Unitary analytic isobar model for the reaction nucleon-meson to nucleon-meson-meson

Abstract

The isobar model for a production amplitude is developed in a construction which incorporates unitarity and analyticity in each of the two-body isobar subenergy channels. The process KN + K T N is considered in order to illustrate and deal with the complications due to spin and unequal masses. The basic aspects of the description are presented in a truncation of the problem to the production of s-wave isobars. The two-body discontinuities in each isobar channel have been derived previously, and are employed here in dispersion relations for the isobar factor amplitudes. A prominent complicating feature is that due to half-angle kinematics; this is investigated without approximation, and factors associated with kinematical singularities are identified and extracted. A coupled system of single-variable integral equations for the isobar factors is obtained by means of a procedure due to Pasquier and ~a s~u i e r .The kernels of the integral equations are evaluated explicitly. These contain the two-body elastic amplitudes in each isobar channel, the parametrization of which propagates into the solution for the isobar production amplitudes. The formal solution of the linear system of equations for the isobar factors is indicated. The final result is unitary and analytic in each subenergy and satisfies two-body unitarity in the total energy as well.

Experimental study of theP11(1440)andD13(1520)Mokeev1, Burkert2, Elouadrhiri3 et al. 2012Phys. Rev. C13231680View full textAdd to dashboardCite

“…The remaining part of the cross sections comes from direct charged pion (2π) production mechanisms, in which the π + π − p final state is created without the formation of unstable hadrons in the intermediate states. The presence of these mechanisms is required by the unitarity of the threebody π + π − p production amplitudes [51]. Their manifestation in π + π − p electroproduction was observed for the first time in our previous analyses of CLAS data [7,47].…”

New results from the studies of theN(1440)1/2+, N(1520)3/2Mokeev1, Burkert2, Carman3 et al. 2016Phys. Rev. C935910View full textAdd to dashboardCite

“…In general, unitarity requires the presence of so-called 2π direct production mechanisms in the π + π − p electroproduction amplitudes, where the final π + π − p state is created without going through the intermediate step of forming unstable hadron states [54]. These 2π direct production processes are beyond the aforementioned contributions from the two-body sub-channels.…”

“…[53]; the model was modified to make it fully consistent with a relativistic Breit-Wigner parameterization of each individual N * state contributions in the JM model [51] that also accounts for the energy-dependent resonance hadronic decay widths. A unitarized Breit-Wigner ansatz accounts for the transition between the same and different resonances in the dressed resonant propagator, which makes the resonant amplitudes consistent with restrictions imposed by a general unitarity condition [43,54]. Quantum number conservation in the strong interaction allows for transitions between the pairs of N * states N (1520)3/2 − ↔ N (1700)3/2 − , N (1535)1/2 − ↔ N (1650)1/2 − , and 3/2 + (1720) ↔ N (1720)3/2 + incorporated into the JM model.…”

Dispersive analysis ofω/ϕ→3π,πγ*

“…(31) (F (s) is given by a contour integral over t as shown in Eq. (19)) can be inverted using the Pasquier method [28,55]. In this method the order of the s and t integration is reversed with the latter deformed onto a real axis that needs can be calculated analytically or numerically only once.…”