Inverse moment of the B s -meson distribution amplitude from QCD sum rule
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Springer
Received: August 17, 2020 Accepted: September 11, 2020 Published: October 7, 2020
Alexander Khodjamirian, Rusa Mandal and Thomas Mannel Theoretische Physik 1, Naturwissenschaftlich-Technische Fakult¨ at, Universit¨ at Siegen, 57068 Siegen, Germany
E-mail: [email protected], [email protected], [email protected] Abstract: We derive a QCD sum rule for the inverse moment of the Bs -meson light-cone distribution amplitude in HQET. Within this method, the SU(3) f l symmetry violation is traced to the strange quark mass and to the difference between strange and nonstrange quark condensate densities. We predict the ratio of inverse moments λBs /λB = 1.19 ± 0.14 which can be used in various applications of these distribution amplitudes to the analyses of Bs -meson decays, provided an accurate value of λB is available from other sources, such as the B → `ν` γ decay. Keywords: Heavy Quark Physics, Nonperturbative Effects, Perturbative QCD ArXiv ePrint: 2008.03935
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)043
JHEP10(2020)043
Inverse moment of the Bs-meson distribution amplitude from QCD sum rule
Contents 1 Introduction
1
2 The method 2.1 Sum rule for the Bs decay constant 2.2 Sum rule for the inverse moment of Bs DA
2 2 6 11
4 Summary
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A Details of the calculation A.1 Perturbative spectral density at LO A.2 Perturbative spectral density at NLO A.3 Nonlocal condensate term
15 15 16 16
1
Introduction
Heavy mesons carrying bottom and strange quantum numbers have attracted increasing attention due to the large data sample which has been collected by the LHCb collaboration over the last years. With the new precise measurements it becomes increasingly important to also get more accurate theoretical predictions. This involves, in particular, reliable estimates of the SU(3) flavour symmetry violation, to be taken into account while analyzing the Bs data and comparing to the results for nonstrange bottom mesons. Among important quantities in the theoretical analyses are the light-cone distribution amplitudes (DAs) of heavy mesons. While these quantities were extensively studied for nonstrange bottom mesons, the SU(3)f l violating effects for Bs have not yet been estimated. The light-cone DAs of B-meson introduced [1] in the framework of Heavy Quark Effective Theory (HQET) (see also [2]) describe momentum distribution of the light quark in a heavy pseudoscalar meson. These DAs enter various factorization formulas for the exclusive decays of B-meson (see e.g. [3–7]). They also provide the main nonperturbative input in one of the versions [8, 9] of QCD light-cone sum rules for B-meson form factors. In all these applications, the key parameter is the inverse moment of the leading (lowest twist) B-meson DA. Evidently, the mass of the light u, d quarks plays no role in the Bu,d meson DAs. It can safely be neglected not only in comparison with any of the large scales involved in an exclusive Bu,d decay, but also with respect to typ
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