Abstract
We revisit light-cone sum rules with pion distribution amplitudes to determine the full set of local \( \overline{B} \) → π form factors. To this end, we determine all duality threshold parameters from a Bayesian fit for the first time. Our results, obtained at small momentum transfer q2, are extrapolated to large q2 where they agree with precise lattice QCD results. We find that a modification to the commonly used BCL parametrization is crucial to interpolate the scalar form factor between the two q2 regions. We provide numerical results for the form factor parameters — including their covariance — based on simultaneous fit of all three form factors to both the sum rule and lattice QCD results. Our predictions for the form factors agree well with measurements of the q2 spectrum of the semileptonic decay \( {\overline{B}}^0\to {\pi}^{+}{\mathrm{\ell}}^{-}{\overline{\nu}}_{\mathrm{\ell}} \). From the world average of the latter we obtain |Vub| = (3.77 ± 0.15) · 10−3, which is in agreement with the most recent inclusive determination at the 1 σ level.
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S.W. Bosch, B.O. Lange, M. Neubert and G. Paz, Factorization and shape function effects in inclusive B meson decays, Nucl. Phys. B 699 (2004) 335 [hep-ph/0402094] [INSPIRE].
S.W. Bosch, M. Neubert and G. Paz, Subleading shape functions in inclusive B decays, JHEP 11 (2004) 073 [hep-ph/0409115] [INSPIRE].
B.O. Lange, M. Neubert and G. Paz, Theory of charmless inclusive B decays and the extraction of Vub, Phys. Rev. D 72 (2005) 073006 [hep-ph/0504071] [INSPIRE].
M. Neubert, Two-loop relations for heavy-quark parameters in the shape-function scheme, Phys. Lett. B 612 (2005) 13 [hep-ph/0412241] [INSPIRE].
M. Neubert, Advanced predictions for moments of the \( \overline{B} \) → Xsγ photon spectrum, Phys. Rev. D 72 (2005) 074025 [hep-ph/0506245] [INSPIRE].
P. Gambino, P. Giordano, G. Ossola and N. Uraltsev, Inclusive semileptonic B decays and the determination of |V(ub)|, JHEP 10 (2007) 058 [arXiv:0707.2493] [INSPIRE].
P. Gambino, B semileptonic moments at NNLO, JHEP 09 (2011) 055 [arXiv:1107.3100] [INSPIRE].
HFLAV collaboration, Averages of b-hadron, c-hadron, and τ-lepton properties as of 2018, Eur. Phys. J. C 81 (2021) 226 [arXiv:1909.12524] [INSPIRE].
P. Gambino et al., Challenges in semileptonic B decays, Eur. Phys. J. C 80 (2020) 966 [arXiv:2006.07287] [INSPIRE].
Belle collaboration, Measurements of Partial Branching Fractions of Inclusive B → Xuℓ+ νℓ Decays with Hadronic Tagging, arXiv:2102.00020 [INSPIRE].
V.M. Braun and I.E. Filyanov, QCD Sum Rules in Exclusive Kinematics and Pion Wave Function, Z. Phys. C 44 (1989) 157 [Sov. J. Nucl. Phys. 50 (1989) 511] [INSPIRE].
I.I. Balitsky, V.M. Braun and A.V. Kolesnichenko, Radiative Decay Σ+ → pγ in Quantum Chromodynamics, Nucl. Phys. B 312 (1989) 509 [INSPIRE].
V.L. Chernyak and I.R. Zhitnitsky, B meson exclusive decays into baryons, Nucl. Phys. B 345 (1990) 137 [INSPIRE].
P. Colangelo and A. Khodjamirian, QCD sum rules, a modern perspective, hep-ph/0010175 [INSPIRE].
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].
G. Duplancic, A. Khodjamirian, T. Mannel, B. Melić and N. Offen, Light-cone sum rules for B → π form factors revisited, JHEP 04 (2008) 014 [arXiv:0801.1796] [INSPIRE].
A. Bharucha, Two-loop Corrections to the Btoπ Form Factor from QCD Sum Rules on the Light-Cone and |Vub|, JHEP 05 (2012) 092 [arXiv:1203.1359] [INSPIRE].
A.V. Rusov, Higher-twist effects in light-cone sum rule for the B → π form factor, Eur. Phys. J. C 77 (2017) 442 [arXiv:1705.01929] [INSPIRE].
G. Duplancic and B. Melić, B(s) → K form factors: An Update of light-cone sum rule results, Phys. Rev. D 78 (2008) 054015 [arXiv:0805.4170] [INSPIRE].
A. Khodjamirian, C. Klein, T. Mannel and N. Offen, Semileptonic charm decays D → \( \pi \mathrm{\ell}{\overline{\nu}}_{\mathrm{\ell}} \) and D → \( K\mathrm{\ell}{\overline{\nu}}_{\mathrm{\ell}} \) from QCD Light-Cone Sum Rules, Phys. Rev. D 80 (2009) 114005 [arXiv:0907.2842] [INSPIRE].
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].
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].
Particle Data Group collaboration, Review of Particle Physics, PTEP 2020 (2020) 083C01 [INSPIRE].
B.L. Ioffe, Condensates in quantum chromodynamics, Phys. Atom. Nucl. 66 (2003) 30 [hep-ph/0207191] [INSPIRE].
Flavour Lattice Averaging Group collaboration, FLAG Review 2019: Flavour Lattice Averaging Group (FLAG), Eur. Phys. J. C 80 (2020) 113 [arXiv:1902.08191] [INSPIRE].
RQCD collaboration, Light-cone distribution amplitudes of pseudoscalar mesons from lattice QCD, JHEP 08 (2019) 065 [Addendum ibid. 11 (2020) 037] [arXiv:1903.08038] [INSPIRE].
A. Khodjamirian, T. Mannel, N. Offen and Y.M. Wang, B → πℓνl Width and |Vub| from QCD Light-Cone Sum Rules, Phys. Rev. D 83 (2011) 094031 [arXiv:1103.2655] [INSPIRE].
P. Ball, V.M. Braun and A. Lenz, Higher-twist distribution amplitudes of the K meson in QCD, JHEP 05 (2006) 004 [hep-ph/0603063] [INSPIRE].
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. 89 (2014) 099901] [Erratum ibid. 91 (2015) 099901] [arXiv:1305.5432] [INSPIRE].
A. Khodjamirian and A.V. Rusov, Bs → Kℓνℓ and B(s) → π(K)ℓ+ℓ− decays at large recoil and CKM matrix elements, JHEP 08 (2017) 112 [arXiv:1703.04765] [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].
C. Bourrely, I. Caprini and L. Lellouch, Model-independent description of B → \( \pi \mathrm{\ell}\overline{\nu } \) decays and a determination of |Vub|, Phys. Rev. D 79 (2009) 013008 [Erratum ibid. 82 (2010) 099902] [arXiv:0807.2722] [INSPIRE].
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].
Fermilab Lattice and MILC collaborations, B → πℓℓ form factors for new-physics searches from lattice QCD, Phys. Rev. Lett. 115 (2015) 152002 [arXiv:1507.01618] [INSPIRE].
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].
A. Bharucha, T. Feldmann and M. Wick, Theoretical and Phenomenological Constraints on Form Factors for Radiative and Semi-Leptonic B-Meson Decays, JHEP 09 (2010) 090 [arXiv:1004.3249] [INSPIRE].
ETM collaboration, Masses and decay constants of \( {D}_{(s)}^{\ast } \) and \( {B}_{(s)}^{\ast } \) mesons with Nf = 2 + 1 + 1 twisted mass fermions, Phys. Rev. D 96 (2017) 034524 [arXiv:1707.04529] [INSPIRE].
A. Khodjamirian, B. Melić, Y.-M. Wang and Y.-B. Wei, The D*Dπ and B*Bπ couplings from light-cone sum rules, JHEP 03 (2021) 016 [arXiv:2011.11275] [INSPIRE].
N. Isgur and M.B. Wise, Influence of the B* Resonance on \( \overline{B}\to \pi e\overline{\nu} \), Phys. Rev. D 41 (1990) 151 [INSPIRE].
C.A. Dominguez, J.G. Korner and K. Schilcher, The scalar form-factor in the exclusive semileptonic decay of B → \( \pi \tau {\overline{\nu}}_{\tau } \), Phys. Lett. B 248 (1990) 399 [INSPIRE].
M.B. Wise, Chiral perturbation theory for hadrons containing a heavy quark, Phys. Rev. D 45 (1992) R2188 [INSPIRE].
G. Burdman and J.F. Donoghue, Union of chiral and heavy quark symmetries, Phys. Lett. B 280 (1992) 287 [INSPIRE].
L. Wolfenstein, General results for the decays D → \( \pi \mathrm{\ell}\overline{\nu } \) and B → \( \pi \mathrm{\ell}\overline{\nu } \), Phys. Lett. B 291 (1992) 177 [INSPIRE].
G. Burdman, Z. Ligeti, M. Neubert and Y. Nir, The Decay B → \( \pi \mathrm{\ell}\overline{\nu } \) in heavy quark effective theory, Phys. Rev. D 49 (1994) 2331 [hep-ph/9309272] [INSPIRE].
E. Dalgic, A. Gray, M. Wingate, C.T.H. Davies, G.P. Lepage and J. Shigemitsu, B meson semileptonic form-factors from unquenched lattice QCD, Phys. Rev. D 73 (2006) 074502 [Erratum ibid. 75 (2007) 119906] [hep-lat/0601021] [INSPIRE].
B. Colquhoun, R.J. Dowdall, J. Koponen, C.T.H. Davies and G.P. Lepage, B → πℓν at zero recoil from lattice QCD with physical u/d quarks, Phys. Rev. D 93 (2016) 034502 [arXiv:1510.07446] [INSPIRE].
Fermilab Lattice and MILC collaborations, Bs → Kℓν decay from lattice QCD, Phys. Rev. D 100 (2019) 034501 [arXiv:1901.02561] [INSPIRE].
H.-Y. Cheng and F.-S. Yu, Masses of Scalar and Axial-Vector B Mesons Revisited, Eur. Phys. J. C 77 (2017) 668 [arXiv:1704.01208] [INSPIRE].
I. Caprini, B. Grinstein and R.F. Lebed, Model-independent constraints on hadronic form factors with above-threshold poles, Phys. Rev. D 96 (2017) 036015 [arXiv:1705.02368] [INSPIRE].
RBC and UKQCD collaborations, The B*Bπ Coupling Using Relativistic Heavy Quarks, Phys. Rev. D 93 (2016) 014510 [arXiv:1506.06413] [INSPIRE].
S. Gonzàlez-Solís and P. Masjuan, Study of B → πℓνℓ and B+ → η(′)ℓ+νℓ decays and determination of |Vub|, Phys. Rev. D 98 (2018) 034027 [arXiv:1805.11262] [INSPIRE].
BaBar collaboration, Study of B → πℓν and B → ρℓν Decays and Determination of |Vub|, Phys. Rev. D 83 (2011) 032007 [arXiv:1005.3288] [INSPIRE].
BaBar collaboration, Branching fraction and form-factor shape measurements of exclusive charmless semileptonic B decays, and determination of |Vub|, Phys. Rev. D 86 (2012) 092004 [arXiv:1208.1253] [INSPIRE].
Belle collaboration, Measurement of the decay B0 → π−ℓf+ν and determination of |Vub|, Phys. Rev. D 83 (2011) 071101 [arXiv:1012.0090] [INSPIRE].
Belle collaboration, Study of Exclusive B → Xuℓν Decays and Extraction of ||Vub|| using Full Reconstruction Tagging at the Belle Experiment, Phys. Rev. D 88 (2013) 032005 [arXiv:1306.2781] [INSPIRE].
T. Becher and R.J. Hill, Comment on form-factor shape and extraction of |Vub| from \( \overline{B}\to \pi \mathrm{\ell}\overline{\nu } \), Phys. Lett. B 633 (2006) 61 [hep-ph/0509090] [INSPIRE].
F.U. Bernlochner, M.F. Sevilla, D.J. Robinson and G. Wormser, Semitauonic b-hadron decays: A lepton flavor universality laboratory, arXiv:2101.08326 [INSPIRE].
D. Bečirević, F. Jaffredo, A. Peñuelas and O. Sumensari, New Physics effects in leptonic and semileptonic decays, JHEP 05 (2021) 175 [arXiv:2012.09872] [INSPIRE].
F.U. Bernlochner, B → \( \pi \tau {\overline{\nu}}_{\tau } \) decay in the context of type-II 2HDM, Phys. Rev. D 92 (2015) 115019 [arXiv:1509.06938] [INSPIRE].
Belle collaboration, Search for B0 → π−τ+ντ with hadronic tagging at Belle, Phys. Rev. D 93 (2016) 032007 [arXiv:1509.06521] [INSPIRE].
C. Bobeth, G. Hiller and G. Piranishvili, Angular distributions of \( \overline{B}\to \overline{K}{\mathrm{\ell}}^{+}{\mathrm{\ell}}^{-} \) decays, JHEP 12 (2007) 040 [arXiv:0709.4174] [INSPIRE].
HPQCD collaboration, Standard Model Predictions for B → Kℓ+ℓ− with Form Factors from Lattice QCD, Phys. Rev. Lett. 111 (2013) 162002 [Erratum ibid. 112 (2014) 149902] [arXiv:1306.0434] [INSPIRE].
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Leljak, D., Melić, B. & van Dyk, D. The \( \overline{B} \) → π form factors from QCD and their impact on |Vub|. J. High Energ. Phys. 2021, 36 (2021). https://doi.org/10.1007/JHEP07(2021)036
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DOI: https://doi.org/10.1007/JHEP07(2021)036