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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 $Lambda_c^+to pK^-pi^+$ decay.
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We calculate the radiative corrections to the Dalitz plot of K_{l3}^pm decays to order (alpha/pi)(q/M_1), where q is the momentum transfer and M_1 is the mass of the kaon. We restrict the analysis to the so-called four-body region, which arises when no discrimination of real photons is made either kinematically or experimentally. We present our results in two ways: the first one with the triple integration over the photon kinematical variables ready to be performed numerically and the second one in a fully analytical form. Our results can be useful in experimental analyses of the Dalitz plot, by evaluating the model-independent coefficients of the quadratic products of the form factors; we provide some numbers as a case example. We find a small, albeit non-negligible, contribution from the four-body region to the radiative correction to the total decay rate of K_{l3}^pm decays.
We calculate the model-independent radiative corrections to the Dalitz plot of K_{l3}^pm decays to order (alpha/pi)(q/M_1), where q is the momentum transfer and M_1 is the mass of the kaon. The final results are presented, first, with the triple integration over the variables of the bremsstrahlung photon ready to be performed numerically and, second, in an analytical form. These two forms are useful to crosscheck on one another and with other calculations. This paper is organized to make it accessible and reliable in the analysis of the Dalitz plot of precision experiments and is not compromised to fixing the form factors at predetermined values. It is assumed that the real photons are kinematically discriminated. Otherwise, our results have a general model-independent applicability.
A model-independent expression for the Dalitz plot of semileptonic decays of neutral kaons, K_{l3}^0, including radiative corrections to order (alpha/pi)(q/M_1), where q is the momentum transfer and M_1 is the mass of the kaon, is presented. The model dependence of radiative corrections is kept in a general form within this approximation, which is suitable for model-independent experimental analyses. Expressions for bremsstrahlung radiative corrections are presented in two forms: one with the triple integral over the kinematical variables of the photon ready to be performed numerically and the other one in a fully analytical form. The final result is restricted to the so-called three-body region of the Dalitz plot and it is not compromised to fixing the values of the form factors at predetermined values.
We present for the first time a measurement of the weak phase 2b+g obtained from a time-dependent Dalitz plot analysis of B^0 -> D-(+) K0 Pi+(-) decays. Using a sample of approximately 347*10^{6} BBbar pairs collected by the BABAR detector at the PEP-II asymmetric-energy storage rings, we obtain 2b+g = (83 +/- 53 +/- 20) degrees and (263 +/- 53 +/- 20) degrees assuming the ratio r of the b -> u and b -> c decay amplitudes to be 0.3. The magnitudes and phases for the resonances associated with the b -> c transitions are also extracted from the fit.
The $g$, $h$, and $k$ Dalitz plot parameters, which are coefficients in a series expansion of the squared module of the matrix element $|M(u,v)|^{2} propto 1 + gu + hu^{2} + kv^{2}$ ($u$, $v$ are invariant variables), have been measured for $K^{pm}to pi^{pm} pi^{0} pi^{0}$ decays using $35 GeV/c$ hadron beams at the IHEP (Protvino) accelerator. Dependences of parameters and fit quality on the $pi^0pi^0$ mass cut were investigated. The results point to the important role of $pi^+pi^- to pi^0pi^0$ charge exchange scattering near the $pi^0pi^0$ mass threshold. The comparison of our data with previous measurements is presented.
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