Measuring Vub and probing SUSY with double ratios of purely leptonic decays of B and D mesons

Open Access


The experimental prospects for precise measurements of the leptonic decays Bu→τνν, Bsμ+μ, Dμν and Dsμν/τν are very promising. Double ratios involving four of these decays can be defined in which the dependence on the values of the decay constants is essentially eliminated, thus enabling complementary measurements of the CKM matrix element Vub with a small theoretical error. We quantify the experimental error in a possible future measurement of ∣Vub∣ using this approach, and show that it is competitive with the anticipated precision from the conventional approaches. Moreover, it is shown that such double ratios can be more effective than the individual leptonic decays as a probe of the parameter space of supersymmetric models. We emphasize that the double ratios have the advantage of using ∣Vub∣ as an input parameter (for which there is experimental information), while the individual decays have an uncertainty from the decay constants (e.g. \( {f_{{B_s}}} \)), and hence a reliance on theoretical techniques such as lattice QCD.


B-Physics Supersymmetric Standard Model Beyond Standard Model 


  1. [1]
    N. Cabibbo, Unitary Symmetry and Leptonic Decays, Phys. Rev. Lett. 10 (1963) 531 [SPIRES].CrossRefADSGoogle Scholar
  2. [2]
    M. Kobayashi and T. Maskawa, CP Violation in the Renormalizable Theory of Weak Interaction, Prog. Theor. Phys. 49 (1973) 652 [SPIRES].CrossRefADSGoogle Scholar
  3. [3]
    L. Wolfenstein, Parametrization of the Kobayashi-Maskawa Matrix, Phys. Rev. Lett. 51 (1983) 1945 [SPIRES].CrossRefADSGoogle Scholar
  4. [4]
    R. Kowalewski and T. Mannel, Determination of V cb and V ub Review of particle physics, in Review of Particle Physics, Phys. Lett. B 667 (2008) 1 [SPIRES].ADSGoogle Scholar
  5. [5]
    B. Grinstein, On a precise calculation of \( {{{\left( {{{{{f_{{B_s}}}}} \left/ {{{f_B}}} \right.}} \right)}} \left/ {{\left( {{{{{f_{{D_s}}}}} \left/ {{{f_D}}} \right.}} \right)}} \right.} \) and its implications on the interpretation of \( B - \overline B \) mixing, Phys. Rev. Lett. 71 (1993) 3067 [hep-ph/9308226] [SPIRES].CrossRefADSGoogle Scholar
  6. [6]
    Z. Ligeti and M.B. Wise, ∣V ubfrom exclusive B and D decays, Phys. Rev. D 53 (1996) 4937 [hep-ph/9512225] [SPIRES].ADSGoogle Scholar
  7. [7]
    Z. Ligeti, ∣V (cb)∣ andV (ub)∣: Theoretical developments, in the proceedings of Flavor Physics and CP Violation (FPCP 2003), Paris France, 3–6 Jun 2003 [hep-ph/0309219] [SPIRES].
  8. [8]
    A. Hocker and Z. Ligeti, CP violation and the CKM matrix, Ann. Rev. Nucl. Part. Sci. 56 (2006) 501 [hep-ph/0605217] [SPIRES].CrossRefADSGoogle Scholar
  9. [9]
    B. Grinstein, Heavy Flavor Theory, arXiv:0910.2422 [SPIRES].
  10. [10]
    Belle collaboration, K. Ikado et al., Evidence of the purely leptonic decay \( {B^{-} } \to {\tau^{-} }{\overline \nu_\tau } \), Phys. Rev. Lett. 97 (2006) 251802 [hep-ex/0604018] [SPIRES].CrossRefADSGoogle Scholar
  11. [11]
    Belle collaboration, I. Adachi et al., Measurement of \( {B^{-} } \to {\tau^{-} }{\overline \nu_\tau } \) Decay With a Semileptonic Tagging Method, arXiv:0809.3834 [SPIRES].
  12. [12]
    Belle collaboration, K. Hara et al., Evidence for \( {B^{-} } \to {\tau^{-} }\overline \nu \) with a Semileptonic Tagging Method, arXiv:1006.4201 [SPIRES].
  13. [13]
    BABAR collaboration, B. Aubert et al., A Search for B +→ τ+ν, Phys. Rev. D 76 (2007) 052002 [arXiv:0705.1820] [SPIRES].ADSGoogle Scholar
  14. [14]
    BABAR collaboration, B. Aubert et al., A Search for B +→τ+ν with Hadronic B tags, Phys. Rev. D 77 (2008) 011107 [arXiv:0708.2260] [SPIRES].ADSGoogle Scholar
  15. [15]
    M. Yamauchi, Super KEKB, a high luminosity upgrade of KEKB, Nucl. Phys. Proc. Suppl. 111 (2002) 96 [SPIRES].CrossRefADSGoogle Scholar
  16. [16]
    I.I. Bigi and A.I. Sanda, Is super-B sufficiently superb? On the motivation for a super-B factory, hep-ph/0401003 [SPIRES].
  17. [17]
    S. Hashimoto et. al., Letter of intent for KEK Super B Factory, KEK-Report-2004-4.Google Scholar
  18. [18]
    SuperKEKB Physics Working Group collaboration, A.G. Akeroyd et al., Physics at super B factory, hep-ex/0406071 [SPIRES].
  19. [19]
    T. Aushev et al., Physics at Super B Factory, arXiv:1002.5012 [SPIRES].
  20. [20]
    T.E. Browder and A. Soni, Search for new physics at a super-B factory, Pramana 63 (2004) 1171 [hep-ph/0410192] [SPIRES].CrossRefADSGoogle Scholar
  21. [21]
    J.L. Hewett, (ed.) et al., The Discovery potential of a Super B Factory. Proceedings, SLAC W orkshops, Stanford, USA, 2003, hep-ph/0503261 [SPIRES].
  22. [22]
    M. Bona et al., SuperB: A High-Luminosity Asymmetric e + e Super Flavor Factory. Conceptual Design Report, arXiv:0709.0451 [SPIRES].
  23. [23]
    T. Browder et al., On the Physics Case of a Super Flavour Factory, JHEP 02 (2008) 110 [arXiv:0710.3799] [SPIRES].CrossRefADSGoogle Scholar
  24. [24]
    T.E. Browder, T. Gershon, D. Pirjol, A. Soni and J. Zupan, New Physics at a Super Flavor Factory, Rev. Mod. Phys. 81 (2009) 1887 [arXiv:0802.3201] [SPIRES].CrossRefADSGoogle Scholar
  25. [25]
    C. Bernard et al., B and D Meson Decay Constants, PoS(LATTICE2008)278 [arXiv:0904.1895] [SPIRES].
  26. [26]
    HPQCD collaboration, E. Gamiz, C.T.H. Davies, G.P. Lepage, J. Shigemitsu and M. Wingate, Neutral B Meson Mixing in Unquenched Lattice QCD, Phys. Rev. D 80 (2009) 014503 [arXiv:0902.1815] [SPIRES].ADSGoogle Scholar
  27. [27]
    J. Laiho, E. Lunghi and R.S. Van de Water, Lattice QCD inputs to the CKM unitarity triangle analysis, Phys. Rev. D 81 (2010) 034503 [arXiv:0910.2928] [SPIRES].ADSGoogle Scholar
  28. [28]
    S.S. Gershtein and M.Y. Khlopov, SU(4) Symmetry Breaking and Lepton Decays of Heavy Pseudoscalar Mesons, JETP Lett. 23 (1976) 338 [SPIRES].ADSGoogle Scholar
  29. [29]
    CLEO collaboration, B.I. Eisenstein et al., Precision Measurement of B (D +μ +ν) and the Pseudoscalar Decay Constant f D+, Phys. Rev. D 78 (2008) 052003 [arXiv:0806.2112] [SPIRES].ADSGoogle Scholar
  30. [30]
    CLEO collaboration, J.P. Alexander et al., Measurement of B (D s+→ℓ+ν) and the Decay Constant \( f_{{D_s}}^{+} \) From 600 pb −1 of e ± Annihilation Data Near 4170 MeV, Phys. Rev. D 79 (2009) 052001 [arXiv:0901.1216] [SPIRES].ADSGoogle Scholar
  31. [31]
    Belle collaboration, K. Abe et al., Measurement of B (D sμν), Phys. Rev. Lett. 100 (2008) 241801 [arXiv:0709.1340] [SPIRES].CrossRefGoogle Scholar
  32. [32]
    BABAR collaboration, B. Aubert et al., Measurement of the pseudoscalar decay constant \( {f_{{D_s}}} \) using charm-tagged events in e + e collisions at \( \sqrt {s} = 10.58\,GeV \), Phys. Rev. Lett. 98 (2007) 141801 [hep-ex/0607094] [SPIRES].CrossRefADSGoogle Scholar
  33. [33]
    CLEO collaboration, P.U.E. Onyisi et al., Improved Measurement of Absolute Branching Fraction of D s→τν, Phys. Rev. D 79 (2009) 052002 [arXiv:0901.1147] [SPIRES].ADSGoogle Scholar
  34. [34]
    CLEO collaboration, P. Naik et al., Measurement of the Pseudoscalar Decay Constant \( {f_{{D_s}}} \) Using \( D_s^{+} \to {\tau^{+} }\nu, \,{\tau^{+} } \to {\rho^{+} }\overline \nu \) Decays, Phys. Rev. D 80 (2009) 112004 [arXiv:0910.3602] [SPIRES].ADSGoogle Scholar
  35. [35]
    The BABAR collaboration, J.P. Lees et al., Measurement of the Branching Fraction for D + s→τ+ντ and Extraction of the Decay Constant \( {f_{{D_s}}} \), arXiv:1003.3063 [SPIRES].
  36. [36]
    H.-B. Li and J.-H. Zou, A possible signature of new physics at BES-III, Chin. Phys. C 33 (2009) 1 [arXiv:0804.1822] [SPIRES].ADSGoogle Scholar
  37. [37]
    D.M. Asner et al., Physics at BES-III, arXiv:0809.1869 [SPIRES].
  38. [38]
    CDF collaboration, Search for B s0μ + μ and B d0μ + μ Decays in 3.7 fb −1 of \( p \bar{p} \) collisions with CDF II, CDF Public Note 9892.Google Scholar
  39. [39]
    W.-S. Hou, Enhanced charged Higgs boson effects in \( {B^{-} } \to \tau \overline \nu \) , \( \mu \overline \nu \) and \( b \to \tau \overline \nu + X \), Phys. Rev. D 48 (1993) 2342 [SPIRES].ADSGoogle Scholar
  40. [40]
    D. Eriksson, F. Mahmoudi and O. Stal, Charged Higgs bosons in Minimal Supersymmetry: Updated constraints and experimental prospects, JHEP 11 (2008) 035 [arXiv:0808.3551] [SPIRES]. CrossRefADSGoogle Scholar
  41. [41]
    J.L. Hewett, Searching for new physics with charm, hep-ph/9505246 [SPIRES].
  42. [42]
    A.G. Akeroyd, Effect of H ± on D sμ ±νμ and D sτ±→ντ, Prog. Theor. Phys. 111 (2004) 295 [hep-ph/0308260] [SPIRES].CrossRefADSGoogle Scholar
  43. [43]
    A.G. Akeroyd and C.H. Chen, Effect of H ± on B ±→τ±ντ and D ± sμ ±νμ , τ±ντ, Phys. Rev. D 75 (2007) 075004 [hep-ph/0701078] [SPIRES].ADSGoogle Scholar
  44. [44]
    A.G. Akeroyd and F. Mahmoudi, Constraints on charged Higgs bosons from D sμ ±ν and D s→τ±ν, JHEP 04 (2009) 121 [arXiv:0902.2393] [SPIRES].CrossRefADSGoogle Scholar
  45. [45]
    S.R. Choudhury and N. Gaur, Dileptonic decay of B smeson in SUSY models with large tan β, Phys. Lett. B 451 (1999) 86 [hep-ph/9810307] [SPIRES].ADSGoogle Scholar
  46. [46]
    K.S. Babu and C.F. Kolda, Higgs mediated B 0μ + μ in minimal supersymmetry, Phys. Rev. Lett. 84 (2000) 228 [hep-ph/9909476] [SPIRES].CrossRefADSGoogle Scholar
  47. [47]
    M. Neubert, QCD based interpretation of the lepton spectrum in inclusive \( \overline B \to X(u) \) lepton anti-neutrino decays, Phys. Rev. D 49 (1994) 3392 [hep-ph/9311325] [SPIRES].ADSGoogle Scholar
  48. [48]
    Belle collaboration, P. Urquijo et al., Measurement OfV ubFrom Inclusive Charmless Semileptonic B Decays, Phys. Rev. Lett. 104 (2010) 021801 [arXiv:0907.0379] [SPIRES].CrossRefADSGoogle Scholar
  49. [49]
    B. Kowalewski, Measurement ofV cbandV ub∣, talk at Flavor Physics and CP V iolation 2010, Torino, Italy, May 25-29.Google Scholar
  50. [50]
    Belle collaboration, T. Hokuue et al., Measurements of branching fractions and q 2 distributions for B→πℓν and B→ρℓν Decays with BD (∗)ℓν Decay Tagging, Phys. Lett. B 648 (2007) 139 [hep-ex/0604024] [SPIRES].ADSGoogle Scholar
  51. [51]
    BABAR collaboration, P. del Amo Sanchez et al., Study of B→πℓν and B→ρℓν Decays and Determination ofVub∣, arXiv:1005.3288 [SPIRES].
  52. [52]
    CKMfitter Group collaboration, 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, updated results and plots available at: [hep-ph/0406184] [SPIRES].CrossRefADSGoogle Scholar
  53. [53]
    UTfit collaboration, M. Bona et al., An Improved Standard Model Prediction Of BR(B→τν) And Its Implications For New Physics, Phys. Lett. B 687 (2010) 61 [arXiv:0908.3470] [SPIRES].ADSGoogle Scholar
  54. [54]
    R.J. Oakes, Ratios of charmed and beauty meson decay constants, Phys. Rev. Lett. 73 (1994) 381 [SPIRES].CrossRefADSGoogle Scholar
  55. [55]
    D.S. Hwang and G.-H. Kim, Ratios of B and D meson decay constants in relativistic quark model, Phys. Rev. D 53 (1996) 3659 [hep-ph/9507340] [SPIRES].ADSGoogle Scholar
  56. [56]
    D.S. Hwang and G.-H. Kim, Ratios of B and D Meson Decay Constants in Improved Mock Meson Model, Phys. Lett. B 367 (1996) 353 [hep-ph/9509291] [SPIRES].ADSGoogle Scholar
  57. [57]
    T. Huang, Z.-H. Li and C.-W. Luo, QCD Sum Rules for The Double Ratio \( {{{\left( {{{{{f_{{B_s}}}}} \left/ {{{f_{{B_d}}}}} \right.}} \right)}} \left/ {{\left( {{{{{f_{{D_s}}}}} \left/ {{{f_{{D_d}}}}} \right.}} \right)}} \right.} \) in HQET, Phys. Lett. B 391 (1997) 451 [hep-ph/9610227] [SPIRES].ADSGoogle Scholar
  58. [58]
    BESIII collaboration, P. Zweber, Charm Factories: Present and Future, AIP Conf. Proc. 1182 (2009) 406 [arXiv:0908.2157] [SPIRES].CrossRefADSGoogle Scholar
  59. [59]
    A.G. Akeroyd and S. Recksiegel, The effect of H ± on B ±→τ±ντ and B ±μ ±ν, J. Phys. G 29 (2003) 2311 [hep-ph/0306037] [SPIRES].ADSGoogle Scholar
  60. [60]
    H. Itoh, S. Komine and Y. Okada, Tauonic B decays in the minimal supersymmetric standard model, Prog. T heor. Phys. 114 (2005) 179 [hep-ph/0409228] [SPIRES].CrossRefADSMATHGoogle Scholar
  61. [61]
    G. Isidori and P. Paradisi, Hints of large tan β in flavour physics, Phys. Lett. B 639 (2006) 499 [hep-ph/0605012] [SPIRES].ADSGoogle Scholar
  62. [62]
    L.J. Hall, R. Rattazzi and U. Sarid, The Top quark mass in supersymmetric SO(10) unification, Phys. Rev. D 50 (1994) 7048 [hep-ph/9306309] [SPIRES].ADSGoogle Scholar
  63. [63]
    R. Hempfling, Yukawa coupling unification with supersymmetric threshold corrections, Phys. Rev. D 49 (1994) 6168 [SPIRES].ADSGoogle Scholar
  64. [64]
    M.S. Carena, M. Olechowski, S. Pokorski and C.E.M. Wagner, Electroweak symmetry breaking and bottom -top Yukawa unification, Nucl. Phys. B 426 (1994) 269 [hep-ph/9402253] [SPIRES].CrossRefADSGoogle Scholar
  65. [65]
    T. Blazek, S. Raby and S. Pokorski, Finite supersymmetric threshold corrections to CKM matrix elements in the large tan β regime, Phys. Rev. D 52 (1995) 4151 [hep-ph/9504364] [SPIRES].ADSGoogle Scholar
  66. [66]
    F. Mahmoudi, SuperIso: A program for calculating the isospin asymmetry of BK γ in the MSSM, Comput. Phys. Commun. 178 (2008) 745 [arXiv:0710.2067] [SPIRES].CrossRefADSGoogle Scholar
  67. [67]
    F. Mahmoudi, SuperIso v2.3: A Program for calculating flavor physics observables in Supersymmetry, Comput. Phys. Commun. 180 (2009) 1579 [arXiv:0808.3144] [SPIRES].CrossRefADSGoogle Scholar
  68. [68]
    Heavy Flavor Averaging Group collaboration, E. Barberio et al., Averages of b-hadron and c-hadron Properties at the End of 2007, arXiv:0808.1297 [SPIRES].
  69. [69]
    B.A. Dobrescu and A.S. Kronfeld, Accumulating evidence for nonstandard leptonic decays of D s mesons, Phys. Rev. Lett. 100 (2008) 241802 [arXiv:0803.0512] [SPIRES].CrossRefADSGoogle Scholar
  70. [70]
    C.T.H. Davies et al., Precise Charm to Strange Mass Ratio and Light Quark Masses from Full Lattice QCD, Phys. Rev. Lett. 104 (2010) 132003 [arXiv:0910.3102] [SPIRES].CrossRefADSGoogle Scholar
  71. [71]
    J.L. Rosner and S. Stone, Leptonic Decays of Charged Pseudoscalar Mesons, arXiv:1002.1655 [SPIRES].
  72. [72]
    HPQCD collaboration, E. Follana, C.T.H. Davies, G.P. Lepage and J. Shigemitsu, High Precision determination of the π,K,D and D s decay constants from lattice QCD, Phys. Rev. Lett. 100 (2008) 062002 [arXiv:0706.1726] [SPIRES].CrossRefADSGoogle Scholar
  73. [73]
    C.T.H. Davies et al., Update: Precision D s decay constant from full lattice QCD using very fine lattices, arXiv:1008.4018 [SPIRES].
  74. [74]
    C. Aubin et al., Charmed meson decay constants in three-flavor lattice QCD, Phys. Rev. Lett. 95 (2005) 122002 [hep-lat/0506030] [SPIRES].CrossRefADSGoogle Scholar
  75. [75]
    Fermilab Lattice and MILC collaboration, A. Bazavov et al., The Dsand D + Leptonic Decay Constants from Lattice QCD, PoS(LAT2009)249 [arXiv:0912.5221] [SPIRES].
  76. [76]
    B. Blossier et al., Pseudoscalar decay constants of kaon and D-mesons from N f=2 twisted mass Lattice QCD, JHEP 07 (2009) 043 [arXiv:0904.0954] [SPIRES].Google Scholar
  77. [77]
    A.J. Schwartz, B + and D s+ Decay Constants from Belle and Babar, AIP Conf. Proc. 1182 (2009) 299 [arXiv:0909.4473] [SPIRES].CrossRefADSGoogle Scholar
  78. [78]
    BaBar collaboration, P. del Amo Sanchez et al., Measurement of the Absolute Branching Fractions for \( D_s^{-} \to {\ell^{-} }\overline \nu \ell \) and Extraction of the Decay Constant \( {f_{{D_s}}} \), arXiv:1008.4080 [SPIRES].
  79. [79]
    M.S. Carena, A. Menon, R. Noriega-Papaqui, A. Szynkman and C.E.M. Wagner, Constraints on B and Higgs physics in minimal low energy supersymmetric models, Phys. Rev. D 74 (2006) 015009 [hep-ph/0603106] [SPIRES].ADSGoogle Scholar
  80. [80]
    J.R. Ellis, S. Heinemeyer, K.A. Olive and G. Weiglein, Light Heavy MSSM Higgs Bosons at Large tan β, Phys. Lett. B 653 (2007) 292 [arXiv:0706.0977] [SPIRES].ADSGoogle Scholar
  81. [81]
    F. Mahmoudi, New constraints on supersymmetric models from bsγ, JHEP 12 (2007) 026 [arXiv:0710.3791] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  82. [82]
    C. Bobeth, T. Ewerth, F. Krüger and J. Urban, Analysis of neutral Higgs boson contributions to the decays \( {\overline B_s} \to {\ell^{+} }{\ell^{-} } \) and \( \overline B \to K{\ell^{+} }{\ell^{-} } \), Phys. Rev. D 64 (2001) 074014 [hep-ph/0104284] [SPIRES].ADSGoogle Scholar
  83. [83]
    M. Lenzi, Rare B decays at LHCb, arXiv:0710.5056 [SPIRES].
  84. [84]
    ATLAS collaboration, M. Smizanska, Prospects for observing CP-violation and rare decays at ATLAS and CMS, arXiv:0810.3618 [SPIRES].
  85. [85]
    LHCb collaboration, D.M. Santos et al., Analysis of the decay B s0μ + μ at LHCb, LHCB-ROADMAP 1-002.Google Scholar
  86. [86]
    B.C. Allanach, SOFTSUSY: aC++ program forcalculatingsupersymmetricspectra, Comput. Phys. Commun. 143 (2002) 305 [hep-ph/0104145] [SPIRES].CrossRefADSMATHGoogle Scholar

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.Department of PhysicsNational Central UniversityJhongliTaiwan
  2. 2.Clermont UniversitéUniversité Blaise Pascal, CNRS/IN2P3, LPCClermont-FerrandFrance

Personalised recommendations