*B* →*P* and *B* →*V* form factors from *B*-meson light-cone sum rules beyond leading twist

- 23 Downloads

## Abstract

We provide results for the full set of form factors describing semileptonic *B*-meson transitions to pseudoscalar mesons *π*, *K*, \( \overline{D} \) and vector mesons *ρ*, *K*^{∗}, \( {\overline{D}}^{\ast } \). Our results are obtained within the framework of QCD Light-Cone Sum Rules with *B*-meson distribution amplitudes. We recalculate and confirm the results for the leading-twist two-particle contributions in the literature. Furthermore, we calculate and provide new expressions for the two-particle contributions up to twist four. Following new developments for the three-particle distribution amplitudes, we calculate and provide new results for the complete set of three-particle contributions up to twist four. The form factors are computed numerically at several phase space points using up-to-date input parameters, including correlations across phase space points and form factors. We use a model ansatz for all contributing *B*-meson distribution amplitudes that is self-consistent up to twist-four accuracy. We find that the higher-twist two-particle contributions have a substantial impact on the results, and dominate over the three-particle contributions. Our numerical results, including correlations, are provided as machine-readable files in the supplementary material. We discuss the qualitative phenomenological impact of our results on the present *b* anomalies.

## Keywords

QCD Phenomenology## Notes

### **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.

## Supplementary material

## References

- [1]J. Albrecht et al.,
*Future prospects for exploring present day anomalies in flavour physics measurements with Belle II and LHCb*, arXiv:1709.10308 [INSPIRE]. - [2]J. Albrecht, S. Reichert and D. van Dyk,
*Status of rare exclusive B meson decays in 2018*,*Int. J. Mod. Phys.***A 33**(2018) 1830016 [arXiv:1806.05010] [INSPIRE].ADSCrossRefGoogle Scholar - [3]
- [4]D. Bigi, P. Gambino and S. Schacht,
*R*(*D*^{∗})*,*|*V*_{cb}|*and the heavy quark symmetry relations between form factors*,*JHEP***11**(2017) 061 [arXiv:1707.09509] [INSPIRE]. - [5]M. Jung and D.M. Straub,
*Constraining new physics in b*→*cℓν transitions*, arXiv:1801.01112 [INSPIRE]. - [6]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]. - [7]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]. - [8]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]. - [9]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]. - [10]S. Cheng, A. Khodjamirian and J. Virto,
*B*→*ππ form factors from light-cone sum rules with B-meson distribution amplitudes*,*JHEP***05**(2017) 157 [arXiv:1701.01633] [INSPIRE]. - [11]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]. - [12]P. Ball and R. Zwicky,
*B*_{d,s}→*ρ, ω, K*^{∗}*,*\( \phi \)*decay form-factors from light-cone sum rules revisited*,*Phys. Rev.***D 71**(2005) 014029 [hep-ph/0412079] [INSPIRE]. - [13]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]. - [14]A. Khodjamirian, T. Mannel, N. Offen and Y.M. Wang,
*B*→*πℓν*_{l}*width and*|*V*_{ub}|*from QCD light-cone sum rules*,*Phys. Rev.***D 83**(2011) 094031 [arXiv:1103.2655] [INSPIRE]. - [15]A. Bharucha,
*Two-loop corrections to the B*→*π form factor from QCD sum rules on the light-cone and*|*V*_{ub}|,*JHEP***05**(2012) 092 [arXiv:1203.1359] [INSPIRE]. - [16]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]. - [17]A. Bharucha, D.M. Straub and R. Zwicky,
*B*→*V ℓ*^{+}*ℓ*^{−}*in the standard model from light-cone sum rules*,*JHEP***08**(2016) 098 [arXiv:1503.05534] [INSPIRE]. - [18]A. Khodjamirian and A.V. Rusov,
*B*_{s}→*Kℓν*_{ℓ}*and B*_{(s)}→*π*(*K*)*ℓ*^{+}*ℓ*^{−}*decays at large recoil and CKM matrix elements*,*JHEP***08**(2017) 112 [arXiv:1703.04765] [INSPIRE]. - [19]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]. - [20]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]. - [21]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]. - [22]Y.-M. Wang, Y.-B. Wei, Y.-L. Shen and C.-D. Lü,
*Perturbative corrections to B*→*D form factors in QCD*,*JHEP***06**(2017) 062 [arXiv:1701.06810] [INSPIRE]. - [23]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].ADSCrossRefGoogle Scholar - [24]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]. - [25]H. Kawamura, J. Kodaira, C.-F. Qiao and K. Tanaka,
*Transverse momentum distribution in B mesons in the heavy quark limit: the Wandzura-Wilczek part*,*Mod. Phys. Lett.***A 18**(2003) 799 [hep-ph/0112174] [INSPIRE]. - [26]S. Faller et al.,
*Disentangling the Decay Observables in*\( {B}^{-}\to {\pi}^{+}{\pi}^{-}{\ell}^{-}{\overline{\nu}}_{\ell } \),*Phys. Rev.***D 89**(2014) 014015 [arXiv:1310.6660] [INSPIRE]. - [27]X.-W. Kang, B. Kubis, C. Hanhart and U.-G. Meissner,
*B*_{l4}*decays and the extraction of*|*V*_{ub}|,*Phys. Rev.***D 89**(2014) 053015 [arXiv:1312.1193] [INSPIRE]. - [28]C. Hambrock and A. Khodjamirian,
*Form factors in*\( {\overline{B}}^0\to \pi \pi \ell {\overline{\nu}}_{\ell } \)*from QCD light-cone sum rules*,*Nucl. Phys.***B 905**(2016) 373 [arXiv:1511.02509] [INSPIRE]. - [29]P. Böer, T. Feldmann and D. van Dyk,
*QCD factorization theorem for B*→*ππℓν decays at large dipion masses*,*JHEP***02**(2017) 133 [arXiv:1608.07127] [INSPIRE]. - [30]S. Cheng, A. Khodjamirian and J. Virto,
*Timelike-helicity B*→*ππ form factor from light-cone sum rules with dipion distribution amplitudes*,*Phys. Rev.***D 96**(2017) 051901 [arXiv:1709.00173] [INSPIRE]. - [31]T. Feldmann, D. Van Dyk and K.K. Vos,
*Revisiting B*→*ππℓν at large dipion masses*,*JHEP***10**(2018) 030 [arXiv:1807.01924] [INSPIRE]. - [32]U.-G. Meissner and W. Wang, \( {B}_s\to {K}^{\left(\ast \right)}\ell \overline{\nu} \)
*, angular analysis, S-wave contributions and*|*V*_{ub}|,*JHEP***01**(2014) 107 [arXiv:1311.5420] [INSPIRE]. - [33]U.-G. Meissner and W. Wang,
*Generalized heavy-to-light form factors in light-cone sum rules*,*Phys. Lett.***B 730**(2014) 336 [arXiv:1312.3087] [INSPIRE]. - [34]D. Das, G. Hiller, M. Jung and A. Shires,
*The*\( \overline{B}\to \overline{K}\pi \ell \ell \)*and*\( {\overline{B}}_s\to \overline{K}K\ell \ell \)*distributions at low hadronic recoil*,*JHEP***09**(2014) 109 [arXiv:1406.6681] [INSPIRE]. - [35]T. Feldmann, B. Müller and D. van Dyk,
*Analyzing b*→*u transitions in semileptonic*\( {\overline{B}}_s\to {K}^{\ast +}\left(\to K\pi \right){\ell}^{-}{\overline{\nu}}_{\ell } \)*decays*,*Phys. Rev.***D 92**(2015) 034013 [arXiv:1503.09063] [INSPIRE]. - [36]S. Descotes-Genon, A. Khodjamirian and J. Virto,
*Light-cone sum rules for B*→*Kπ form factors and applications to rare decays*, to appear.Google Scholar - [37]S. Descotes-Genon, A. Khodjamirian, J. Virto and K. K. Vos,
*Light-cone sum rules for S-wave B*→*M*_{1}*M*_{2}*form factors*, work in progress.Google Scholar - [38]W.-F. Wang, H.-n. Li, W. Wang and C.-D. Lü,
*S-wave resonance contributions to the B*_{( s)}^{0}→*J*/*ψπ*^{+}*π*^{−}*and B*_{s}→*π*^{+}*π*^{−}*μ*^{+}*μ*^{−}*decays*,*Phys. Rev.***D 91**(2015) 094024 [arXiv:1502.05483] [INSPIRE]. - [39]S. Kränkl, T. Mannel and J. Virto,
*Three-body non-leptonic B decays and QCD factorization*,*Nucl. Phys.***B 899**(2015) 247 [arXiv:1505.04111] [INSPIRE]. - [40]J.T. Daub, C. Hanhart and B. Kubis,
*A model-independent analysis of final-state interactions in*\( {\overline{B}}_{d/s}^0\to J/\psi \pi \pi \),*JHEP***02**(2016) 009 [arXiv:1508.06841] [INSPIRE]. - [41]H.-Y. Cheng, C.-K. Chua and Z.-Q. Zhang,
*Direct CP-violation in charmless three-body decays of B mesons*,*Phys. Rev.***D 94**(2016) 094015 [arXiv:1607.08313] [INSPIRE]. - [42]W.-F. Wang and H.-n. Li,
*Quasi-two-body decays B*→*Kρ*→*Kππ in perturbative QCD approach*,*Phys. Lett.***B 763**(2016) 29 [arXiv:1609.04614] [INSPIRE]. - [43]M. Albaladejo et al.,
*How to employ*\( {\overline{B}}_d^0\to J/\psi \left(\pi \eta,\ \overline{K}K\right) \)*decays to extract information on πη scattering*,*JHEP***04**(2017) 010 [arXiv:1611.03502] [INSPIRE]. - [44]R. Klein, T. Mannel, J. Virto and K.K. Vos,
*CP violation in multibody B decays from QCD factorization*,*JHEP***10**(2017) 117 [arXiv:1708.02047] [INSPIRE].ADSCrossRefGoogle Scholar - [45]I.I. Balitsky and V.M. Braun,
*Nonlocal operator expansion for structure functions of e*^{+}*e*^{−}*annihilation*,*Phys. Lett.***B 222**(1989) 123 [INSPIRE]. - [46]D. van Dyk et al.,
*EOS release v0.2.3*, https://github.com/eos/eos/releases/tag/v0.2.3. - [47]D. van Dyk et al.,
*EOS — A HEP program for flavor observables*(2018).Google Scholar - [48]M. Beneke, V.M. Braun, Y. Ji and Y.-B. Wei,
*Radiative leptonic decay B*→*γℓν*_{ℓ}*with subleading power corrections*,*JHEP***07**(2018) 154 [arXiv:1804.04962] [INSPIRE]. - [49]A. Bazavov et al.,
*B- and D-meson leptonic decay constants from four-flavor lattice QCD*,*Phys. Rev.***D 98**(2018) 074512 [arXiv:1712.09262] [INSPIRE]. - [50]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]. - [51]M.A. Shifman, A.I. Vainshtein and V.I. Zakharov,
*QCD and resonance physics. Theoretical foundations*,*Nucl. Phys.***B 147**(1979) 385 [INSPIRE]. - [52]
- [53]A. Khodjamirian, T. Mannel and M. Melcher,
*Flavor*SU(3)*symmetry in charmless B decays*,*Phys. Rev.***D 68**(2003) 114007 [hep-ph/0308297] [INSPIRE]. - [54]S. Aoki et al.,
*Review of lattice results concerning low-energy particle physics*,*Eur. Phys. J.***C 77**(2017) 112 [arXiv:1607.00299] [INSPIRE]. - [55]HPQCD, UKQCD collaboration,
*High Precision determination of the pi, K, D and D*_{s}*decay constants from lattice QCD*,*Phys. Rev. Lett.***100**(2008) 062002 [arXiv:0706.1726] [INSPIRE]. - [56]MILC collaboration,
*Results for light pseudoscalar mesons*, PoS(LATTICE 2010) 074 [arXiv:1012.0868] [INSPIRE]. - [57]RBC, UKQCD collaboration,
*Domain wall QCD with near-physical pions*,*Phys. Rev.***D 87**(2013) 094514 [arXiv:1208.4412] [INSPIRE]. - [58]R.J. Dowdall, C.T.H. Davies, G.P. Lepage and C. McNeile,
*Vus from π and K decay constants in full lattice QCD with physical u, d, s and c quarks*,*Phys. Rev.***D 88**(2013) 074504 [arXiv:1303.1670] [INSPIRE]. - [59]N. Carrasco et al.,
*Leptonic decay constants f*_{K}*, f*_{D}*, and f*_{Ds}*with N*_{f}= 2 + 1 + 1*twisted-mass lattice QCD*,*Phys. Rev.***D 91**(2015) 054507 [arXiv:1411.7908] [INSPIRE]. - [60]Fermilab Lattice, MILC collaboration,
*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]. - [61]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] [arXiv:1305.5432] [INSPIRE]. - [62]V. Braun, private communications.Google Scholar
- [63]C.-D. Lü, Y.-L. Shen, Y.-M. Wang and Y.-B. Wei,
*QCD calculations of B*→*π, K form factors with higher-twist corrections*, arXiv:1810.00819 [INSPIRE]. - [64]HPQCD collaboration,
*Rare decay B*→*Kℓ*^{+}*ℓ*^{−}*form factors from lattice QCD*,*Phys. Rev.***D 88**(2013) 054509 [*Erratum ibid.***D 88**(2013) 079901] [arXiv:1306.2384] [INSPIRE]. - [65]R.R. Horgan, Z. Liu, S. Meinel and M. Wingate,
*Lattice QCD calculation of form factors describing the rare decays B*→*K*^{∗}*ℓ*^{+}*ℓ*^{−}*and B*_{s}→ \( \phi \)*ℓ*^{+}*ℓ*^{−},*Phys. Rev.***D 89**(2014) 094501 [arXiv:1310.3722] [INSPIRE]. - [66]Fermilab Lattice, MILC collaboration,
*Update of*|*V*_{cb}|*from the*\( \overline{B}\to {D}^{\ast}\ell \overline{\nu} \)*form factor at zero recoil with three-flavor lattice QCD*,*Phys. Rev.***D 89**(2014) 114504 [arXiv:1403.0635] [INSPIRE]. - [67]R.R. Horgan, Z. Liu, S. Meinel and M. Wingate,
*Rare B decays using lattice QCD form factors*,*PoS***LATTICE2014**(2015) 372 [arXiv:1501.00367] [INSPIRE]. - [68]HPQCD collaboration,
*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]. - [69]Fermilab Lattice, MILC collaboration, |
*V*_{ub}|*from B*→*πℓν decays and*(2 + 1)*-flavor lattice QCD*,*Phys. Rev.***D 92**(2015) 014024 [arXiv:1503.07839] [INSPIRE]. - [70]HPQCD collaboration,
*Lattice QCD calculation of the B*_{(s)}→*D*_{( s)}^{*}*ℓν form factors at zero recoil and implications for*|*V*_{cb}|,*Phys. Rev.***D 97**(2018) 054502 [arXiv:1711.11013] [INSPIRE]. - [71]D.M. Straub,
*flavio: a Python package for flavour and precision phenomenology in the Standard Model and beyond*, arXiv:1810.08132 [INSPIRE]. - [72]W. Detmold, C. Lehner and S. Meinel, \( {\varLambda}_b\to p{\ell}^{-}{\overline{\nu}}_{\ell } \)
*and*\( {\varLambda}_b\to\ {\varLambda}_c{\ell}^{-}{\overline{\nu}}_{\ell } \)*form factors from lattice QCD with relativistic heavy quarks*,*Phys. Rev.***D 92**(2015) 034503 [arXiv:1503.01421] [INSPIRE]. - [73]LHCb collaboration,
*Differential branching fractions and isospin asymmetries of B*→*K*^{(∗)}*μ*^{+}*μ*^{−}*decays*,*JHEP***06**(2014) 133 [arXiv:1403.8044] [INSPIRE]. - [74]LHCb collaboration,
*Angular analysis and differential branching fraction of the decay B*_{s}^{0}→*ϕμ*^{+}*μ*^{−},*JHEP***09**(2015) 179 [arXiv:1506.08777] [INSPIRE]. - [75]LHCb collaboration,
*Measurements of the S-wave fraction in B*^{0}→*K*^{+}*π*^{−}*μ*^{+}*μ*^{−}*decays and the B*^{0}→*K*^{∗}(892)^{0}*μ*^{+}*μ*^{−}*differential branching fraction*,*JHEP***11**(2016) 047 [*Erratum ibid.***04**(2017) 142] [arXiv:1606.04731] [INSPIRE]. - [76]LHCb collaboration,
*Differential branching fraction and angular analysis of*Λ_{b}^{0}→ Λ*μ*^{+}*μ*^{−}*decays*,*JHEP***06**(2015) 115 [*Erratum ibid.***09**(2018) 145] [arXiv:1503.07138] [INSPIRE]. - [77]LHCb collaboration,
*Angular analysis of the B*^{0}→*K*^{∗0}*μ*^{+}*μ*^{−}*decay using*3*fb*^{−1}*of integrated luminosity*,*JHEP***02**(2016) 104 [arXiv:1512.04442] [INSPIRE]. - [78]CMS collaboration,
*Angular analysis of the decay B*^{0}→*K*^{∗0}*μ*+*μ*−*from pp collisions at*\( \sqrt{s}=8 \)*TeV*,*Phys. Lett.***B 753**(2016) 424 [arXiv:1507.08126] [INSPIRE]. - [79]ATLAS collaboration,
*Angular analysis of B*_{d}^{0}→*K*^{∗}*μ*^{+}*μ*^{−}*decays in pp collisions at*\( \sqrt{s}=8 \)*TeV with the ATLAS detector*,*JHEP***10**(2018) 047 [arXiv:1805.04000] [INSPIRE]. - [80]LHCb collaboration,
*Test of lepton universality using B*^{+}→*K*^{+}*ℓ*^{+}*ℓ*^{−}*decays*,*Phys. Rev. Lett.***113**(2014) 151601 [arXiv:1406.6482] [INSPIRE]. - [81]LHCb collaboration,
*Test of lepton universality with B*^{0}→*K*^{∗0}*ℓ*^{+}*ℓ*^{−}*decays*,*JHEP***08**(2017) 055 [arXiv:1705.05802] [INSPIRE]. - [82]S. Descotes-Genon, J. Matias and J. Virto,
*Understanding the B*→*K*^{∗}*μ*^{+}*μ*^{−}*anomaly*,*Phys. Rev.***D 88**(2013) 074002 [arXiv:1307.5683] [INSPIRE]. - [83]W. Altmannshofer and D.M. Straub,
*New physics in B*→*K*^{∗}*μμ?*,*Eur. Phys. J.***C 73**(2013) 2646 [arXiv:1308.1501] [INSPIRE]. - [84]F. Beaujean, C. Bobeth and D. van Dyk,
*Comprehensive Bayesian analysis of rare (semi)leptonic and radiative B decays*,*Eur. Phys. J.***C 74**(2014) 2897 [*Erratum ibid.***C 74**(2014) 3179] [arXiv:1310.2478] [INSPIRE]. - [85]T. Hurth and F. Mahmoudi,
*On the LHCb anomaly in B*→*K*^{∗}*ℓ*^{+}*ℓ*^{−},*JHEP***04**(2014) 097 [arXiv:1312.5267] [INSPIRE]. - [86]S. Descotes-Genon, L. Hofer, J. Matias and J. Virto,
*Global analysis of b*→*sℓℓ anomalies*,*JHEP***06**(2016) 092 [arXiv:1510.04239] [INSPIRE]. - [87]W. Altmannshofer, C. Niehoff, P. Stangl and D.M. Straub,
*Status of the B*→*K*^{∗}*μ*^{+}*μ*^{−}*anomaly after Moriond 2017*,*Eur. Phys. J.***C 77**(2017) 377 [arXiv:1703.09189] [INSPIRE]. - [88]W. Altmannshofer, P. Stangl and D.M. Straub,
*Interpreting hints for lepton flavor universality violation*,*Phys. Rev.***D 96**(2017) 055008 [arXiv:1704.05435] [INSPIRE]. - [89]B. Capdevila et al.,
*Patterns of new physics in b*→*sℓ*^{+}*ℓ*^{−}*transitions in the light of recent data*,*JHEP***01**(2018) 093 [arXiv:1704.05340] [INSPIRE]. - [90]L.-S. Geng et al.,
*Towards the discovery of new physics with lepton-universality ratios of b*→*sℓℓ decays*,*Phys. Rev.***D 96**(2017) 093006 [arXiv:1704.05446] [INSPIRE]. - [91]M. Ciuchini et al.,
*On flavourful easter eggs for new physics hunger and lepton flavour universality violation*,*Eur. Phys. J.***C 77**(2017) 688 [arXiv:1704.05447] [INSPIRE]. - [92]F. Mahmoudi, T. Hurth and S. Neshatpour,
*Updated fits to the present b*→*sℓ*^{+}*ℓ*^{−}*data*,*Acta Phys. Polon.***B 49**(2018) 1267 [INSPIRE]. - [93]G. Hiller and F. Krüger,
*More model-independent analysis of b*→*s processes*,*Phys. Rev.***D 69**(2004) 074020 [hep-ph/0310219] [INSPIRE]. - [94]C. Bobeth, G. Hiller and G. Piranishvili,
*Angular distributions of*\( \overline{B}\to \overline{K}{\ell}^{+}{\ell}^{-} \)*decays*,*JHEP***12**(2007) 040 [arXiv:0709.4174] [INSPIRE]. - [95]M. Bordone, G. Isidori and A. Pattori,
*On the standard model predictions for R*_{K}*and R*_{K}∗ ,*Eur. Phys. J.***C 76**(2016) 440 [arXiv:1605.07633] [INSPIRE]. - [96]J. Charles et al.,
*Heavy to light form-factors in the heavy mass to large energy limit of QCD*,*Phys. Rev.***D 60**(1999) 014001 [hep-ph/9812358] [INSPIRE]. - [97]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]. - [98]C. Bobeth, M. Chrzaszcz, D. van Dyk and J. Virto,
*Long-distance effects in B*→*K*^{∗}*ℓℓ from analyticity*,*Eur. Phys. J.***C 78**(2018) 451 [arXiv:1707.07305] [INSPIRE]. - [99]R.R. Horgan, Z. Liu, S. Meinel and M. Wingate,
*Calculation of B*^{0}→*K*^{∗0}*μ*^{+}*μ*^{−}*and B*_{s}^{0}→*ϕμ*^{+}*μ*^{−}*observables using form factors from lattice QCD*,*Phys. Rev. Lett.***112**(2014) 212003 [arXiv:1310.3887] [INSPIRE]. - [100]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]. - [101]I. Caprini, L. Lellouch and M. Neubert,
*Dispersive bounds on the shape of*\( \overline{B}\to {D}^{\left(\ast \right)} \)*lepton anti-neutrino form-factors*,*Nucl. Phys.***B 530**(1998) 153 [hep-ph/9712417] [INSPIRE]. - [102]S. Fajfer, J.F. Kamenik and I. Nisandzic,
*On the*\( B\to {D}^{\ast}\tau {\overline{\nu}}_{\tau } \)*sensitivity to new physics*,*Phys. Rev.***D 85**(2012) 094025 [arXiv:1203.2654] [INSPIRE]. - [103]F.U. Bernlochner, Z. Ligeti, M. Papucci and D.J. Robinson,
*Combined analysis of semileptonic B decays to D and D*^{∗}*: R*(*D*^{(∗)})*,*|*V*_{cb}|*and new physics*,*Phys. Rev.***D 95**(2017) 115008 [*Erratum ibid.***D 97**(2018) 059902] [arXiv:1703.05330] [INSPIRE]. - [104]A.G. Grozin and M. Neubert,
*Asymptotics of heavy meson form-factors*,*Phys. Rev.***D 55**(1997) 272 [hep-ph/9607366] [INSPIRE].