|Vub| determination and testing of lepton flavour universality in semileptonic Bc → D(∗) decays

Abstract

In light of prospects for measurements of Bc → D(∗)lv decays in the upcoming Upgrade II of the LHC, we show that by using calculated Bc → D(∗) form factors a competitive extraction of the |Vub| CKM matrix element from the \( {B}_c\to D\mu {\overline{v}}_{\mu } \) decay might be possible. To minimize experimental and theoretical uncertainties we provide the ratio |Vub|/|Vcb| by normalizing the \( {B}_c\to {D}^{\left(\ast \right)}\mu {\overline{v}}_{\mu } \) to \( {B}_c\to J/\psi \mu {\overline{v}}_{\mu } \) decay. We also briefly examine the suggestion to extract |Vub|/|Vcs| from the theoretically interesting ratio of \( {B}_c\to {D}^0e{\overline{v}}_e \) and \( {B}_c\to {B}_se{\overline{v}}_e \) decay rates in the zero-recoil limit. With the present average value of |Vub|, the predicted branching ratios are estimated to be \( BR\left({B}_c\to {D}^0\mu {\overline{\nu}}_{\mu}\right)=\left(2.4\pm 0.4\right)\cdotp {10}^{-5} \) and \( BR\left({B}_c\to {D}^{\ast}\mu {\overline{\nu}}_{\mu}\right)=\left(7\pm 3\right)\cdotp {10}^{-5}, \) and the semileptonic ratios for testing the lepton flavour universality in these Bc decays are Rc(D0) = 0.64 ± 0.05 and Rc(D) = 0.55 ± 0.05. We also provide q2 distributions and various angular observables of Bc → D() decays.

A preprint version of the article is available at ArXiv.

References

  1. [1]

    Particle Data Group, Review of Particle Physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].

  2. [2]

    D. Bigi and P. Gambino, Revisiting B → Dℓv, Phys. Rev. D 94 (2016) 094008 [arXiv:1606.08030] [INSPIRE].

  3. [3]

    D. Bigi, P. Gambino and S. Schacht, A fresh look at the determination of |Vcb| fromB → Dℓv, Phys. Lett. B 769 (2017) 441 [arXiv:1703.06124] [INSPIRE].

    ADS  Article  Google Scholar 

  4. [4]

    F.U. Bernlochner, Z. Ligeti and D.J. Robinson, N = 5, 6, 7, 8: Nested hypothesis tests and truncation dependence of |Vcb|, Phys. Rev. D 100 (2019) 013005 [arXiv:1902.09553] [INSPIRE].

  5. [5]

    C.G. Boyd, B. Grinstein and R.F. Lebed, Model independent determinations of \( \overline{B} \)→ Dl\( \overline{v} \), D l\( \overline{v} \) form-factors, Nucl. Phys. B 461 (1996) 493 [hep-ph/9508211] [INSPIRE].

  6. [6]

    C.G. Boyd, B. Grinstein and R.F. Lebed, Precision corrections to dispersive bounds on form-factors, Phys. Rev. D 56 (1997) 6895 [hep-ph/9705252] [INSPIRE].

  7. [7]

    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].

  8. [8]

    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].

    ADS  Article  Google Scholar 

  9. [9]

    I. Sentitemsu Imsong, A. Khodjamirian, T. Mannel and D. van Dyk, Extrapolation and unitarity bounds for the B → π form factor, JHEP 02 (2015) 126 [arXiv:1409.7816] [INSPIRE].

    ADS  Article  Google Scholar 

  10. [10]

    J.M. Flynn et al., B → πℓν and Bs → Kℓν form factors and |Vub| from 2 + 1-flavor lattice QCD with domain-wall light quarks and relativistic heavy quarks, Phys. Rev. D 91 (2015) 074510 [arXiv:1501.05373] [INSPIRE].

  11. [11]

    Fermilab Lattice and MILC collaborations, |Vub| from B → πℓν decays and (2 + 1)-flavor lattice QCD, Phys. Rev. D 92 (2015) 014024 [arXiv:1503.07839] [INSPIRE].

  12. [12]

    S. Gonzàlez-Solís and P. Masjuan, Study of B → πℓv and B+ → η(′) + v decays and determination of |Vcb|, Phys. Rev. D 98 (2018) 034027 [arXiv:1805.11262] [INSPIRE].

  13. [13]

    LHCb collaboration, Determination of the quark coupling strength |Vub| using baryonic decays, Nature Phys. 11 (2015) 743 [arXiv:1504.01568] [INSPIRE].

  14. [14]

    W. Detmold, C. Lehner and S. Meinel, Λb → pℓ \( {\overline{v}}_{\ell } \) and Λb Λc\( {\overline{v}}_{\ell } \) form factors from lattice QCD with relativistic heavy quarks, Phys. Rev. D 92 (2015) 034503 [arXiv:1503.01421] [INSPIRE].

  15. [15]

    A. Cerri et al., Report from Working Group 4, CERN Yellow Rep. Monogr. 7 (2019) 867 [arXiv:1812.07638] [INSPIRE].

    Google Scholar 

  16. [16]

    LHCb collaboration, Physics case for an LHCb Upgrade II — Opportunities in flavour physics and beyond, in the HL-LHC era, arXiv:1808.08865 [INSPIRE].

  17. [17]

    M. Calvi and M.W. Kenzie, private communication.

  18. [18]

    LHCb collaboration, Measurement of the ratio of branching fractions \( \mathcal{B}\left({B}_c^{+}\to J/\psi {\tau}^{+}{v}_{\tau}\right)/\mathcal{B}\left({B}_c^{+}\to J/\psi {\mu}^{+}{v}_{\mu}\right), \) Phys. Rev. Lett. 120 (2018) 121801 [arXiv:1711.05623] [INSPIRE].

  19. [19]

    D. Leljak, B. Melic and M. Patra, On lepton flavour universality in semileptonic Bc → ηc, J/ψ decays, JHEP 05 (2019) 094 [arXiv:1901.08368] [INSPIRE].

    ADS  Article  Google Scholar 

  20. [20]

    T.D. Cohen, H. Lamm and R.F. Lebed, Model-independent bounds on R(J/ψ), JHEP 09 (2018) 168 [arXiv:1807.02730] [INSPIRE].

    ADS  Article  Google Scholar 

  21. [21]

    A.I. Vainshtein, M.B. Voloshin, V.I. Zakharov, V.A. Novikov, L.B. Okun and M.A. Shifman, Sum Rules for Light Quarks in Quantum Chromodynamics, Sov. J. Nucl. Phys. 27 (1978) 274 [INSPIRE].

    Google Scholar 

  22. [22]

    P. Ball and V.M. Braun, Use and misuse of QCD sum rules in heavy to light transitions: The Decay B → ρeν reexamined, Phys. Rev. D 55 (1997) 5561 [hep-ph/9701238] [INSPIRE].

  23. [23]

    P. Colangelo and F. De Fazio, Using heavy quark spin symmetry in semileptonic Bc decays, Phys. Rev. D 61 (2000) 034012 [hep-ph/9909423] [INSPIRE].

  24. [24]

    S.J. Brodsky, T. Huang and G.P. Lepage, Hadronic wave functions and high momentum transfer interactions in quantum chromodynamics, Conf. Proc. C 810816 (1981) 143 [INSPIRE].

    Google Scholar 

  25. [25]

    T. Huang and F. Zuo, Semileptonic Bc decays and charmonium distribution amplitude, Eur. Phys. J. C 51 (2007) 833 [hep-ph/0702147] [INSPIRE].

  26. [26]

    P. Ball, V.M. Braun and H.G. Dosch, Form-factors of semileptonic D decays from QCD sum rules, Phys. Rev. D 44 (1991) 3567 [INSPIRE].

    ADS  Google Scholar 

  27. [27]

    M. Wirbel, B. Stech and M. Bauer, Exclusive Semileptonic Decays of Heavy Mesons, Z. Phys. C 29 (1985) 637 [INSPIRE].

    ADS  Google Scholar 

  28. [28]

    S.V. Mikhailov and A.V. Radyushkin, Quark Condensate Nonlocality and Pion Wave Function in QCD: General Formalism, Sov. J. Nucl. Phys. 49 (1989) 494 [Yad. Fiz. 49 (1988) 794] [INSPIRE].

  29. [29]

    S.V. Mikhailov and A.V. Radyushkin, The Pion wave function and QCD sum rules with nonlocal condensates, Phys. Rev. D 45 (1992) 1754 [INSPIRE].

    ADS  Google Scholar 

  30. [30]

    V.M. Braun, P. Gornicki, L. Mankiewicz and A. Schafer, Gluon form-factor of the proton from QCD sum rules, Phys. Lett. B 302 (1993) 291 [INSPIRE].

    ADS  Article  Google Scholar 

  31. [31]

    V. Braun, P. Gornicki and L. Mankiewicz, Ioffe-time distributions instead of parton momentum distributions in description of deep inelastic scattering, Phys. Rev. D 51 (1995) 6036 [hep-ph/9410318] [INSPIRE].

  32. [32]

    A.P. Bakulev and S.V. Mikhailov, QCD sum rules for pion wave function revisited, Z. Phys. C 68 (1995) 451 [hep-ph/9412366] [INSPIRE].

  33. [33]

    V.M. Braun, D.Y. Ivanov and G.P. Korchemsky, The B meson distribution amplitude in QCD, Phys. Rev. D 69 (2004) 034014 [hep-ph/0309330] [INSPIRE].

  34. [34]

    V.V. Kiselev, A.K. Likhoded and A.I. Onishchenko, Semileptonic Bc meson decays in sum rules of QCD and NRQCD, Nucl. Phys. B 569 (2000) 473 [hep-ph/9905359] [INSPIRE].

  35. [35]

    P. Gelhausen, A. Khodjamirian, A.A. Pivovarov and D. Rosenthal, Decay constants of heavy-light vector mesons from QCD sum rules, Phys. Rev. D 88 (2013) 014015 [Erratum ibid. D 89 (2014) 099901] [Erratum ibid. D 91 (2015) 099901] [arXiv:1305.5432] [INSPIRE].

  36. [36]

    C. McNeile, C.T.H. Davies, E. Follana, K. Hornbostel and G.P. Lepage, Heavy meson masses and decay constants from relativistic heavy quarks in full lattice QCD, Phys. Rev. D 86 (2012) 074503 [arXiv:1207.0994] [INSPIRE].

  37. [37]

    HPQCD collaboration, B-meson decay constants: a more complete picture from full lattice QCD, Phys. Rev. D 91 (2015) 114509 [arXiv:1503.05762] [INSPIRE].

  38. [38]

    Fermilab Lattice and MILC collaborations, Charmed and Light Pseudoscalar Meson Decay Constants from Four-Flavor Lattice QCD with Physical Light Quarks, Phys. Rev. D 90 (2014) 074509 [arXiv:1407.3772] [INSPIRE].

  39. [39]

    N. Carrasco et al., Leptonic decay constants fK , fD , and fDs with Nf = 2 + 1 + 1 twisted-mass lattice QCD, Phys. Rev. D 91 (2015) 054507 [arXiv:1411.7908] [INSPIRE].

  40. [40]

    D. Becirevic, V. Lubicz, F. Sanfilippo, S. Simula and C. Tarantino, D-meson decay constants and a check of factorization in non-leptonic B-decays, JHEP 02 (2012) 042 [arXiv:1201.4039] [INSPIRE].

    ADS  Article  Google Scholar 

  41. [41]

    ETM collaboration, Masses and decay constants of D*(s) and B*(s) mesons with Nf = 2 + 1 + 1 twisted mass fermions, Phys. Rev. D 96 (2017) 034524 [arXiv:1707.04529] [INSPIRE].

  42. [42]

    P. Ball, V.M. Braun and H.G. Dosch, Form-factors of semileptonic D decays from QCD sum rules, Phys. Rev. D 44 (1991) 3567 [INSPIRE].

    ADS  Google Scholar 

  43. [43]

    M. Beneke, A Quark mass definition adequate for threshold problems, Phys. Lett. B 434 (1998) 115 [hep-ph/9804241] [INSPIRE].

  44. [44]

    A.H. Hoang, Bottom quark mass from ϒ mesons, Phys. Rev. D 59 (1999) 014039 [hep-ph/9803454] [INSPIRE].

  45. [45]

    I.I.Y. Bigi, M.A. Shifman, N. Uraltsev and A.I. Vainshtein, High power n of mb in beauty widths and n = 5 → ∞ limit, Phys. Rev. D 56 (1997) 4017 [hep-ph/9704245] [INSPIRE].

  46. [46]

    M. Neubert, Two-loop relations for heavy-quark parameters in the shape-function scheme, Phys. Lett. B 612 (2005) 13 [hep-ph/0412241] [INSPIRE].

  47. [47]

    S. Aoki et al., Review of lattice results concerning low-energy particle physics, Eur. Phys. J. C 77 (2017) 112 [arXiv:1607.00299] [INSPIRE].

    ADS  Article  Google Scholar 

  48. [48]

    Fermilab Lattice, MILC and TUMQCD collaborations, Up-, down-, strange-, charm- and bottom-quark masses from four-flavor lattice QCD, Phys. Rev. D 98 (2018) 054517 [arXiv:1802.04248] [INSPIRE].

  49. [49]

    B.L. Ioffe and K.N. Zyablyuk, Gluon condensate in charmonium sum rules with three loop corrections, Eur. Phys. J. C 27 (2003) 229 [hep-ph/0207183] [INSPIRE].

  50. [50]

    V.V. Kiselev, Exclusive decays and lifetime of Bc meson in QCD sum rules, hep-ph/0211021 [INSPIRE].

  51. [51]

    S. Dubnicka, A.Z. Dubnickova, A. Issadykov, M.A. Ivanov and A. Liptaj, Study of Bc decays into charmonia and D mesons, Phys. Rev. D 96 (2017) 076017 [arXiv:1708.09607] [INSPIRE].

  52. [52]

    A. Issadykov, M.A. Ivanov and G. Nurbakova, Semileptonic decays of Bc mesons into charmonium states, EPJ Web Conf. 158 (2017) 03002 [arXiv:1907.13210] [INSPIRE].

  53. [53]

    W.-F. Wang, X. Yu, C.-D. Lü and Z.-J. Xiao, Semileptonic decays \( {B}_c^{+}\to {D}_s^{\left(\ast \right)}\left({l}^{+}{v}_l,{l}^{+}{l}^{-},v\overline{v}\right) \) in the perturbative QCD approach, Phys. Rev. D 90 (2014) 094018 [arXiv:1401.0391] [INSPIRE].

  54. [54]

    D. Ebert, R.N. Faustov and V.O. Galkin, Weak decays of the Bc meson to charmonium and D mesons in the relativistic quark model, Phys. Rev. D 68 (2003) 094020 [hep-ph/0306306] [INSPIRE].

  55. [55]

    M.A. Nobes and R.M. Woloshyn, Decays of the Bc meson in a relativistic quark meson model, J. Phys. G 26 (2000) 1079 [hep-ph/0005056] [INSPIRE].

  56. [56]

    W. Wang, Y.-L. Shen and C.-D. Lü, Covariant Light-Front Approach for Bc transition form factors, Phys. Rev. D 79 (2009) 054012 [arXiv:0811.3748] [INSPIRE].

  57. [57]

    D.-s. Du and Z. Wang, Predictions of the Standard Model for \( {B}_c^{\pm } \) Weak Decays, Phys. Rev. D 39 (1989) 1342 [INSPIRE].

    ADS  Google Scholar 

  58. [58]

    P. Colangelo, G. Nardulli and N. Paver, QCD sum rules calculation of Bc decays, Z. Phys. C 57 (1993) 43 [INSPIRE].

    ADS  Google Scholar 

  59. [59]

    R. Dhir and R.C. Verma, Bc Meson Form-factors and Bc → P V Decays Involving Flavor Dependence of Transverse Quark Momentum, Phys. Rev. D 79 (2009) 034004 [arXiv:0810.4284] [INSPIRE].

  60. [60]

    C. Bourrely, I. Caprini and L. Lellouch, Model-independent description of B → πlν decays and a determination of |Vub |, Phys. Rev. D 79 (2009) 013008 [Erratum ibid. D 82 (2010) 099902] [arXiv:0807.2722] [INSPIRE].

  61. [61]

    S. Godfrey, K. Moats and E.S. Swanson, B and Bs Meson Spectroscopy, Phys. Rev. D 94 (2016) 054025 [arXiv:1607.02169] [INSPIRE].

  62. [62]

    J.G. Korner and G.A. Schuler, Exclusive Semileptonic Heavy Meson Decays Including Lepton Mass Effects, Z. Phys. C 46 (1990) 93 [INSPIRE].

    ADS  Google Scholar 

  63. [63]

    M.A. Ivanov, J.G. Korner and P. Santorelli, Exclusive semileptonic and nonleptonic decays of the Bc meson, Phys. Rev. D 73 (2006) 054024 [hep-ph/0602050] [INSPIRE].

  64. [64]

    D. Scora and N. Isgur, Semileptonic meson decays in the quark model: An update, Phys. Rev. D 52 (1995) 2783 [hep-ph/9503486] [INSPIRE].

  65. [65]

    A. Abd El-Hady, J.H. Muñoz and J.P. Vary, Semileptonic and nonleptonic Bc decays, Phys. Rev. D 62 (2000) 014019 [hep-ph/9909406] [INSPIRE].

  66. [66]

    R. Dutta, Predictions of Bc (D, D )τ ν decay observables in the standard model, J. Phys. G 46 (2019) 035008 [arXiv:1809.08561] [INSPIRE].

  67. [67]

    HPQCD collaboration, Bc decays from highly improved staggered quarks and NRQCD, PoS(LATTICE2016)281 (2016) [arXiv:1611.01987] [INSPIRE].

  68. [68]

    E.E. Jenkins, M.E. Luke, A.V. Manohar and M.J. Savage, Semileptonic Bc decay and heavy quark spin symmetry, Nucl. Phys. B 390 (1993) 463 [hep-ph/9204238] [INSPIRE].

  69. [69]

    G.C. Donald et al., Precision tests of the J/ψ from full lattice QCD: mass, leptonic width and radiative decay rate to ηc , Phys. Rev. D 86 (2012) 094501 [arXiv:1208.2855] [INSPIRE].

  70. [70]

    G. Bailas, B. Blossier and V. Morénas, Some hadronic parameters of charmonia in Nf = 2 lattice QCD, Eur. Phys. J. C 78 (2018) 1018 [arXiv:1803.09673] [INSPIRE].

    ADS  Article  Google Scholar 

  71. [71]

    ETM collaboration, Mass of the b quark and B-meson decay constants from Nf = 2 + 1 + 1 twisted-mass lattice QCD, Phys. Rev. D 93 (2016) 114505 [arXiv:1603.04306] [INSPIRE].

  72. [72]

    P. Ball and R. Zwicky, Bd,s → ρ, ω, K , ø decay form-factors from light-cone sum rules revisited, Phys. Rev. D 71 (2005) 014029 [hep-ph/0412079] [INSPIRE].

  73. [73]

    E.J. Eichten and C. Quigg, Mesons with beauty and charm: Spectroscopy, Phys. Rev. D 49 (1994) 5845 [hep-ph/9402210] [INSPIRE].

  74. [74]

    V.A. Novikov, M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Calculations in External Fields in Quantum Chromodynamics. Technical Review, Fortsch. Phys. 32 (1984) 585 [INSPIRE].

  75. [75]

    G. Duplancic and B. Nizic, Reduction method for dimensionally regulated one loop N point Feynman integrals, Eur. Phys. J. C 35 (2004) 105 [hep-ph/0303184] [INSPIRE].

Download references

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

Author information

Affiliations

Authors

Corresponding author

Correspondence to Domagoj Leljak.

Additional information

ArXiv ePrint: 1909.01213

Rights and permissions

Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Leljak, D., Melić, B. |Vub| determination and testing of lepton flavour universality in semileptonic Bc → D(∗) decays. J. High Energ. Phys. 2020, 171 (2020). https://doi.org/10.1007/JHEP02(2020)171

Download citation

Keywords

  • Heavy Quark Physics
  • Nonperturbative Effects