Abstract
We compute perturbative QCD corrections to B → D form factors at leading power in Λ/m b , at large hadronic recoil, from the light-cone sum rules (LCSR) with B-meson distribution amplitudes in HQET. QCD factorization for the vacuum-to-B-meson correlation function with an interpolating current for the D-meson is demonstrated explicitly at one loop with the power counting scheme \( {m}_c\sim \mathcal{O}\left(\sqrt{\Lambda {m}_b}\right) \). The jet functions encoding information of the hard-collinear dynamics in the above-mentioned correlation function are complicated by the appearance of an additional hard-collinear scale m c , compared to the counterparts entering the factorization formula of the vacuum-to-B-meson correction function for the construction of B → π from factors. Inspecting the next-to-leading-logarithmic sum rules for the form factors of B → Dℓν indicates that perturbative corrections to the hard-collinear functions are more profound than that for the hard functions, with the default theory inputs, in the physical kinematic region. We further compute the subleading power correction induced by the three-particle quark-gluon distribution amplitudes of the B-meson at tree level employing the background gluon field approach. The LCSR predictions for the semileptonic B → Dℓν form factors are then extrapolated to the entire kinematic region with the z-series parametrization. Phenomenological implications of our determinations for the form factors f +,0 BD (q 2) are explored by investigating the (differential) branching fractions and the R(D) ratio of B → Dℓν and by determining the CKM matrix element |V cb | from the total decay rate of B → Dμν μ .
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Particle Data Group collaboration, K.A. Olive et al., Review of particle physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
Y. Amhis et al., Averages of b-hadron, c-hadron and τ-lepton properties as of summer 2016, arXiv:1612.07233 [INSPIRE].
M. Neubert, Heavy quark symmetry, Phys. Rept. 245 (1994) 259 [hep-ph/9306320] [INSPIRE].
MILC collaboration, J.A. Bailey et al., B → Dℓν form factors at nonzero recoil and |V cb | from 2 + 1-flavor lattice QCD, Phys. Rev. D 92 (2015) 034506 [arXiv:1503.07237] [INSPIRE].
HPQCD collaboration, H. Na, C.M. Bouchard, G.P. Lepage, C. Monahan and J. Shigemitsu, B → Dℓν form factors at nonzero recoil and extraction of |V cb |, Phys. Rev. D 92 (2015) 054510 [Erratum ibid. D 93 (2016) 119906] [arXiv:1505.03925] [INSPIRE].
A. Khodjamirian, T. Mannel and N. Offen, B-meson distribution amplitude from the B → π form-factor, Phys. Lett. B 620 (2005) 52 [hep-ph/0504091] [INSPIRE].
A. Khodjamirian, T. Mannel and N. Offen, Form-factors from light-cone sum rules with B-meson distribution amplitudes, Phys. Rev. D 75 (2007) 054013 [hep-ph/0611193] [INSPIRE].
F. De Fazio, T. Feldmann and T. Hurth, Light-cone sum rules in soft-collinear effective theory, Nucl. Phys. B 733 (2006) 1 [Erratum ibid. B 800 (2008) 405] [hep-ph/0504088] [INSPIRE].
F. De Fazio, T. Feldmann and T. Hurth, SCET sum rules for B → P and B → V transition form factors, JHEP 02 (2008) 031 [arXiv:0711.3999] [INSPIRE].
S. Faller, A. Khodjamirian, C. Klein and T. Mannel, B → D (*) form factors from QCD light-cone sum rules, Eur. Phys. J. C 60 (2009) 603 [arXiv:0809.0222] [INSPIRE].
H. Boos, T. Feldmann, T. Mannel and B.D. Pecjak, Shape functions from \( \overline{B}\to {X}_c\ell {\overline{\nu}}_{\ell } \), Phys. Rev. D 73 (2006) 036003 [hep-ph/0504005] [INSPIRE].
H. Boos, T. Feldmann, T. Mannel and B.D. Pecjak, Can \( \overline{B}\to {X}_c\ell \overline{n}{u}_{\ell } \) help us extract |V ub |?, JHEP 05 (2006) 056 [hep-ph/0512157] [INSPIRE].
P. Gambino, T. Mannel and N. Uraltsev, B → D * zero-recoil formfactor and the heavy quark expansion in QCD: a systematic study, JHEP 10 (2012) 169 [arXiv:1206.2296] [INSPIRE].
M. Beneke, G. Buchalla, M. Neubert and C.T. Sachrajda, QCD factorization for exclusive, nonleptonic B meson decays: general arguments and the case of heavy light final states, Nucl. Phys. B 591 (2000) 313 [hep-ph/0006124] [INSPIRE].
Y.-M. Wang and Y.-L. Shen, QCD corrections to B → π form factors from light-cone sum rules, Nucl. Phys. B 898 (2015) 563 [arXiv:1506.00667] [INSPIRE].
I.Z. Rothstein, Factorization, power corrections and the pion form-factor, Phys. Rev. D 70 (2004) 054024 [hep-ph/0301240] [INSPIRE].
A.K. Leibovich, Z. Ligeti and M.B. Wise, Comment on quark masses in SCET, Phys. Lett. B 564 (2003) 231 [hep-ph/0303099] [INSPIRE].
M. Beneke and V.A. Smirnov, Asymptotic expansion of Feynman integrals near threshold, Nucl. Phys. B 522 (1998) 321 [hep-ph/9711391] [INSPIRE].
Y.-M. Wang and Y.-L. Shen, Perturbative corrections to Λ b → Λ form factors from QCD light-cone sum rules, JHEP 02 (2016) 179 [arXiv:1511.09036] [INSPIRE].
Y.-M. Wang, Factorization and dispersion relations for radiative leptonic B decay, JHEP 09 (2016) 159 [arXiv:1606.03080] [INSPIRE].
H.-B. Fu, X.-G. Wu, H.-Y. Han, Y. Ma and T. Zhong, |V cb | from the semileptonic decay \( B\to D\ell {\overline{\nu}}_{\ell } \) and the properties of the D meson distribution amplitude, Nucl. Phys. B 884 (2014) 172 [arXiv:1309.5723] [INSPIRE].
R.-H. Li, C.-D. Lü and Y.-M. Wang, Exclusive B s decays to the charmed mesons D + s (1968, 2317) in the Standard Model, Phys. Rev. D 80 (2009) 014005 [arXiv:0905.3259] [INSPIRE].
H.-N. Li, Applicability of perturbative QCD to B → D decays, Phys. Rev. D 52 (1995) 3958 [hep-ph/9412340] [INSPIRE].
T. Kurimoto, H.-N. Li and A.I. Sanda, B → D (*) form-factors in perturbative QCD, Phys. Rev. D 67 (2003) 054028 [hep-ph/0210289] [INSPIRE].
Y.-Y. Fan, W.-F. Wang, S. Cheng and Z.-J. Xiao, Semileptonic decays B → D (*) ℓν in the perturbative QCD factorization approach, Chin. Sci. Bull. 59 (2014) 125 [arXiv:1301.6246] [INSPIRE].
H.-N. Li, Y.-L. Shen, Y.-M. Wang and H. Zou, Next-to-leading-order correction to pion form factor in k T factorization, Phys. Rev. D 83 (2011) 054029 [arXiv:1012.4098] [INSPIRE].
H.-N. Li, Y.-L. Shen and Y.-M. Wang, Next-to-leading-order corrections to B → π form factors in k T factorization, Phys. Rev. D 85 (2012) 074004 [arXiv:1201.5066] [INSPIRE].
H.-N. Li, Y.-L. Shen and Y.-M. Wang, Resummation of rapidity logarithms in B meson wave functions, JHEP 02 (2013) 008 [arXiv:1210.2978] [INSPIRE].
H.-N. Li, Y.-L. Shen and Y.-M. Wang, Joint resummation for pion wave function and pion transition form factor, JHEP 01 (2014) 004 [arXiv:1310.3672] [INSPIRE].
Y.-M. Wang, Non-dipolar gauge links for transverse-momentum-dependent pion wave functions, EPJ Web Conf. 112 (2016) 01021 [arXiv:1512.08374] [INSPIRE].
H.-N. Li and Y.-M. Wang, Non-dipolar Wilson links for transverse-momentum-dependent wave functions, JHEP 06 (2015) 013 [arXiv:1410.7274] [INSPIRE].
C. Bourrely, I. Caprini and L. Lellouch, Model-independent description of B → πℓν decays and a determination of |V ub |, Phys. Rev. D 79 (2009) 013008 [Erratum ibid. D 82 (2010) 099902] [arXiv:0807.2722] [INSPIRE].
I. Caprini, L. Lellouch and M. Neubert, Dispersive bounds on the shape of \( \overline{B}\to {D}^{\left(\ast \right)}\ell \overline{\nu} \) form-factors, Nucl. Phys. B 530 (1998) 153 [hep-ph/9712417] [INSPIRE].
A.G. Grozin and M. Neubert, Asymptotics of heavy meson form-factors, Phys. Rev. D 55 (1997) 272 [hep-ph/9607366] [INSPIRE].
M. Beneke and T. Feldmann, Symmetry breaking corrections to heavy to light B meson form-factors at large recoil, Nucl. Phys. B 592 (2001) 3 [hep-ph/0008255] [INSPIRE].
G. Bell, T. Feldmann, Y.-M. Wang and M.W.Y. Yip, Light-cone distribution amplitudes for heavy-quark hadrons, JHEP 11 (2013) 191 [arXiv:1308.6114] [INSPIRE].
K.G. Chetyrkin, Quark mass anomalous dimension to O(α 4 S ), Phys. Lett. B 404 (1997) 161 [hep-ph/9703278] [INSPIRE].
J.A.M. Vermaseren, S.A. Larin and T. van Ritbergen, The four loop quark mass anomalous dimension and the invariant quark mass, Phys. Lett. B 405 (1997) 327 [hep-ph/9703284] [INSPIRE].
G. Bell and T. Feldmann, Modelling light-cone distribution amplitudes from non-relativistic bound states, JHEP 04 (2008) 061 [arXiv:0802.2221] [INSPIRE].
S. Descotes-Genon and N. Offen, Three-particle contributions to the renormalisation of B-meson light-cone distribution amplitudes, JHEP 05 (2009) 091 [arXiv:0903.0790] [INSPIRE].
M. Beneke and J. Rohrwild, B meson distribution amplitude from B → γℓν, Eur. Phys. J. C 71 (2011) 1818 [arXiv:1110.3228] [INSPIRE].
M. Beneke and T. Feldmann, Factorization of heavy to light form-factors in soft collinear effective theory, Nucl. Phys. B 685 (2004) 249 [hep-ph/0311335] [INSPIRE].
M. Beneke and D. Yang, Heavy-to-light B meson form-factors at large recoil energy: spectator-scattering corrections, Nucl. Phys. B 736 (2006) 34 [hep-ph/0508250] [INSPIRE].
C.W. Bauer, S. Fleming, D. Pirjol and I.W. Stewart, An effective field theory for collinear and soft gluons: heavy to light decays, Phys. Rev. D 63 (2001) 114020 [hep-ph/0011336] [INSPIRE].
C.W. Bauer, D. Pirjol and I.W. Stewart, Factorization and endpoint singularities in heavy to light decays, Phys. Rev. D 67 (2003) 071502 [hep-ph/0211069] [INSPIRE].
I.I. Balitsky and V.M. Braun, Evolution equations for QCD string operators, Nucl. Phys. B 311 (1989) 541 [INSPIRE].
A. Khodjamirian, T. Mannel, A.A. Pivovarov and Y.-M. Wang, Charm-loop effect in B → K (*) ℓ + ℓ − and B → K * γ, JHEP 09 (2010) 089 [arXiv:1006.4945] [INSPIRE].
A. Khodjamirian, T. Mannel and Y.M. Wang, B → Kℓ + ℓ − decay at large hadronic recoil, JHEP 02 (2013) 010 [arXiv:1211.0234] [INSPIRE].
H. Kawamura, J. Kodaira, C.-F. Qiao and K. Tanaka, B-meson light cone distribution amplitudes in the heavy quark limit, Phys. Lett. B 523 (2001) 111 [Erratum ibid. B 536 (2002) 344] [hep-ph/0109181] [INSPIRE].
B. Geyer and O. Witzel, B-meson distribution amplitudes of geometric twist vs. dynamical twist, Phys. Rev. D 72 (2005) 034023 [hep-ph/0502239] [INSPIRE].
V.M. Braun, A.N. Manashov and N. Offen, Evolution equation for the higher-twist B-meson distribution amplitude, Phys. Rev. D 92 (2015) 074044 [arXiv:1507.03445] [INSPIRE].
S.J. Lee and M. Neubert, Model-independent properties of the B-meson distribution amplitude, Phys. Rev. D 72 (2005) 094028 [hep-ph/0509350] [INSPIRE].
T. Feldmann, B.O. Lange and Y.-M. Wang, B-meson light-cone distribution amplitude: perturbative constraints and asymptotic behavior in dual space, Phys. Rev. D 89 (2014) 114001 [arXiv:1404.1343] [INSPIRE].
P. Ball, QCD sum rules on the light cone, factorization and SCET, hep-ph/0308249 [INSPIRE].
V.M. Braun, D. Yu. Ivanov and G.P. Korchemsky, The B meson distribution amplitude in QCD, Phys. Rev. D 69 (2004) 034014 [hep-ph/0309330] [INSPIRE].
B.O. Lange and M. Neubert, Renormalization group evolution of the B meson light cone distribution amplitude, Phys. Rev. Lett. 91 (2003) 102001 [hep-ph/0303082] [INSPIRE].
T. Nishikawa and K. Tanaka, QCD sum rules for quark-gluon three-body components in the B meson, Nucl. Phys. B 879 (2014) 110 [arXiv:1109.6786] [INSPIRE].
S. Aoki et al., Review of lattice results concerning low-energy particle physics, Eur. Phys. J. C 77 (2017) 112 [arXiv:1607.00299] [INSPIRE].
M. Beneke, A. Maier, J. Piclum and T. Rauh, The bottom-quark mass from non-relativistic sum rules at NNNLO, Nucl. Phys. B 891 (2015) 42 [arXiv:1411.3132] [INSPIRE].
B. Dehnadi, A.H. Hoang and V. Mateu, Bottom and charm mass determinations with a convergence test, JHEP 08 (2015) 155 [arXiv:1504.07638] [INSPIRE].
A. Khodjamirian, C. Klein, T. Mannel and N. Offen, Semileptonic charm decays D → πℓν ℓ and D → Kℓν ℓ from QCD light-cone sum rules, Phys. Rev. D 80 (2009) 114005 [arXiv:0907.2842] [INSPIRE].
Y.-M. Wang, Subleading power corrections in radiative leptonic B decay, Nucl. Part. Phys. Proc. 285-286 (2017) 75 [arXiv:1609.09813] [INSPIRE].
P. Ball and E. Kou, B → γeν transitions from QCD sum rules on the light cone, JHEP 04 (2003) 029 [hep-ph/0301135] [INSPIRE].
C. Bourrely, B. Machet and E. de Rafael, Semileptonic decays of pseudoscalar particles (M → M′ + ℓ + ν ℓ ) and short distance behavior of quantum chromodynamics, Nucl. Phys. B 189 (1981) 157 [INSPIRE].
E.B. Gregory et al., A prediction of the B * c mass in full lattice QCD, Phys. Rev. Lett. 104 (2010) 022001 [arXiv:0909.4462] [INSPIRE].
C.G. Boyd, B. Grinstein and R.F. Lebed, Model independent extraction of |V cb | using dispersion relations, Phys. Lett. B 353 (1995) 306 [hep-ph/9504235] [INSPIRE].
D. Bigi and P. Gambino, Revisiting B → Dℓν, Phys. Rev. D 94 (2016) 094008 [arXiv:1606.08030] [INSPIRE].
C. DeTar, LQCD: flavor physics and spectroscopy, PoS(LeptonPhoton2015)023 [arXiv:1511.06884] [INSPIRE].
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 [INSPIRE].
N. Carrasco et al., QED corrections to hadronic processes in lattice QCD, Phys. Rev. D 91 (2015) 074506 [arXiv:1502.00257] [INSPIRE].
Belle collaboration, R. Glattauer et al., Measurement of the decay B → Dℓν ℓ in fully reconstructed events and determination of the Cabibbo-Kobayashi-Maskawa matrix element |V cb |, Phys. Rev. D 93 (2016) 032006 [arXiv:1510.03657] [INSPIRE].
BaBar collaboration, J.P. Lees et al., Measurement of an excess of \( \overline{B}\to {D}^{\left(\ast \right)}{\tau}^{-}{\overline{\nu}}_{\tau } \) decays and implications for charged Higgs bosons, Phys. Rev. D 88 (2013) 072012 [arXiv:1303.0571] [INSPIRE].
BaBar collaboration, B. Aubert et al., Measurement of |V cb | and the form-factor slope in \( \overline{B}\to D{\ell}^{-}\overline{n}{u}_{\ell } \) decays in events tagged by a fully reconstructed B meson, Phys. Rev. Lett. 104 (2010) 011802 [arXiv:0904.4063] [INSPIRE].
A. Celis, M. Jung, X.-Q. Li and A. Pich, Scalar contributions to b → c(u)τν transitions, Phys. Lett. B 771 (2017) 168 [arXiv:1612.07757] [INSPIRE].
J.F. Kamenik and F. Mescia, B → Dτν branching ratios: opportunity for lattice QCD and hadron colliders, Phys. Rev. D 78 (2008) 014003 [arXiv:0802.3790] [INSPIRE].
D. Bečirević, N. Košnik and A. Tayduganov, \( \overline{B}\to D\tau {\overline{\nu}}_{\tau } \) vs. \( \overline{B}\to D\mu {\overline{\nu}}_{\mu } \), Phys. Lett. B 716 (2012) 208 [arXiv:1206.4977] [INSPIRE].
X.-Q. Li, Y.-D. Yang and X. Zhang, Revisiting the one leptoquark solution to the R(D (*)) anomalies and its phenomenological implications, JHEP 08 (2016) 054 [arXiv:1605.09308] [INSPIRE].
V.M. Braun, Y. Ji and A.N. Manashov, Higher-twist B-meson distribution amplitudes in HQET, JHEP 05 (2017) 022 [arXiv:1703.02446] [INSPIRE].
Z. Ligeti, M. Papucci and D.J. Robinson, New physics in the visible final states of B → D (*) τν, JHEP 01 (2017) 083 [arXiv:1610.02045] [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
ArXiv ePrint: 1701.06810
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Wang, YM., Wei, YB., Shen, YL. et al. Perturbative corrections to B → D form factors in QCD. J. High Energ. Phys. 2017, 62 (2017). https://doi.org/10.1007/JHEP06(2017)062
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2017)062