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Parametrizations of three-body hadronic $B$ - and $D$ -decay amplitudes in terms of analytic and unitary meson-meson form factors

D. Boito¹, J.-P. Dedonder², B. El-Bennich³, R. Escribano⁴, R. Kamiński⁵, L. Leśniak⁵, and B. Loiseau²

¹Instituto de Física de São Carlos, Universidade de São Paulo, CP 369, 13560-970 São Carlos, SP, Brazil
²Sorbonne Universités, Université Pierre et Marie Curie, Sorbonne Paris Cité, Université Paris Diderot, et IN2P3-CNRS, UMR 7585, Laboratoire de Physique Nucléaire et de Hautes Énergies, 4 place Jussieu, 75252 Paris, France
³Laboratório de Física Teòrica e Computacional, Universidade Cruzeiro do Sul, Rua Galvão Bueno 868, 01506-000 São Paulo, São Paulo, Brazil
⁴Grup de Física Teòrica (Departament de Física) and Institut de Física d’Altes Energies (IFAE), Universitat Autònoma de Barcelona, E-08193 Bellaterra (Barcelona), Spain
⁵Division of Theoretical Physics, The Henryk Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences, 31-342 Kraków, Poland

Phys. Rev. D 96, 113003 – Published 12 December, 2017

DOI: https://doi.org/10.1103/PhysRevD.96.113003

Abstract

We introduce parametrizations of hadronic three-body $B$ and $D$ weak decay amplitudes that can be readily implemented in experimental analyses and are a sound alternative to the simplistic and widely used sum of Breit-Wigner type amplitudes, also known as the isobar model. These parametrizations can be particularly useful in the interpretation of $C P$ asymmetries in the Dalitz plots. They are derived from previous calculations based on a quasi-two-body factorization approach in which two-body hadronic final-state interactions are fully taken into account in terms of unitary $S$ - and $P$ -wave $π π$ , $π K$ , and $K \bar{K}$ form factors. These form factors can be determined rigorously, fulfilling fundamental properties of quantum field-theory amplitudes such as analyticity and unitarity, and are in agreement with the low-energy behavior predicted by effective theories of QCD. They are derived from sets of coupled-channel equations using $T$ -matrix elements constrained by experimental meson-meson phase shifts and inelasticities, chiral symmetry, and asymptotic QCD. We provide explicit amplitude expressions for the decays $B^{\pm} \to π^{+} π^{-} π^{\pm}$ , $B \to K π^{+} π^{-}$ , $B^{\pm} \to K^{+} K^{-} K^{\pm}$ , $D^{+} \to π^{-} π^{+} π^{+}$ , $D^{+} \to K^{-} π^{+} π^{+}$ , and $D^{0} \to K_{S}^{0} π^{+} π^{-}$ , for which we have shown in previous studies that this approach is phenomenologically successful; in addition, we provide expressions for the $D^{0} \to K_{S}^{0} K^{+} K^{-}$ decay. Other three-body hadronic channels can be parametrized likewise.

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References (89)

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Parametrizations of three-body hadronic $B$ - and $D$ -decay amplitudes in terms of analytic and unitary meson-meson form factors

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Parametrizations of three-body hadronic B- and D-decay amplitudes in terms of analytic and unitary meson-meson form factors

Abstract

Physics Subject Headings (PhySH)

Article Text

References (89)

Parametrizations of three-body hadronic $B$ - and $D$ -decay amplitudes in terms of analytic and unitary meson-meson form factors