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, which 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 line shapes 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 ${\mathrm{\ensuremath{\Lambda}}}_{c}^{+}\ensuremath{\rightarrow}p{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ decay.