Three-body non-leptonic heavy-to-heavy B decays at NNLO in QCD
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Springer
Received: August Revised: September Accepted: October Published: November
10, 29, 10, 20,
2020 2020 2020 2020
Tobias Huber,a Javier Virtob and K. Keri Vosc a
Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany b Departament de Física Quàntica i Astrofísica, Institut de Ciències del Cosmos, Universitat de Barcelona, Martí Franquès 1, E08028 Barcelona, Catalunya, Spain c Physics Department T31, Technische Universität München, James Franck-Straße 1, D-85748 Garching, Germany
E-mail: [email protected], [email protected], [email protected] Abstract: Exclusive non-leptonic two-body decays of B mesons have been studied extensively in the past two decades within the framework of factorization. However, the exploration of the corresponding three-body case has only started recently, in part motivated by new data. We consider here the simplest non-leptonic three-body B decays from the point of view of factorization, namely heavy-to-heavy transitions. We provide a careful derivation of the SCET/QCDF factorized amplitudes to NNLO in αs , and discuss the numerical impact of NLO and NNLO corrections. We then study the narrow-width limit, showing that the three-body amplitude reproduces analytically the known quasi-two-body decay amplitudes, and compute finite-width corrections. Finally, we discuss certain observables that are sensitive to perturbative NLO and NNLO corrections and to higher Gegenbauer moments of the dimeson LCDAs. This is the first study of non-leptonic three-body B decays to NNLO in QCD. Keywords: CP violation, Effective Field Theories, Heavy Quark Physics, Perturbative QCD ArXiv ePrint: 2007.08881
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP11(2020)103
JHEP11(2020)103
Three-body non-leptonic heavy-to-heavy B decays at NNLO in QCD
Contents 1 Introduction
1
2 Kinematics and phase space of the three-body decay
3 4 4 5 7 9 10 12
4 Narrow-width limit and finite-width effects 4.1 Narrow-width limit 4.2 Leading corrections to the narrow-width limit
14 14 15
5 Probing higher-order QCD effects 5.1 Di-pion system 5.2 Kπ system
18 18 20
6 Discussion and conclusions
20
1
Introduction
For more than two decades, non-leptonic decays of B mesons have been known to provide unique information on three fronts: CP violation and the angles of the CKM matrix, the structure of QCD in the presence of heavy quarks and energetic light particles, and beyond-the-Standard Model physics in the quark sector. Experimental information on non-leptonic B decays has been collected progressively over the years, at CLEO, the B-factories BaBar and Belle [1], the Tevatron, and currently at the LHC, most prominently at LHCb. Future experimental programs at the upgraded LHC and at Belle II also include serious plans for analyses of non-leptonic B decays [2, 3]. On the theory side, the calculation of the complicated non-perturbative matrix elements which are present in the amplitude is the bottleneck to precision prediction
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