Super Flavor Factory. Conceptual Design Report, arXiv:0709.0451 [SPIRES].

Copyright information

© The Author(s) 2010

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  1. 1.CERN, Theory DivisionGeneva 23Switzerland

Personalised recommendations