Width effects in resonant three-body decays: $B$ decay as an example

Abstract

For three-body hadron decays mediated by intermediate resonances with large widths, we show how to properly extract the quasi-two-body decay rates for a meaningful comparison with the corresponding theoretical estimates, using several $B$ decays as explicit examples. We compute the correction factor from finite width effects in the QCD factorization approach, and make a comparison with that using the experimental parameterization in which the momentum dependence in the weak dynamics is absent. Although the difference is generally less than $10\%$ for tensor and vector resonances, it can be as large as $(25-40)\%$ for scalar resonances. Our finding can in fact be applied to general quasi-two-body decays.

5 pages, 2 figures, title changed, version to appear in Phys. Lett. B

References in corpus (8)

• QCD Factorization for $B\to \pi \pi$ Decays: Strong Phases and CP Violation in the Heavy Quark Limit
• QCD factorization for exclusive, non-leptonic B meson decays: General arguments and the case of heavy-light final states
• QCD factorization for B->PP and B->PV decays
• Final State Interactions in Hadronic B Decays
• Dalitz Plot Analysis of B+- --> pi+-pi+-pi-+ Decays
• Amplitude analysis of the $B^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ decay
• Observation of several sources of $CP$ violation in $B^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ decays
• Branching Fractions and CP Violation in $B^{-}\to K^{+}{K}^{-}{\pi }^{-}$ and $B^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{-}$ Decays

Cited by in corpus (11)

• Finite-Width Effects in Three-Body B Decays
• Hadronic three-body D decays mediated by scalar resonances
• Contributions for the kaon pair from $\rho (770)$, $\omega (782)$ and their excited states in the $B\to K\bar{K}h$ decays
• Direct $CP$ violation of three bodies decay process from the resonance effect
• Two- and three-body hadronic decays of charmed mesons involving a tensor meson
• CP violation in the interference between $\rho (770{)}^0$ and $S$-wave in $B^{\pm }\to {\pi }^{+}{\pi }^{-}{\pi }^{\pm }$ decays and its implication for CP asymmetry in $B^{\pm }\to {\rho }^0{\pi }^{\pm }$
• $CP$-violating observables in four-body $B\to \varphi (\to K\bar{K})K^{\ast }(\to K\pi )$ decays
• Pure annihilation decays of $B_s^0\to a_0^{+}{a}_0^{-}$ and $B_d^0\to K_0^{\ast +}{K}_0^{\ast -}$ in the PQCD approach
• Family Non-universal $Z^{\prime }$ Effects on $B_{d,s}\to K^{\ast 0}{\overline{K}}^{\ast 0}$ Decays in Perturbative QCD Approach
• Measurement of the branching fraction of $J/\psi \to \rho \pi$ at KEDR
• Contributions of the subprocess $K_0^{\ast }(1430)\to K{\eta }^{\prime }$ in the charmless three-body $B$ meson decays