Are there important unitarity corrections to the isobar model?

Aitchison, I. J. R.; Brehm, J.J.

doi:10.1016/0370-2693(79)90056-x

Cited by 19 publications

(10 citation statements)

References 11 publications

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“…If the quasi two-body state, however, is dominated by a low-mass, narrow resonance, then the overlap between the resonance and the spectator pion wave functions is expected to be small. Indeed, in the case of the ππN final state at a total center of mass energy below 2 GeV [4,5] (one of the very few phenomenological analyses of re-scattering effects in threeparticle systems that we are aware of), the re-scattering corrections were found to not exceed 20% [6]. In the case of the J/ψ with even higher center of mass energy and with a pronounced ρ resonance in ππ, we expect these effects to be even smaller.…”

Section: IImentioning

confidence: 99%

Role ofP-wave inelasticity inJ/ψ→π+π−π0

2010

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We discuss the importance of inelasticity in the P -wave ππ amplitude on the Dalitz distribution of 3π events in J/ψ decay. The inelasticity, which becomes sizable for ππ masses above 1.4 GeV, is attributed to KK → ππ re-scattering. We construct an analytical model for the two-channel scattering amplitude and use it to solve the dispersion relation for the isobar amplitudes that parametrize the J/ψ decay. We present comparisons between theoretical predictions for the Dalitz distribution of 3π events with available experimental data.Here is the polarization vector of the J/ψ, the Dalitz invariants are defined by s ij = (p i + p j ) 2 for i, j = ±, 0 and satisfy s +− + s 0+ + s −0 = M 2 + 3m 2 π ,p i = p i /|p i |, and the scalar form factor F describes the dynamics of

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Section: IImentioning

confidence: 99%

Role ofP-wave inelasticity inJ/ψ→π+π−π0

2010

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“…In particular, one can separate the genuine three-body unitary from the subchannel unitarity related to rescattering between different isobars. These processes modify the line shape of the subchannel amplitudes [47][48][49][50][51][52][53]. A good example is the ρπ-dynamics studied in the 1 −− sector in the decay of ω/φ [48,50], where the final-state interaction were found to shift and skew the ρ-meson peak.…”

Section: The Reaction Modelmentioning

confidence: 99%

Pole position of the a1(1260) from τ -decay

et al. 2018

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We perform an analysis of the three-pion system with quantum numbers J P C = 1 ++ produced in the weak decay of τ leptons. The interaction is known to be dominated by the axial meson a1(1260). We build a model based on approximate three-body unitary and fix the free parameters by fitting it to the ALEPH data on τ − → π − π + π − ντ decay. We then perform the analytic continuation of the amplitude to the complex energy plane. The singularity structures related to the ππ subchannel resonances are carefully addressed. Finally, we extract the a1(1260) pole position m (a 1 (1260)) p − iΓ (a 1 (1260)) p /2 with m (a 1 (1260)) p = (1209 ± 4 +12 −9 ) MeV, Γ (a 1 (1260)) p = (576 ± 11 +89 −20 ) MeV.

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“…[27][28][29]. However, in the works of Graves-Morris [35] and Aitchison and collaborators [36][37][38], the possible existence of an additional real, or even complex, contribution was considered within the K-matrix formalism. Here, an inhomogeneous real term follows straightforwardly from the reasonable assumption that the produced meson pair originates from an initial q q pair.…”

Section: The Lowest-order Termmentioning

confidence: 99%

“…which is nothing but a Breit-Wigner [41] expansion over a series of resonances, as employed in the isobar formalism [38,[42][43][44][45].…”

Section: Breit-wigner Resonancesmentioning

confidence: 99%

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

Beveren

Rupp

2008

Annals of Physics

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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.

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Are there important unitarity corrections to the isobar model?

Cited by 19 publications

References 11 publications

Role ofP-wave inelasticity inJ/ψ→π+π−π0

Role ofP-wave inelasticity inJ/ψ→π+π−π0

Pole position of the a1(1260) from τ -decay

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

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