Form factors \( f_{ + }^{{B \to \pi }}(0) \) and \( f_{ + }^{{D \to \pi }}(0) \) in QCD and determination of |V ub | and |V cd |

Article

Abstract

We present a QCD study on B, Dπ semileptonic transitions at zero momentum transfer and an estimate of magnitudes of the associated CKM matrix elements. Light cone sum rules (LCSRs) with chiral correlator are applied to calculate the form factors \( f_{ + }^{{B \to \pi }}(0) \) and \( f_{ + }^{{D \to \pi }}(0) \). We show that there is no twist-3 and-5 component involved in the light-cone expansions such that the resulting sum rules have a good convergence and offer an understanding of these form factors at twist-5 level. A detailed \( \mathcal{O}\left( {{\alpha_s}} \right) \) computation is carried out in leading twist-2 approximation and the \( \overline {MS} \) masses are employed for the underlying heavy quarks. With the updated inputs and experimental data, we have \( f_{ + }^{{B \to \pi }}(0) = 0.28_{{ - 0.02}}^{{ + 0.05}} \) and \( \left| {{V_{{ub}}}} \right| = \left( {3.4_{{ - 0.6}}^{{ + 0.2}}\pm 0.1\pm 0.1} \right) \times {10^{{ - 3}}};f_{ + }^{{D \to \pi }}(0) = 0.62\pm 0.03 \) and \( \left| {{V_{{cd}}}} \right| = 0.244\pm 0.005\pm 0.003\pm 0.008 \). As a by-product, a numerical estimate for the decay constant f D is yielded as \( {f_D} = 190_{{ - 11}}^{{ + 15}}{\text{MeV}} \).

Keywords

QCD Phenomenology NLO Computations 

References

  1. [1]
    BABAR collaboration, P. del Amo Sanchez et al., Measurement of the B 0π + ν and B +η (′) + ν branching fractions, the B 0π + ν and B +ηℓ + ν form-factor shapes and determination of |V ub |, Phys. Rev. D 83 (2011) 052011 [arXiv:1010.0987] [INSPIRE].ADSGoogle Scholar
  2. [2]
    BABAR collaboration, P. del Amo Sanchez et al., Study of Bπℓν and Bρℓν decays and determination of |V ub |, Phys. Rev. D 83 (2011) 032007 [arXiv:1005.3288] [INSPIRE].ADSGoogle Scholar
  3. [3]
    CLEO collaboration, D. Besson et al., Improved measurements of D meson semileptonic decays to π and K mesons, Phys. Rev. D 80 (2009) 032005 [arXiv:0906.2983] [INSPIRE].ADSGoogle Scholar
  4. [4]
    CLEO collaboration, B. 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] [INSPIRE].ADSGoogle Scholar
  5. [5]
    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 [hep-ph/0406184] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    UTfit collaboration, A. Bevan et al., Update of the unitarity triangle analysis, PoS(ICHEP 2010)270 [arXiv:1010.5089] [INSPIRE].
  7. [7]
    BaBar collaboration, F. Palombo, Recent CKM and CP results from BaBar, arXiv:1110.5024 [INSPIRE].
  8. [8]
    T. Gershon, Overview of the CKM matrix, arXiv:1112.1984 [INSPIRE].
  9. [9]
    I. Balitsky, V.M. Braun and A. Kolesnichenko, Radiative decay Σ+pγ in quantum chromodynamics, Nucl. Phys. B 312 (1989) 509 [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    V.L. Chernyak and I.R. Zhitnitsky, B-meson exclusive decays into baryons, Nucl. Phys. B 345 (1990) 137 [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    V. Belyaev, A. Khodjamirian and R. Rückl, QCD calculation of the Bπ, K form-factors, Z. Phys. C 60 (1993) 349 [hep-ph/9305348] [INSPIRE].ADSGoogle Scholar
  12. [12]
    V. Belyaev, V.M. Braun, A. Khodjamirian and R. Rückl, D Dπ and B Bπ couplings in QCD, Phys. Rev. D 51 (1995) 6177 [hep-ph/9410280] [INSPIRE].ADSGoogle Scholar
  13. [13]
    A. Khodjamirian, R. Rückl, S. Weinzierl and O.I. Yakovlev, Perturbative QCD correction to the Bπ transition form-factor, Phys. Lett. B 410 (1997) 275 [hep-ph/9706303] [INSPIRE].ADSGoogle Scholar
  14. [14]
    E. Bagan, P. Ball and V.M. Braun, Radiative corrections to the decay Bπeν and the heavy quark limit, Phys. Lett. B 417 (1998) 154 [hep-ph/9709243] [INSPIRE].ADSGoogle Scholar
  15. [15]
    P. Ball, Bπ and BK transitions from QCD sum rules on the light cone, JHEP 09 (1998) 005 [hep-ph/9802394] [INSPIRE].
  16. [16]
    P. Ball and R. Zwicky, Improved analysis of Bπeν from QCD sum rules on the light cone, JHEP 10 (2001) 019 [hep-ph/0110115] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    A. Khodjamirian, R. Rückl, S. Weinzierl, C. Winhart and O.I. Yakovlev, Predictions on Bπ \( \overline \ell \) ν , Dπ \( \overline \ell \) ν and D → K \( \overline \ell \) ν from QCD light cone sum rules, Phys. Rev. D 62 (2000) 114002 [hep-ph/0001297] [INSPIRE].ADSGoogle Scholar
  18. [18]
    P. Ball and R. Zwicky, New results on B → π, K, η decay formfactors from light-cone sum rules, Phys. Rev. D 71 (2005) 014015 [hep-ph/0406232] [INSPIRE].ADSGoogle Scholar
  19. [19]
    P. Ball and R. Zwicky, |V ub | and constraints on the leading-twist pion distribution amplitude from Bπℓν, Phys. Lett. B 625 (2005) 225 [hep-ph/0507076] [INSPIRE].ADSGoogle Scholar
  20. [20]
    G. Duplancic, A. Khodjamirian, T. Mannel, B. Melic and N. Offen, Light-cone sum rules for B → π form factors revisited, JHEP 04 (2008) 014 [arXiv:0801.1796] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    A. Khodjamirian, T. Mannel, N. Offen and Y.-M. Wang, Bπℓν l width and |V ub | from QCD light-cone sum rules, Phys. Rev. D 83 (2011) 094031 [arXiv:1103.2655] [INSPIRE].ADSGoogle Scholar
  22. [22]
    T. Huang, Z.-H. Li and X.-Y. Wu, Improved approach to the heavy to light form-factors in the light cone QCD sum rules, Phys. Rev. D 63 (2001) 094001 [INSPIRE].ADSGoogle Scholar
  23. [23]
    X.-G. Wu and T. Huang, Radiative corrections on the BP form factors with chiral current in the light-cone sum rules, Phys. Rev. D 79 (2009) 034013 [arXiv:0901.2636] [INSPIRE].ADSGoogle Scholar
  24. [24]
    P. Ball, Testing QCD sum rules on the light-cone in D → (π, K)ℓν decays, Phys. Lett. B 641 (2006) 50 [hep-ph/0608116] [INSPIRE].ADSGoogle Scholar
  25. [25]
    A. Khodjamirian, C. Klein, T. Mannel and N. Offen, Semileptonic charm decays D → πℓν and D → Kℓν from QCD light-cone sum rules, Phys. Rev. D 80 (2009) 114005 [arXiv:0907.2842] [INSPIRE].ADSGoogle Scholar
  26. [26]
    G.P. Lepage and S.J. Brodsky, Exclusive processes in quantum chromodynamics: evolution equations for hadronic wave functions and the form-factors of mesons, Phys. Lett. B 87 (1979) 359 [INSPIRE].ADSGoogle Scholar
  27. [27]
    G.P. Lepage and S.J. Brodsky, Exclusive processes in perturbative quantum chromodynamics, Phys. Rev. D 22 (1980) 2157 [INSPIRE].ADSGoogle Scholar
  28. [28]
    P. Ball and A.N. Talbot, Models for light-cone meson distribution amplitudes, JHEP 06 (2005) 063 [hep-ph/0502115] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    S. Agaev, V. Braun, N. Offen and F. Porkert, Light cone sum rules for the π 0 γ γ form factor revisited, Phys. Rev. D 83 (2011) 054020 [arXiv:1012.4671] [INSPIRE].ADSGoogle Scholar
  30. [30]
    P. Ball, V. Braun and A. Lenz, Twist-4 distribution amplitudes of the K and ϕ mesons in QCD, JHEP 08 (2007) 090 [arXiv:0707.1201] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  31. [31]
    J.H. Kühn, M. Steinhauser and C. Sturm, Heavy quark masses from sum rules in four-loop approximation, Nucl. Phys. B 778 (2007) 192 [hep-ph/0702103] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    R. Boughezal, M. Czakon and T. Schutzmeier, Charm and bottom quark masses from perturbative QCD, Phys. Rev. D 74 (2006) 074006 [hep-ph/0605023] [INSPIRE].ADSGoogle Scholar
  33. [33]
    Particle Data Group collaboration, K. Nakamura et al., Review of particle physics, J. Phys. G 37 (2010) 075021 [INSPIRE].ADSGoogle Scholar
  34. [34]
    BABAR collaboration, R. Barlow, Experimental status of B → τν and B → ℓν(γ), arXiv:1102.1267 [INSPIRE].
  35. [35]
    T. Huang and Z.-H. Li, The binding energy of the excited heavy light mesons in HQET, Phys. Lett. B 438 (1998) 159 [INSPIRE].ADSGoogle Scholar
  36. [36]
    QCDSF collaboration, A. Al-Haydari et al., Semileptonic form factors D → π, K and B → π, K from a fine lattice, Eur. Phys. J. A 43 (2010) 107 [arXiv:0903.1664] [INSPIRE].ADSGoogle Scholar
  37. [37]
    Fermilab Lattice, MILC and HPQCD collaborations, C. Aubin et al., Semileptonic decays of D mesons in three-flavor lattice QCD, Phys. Rev. Lett. 94 (2005) 011601 [hep-ph/0408306] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    C. Bernard, C. DeTar, M. Di Pierro, A. El-Khadra, R. Evans, et al., Visualization of semileptonic form factors from lattice QCD, Phys. Rev. D 80 (2009) 034026 [arXiv:0906.2498] [INSPIRE].ADSGoogle Scholar
  39. [39]
    A. Abada et al., Heavy to light semileptonic decays of pseudoscalar mesons from lattice QCD, Nucl. Phys. B 619 (2001) 565 [hep-lat/0011065] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    H. Na et al., D → π, ℓν semileptonic decays, |V cd | and 2 nd row unitarity from lattice QCD, Phys. Rev. D 84 (2011) 114505 [arXiv:1109.1501] [INSPIRE].ADSGoogle Scholar
  41. [41]
    S. Di Vita et al., Form factors of the D → π and D → K semileptonic decays with N f = 2 twisted mass lattice QCD, PoS(LATTICE 2010)301 [arXiv:1104.0869] [INSPIRE].
  42. [42]
    ETM collaboration, 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] [INSPIRE].Google Scholar
  43. [43]
    Fermilab Lattice and MILC collaborations, A. Bazavov et al., B- and D-meson decay constants from three-flavor lattice QCD, arXiv:1112.3051 [INSPIRE].
  44. [44]
    C. Davies et al., Update: precision D s decay constant from full lattice QCD using very fine lattices, Phys. Rev. D 82 (2010) 114504 [arXiv:1008.4018] [INSPIRE].ADSGoogle Scholar
  45. [45]
    S. Narison, Light and heavy quark masses, flavor breaking of chiral condensates, meson weak leptonic decay constants in QCD, hep-ph/0202200 [INSPIRE].
  46. [46]
    A. Penin and M. Steinhauser, Heavy light meson decay constant from QCD sum rules in three loop approximation, Phys. Rev. D 65 (2002) 054006 [hep-ph/0108110] [INSPIRE].ADSGoogle Scholar
  47. [47]
    J. Bordes, J. Penarrocha and K. Schilcher, D and D S decay constants from QCD duality at three loops, JHEP 11 (2005) 014 [hep-ph/0507241] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • Zuo-Hong Li
    • 1
  • Nan Zhu
    • 1
  • Xiao-Jiao Fan
    • 1
  • Tao Huang
    • 1
    • 2
  1. 1.Department of PhysicsYantai UniversityYantaiP.R. China
  2. 2.Institute of High Energy Physics and Theoretical Physics Enter for Science Facilities, Chinese Academy of SciencesBeijingP.R. China

Personalised recommendations