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 Zc(4430), the pentaquarks Pc, and the intriguing Λ + c → pK − π + decay.
I. INTRODUCTIONPartial-wave decomposition of reaction amplitudes is widely used in the analysis of both fixed target (e.g. COM-PASS, VES, CLAS, GlueX), and collider (e.g. LHCb, BESIII, Belle, BaBar) experiments. It is the most powerful way to account for spin and parity, J P , of various contributions, thus required in quantum number determinations of newly observed resonances. It also provides for the most sensitive way of distinguishing exotic hadrons, including the XY Z states and pentaquark candidates in the heavy quarkonium sector, from usually large contributions by ordinary mesons and baryons. To establish the existence of a resonance in a given partial wave, it is desired to have a representation of the reaction amplitude consistent with the S-matrix principles of unitarity, analyticity and Lorentz invariance. This is nontrivial when dealing with particles with spin, which introduce kinematical singularities and (pseudo)threshold relations between partial waves. Amplitude analysis in the context of the S-matrix constraints has been extensively studied in the past using both covariant [1-3] and noncovariant methods [4][5][6][7]. When several particles with spin are involved, the noncovariant approach is more practical, because spin is universally accounted for through the simple Wigner D-functions. In this paper, we take a step to simplify amplitude construction and discuss a convenient framework which incorporates dynamic subchannel resonances for a multiparticle decay. We present a universal amplitude formula which describes the decay of an arbitrary spin state to three particles, each also with arbitrary spin. Specifically, we write the amplitudes in a factorized form to separate the dependence on the angles that characterize the orientation of the final-state particles (and thus the information about the polarization of the parent particle) from the Dalitz-plot variables that encode the information on the intermediate resonances in the multiparticle final state. We do not focus on details of the two-particle dynamics merely giving ...