Final-State Interaction Effects in Weak Three-Body Decays

Abstract

An exactly soluble model of the weak decay of a 0"^ particle to three strongly interacting 0"^ decay products is investigated numerically in order to explore the effects of final-state interactions (FSI) on the decay and the way in which the resonant-pair interaction information is distributed over the three-body final state. We find that moderately strong attractive pairwise FSI can produce very large enhancements or de-enhancements in the decay rate, but we find no effect of rescattering singularities. We find that large effects on the decay rate can be accompanied by pure phase-space single-particle spectra. The effects of interference between various terms in the amplitude make the extraction of pair-resonance parameters from singles spectra chancy, and there is no obvious trend in the deviation from the input resonance parameters. These interference effects also produce striking and possibly misleading patterns in the Dalitz plots.

Scattering ofDandD*mesons off theX(3872)

“…Typically, (e.g., Ref. [58]) there will be an enhancement or deenhancement of the total cross section relative to the situation where three body scattering does not occur in the final state. In particular, the behavior of the X(3872) produced in isolation should be distinguishable from its behavior when in the presence of S = D 0 , D * 0 , D0 , or D * 0 , a situation that may be accessible in the rich environment of the LHC.…”

Final State Interactions in Weak Three-Body Decays Calculated in the Impulse Approximation

“…An increase in our fundamental knowledge of the three-body decay mechanism has been made by Amado and Noble 1 l' 2 ) who have studied the non-relativistic weak decay of a o+ particle (the G's or Gedanken) into three o+ particles (the H's) which interact strongly. The problem was facilitated by the choice of a separable two-body interaction between the final state H's.…”

“…Of the three commonly used models for resonant three-body decay-the Born approximation, the Breit-Wigner model and the impulse model-the last is the most accurate as it includes the effects of interference between the break-up and the :first scattering terms. This model is a non-relativistic analogue of the dispersion treatment of Khuri (2) where <3H/ is the plane wave state, E the total energy of the G particle, TSH(E) the three-body T matrix and G0 (E) the free Green's function (E-H 0) -1 • Following Faddeev the three-body T matrix may be decomposed as 3 Tan…”