Simultaneous extraction of the Fermi constant and PMNS matrix elements in the presence of a fourth generation

Article

Abstract

Several recent studies performed on constraints of a fourth generation of quarks and leptons suffer from the ad-hoc assumption that 3 × 3 unitarity holds for the first three generations in the neutrino sector. Only under this assumption is one able to determine the Fermi constant GF from the muon lifetime measurement with the claimed precision of GF = 1.16637(1) × 10−5 GeV−2. We study how well GF can be extracted within the framework of four generations from leptonic and radiative μ and τ decays, as well as from Kℓ3 decays and leptonic decays of charged pions, and we discuss the role of lepton universality tests in this context. In the combined fit to leptonic and radiative μ and τ decays, Kℓ3 decays and leptonic decays of charged pions we find a p-value of 2.6 % for the fourth generation matrix element |Ue4| = 0 of the neutrino mixing matrix. We emphasize that constraints on a fourth generation from quark and lepton flavour observables and from electroweak precision observables can only be obtained in a consistent way if these three sectors are considered simultaneously.

Keywords

Rare Decays Beyond Standard Model Neutrino Physics Kaon Physics 

References

  1. [1]
    A. Arhrib and W.S. Hou, Effect of fourth generation CP phase on bs transitions, Eur. Phys. J. C 27 (2003) 555 [hep-ph/0211267] [SPIRES].ADSGoogle Scholar
  2. [2]
    W.S. Hou, M. Nagashima and A. Soddu, Large Time-dependent CP Violation in B 0 s System and Finite \( {D^0} - {\bar{D}^0} \) Mass Difference in Four Generation Standard Model, Phys. Rev. D 76 (2007) 016004 [hep-ph/0610385] [SPIRES].ADSGoogle Scholar
  3. [3]
    W.-S. Hou, M. Nagashima and A. Soddu, Enhanced \( K(L) \to {\pi^0}\nu \overline \nu \) from direct CP-violation in BKπ with four generations, Phys. Rev. D 72 (2005) 115007 [hep-ph/0508237] [SPIRES].ADSGoogle Scholar
  4. [4]
    W.-S. Hou, H.-n. Li, S. Mishima and M. Nagashima, Fourth generation CP-violation effect on BKπ, φK and ρK in NLO PQCD, Phys. Rev. Lett. 98 (2007) 131801 [hep-ph/0611107] [SPIRES].CrossRefADSGoogle Scholar
  5. [5]
    A. Soni, A.K. Alok, A. Giri, R. Mohanta and S. Nandi, The Fourth family: A Natural explanation for the observed pattern of anomalies in B CP asymmetries, Phys. Lett. B 683 (2010) 302 [arXiv:0807.1971] [SPIRES].ADSGoogle Scholar
  6. [6]
    F.J. Botella, G.C. Branco and M. Nebot, Small violations of 3 × 3 unitarity, the phase in B0(S) - anti-B0(S) mixing and visible tcZ decays at the LHC, J. Phys. Conf. Ser. 171 (2009) 012058.CrossRefADSGoogle Scholar
  7. [7]
    M. Bobrowski, A. Lenz, J. Riedl and J. Rohrwild, How much space is left for a new family of fermions?, Phys. Rev. D 79 (2009) 113006 [arXiv:0902.4883] [SPIRES].ADSGoogle Scholar
  8. [8]
    A. Soni, A.K. Alok, A. Giri, R. Mohanta and S. Nandi, SM with four generations: Selected implications for rare B and K decays, 1002.0595 [SPIRES].
  9. [9]
    A.J. Buras et al., Patterns of Flavour Violation in the Presence of a Fourth Generation of Quarks and Leptons, 1002.2126 [SPIRES].
  10. [10]
    H.-J. He, N. Polonsky and S.-f. Su, Extra families, Higgs spectrum and oblique corrections, Phys. Rev. D 64 (2001) 053004 [hep-ph/0102144] [SPIRES].ADSGoogle Scholar
  11. [11]
    G.D. Kribs, T. Plehn, M. Spannowsky and T.M.P. Tait, Four generations and Higgs physics, Phys. Rev. D 76 (2007) 075016 [arXiv:0706.3718] [SPIRES].ADSGoogle Scholar
  12. [12]
    V.A. Novikov, L.B. Okun, A.N. Rozanov and M.I. Vysotsky, Mass of the Higgs versus fourth generation masses, JETP Lett. 76 (2002) 127 [hep-ph/0203132] [SPIRES].CrossRefADSGoogle Scholar
  13. [13]
    M.I. Vysotsky, Fourth quark-lepton generation and precision measurements, arXiv:0910.3100 [SPIRES].
  14. [14]
    M.S. Chanowitz, Bounding CKM Mixing with a Fourth Family, Phys. Rev. D 79 (2009) 113008 [arXiv:0904.3570] [SPIRES].ADSGoogle Scholar
  15. [15]
    N. Cabibbo, Unitary Symmetry and Leptonic Decays, Phys.Rev. Lett. 10 (1963) 531 [SPIRES].CrossRefADSGoogle Scholar
  16. [16]
    M. Kobayashi and T. Maskawa, CP Violation in the Renormalizable Theory of Weak Interaction, Prog. Theor. Phys. 49 (1973) 652 [SPIRES].CrossRefADSGoogle Scholar
  17. [17]
    W.-S. Hou, F.-F. Lee and C.-Y. Ma, Fourth Generation Leptons and Muon g - 2, Phys. Rev. D 79 (2009) 073002 [arXiv:0812.0064] [SPIRES].ADSGoogle Scholar
  18. [18]
    Z. Maki, M. Nakagawa and S. Sakata, Remarks on the unified model of elementary particles, Prog. Theor. Phys. 28 (1962) 870 [SPIRES].MATHCrossRefADSGoogle Scholar
  19. [19]
    B. Pontecorvo, Neutrino experiments and the question of leptonic-charge conservation, Zh. Eksp. Teor. Fiz. 53 (1967) 1717 [Sov. Phys. JETP 26 (1968) 984] [SPIRES].Google Scholar
  20. [20]
    ALEPH collaboration, Precision electroweak measurements on the Z resonance, Phys. Rept. 427 (2006) 257 [hep-ex/0509008] [SPIRES].ADSGoogle Scholar
  21. [21]
    The CKMfitter Group, J. Charles et al., CP violation and the CKM matrix: Assessing the impact of the asymmetric B factories, Eur. Phys. J. C 41 (2005) 1 [hep-ph/0406184] [SPIRES], updated at http://ckmfitter.in2p3.fr/.CrossRefADSGoogle Scholar
  22. [22]
    The CKMfitter Group, A. Höcker et al., A New Approach to a Global Fit of the CKM Matrix, Eur. Phys. J. C 21 (2001) 225 [hep-ph/0104062] [SPIRES].CrossRefGoogle Scholar
  23. [23]
    B.W. Lee and R.E. Shrock, Natural Suppression of Symmetry Violation in Gauge Theories: Muon - Lepton and Electron Lepton Number Nonconservation, Phys. Rev. D 16 (1977) 1444 [SPIRES].ADSGoogle Scholar
  24. [24]
    R.E. Shrock and L.L. Wang, New, Generalized Cabibbo Fit and Application to Quark Mixing Angles in the Sequential Weinberg-Salam Model, Phys. Rev. Lett. 41 (1978) 1692.CrossRefADSGoogle Scholar
  25. [25]
    R.E. Shrock, S.B. Treiman and L.-L. Wang, Bounds on Quark Mixing Angles in the Standard Six Quark Model, Phys. Rev. Lett. 42 (1979) 1589 [SPIRES].CrossRefADSGoogle Scholar
  26. [26]
    R.E. Shrock, General Theory of Weak Leptonic and Semileptonic Decays. 1. Leptonic Pseudoscalar Meson Decays, with Associated Tests For and Bounds on, Neutrino Masses and Lepton Mixing, Phys. Rev. D 24 (1981) 1232 [SPIRES].ADSGoogle Scholar
  27. [27]
    R.E. Shrock, General Theory of Weak Processes Involving Neutrinos. 2. Pure Leptonic Decays, Phys. Rev. D 24 (1981) 1275 [SPIRES].ADSGoogle Scholar
  28. [28]
    T. Appelquist, M. Piai and R. Shrock, Fermion masses and mixing in extended technicolor models, Phys. Rev. D 69 (2004) 015002 [hep-ph/0308061] [SPIRES].ADSGoogle Scholar
  29. [29]
    P. Langacker and D. London, Lepton Number Violation and Massless Nonorthogonal Neutrinos, Phys. Rev. D 38 (1988) 907 [SPIRES].ADSGoogle Scholar
  30. [30]
    D. Tommasini, G. Barenboim, J. Bernabeu and C. Jarlskog, Non-decoupling of Heavy Neutrinos and Lepton Flavour Violation, Nucl. Phys. B 444 (1995) 451 [hep-ph/9503228] [SPIRES].CrossRefADSGoogle Scholar
  31. [31]
    S. Antusch, C. Biggio, E. Fernandez-Martinez, M.B. Gavela and J. Lopez-Pavon, Unitarity of the Leptonic Mixing Matrix, JHEP 10 (2006) 084 [hep-ph/0607020] [SPIRES].CrossRefADSGoogle Scholar
  32. [32]
    S. Antusch, J.P. Baumann and E. Fernandez-Martinez, Non-Standard Neutrino Interactions with Matter from Physics Beyond the Standard Model, Nucl. Phys. B 810 (2009) 369 [arXiv:0807.1003] [SPIRES].CrossRefADSGoogle Scholar
  33. [33]
    E. Fernandez-Martinez, M.B. Gavela, J. Lopez-Pavon and O. Yasuda, CP-violation from non-unitary leptonic mixing, Phys. Lett. B 649 (2007) 427 [hep-ph/0703098] [SPIRES].ADSGoogle Scholar
  34. [34]
    S. Antusch, M. Blennow, E. Fernandez-Martinez and J. Lopez-Pavon, Probing non-unitary mixing and CP-violation at a Neutrino Factory, Phys. Rev. D 80 (2009) 033002 [arXiv:0903.3986] [SPIRES].ADSGoogle Scholar
  35. [35]
    F.J. Botella and L.-L. Chau, Anticipating the Higher Generations of Quarks from Rephasing Invariance of the Mixing Matrix, Phys. Lett. B 168 (1986) 97 [SPIRES].ADSGoogle Scholar
  36. [36]
    T. Kinoshita and A. Sirlin, Radiative corrections toFermi interactions, Phys. Rev. 113 (1959) 1652 [SPIRES].CrossRefADSGoogle Scholar
  37. [37]
    A. Sirlin, Current Algebra Formulation of Radiative Corrections in Gauge Theories and the Universality of the Weak Interactions, Rev. Mod. Phys. 50 (1978) 573 [Erratum ibid. 50 (1978) 905] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  38. [38]
    W.J. Marciano and A. Sirlin, Electroweak radiative corrections to τ decay, Phys. Rev. 61 (1988) 1815.ADSGoogle Scholar
  39. [39]
    T. van Ritbergen and R.G. Stuart, Complete 2-loop quantum electrodynamic contributions to the muon lifetime in theFermi model, Phys. Rev. Lett. 82 (1999) 488 [hep-ph/9808283] [SPIRES].CrossRefADSGoogle Scholar
  40. [40]
    MuLan collaboration, D.B. Chitwood et al., Improved Measurement of the Positive Muon Lifetime and Determination of theFermi Constant, Phys. Rev. Lett. 99 (2007) 032001 [arXiv:0704.1981] [SPIRES].CrossRefADSGoogle Scholar
  41. [41]
    FAST collaboration, A. Barczyk et al., Measurement of theFermi Constant by FAST, Phys. Lett. B 663 (2008) 172 [arXiv:0707.3904] [SPIRES].ADSGoogle Scholar
  42. [42]
    Particle Data Group, C. Amsler et al., Review of particle physics, Phys. Lett. B 667 (2008) 1 [SPIRES] and 2009 partial update for the 2010 edition Review of particle physics.ADSGoogle Scholar
  43. [43]
    T. Sjostrand, Function ”ULALEM(Q2)”, taken from JETSET74, CERN (1993).Google Scholar
  44. [44]
    BABAR collaboration, B. Aubert et al., Measurements of Charged Current Lepton Universality and |V us| using Tau Lepton Decays to \( {e^{-} }{\overline \nu_e}{\nu_\tau },\,{\mu^{-} }\overline \nu \mu {\nu_\tau } \) and K ντ, arXiv:0912.0242 [SPIRES].
  45. [45]
    G. Altarelli, L. Baulieu, N. Cabibbo, L. Maiani and R. Petronzio, Muon Number Nonconserving Processes in Gauge Theories of Weak Interactions, Nucl. Phys. B 125 (1977) 285 [SPIRES].CrossRefADSGoogle Scholar
  46. [46]
    L3 collaboration, P. Achard et al., Search for heavy neutral and charged leptons in e + e annihilation at LEP, Phys. Lett. B 517 (2001) 75 [hep-ex/0107015] [SPIRES].ADSGoogle Scholar
  47. [47]
    MEGA collaboration, M.L. Brooks et al., New Limit for the Family-Number Non-conserving Decay mu+ → e+γ, Phys. Rev. Lett. 83 (1999) 1521 [hep-ex/9905013] [SPIRES].CrossRefADSGoogle Scholar
  48. [48]
    BABAR collaboration, B. Aubert et al., Searches for Lepton Flavor Violation in the Decays τ → eγ and τ → μγ, Phys. Rev. Lett. 104 (2010) 021802 [arXiv:0908.2381] [SPIRES].CrossRefADSGoogle Scholar
  49. [49]
    E. Goudzovski and T. Spadaro, Prospects for lepton universality test with K e2/K μ2, talk at the NA62 Physics Handbook Workshop, CERN, 11 December 2009.Google Scholar
  50. [50]
    V. Cirigliano and I. Rosell, π/K → eν branching ratios to O(e 2 p 4) in Chiral Perturbation Theory, JHEP 10 (2007) 005 [arXiv:0707.4464] [SPIRES].CrossRefADSGoogle Scholar
  51. [51]
    FlaviaNet Working Group on Kaon Decays collaboration, M. Antonelli et al., Precision tests of the Standard Model with leptonic and semileptonic kaon decays, arXiv:0801.1817 [SPIRES].
  52. [52]
    E. Blucher et al., Status of the Cabibbo angle, hep-ph/0512039 [SPIRES].
  53. [53]
    A. Sirlin, Large m(W),m(Z) Behavior of the O(α) Corrections to Semileptonic Processes Mediated by W, Nucl. Phys. B 196 (1982) 83 [SPIRES].CrossRefADSGoogle Scholar
  54. [54]
    V. Cirigliano, H. Neufeld and H. Pichl, K e3 decays and CKM unitarity, Eur. Phys. J. C 35 (2004) 53 [hep-ph/0401173] [SPIRES].ADSGoogle Scholar
  55. [55]
    V. Cirigliano, M. Knecht, H. Neufeld, H. Rupertsberger and P. Talavera, Radiative corrections to K l3 decays, Eur. Phys. J. C 23 (2002) 121 [hep-ph/0110153] [SPIRES].ADSGoogle Scholar
  56. [56]
    T.C. Andre, Radiative corrections to K0(l3) decays, Annals Phys. 322 (2007) 2518 [hep-ph/0406006] [SPIRES].MATHCrossRefADSGoogle Scholar
  57. [57]
    V. Cirigliano, M. Giannotti and H. Neufeld, Electromagnetic effects in Kl3 decays, JHEP 11 (2008) 006 [arXiv:0807.4507] [SPIRES].CrossRefADSGoogle Scholar
  58. [58]
    G. Czapek et al., Branching ratio for the rare pion decay into positron and neutrino, Phys. Rev. Lett. 70 (1993) 17 [SPIRES].CrossRefADSGoogle Scholar
  59. [59]
    D.I. Britton et al., Measurement of the π+e +ν branching ratio, Phys. Rev. Lett. 68 (1992) 3000 [SPIRES].CrossRefADSGoogle Scholar
  60. [60]
    D.I. Britton et al., Measurement of the π+e + neutrino branching ratio, Phys. Rev. D 49 (1994) 28 [SPIRES].ADSGoogle Scholar
  61. [61]
    D.A. Bryman et al., Measurement of the π → electron-neutrino branching ratio, Phys. Rev. D 33 (1986) 1211 [SPIRES].ADSGoogle Scholar
  62. [62]
    D.A. Bryman et al., New Measurement of the π → e neutrino branching ratio, Phys. Rev. Lett. 50 (1983) 7 [SPIRES].CrossRefADSGoogle Scholar
  63. [63]
    M. Finkemeier, Radiative corrections to π(l2) and K(l2) decays, Phys. Lett. B 387 (1996) 391 [hep-ph/9505434] [SPIRES].ADSGoogle Scholar
  64. [64]
    J.C. Hardy and I.S. Towner, Superallowed 0+ → 0+ nuclear beta decays: A new survey with precision tests of the conserved vector current hypothesis and the standard model, Phys. Rev. C 79 (2009) 055502 [arXiv:0812.1202] [SPIRES].ADSGoogle Scholar
  65. [65]
    H. Abramowicz et al., Experimental Study of Opposite Sign Dimuons Produced in Neutrino and anti-neutrinos Interactions, Z. Phys. C 15 (1982) 19 [SPIRES].ADSGoogle Scholar
  66. [66]
    CCFR collaboration, A.O. Bazarko et al., Determination of the strange quark content of the nucleon from a next-to-leading order QCD analysis of neutrino charm production, Z. Phys. C 65 (1995) 189 [hep-ex/9406007] [SPIRES].ADSGoogle Scholar
  67. [67]
    CHARM II collaboration, P. Vilain et al., Leading order QCD analysis of neutrino induced dimuon events, Eur. Phys. J. C 11 (1999) 19 [SPIRES=].CrossRefADSGoogle Scholar
  68. [68]
    T. Bolton, Determining the CKM parameter |V cd| from νN charm production, hep-ex/9708014 [SPIRES].
  69. [69]
    Fermilab E531 collaboration, N. Ushida et al., Cross-Sections For Neutrino Production Of Charmed Particles, Phys. Lett. B 206 (1988) 375 [SPIRES].
  70. [70]
    CLEO collaboration, Y. Kubota et al., Measurements of the inclusive semielectronic D0 branching fraction, Phys. Rev. D 54 (1996) 2994 [hep-ex/9511014] [SPIRES].Google Scholar
  71. [71]
    M.T. Dova, J. Swain and L. Taylor, Constraints on anomalous charged current couplings, τ- neutrino mass and fourth generation mixing from τ leptonic branching fractions, Nucl. Phys. Proc. Suppl. 76 (1999) 133 [hep-ph/9811209] [SPIRES].CrossRefADSGoogle Scholar
  72. [72]
    J. Swain and L. Taylor, Constraints on the τ neutrino mass and mixing from precise measurements of τ decay rates, Phys. Rev. D 55 (1997) 1 [hep-ph/9610242] [SPIRES].ADSGoogle Scholar
  73. [73]
    J. Swain and L. Taylor, New constraints on the τ neutrino mass and fourth generation mixing, hep-ph/9712383 [SPIRES].
  74. [74]
    M. Breskvar, D. Lukman and N.S. Mankoc Borstnik, On the origin of families of fermions and their mass matrices: Approximate analyses of properties of four families within approach unifying spins and charges, hep-ph/0606159 [SPIRES].
  75. [75]
    S. Weinberg, The Problem of Mass, Ann. N.Y. Acad. Sci. 38 (1977) 185.Google Scholar
  76. [76]
    H. Fritzsch, Quark Masses and Flavor Mixing, Nucl. Phys. B 155 (1979) 189 [SPIRES].CrossRefADSGoogle Scholar
  77. [77]
    H. Fritzsch, Hierarchical Chiral Symmetries and the Quark Mass Matrix, Phys. Lett. B 184 (1987) 391 [SPIRES].ADSGoogle Scholar
  78. [78]
    P. H. Frampton, P. Q. Hung and M. Sher, Quarks and leptons beyond the third generation, Phys. Rept. 330 (2000) 263 [hep-ph/9903387] [SPIRES].CrossRefADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  1. 1.Humboldt-Universität zu BerlinInstitut für PhysikBerlinGermany

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