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

2017/09/30 by D. Boito, Diogo Boito, J. -P. Dedonder +10
Mathematics · Physics and Astronomy · #Algorithm #Amplitude #Factorization #Hadron #High-Energy Particle Collisions Research #Mathematical physics #Mathematics #Meson #Particle physics #Particle physics theoretical and experimental studies #Perturbative QCD #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Unitarity #hep-ex #hep-ph

paper · pdf · doi:10.1103/physrevd.96.113003

published as Phys. Rev. D 96, 113003 (2017) · 38 pages. Extended discussions and several references added. Accepted for publication in Physical Review D

openalex created_date 2017/10/06 · arxiv created 2017/11/13 · openalex publication_date 2017/12/12 · arxiv updated 2017/12/20 · openalex updated_date 2026/08/06

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 CP 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 \ensuremathπ\ensuremathπ, \ensuremathπK, and KK 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^\ifmmode±\else\textpm\fi\ensuremath→\ensuremathπ⁺\ensuremathπ^\ensuremath-\ensuremathπ^\ifmmode±\else\textpm\fi, B\ensuremath→K\ensuremathπ⁺\ensuremathπ^\ensuremath-, B^\ifmmode±\else\textpm\fi\ensuremath→K⁺K^\ensuremath-K^\ifmmode±\else\textpm\fi, D⁺\ensuremath→\ensuremathπ^\ensuremath-\ensuremathπ⁺\ensuremathπ⁺, D⁺\ensuremath→K^\ensuremath-\ensuremathπ⁺\ensuremathπ⁺, and D⁰\ensuremath→K_S⁰\ensuremathπ⁺\ensuremathπ^\ensuremath-, for which we have shown in previous studies that this approach is phenomenologically successful; in addition, we provide expressions for the D⁰\ensuremath→K_S⁰K⁺K^\ensuremath- decay. Other three-body hadronic channels can be parametrized likewise.

Citations

• Study of τ−→KSπ−ντ decay at Belle
• Bd,s→ρ,ω,K*,ϕdecay form factors from light-cone sum rules reexamined
• Dalitz plot analysis of the decayB±→K±K±K∓
• The K* 0(800) scalar resonance from Roy–Steiner representations of πK scattering
• QCD factorization in B→πK, ππ decays and extraction of Wolfenstein parameters
• Rescattering and chiral dynamics inB→ρπdecay
• Form factors from light-cone sum rules withB-meson distribution amplitudes
• Heavy-to-light form factors on the light cone
• Towards three-body unitarity inD+→K−π+π+
• Dalitz plot analysis ofB±→π±π±π∓decays
• Charmless three-body decays ofBmesons
• Chiral dynamics and S-wave contributions in semileptonicDs/Bsdecays intoπ+π−
• Search for CP violation in the decay D+→π−π+π+
• Interference betweenf0(980)andρ(770)0resonances inB→π+π−Kdecays
• CP violation in multibody B decays from QCD factorization
• Dalitz plot analysis of theD+→π−π+π+decay
• K π vector form factor, dispersive constraints and τ→ν τ K π decays
• Review of Multibody Charm Analyses
• Review of Particle Physics
• Summary of the 2015 LHCb workshop on multi-body decays of D and B mesons