Abstract
We investigate the semi-leptonic decays of \( B\to {D}^{\left(\ast \right)}\mathrm{\ell}\overline{\nu } \) in terms of the Heavy-Quark-Effective-Theory (HQET) parameterization for the form factors, which is described with the heavy quark expansion up to \( \mathcal{O}\left(1/{m}_c^2\right) \) beyond the simple approximation considered in the original CLN parameterization. An analysis with this setup was first given in the literature, and then we extend it to the comprehensive analyses including (i) simultaneous fit of |Vcb| and the HQET parameters to available experimental full distribution data and theory constraints, and (ii) New Physics (NP) contributions of the V2 and T types, such as \( \left(\overline{c}{\upgamma}^{\mu }{P}_Rb\right)\left(\overline{\mathrm{\ell}}{\gamma}_{\mu }{P}_L\nu \mathrm{\ell}\right)\kern0.5em \mathrm{and}\kern0.5em \left(\overline{c}{\sigma}^{\mu \nu}{P}_Lb\right)\left(\overline{\mathrm{\ell}}{\sigma}_{\mu \nu}{P}_L{\nu}_{\mathrm{\ell}}\right) \), to the decay distributions and rates. For this purpose, we perform Bayesian fit analyses by using Stan program, a state-of-the-art public platform for statistical computation. Then, we show that our |Vcb| fit results for the SM scenarios are close to the PDG combined average from the exclusive mode, and indicate significance of the angular distribution data. In turn, for the SM + NP scenarios, our fit analyses find that non-zero NP contribution is favored at the best fit point for both SM + V2 and SM + T depending on the HQET parameterization model. A key feature is then realized in the \( \overline{B}\to {D}^{\left(\ast \right)}\tau \overline{\nu} \) observables. Our fit result of the HQET parameters in the SM(+T) produces a consistent value for RD while smaller for \( {R}_{D^{\ast }} \), compared with the previous SM prediction in the HFLAV report. On the other hand, SM + V2 points to smaller and larger values for RD and \( {R}_{D^{\ast }} \) than the SM predictions. In particular, the \( {R}_{D^{\ast }} \) deviation from the experimental measurement becomes smaller, which could be interesting for future improvement on measurements at the Belle II experiment.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Cabibbo, Unitary Symmetry and Leptonic Decays, Phys. Rev. Lett. 10 (1963) 531 [INSPIRE].
M. Kobayashi and T. Maskawa, CP Violation in the Renormalizable Theory of Weak Interaction, Prog. Theor. Phys. 49 (1973) 652 [INSPIRE].
Belle-II collaboration, The Belle II Physics Book, Prog. Theor. Exp. Phys. 2019 (2019) 123C01 [Erratum ibid. 2020 (2020) 029201] [arXiv:1808.10567] [INSPIRE].
I. Caprini, L. Lellouch and M. Neubert, Dispersive bounds on the shape of \( \overline{B}\to {D}^{\left(\ast \right)}\mathrm{\ell}\overline{\nu } \) form-factors, Nucl. Phys. B 530 (1998) 153 [hep-ph/9712417] [INSPIRE].
N. Isgur and M.B. Wise, Weak Decays of Heavy Mesons in the Static Quark Approximation, Phys. Lett. B 232 (1989) 113 [INSPIRE].
M. Neubert, Heavy quark symmetry, Phys. Rept. 245 (1994) 259 [hep-ph/9306320] [INSPIRE].
C. 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].
F.U. Bernlochner, Z. Ligeti, M. Papucci and D.J. Robinson, Combined analysis of semileptonic B decays to D and D*: R(D(*)), |Vcb| and new physics, Phys. Rev. D 95 (2017) 115008 [Erratum ibid. 97 (2018) 059902] [arXiv:1703.05330] [INSPIRE].
D. Bigi and P. Gambino, Revisiting B → Dℓν, Phys. Rev. D 94 (2016) 094008 [arXiv:1606.08030] [INSPIRE].
D. Bigi, P. Gambino and S. Schacht, A fresh look at the determination of |Vcb| from B → D*ℓν, Phys. Lett. B 769 (2017) 441 [arXiv:1703.06124] [INSPIRE].
B. Grinstein and A. Kobach, Model-Independent Extraction of |Vcb| from \( \overline{B}\to {D}^{\ast}\mathrm{\ell}\overline{\nu } \), Phys. Lett. B 771 (2017) 359 [arXiv:1703.08170] [INSPIRE].
S. Jaiswal, S. Nandi and S.K. Patra, Extraction of |Vcb| from B → D(*)ℓνℓ and the Standard Model predictions of R(D(*)), JHEP 12 (2017) 060 [arXiv:1707.09977] [INSPIRE].
F.U. Bernlochner, Z. Ligeti, M. Papucci and D.J. Robinson, Tensions and correlations in |Vcb| determinations, Phys. Rev. D 96 (2017) 091503 [arXiv:1708.07134] [INSPIRE].
D. Bigi, P. Gambino and S. Schacht, R(D*), |Vcb| and the Heavy Quark Symmetry relations between form factors, JHEP 11 (2017) 061 [arXiv:1707.09509] [INSPIRE].
P. Gambino, M. Jung and S. Schacht, The Vcb puzzle: An update, Phys. Lett. B 795 (2019) 386 [arXiv:1905.08209] [INSPIRE].
M. Jung and D.M. Straub, Constraining new physics in b → cℓν transitions, JHEP 01 (2019) 009 [arXiv:1801.01112] [INSPIRE].
M. Bordone, M. Jung and D. van Dyk, Theory determination of \( \overline{B}\to {D}^{\left(\ast \right)}{\mathrm{\ell}}^{-}\overline{\nu} \) form factors at \( \mathcal{O}\left(1/{m}_c^2\right) \), Eur. Phys. J. C 80 (2020) 74 [arXiv:1908.09398] [INSPIRE].
Particle Data Group, Review of Particle Physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].
Belle collaboration, Measurement of the decay B → Dℓνℓ in fully reconstructed events and determination of the Cabibbo-Kobayashi-Maskawa matrix element |Vcb|, Phys. Rev. D 93 (2016) 032006 [arXiv:1510.03657] [INSPIRE].
Belle collaboration, Precise determination of the CKM matrix element |Vcb| with \( {\overline{B}}^0\to {D}^{\ast +}{\mathrm{\ell}}^{-}{\overline{\nu}}_{\mathrm{\ell}} \) decays with hadronic tagging at Belle, arXiv:1702.01521 [INSPIRE].
Belle collaboration, Measurement of the CKM matrix element |Vcb| from B0 → D∗−ℓ+νℓ at Belle, Phys. Rev. D 100 (2019) 052007 [arXiv:1809.03290] [INSPIRE].
BaBar collaboration, Extraction of form Factors from a Four-Dimensional Angular Analysis of \( \overline{B}\to {D}^{\ast }{\mathrm{\ell}}^{-}{\overline{\nu}}_{\mathrm{\ell}} \), Phys. Rev. Lett. 123 (2019) 091801 [arXiv:1903.10002] [INSPIRE].
B. Carpenter, M.D. Hoffman, M. Brubaker, D. Lee, P. Li and M. Betancourt, The Stan Math Library: Reverse-Mode Automatic Differentiation in C++, arXiv:1509.07164.
B. Carpenter et al., Stan: A probabilistic programming language, J. Stat. Software 76 (2017) 1 and online at https://mc-stan.org/.
A. Gelman, J. Hwang and A. Vehtari, Understanding predictive information criteria for Bayesian models, arXiv:1307.5928.
A.F. Falk and M. Neubert, Second order power corrections in the heavy quark effective theory. 1. Formalism and meson form-factors, Phys. Rev. D 47 (1993) 2965 [hep-ph/9209268] [INSPIRE].
A. Sirlin, Large mW, mZ Behavior of the O(α) Corrections to Semileptonic Processes Mediated by W, Nucl. Phys. B 196 (1982) 83 [INSPIRE].
Fermilab Lattice and MILC collaborations, Update of |Vcb| from the \( \overline{B}\to {D}^{\ast}\mathrm{\ell}\overline{\nu } \) form factor at zero recoil with three-flavor lattice QCD, Phys. Rev. D 89 (2014) 114504 [arXiv:1403.0635] [INSPIRE].
M. Tanaka and R. Watanabe, New physics in the weak interaction of \( \overline{B}\to {D}^{\left(\ast \right)}\tau \overline{\nu} \), Phys. Rev. D 87 (2013) 034028 [arXiv:1212.1878] [INSPIRE].
Y. Sakaki, M. Tanaka, A. Tayduganov and R. Watanabe, Testing leptoquark models in \( \overline{B}\to {D}^{\left(\ast \right)}\tau \overline{\nu} \), Phys. Rev. D 88 (2013) 094012 [arXiv:1309.0301] [INSPIRE].
Y. Sakaki, M. Tanaka, A. Tayduganov and R. Watanabe, Probing New Physics with q2 distributions in \( \overline{B}\to {D}^{\left(\ast \right)}\tau \overline{\nu} \), Phys. Rev. D 91 (2015) 114028 [arXiv:1412.3761] [INSPIRE].
MILC collaboration, B → Dℓν form factors at nonzero recoil and |Vcb| from 2 + 1-flavor lattice QCD, Phys. Rev. D 92 (2015) 034506 [arXiv:1503.07237] [INSPIRE].
HPQCD collaboration, B → Dlν form factors at nonzero recoil and extraction of |Vcb|, Phys. Rev. D 92 (2015) 054510 [Erratum ibid. 93 (2016) 119906] [arXiv:1505.03925] [INSPIRE].
Flavour Lattice Averaging Group, FLAG Review 2019: Flavour Lattice Averaging Group (FLAG), Eur. Phys. J. C 80 (2020) 113 [arXiv:1902.08191] [INSPIRE].
N. Gubernari, A. Kokulu and D. van Dyk, B → P and B → V Form Factors from B-Meson Light-Cone Sum Rules beyond Leading Twist, JHEP 01 (2019) 150 [arXiv:1811.00983] [INSPIRE].
M. Neubert, Z. Ligeti and Y. Nir, QCD sum rule analysis of the subleading Isgur-Wise form-factor χ2(v · v′), Phys. Lett. B 301 (1993) 101 [hep-ph/9209271] [INSPIRE].
M. Neubert, Z. Ligeti and Y. Nir, The Subleading Isgur-Wise form-factor χ3(v · v′) to order αs in QCD sum rules, Phys. Rev. D 47 (1993) 5060 [hep-ph/9212266] [INSPIRE].
Z. Ligeti, Y. Nir and M. Neubert, The Subleading Isgur-Wise form-factor ξ3(v · v′) and its implications for the decays \( \overline{B}\to {D}^{\left(\ast \right)}\mathrm{\ell}\overline{\nu } \), Phys. Rev. D 49 (1994) 1302 [hep-ph/9305304] [INSPIRE].
E.J. Eichten and C. Quigg, Mesons with Beauty and Charm: New Horizons in Spectroscopy, Phys. Rev. D 99 (2019) 054025 [arXiv:1902.09735] [INSPIRE].
Q. Li, M.-S. Liu, L.-S. Lu, Q.-F. Lü, L.-C. Gui and X.-H. Zhong, Excited bottom-charmed mesons in a nonrelativistic quark model, Phys. Rev. D 99 (2019) 096020 [arXiv:1903.11927] [INSPIRE].
V. Picaud, MathematicaStan, (2020) https://mc-stan.org/users/interfaces/mathematica-stan.
HFLAV collaboration, Averages of b-hadron, c-hadron and τ-lepton properties as of 2018, arXiv:1909.12524 [INSPIRE].
Belle collaboration, Measurement of the D∗− polarization in the decay B0 → D∗−τ+ντ, in proceedings of the 10th International Workshop on the CKM Unitarity Triangle (CKM 2018), Heidelberg, Germany, 17–21 September 2018, [arXiv:1903.03102] [INSPIRE].
A. Crivellin, Effects of right-handed charged currents on the determinations of |Vub| and |Vcb|, Phys. Rev. D 81 (2010) 031301 [arXiv:0907.2461] [INSPIRE].
A. Crivellin and S. Pokorski, Can the differences in the determinations of Vub and Vcb be explained by New Physics?, Phys. Rev. Lett. 114 (2015) 011802 [arXiv:1407.1320] [INSPIRE].
A. Greljo, J. Martin Camalich and J.D. Ruiz-Álvarez, Mono-τ Signatures at the LHC Constrain Explanations of B-decay Anomalies, Phys. Rev. Lett. 122 (2019) 131803 [arXiv:1811.07920] [INSPIRE].
ATLAS collaboration, Search for High-Mass Resonances Decaying to τν in pp Collisions at \( \sqrt{s} \) = 13 TeV with the ATLAS Detector, Phys. Rev. Lett. 120 (2018) 161802 [arXiv:1801.06992] [INSPIRE].
CMS collaboration, Search for a W′ boson decaying to a τ lepton and a neutrino in proton-proton collisions at \( \sqrt{s} \) = 13 TeV, Phys. Lett. B 792 (2019) 107 [arXiv:1807.11421] [INSPIRE].
W. Altmannshofer, P.S. Bhupal Dev and A. Soni, \( {R}_{D^{\left(\ast \right)}} \) anomaly: A possible hint for natural supersymmetry with R-parity violation, Phys. Rev. D 96 (2017) 095010 [arXiv:1704.06659] [INSPIRE].
S. Iguro and K. Tobe, R(D(∗)) in a general two Higgs doublet model, Nucl. Phys. B 925 (2017) 560 [arXiv:1708.06176] [INSPIRE].
M. Abdullah, J. Calle, B. Dutta, A. Flórez and D. Restrepo, Probing a simplified, W t model of R(D(∗)) anomalies using b-tags, τ leptons and missing energy, Phys. Rev. D 98 (2018) 055016 [arXiv:1805.01869] [INSPIRE].
S. Iguro, Y. Omura and M. Takeuchi, Test of the R(D(∗)) anomaly at the LHC, Phys. Rev. D 99 (2019) 075013 [arXiv:1810.05843] [INSPIRE].
M.J. Baker, J. Fuentes-Martín, G. Isidori and M. König, High-pT signatures in vector-leptoquark models, Eur. Phys. J. C 79 (2019) 334 [arXiv:1901.10480] [INSPIRE].
ATLAS collaboration, Search for a heavy charged boson in events with a charged lepton and missing transverse momentum from pp collisions at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, Phys. Rev. D 100 (2019) 052013 [arXiv:1906.05609] [INSPIRE].
S. Iguro, T. Kitahara, Y. Omura, R. Watanabe and K. Yamamoto, D* polarization vs. \( {R}_{D^{\left(\ast \right)}} \) anomalies in the leptoquark models, JHEP 02 (2019) 194 [arXiv:1811.08899] [INSPIRE].
M. Blanke et al., Impact of polarization observables and Bc → τν on new physics explanations of the b → cτν anomaly, Phys. Rev. D 99 (2019) 075006 [arXiv:1811.09603] [INSPIRE].
Belle collaboration, Measurement of the τ lepton polarization and R(D*) in the decay \( \overline{B}\to {D}^{\ast }{\tau}^{-}{\nu}_{\tau } \), Phys. Rev. Lett. 118 (2017) 211801 [arXiv:1612.00529] [INSPIRE].
C. Murgui, A. Peñuelas, M. Jung and A. Pich, Global fit to b → cτν transitions, JHEP 09 (2019) 103 [arXiv:1904.09311] [INSPIRE].
S. Jaiswal, S. Nandi and S.K. Patra, Updates on extraction of |Vcb| and SM prediction of R(D*) in B → D*ℓνℓ decays, JHEP 06 (2020) 165 [arXiv:2002.05726] [INSPIRE].
K. Cheung, Z.-R. Huang, H.-D. Li, C.-D. Lü, Y.-N. Mao and R.-Y. Tang, Revisit to the b → cτν transition: in and beyond the SM, arXiv:2002.07272 [INSPIRE].
J. De Blas et al., HEPfit: a code for the combination of indirect and direct constraints on high energy physics models, Eur. Phys. J. C 80 (2020) 456 [arXiv:1910.14012] [INSPIRE].
B. Bhattacharya, A. Datta, S. Kamali and D. London, CP Violation in \( {\overline{B}}^0\to {D}^{\ast +}{\mu}^{-}{\overline{\nu}}_{\mu } \), JHEP 05 (2019) 191 [arXiv:1903.02567] [INSPIRE].
S. de Boer, T. Kitahara and I. Nisandzic, Soft-Photon Corrections to \( \overline{B}\to D{\tau}^{-}{\overline{\nu}}_{\tau } \) Relative to \( \overline{B}\to D{\mu}^{-}{\overline{\nu}}_{\mu } \) , Phys. Rev. Lett. 120 (2018) 261804 [arXiv:1803.05881] [INSPIRE].
P. Colangelo and A. Khodjamirian, QCD sum rules, a modern perspective, in At the frontier of particle physics. Volume 3 , M. Shifman ed., World Scientific (2001), pp. 1495–1576 [hep-ph/0010175] [INSPIRE].
B.L. Ioffe, QCD at low energies, Prog. Part. Nucl. Phys. 56 (2006) 232 [hep-ph/0502148] [INSPIRE].
Z.-G. Wang, Analysis of the decay constants of the heavy pseudoscalar mesons with QCD sum rules, JHEP 10 (2013) 208 [arXiv:1301.1399] [INSPIRE].
S. Narison, QCD parameter correlations from heavy quarkonia, Int. J. Mod. Phys. A 33 (2018) 1850045 [Addendum ibid. 33 (2018) 1892004] [arXiv:1801.00592] [INSPIRE].
V.M. Belyaev and B.L. Ioffe, Determination of Baryon and Baryonic Resonance Masses from QCD Sum Rules. 1. Nonstrange Baryons, Sov. Phys. JETP 56 (1982) 493 [Zh. Eksp. Teor. Fiz. 83 (1982) 876] [INSPIRE].
H.G. Dosch and S. Narison, Direct extraction of the chiral quark condensate and bounds on the light quark masses, Phys. Lett. B 417 (1998) 173 [hep-ph/9709215] [INSPIRE].
A. Di Giacomo and Y. Simonov, The Quark gluon mixed condensate calculated via field correlators, Phys. Lett. B 595 (2004) 368 [hep-ph/0404044] [INSPIRE].
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
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2004.10208
Electronic supplementary material
ESM 1
(TGZ 3 kb)
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Iguro, S., Watanabe, R. Bayesian fit analysis to full distribution data of \( \overline{\mathrm{B}}\to {\mathrm{D}}^{\left(\ast \right)}\mathrm{\ell}\overline{\nu }:\left|{\mathrm{V}}_{\mathrm{cb}}\right| \) determination and new physics constraints. J. High Energ. Phys. 2020, 6 (2020). https://doi.org/10.1007/JHEP08(2020)006
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2020)006