7 Search Results

In this study, a unitary coupled-channels model is presented for investigating the decays of heavy mesons and excited meson states into three light pseudoscalar mesons. The model accounts for the three-mesons final state interactions in the decay processes, as required by both the three-body and two-body unitarity conditions. In the absence of the Z-diagram mechanisms that are necessary consequences of the three-body unitarity, our decay amplitudes are reduced to a form similar to those used in the so-called isobar-model analysis. We apply our coupled-channels model to the three-pions decays of α₁(1260), π₂(1670), π₂(2100), and D⁰ mesons, and show that themore » Z-diagram mechanisms can contribute to the calculated Dalitz plot distributions by as much as 30% in magnitudes in the regions where f₀(600), ρ(770), and f₂(1270) dominate the distributions. Also, by fitting to the same Dalitz plot distributions, we demonstrate that the decay amplitudes obtained with the unitary model and the isobar model can be rather different, particularly in the phase that plays a crucial role in extracting the CKM CP-violating phase from the data of B meson decays. Our results indicate that the commonly used isobar model analysis must be extended to account for the final state interactions required by the three-body unitarity to reanalyze the three-mesons decays of heavy mesons, thereby exploring hybrid or exotic mesons, and signatures of physics beyond the standard model.« less

Around $$\theta_{\pi}=$$90$$^\circ$$, the coupling to the $$\rho^\circ N$$ channel leads to a good accounting of the charged pion exclusive photoproduction cross section in the energy range 3 < E_γ < 10 GeV, where experimental data exist. Starting from a Regge Pole approach that successfully describes vector meson production, the singular part of the corresponding box diagrams (where the intermediate vector meson-baryon pair propagates on-shell) is evaluated without any further assumptions (unitarity). Such a treatment provides an explanation of the $$s^{-7}$$ scaling of the cross section. Furthermore, elastic rescattering of the charged pion improves the basic Regge pole model at forwardmore » and backward angles.« less

Here a simple and systematic procedure is established for directly generating perturbation theory for the $$σ$$ model order by order in the number of loops rather than in powers of the bare coupling constant. This self-consistent Green's-function method is demonstrated by deriving the already known tree and one-loop approximations, and then is applied to the much more complex problem of the two-loop approximations to the propagators. The explicit form is displayed for these, and it is demonstrated that in the limit of no symmetry breaking and zero pion bare mass, the renormalized pion mass remains at zero as is requiredmore » by the Goldstone theorem. These are the essential first steps toward calculating a unitary pion-pion scattering amplitude with this model to the two-loop order.« less

The unitary irreducible representations of SU(2, 2), the covering group of the conformal group, are reduced with respect to an iso-Poincaré subgroup E(3, 1). Explicit representations of the 15 generators of SU(2, 2) in terms of differential operators in the function space of |η,ξ,ε;s,t,m$$\rangle$$, |ω,ξ,ε;r,t,m$$\rangle$$, and |ξ,ε;t,m$$\rangle$$, the basis vectors for "timelike,'' "spacelike,'' and "lightlike'' UIR's of E(3, 1), respectively, are given. The matrix elements between a basis vector in the maximal compact subgroup SU(2) × SU(2) × U(1) and a basis vector in E(3, 1) are calculated for all 14 different classes of UIR's of SU(2, 2). He wemore » find that two classes are reducible with respect to "lightlike'' representations, two classes are reducible with respect to "timelike'' representations, eight classes are reducible with respect to ``spacelike'' representations, and two classes contain both "timelike'' and "spacelike'' representations of E(3, 1).« less

In this work, under the general assumptions of analyticity, unitarity, temperedness, and normal threshold behavior, the relation between the number of zeros and the high-energy behavior of the partial-wave scattering amplitude is studied. If the left-hand-cut discontinuity makes a finite number of sign changes, the maximum and minimum numbers of zeros can be determined by the high-energy upper and lower bound of the partial-wave respectively. In particular, for C⁢|s|^–1+ε < |f_l⁡(s)| < C, the number of zeros is determined. After having determined the number of zeros, the number of subtractions as well as the sign of the scattering length ismore » obtained for given number and character of zeros of the left-hand discontinuity Δ⁢f_l⁡(s).« less

A soluble model obtained by a slight extension of the Lee model is considered in a study of the bootstrap mechanism. By examining the general solution that is obtained by using properties of the Herglotz function, it is found that the bootstrap mechanism can be achieved if and only if two further restrictions in addition to the general requirements of analyticity, unitarity, and crossing symmetry are imposed on the solution. They are that (i) the scattering amplitude satisfy the asymptotic condition limit of ω^–2⁢t^–1⁡(ω) as ω →∞ = 0 and (ii) the scattering amplitude have no Castillejo-Dalitz-Dyson (C.D.D.) zeros. Itmore » is also proved that the condition (i) is equivalent to limit of ω^–1⁢D⁡(ω) as ω →∞ = 0 when N⁡(ω) =O⁡(ω^–1) as ω →∞ or Z₃ = 0 or the Levinson theorem holds, while condition (ii) is equivalent to assuming the two familiar bootstrap equations based on the $$\frac{N}{D}$$ method and implies in particular a nonpositive scattering length. Either of the conditions (i) and (ii) alone gives in general only an inequality between the mass and coupling constant, and it is therefore concluded that the possibility of the bootstrap mechanism depends in a very sensitive way on the low-energy behavior as well as the high-energy behavior of the scattering amplitude. Finally, it is further argued that destroying the crossing symmetry in the approximate solutions will not give any physically meaningful conditions for determining the parameters unless one introduces a subtraction or one C.D.D. zero in the Low equation.« less

Here we propose a model in which inelasticity can be calculated dynamically. By this we mean, given the left-hand cut contribution (or force), our model gives a prescription for calculating inelasticity $$η_l⁡(=e^{–2⁢δ_l^I}$$ where $$δ_l^I$$ is ⁢the ⁢imaginary ⁢part⁢ of ⁢the⁢ phase ⁢shift). The basic assumption of the model is that there is one inelastic v_i above which a large number of reaction channels open, so that the partial-wave amplitude is essentially imaginary in the inelastic region. Our amplitude satisfies elastic unitarity below the inelastic threshold and inelastic unitarity above it. We illustrate the use of the model by applying itmore » to the π –π p-wave system, where we approximate the left-hand-cut contribution by one pole and by two poles.« less