Abstract
We study the impact of third-order QCD corrections for several kinematic moments of the inclusive semileptonic B decays, to first order in the 1/mb expansion. We consider the first four moments of the charged-lepton energy ER spectrum, the total leptonic invariant mass q2 and the hadronic invariant mass \( {M}_X^2 \). No experimental cuts are applied. Our analytic results are obtained via an asymptotic expansion around the limit mb ~ mc. After converting the scheme for the bottom mass to the kinetic scheme we compare the size of higher QCD corrections to the contributions from 1/\( {m}_b^2 \) and 1/\( {m}_b^3 \) power corrections and to the relative uncertainties.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
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.V. Manohar and M.B. Wise, Heavy quark physics, in Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology 10, Cambridge University Press, Cambridge, U.K. (2000).
D. Benson, I.I. Bigi, T. Mannel and N. Uraltsev, Imprecated, yet impeccable: On the theoretical evaluation of Γ(B → Xcℓν), Nucl. Phys. B 665 (2003) 367 [hep-ph/0302262] [INSPIRE].
C.W. Bauer, Z. Ligeti, M. Luke, A.V. Manohar and M. Trott, Global analysis of inclusive B decays, Phys. Rev. D 70 (2004) 094017 [hep-ph/0408002] [INSPIRE].
P. Gambino and C. Schwanda, Inclusive semileptonic fits, heavy quark masses, and Vcb, Phys. Rev. D 89 (2014) 014022 [arXiv:1307.4551] [INSPIRE].
A. Pak and A. Czarnecki, Heavy-to-heavy quark decays at NNLO, Phys. Rev. D 78 (2008) 114015 [arXiv:0808.3509] [INSPIRE].
K. Melnikov, O(\( {\alpha}_s^2 \)) corrections to semileptonic decay b → \( c\ell \overline{\nu} \), Phys. Lett. B 666 (2008) 336 [arXiv:0803.0951] [INSPIRE].
S. Biswas and K. Melnikov, Second order QCD corrections to inclusive semileptonic b → \( {X}_c\ell \overline{\nu} \) decays with massless and massive lepton, JHEP 02 (2010) 089 [arXiv:0911.4142] [INSPIRE].
P. Gambino, B semileptonic moments at NNLO, JHEP 09 (2011) 055 [arXiv:1107.3100] [INSPIRE].
T. Becher, H. Boos and E. Lunghi, Kinetic corrections to B → \( {X}_c\ell \overline{\nu} \) at one loop, JHEP 12 (2007) 062 [arXiv:0708.0855] [INSPIRE].
A. Alberti, T. Ewerth, P. Gambino and S. Nandi, Kinetic operator effects in \( \overline{B}\to {X}_c\ell \overline{\nu} \) at O(αs), Nucl. Phys. B 870 (2013) 16 [arXiv:1212.5082] [INSPIRE].
A. Alberti, P. Gambino and S. Nandi, Perturbative corrections to power suppressed effects in semileptonic B decays, JHEP 01 (2014) 147 [arXiv:1311.7381] [INSPIRE].
M. Fael, T. Mannel and K. Keri Vos, Vcb determination from inclusive b → c decays: an alternative method, JHEP 02 (2019) 177 [arXiv:1812.07472] [INSPIRE].
T. Mannel, D. Moreno and A.A. Pivovarov, NLO QCD corrections to inclusive b → \( c\ell \overline{\nu} \) decay spectra up to 1/\( {m}_Q^3 \), Phys. Rev. D 105 (2022) 054033 [arXiv:2112.03875] [INSPIRE].
M. Fael, K. Schönwald and M. Steinhauser, Third order corrections to the semileptonic b → c and the muon decays, Phys. Rev. D 104 (2021) 016003 [arXiv:2011.13654] [INSPIRE].
M. Fael, K. Schönwald and M. Steinhauser, Kinetic Heavy Quark Mass to Three Loops, Phys. Rev. Lett. 125 (2020) 052003 [arXiv:2005.06487] [INSPIRE].
M. Fael, K. Schönwald and M. Steinhauser, Relation between the \( \overline{MS} \) and the kinetic mass of heavy quarks, Phys. Rev. D 103 (2021) 014005 [arXiv:2011.11655] [INSPIRE].
M. Dowling, J.H. Piclum and A. Czarnecki, Semileptonic decays in the limit of a heavy daughter quark, Phys. Rev. D 78 (2008) 074024 [arXiv:0810.0543] [INSPIRE].
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].
A. Czarnecki, K. Melnikov and N. Uraltsev, NonAbelian dipole radiation and the heavy quark expansion, Phys. Rev. Lett. 80 (1998) 3189 [hep-ph/9708372] [INSPIRE].
M. Beneke and V.A. Smirnov, Asymptotic expansion of Feynman integrals near threshold, Nucl. Phys. B 522 (1998) 321 [hep-ph/9711391] [INSPIRE].
V.A. Smirnov, Analytic tools for Feynman integrals, in Springer Tracts in Modern Physics, Springer, Berlin, Germany (2012).
M. Czakon, A. Czarnecki and M. Dowling, Three-loop corrections to the muon and heavy quark decay rates, Phys. Rev. D 103 (2021) L111301 [arXiv:2104.05804] [INSPIRE].
A. Pak and A. Smirnov, Geometric approach to asymptotic expansion of Feynman integrals, Eur. Phys. J. C 71 (2011) 1626 [arXiv:1011.4863] [INSPIRE].
F. Herren, Precision Calculations for Higgs Boson Physics at the LHC. Four-Loop Corrections to Gluon-Fusion Processes and Higgs Boson Pair-Production at NNLO, Ph.D. Thesis, KIT, Karlsruhe, Germany (2020) [10.5445/IR/1000125521].
R.N. Lee and V.A. Smirnov, Analytic ϵ-expansions of Master Integrals Corresponding to Massless Three-Loop Form Factors and Three-Loop g − 2 up to Four-Loop Transcendentality Weight, JHEP 02 (2011) 102 [arXiv:1010.1334] [INSPIRE].
B. Ruijl, T. Ueda and J. Vermaseren, FORM version 4.2, arXiv:1707.06453 [INSPIRE].
A.V. Smirnov and F.S. Chuharev, FIRE6: Feynman Integral REduction with Modular Arithmetic, Comput. Phys. Commun. 247 (2020) 106877 [arXiv:1901.07808] [INSPIRE].
R.N. Lee, Presenting LiteRed: a tool for the Loop InTEgrals REDuction, arXiv:1212.2685 [INSPIRE].
S.A. Larin, The Renormalization of the axial anomaly in dimensional regularization, Phys. Lett. B 303 (1993) 113 [hep-ph/9302240] [INSPIRE].
S.A. Larin and J.A.M. Vermaseren, The \( {\alpha}_s^3 \) corrections to the Bjorken sum rule for polarized electroproduction and to the Gross-Llewellyn Smith sum rule, Phys. Lett. B 259 (1991) 345 [INSPIRE].
S.M. Berman and A. Sirlin, Some considerations on the radiative corrections to muon and neutron decay, Ann. Phys. 20 (1962) 20.
M. Roos and A. Sirlin, Remarks on the radiative corrections of order α2 to muon decay and the determination of Gμ, Nucl. Phys. B 29 (1971) 296 [INSPIRE].
A. Alberti, P. Gambino, K.J. Healey and S. Nandi, Precision Determination of the Cabibbo-Kobayashi-Maskawa Element Vcb, Phys. Rev. Lett. 114 (2015) 061802 [arXiv:1411.6560] [INSPIRE].
M. Bordone, B. Capdevila and P. Gambino, Three loop calculations and inclusive Vcb, Phys. Lett. B 822 (2021) 136679 [arXiv:2107.00604] [INSPIRE].
Belle collaboration, Measurements of q2 Moments of Inclusive B → Xcℓ+νℓ Decays with Hadronic Tagging, Phys. Rev. D 104 (2021) 112011 [arXiv:2109.01685] [INSPIRE].
Belle collaboration, Moments of the electron energy spectrum and partial branching fraction of B → Xceν decays at Belle, Phys. Rev. D 75 (2007) 032001 [hep-ex/0610012] [INSPIRE].
P. Gambino, K.J. Healey and S. Turczyk, Taming the higher power corrections in semileptonic B decays, Phys. Lett. B 763 (2016) 60 [arXiv:1606.06174] [INSPIRE].
DELPHI collaboration, Determination of heavy quark non-perturbative parameters from spectral moments in semileptonic B decays, Eur. Phys. J. C 45 (2006) 35 [hep-ex/0510024] [INSPIRE].
J.A.M. Vermaseren, Axodraw, Comput. Phys. Commun. 83 (1994) 45 [INSPIRE].
D. Binosi and L. Theussl, JaxoDraw: A Graphical user interface for drawing Feynman diagrams, Comput. Phys. Commun. 161 (2004) 76 [hep-ph/0309015] [INSPIRE].
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: 2205.03410
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.
About this article
Cite this article
Fael, M., Schönwald, K. & Steinhauser, M. A first glance to the kinematic moments of B → Xcℓν at third order. J. High Energ. Phys. 2022, 39 (2022). https://doi.org/10.1007/JHEP08(2022)039
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2022)039