S -wave and P -wave ππ and K π contributions to three-body decay processes in the Resonance- Spectrum Expansion

2008

Annals of Physics

Self Cite

Relations between scattering and production amplitudes are studied in a microscopic multichannel model for meson-meson scattering, with coupling to confined quark-antiquark channels. Overlapping resonances and a proper threshold behaviour are treated exactly in the model. Under the spectator assumption, it is found that the two-particle production amplitude shares a common denominator with the elastic scattering amplitude, besides a numerator consisting of a linear combination of all elastic and some inelastic matrix elements. The coefficients in these linear combinations are shown to be generally complex. Finally, the standard operator expressions relating production and scattering amplitudes, viz. A ¼ T =V and ImðAÞ ¼ T Ã A, are fulfilled, while in the small-coupling limit the usual isobar model is recovered.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Note that the process giving rise to the initial q q pair plus the spectator meson can be either weak or strong yet OZI-suppressed (see Ref. [1] for some examples).…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Relating multichannel scattering and production amplitudes in a microscopic OZI-based model

2008

Annals of Physics

Self Cite

“…Furthermore, in Ref. [2] we showed that such a twoparticle production amplitude can reasonably describe experiment in an energy region where no additional resonances from possible rescattering with the spectator particle exist. Moreover, no need to treat a sizable fraction of the experimental signal as background was noticed.…”

mentioning

confidence: 81%

The complex relation between production and scattering amplitudes

2008

Europhys. Lett.

Reply to the comment by M. R. Pennington and D. J. Wilson

2008

Europhys. Lett.

Before replying directly to the Comment [1] of Pennington and Wilson (PW) on our paper [2] about a complex relation between production and scattering amplitudes [3], let us first recapitulate some of the essential features of our approach, for readers who are not so familiar with it.The analysis of two-body subamplitudes in processes of strong decay is often carried out under the spectator assumption [4][5][6]. In such cases, one may express the twobody production subamplitude P as a linear combination of elements of the two-body scattering amplitude T . The latter quantities, which contain the full two-body dynamics, are then supposed to be known, either from experiment, or from theoretical considerations.The amputated scattering amplitude t is, in the loopexpansion approximation, given by t = V + V ωt, where V and ω represent the vertex and loop functions, respectively. The vertex function is supposed to be real and symmetric, whereas the loop function is diagonal. Moreover, in order to ensure that resonance poles come out in the correct Riemann sheet for weak coupling, the loop function satisfies the condition m(ω) 0. The latter condition allows us to define the quantity Z given by ω = Z m(Z).Like the loop function, Z can be chosen diagonal as well. It is straightforward to show that the scattering amplitude T, defined by T = m(Z)t m(Z), satisfies the unitarity condition 2iT T * = 2iT * T = T − T * . We have shown in refs. [7,8] that it also has the correct behaviour at threshold, recently confirmed in ref. [9].The two-particle amputated production amplitude p is, in the loop expansion, given by p = 1 + V ω + V ωV ω + . . . = 1 + tω.(1)