Dalitz-plot decomposition for three-body decays

Abstract

We present a general formalism to write the decay amplitude for multibody reactions with explicit separation of the rotational degrees of freedom, which are well controlled by the spin of the decay particle, and dynamic functions on the subchannel invariant masses, which require modeling. Using the three-particle kinematics we demonstrate the proposed factorization, named the Dalitz-plot decomposition. The Wigner rotations, that are subtle factors needed by the isobar modeling in the helicity framework, are simplified with the proposed decomposition. Consequently, we are able to provide them in an explicit form suitable for the general case of arbitrary spins. The only unknown model-dependent factors are the isobar lineshapes that describe the subchannel dynamics. The advantages of the new decomposition are shown through three examples relevant for the recent discovery of the exotic charmonium candidate $Z_c(4430)$, the pentaquarks $P_c$, and the intriguing ${\Lambda }_c^{+}\to p{K}^{-}{\pi }^{+}$ decay.

14 pages, 7 figures

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Cited by in corpus (20)

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• Observation of a $J/\psi \Lambda$ resonance consistent with a strange pentaquark candidate in $B^{-}\to J/\psi \Lambda \bar{p}$ decays
• Evidence for a new structure in the $J/\psi p$ and $J/\psi \bar{p}$ systems in $B_s^0\to J/\psi p\bar{p}$ decays
• Novel approaches in Hadron Spectroscopy
• Pole position of the $a_1(1260)$ resonance in a three-body unitary framework
• Dalitz plots and lineshape of $a_1(1260)$ from a relativistic three-body unitary approach
• Amplitude analysis of the ${\Lambda }_c^{+}\to p{K}^{-}{\pi }^{+}$ decay and ${\Lambda }_c^{+}$ baryon polarization measurement in semileptonic beauty hadron decays
• Exotic Hadrons at LHCb
• Search for $CP$ violation in ${\Xi }_b^{-}\to p{K}^{-}{K}^{-}$ decays
• Khuri-Treiman equations for $3\pi$ decays of particles with spin
• A novel method to test particle ordering and final state alignment in helicity formalism
• Helicity amplitudes for generic multi-body particle decays featuring multiple decay chains
• Dispersive $\pi \pi \to K\bar{K}$ amplitude and giant CP violation in B to three light-meson decays at LHCb
• Extracting maximum information from polarised baryon decays via amplitude analysis: the ${\Lambda }_c^{+}\to p{K}^{-}{\pi }^{+}$ case
• ${\Lambda }_{\mathrm{c}}^{+}$ polarimetry using the dominant hadronic mode
• Towards an amplitude analysis of the decay ${\Lambda }_b^0\to p{K}^{-}\gamma$
• Spin-orbit amplitudes for decays with arbitrary spin
• Dalitz-plot decomposition for the $e^{+}{e}^{-}\to J/\psi \pi \pi (K\bar{K})$ and $e^{+}{e}^{-}\to h_c\pi \pi$ processes
• Scattering Theory
• Wigner rotations for cascade reactions