Unitarity and the Bethe-Salpeter equation

Lahiff, A. D.; Afnan, I. R.

doi:10.1103/physrevc.66.044001

Cited by 12 publications

(9 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Retaining the t-dependence in the kernel implies additional analytical structures [87] which prevent us from obtaining the scattering amplitudes by solving the Bethe-Salpeter (BS) equation using on-shell amplitudes only. Instead, we incorporate the t-dependence within a more general four-dimensional integration scheme, which we reduce to a three-dimensional equation of the "Lippmann-Schwinger" type.…”

Section: Formalismmentioning

confidence: 99%

Dynamically generated open-charm baryons beyond the zero-range approximation

2009

View full text Add to dashboard Cite

The interaction of the low-lying pseudoscalar mesons with the ground-state baryons in the charm sector is studied within a coupled-channel approach using a t-channel vector-exchange driving force. The amplitudes describing the scattering of the pseudoscalar mesons off the ground-state baryons are obtained by solving the Lippmann-Schwinger equation. We analyze in detail the effects of going beyond the t = 0 approximation. Our model predicts the dynamical generation of several open-charm baryon resonances in different isospin and strangeness channels, some of which can be clearly identified with recently observed states.

show abstract

Section: Formalismmentioning

confidence: 99%

Dynamically generated open-charm baryons beyond the zero-range approximation

2009

View full text Add to dashboard Cite

show abstract

“…(5) are well known, as discussed in, for example, Ref. [19] for πN scattering. Thus approximations, such as those used [15] in obtaining Eqs.…”

Section: Introductionmentioning

confidence: 97%

Nucleon resonances with hidden charm in coupled-channels models

2012

View full text Add to dashboard Cite

The model dependence of the predictions of nucleon resonances with hidden charm is investigated. We consider several coupled-channel models which are derived from relativistic quantum field theory by using (1) a unitary transformation method and (2) the three-dimensional reductions of the Bethe-Salpeter equation. With the same vector-meson exchange mechanism, we find that all models give very narrow molecularlike nucleon resonances with hidden charm in the mass range of 4.3 < M R < 4.5 GeV, consistent with the previous predictions.

show abstract

“…The appearance of the projection operator P ππN in Eqs. (21) and (26) is the consequence of the unitarity condition Eq. (13).…”

Section: Dynamical Coupled-channel Equationsmentioning

confidence: 99%

“…In addition to the two-body unitarity cut, it has a selected set of n-body unitarity cuts, as explained in great detail in Ref. [21]. Considerable numerical efforts are already needed to solve the Ladder BS equation for πN elastic scattering, as can be seen in the work of Lahiff and Afnan [22].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamical coupled-channel model of meson production reactions in the nucleon resonance region

2007

View full text Add to dashboard Cite

A dynamical coupled-channel model is presented for investigating the nucleon resonances (N * ) in the meson production reactions induced by pions and photons. Our objective is to extract the N * parameters and to investigate the meson production reaction mechanisms for mapping out the quark-gluon substructure of N * from the data. The model is based on an energy-independent Hamiltonian which is derived from a set of Lagrangians by using a unitary transformation method. The constructed model Hamiltonian consists of (a) Γ V for describing the vertex interactions N * ↔ M B, ππN with M B = γN, πN, ηN, π∆, ρN, σN , and ρ ↔ ππ and σ ↔ ππ, (b) v 22 for the non-resonant M B → M ′ B ′ and ππ → ππ interactions, (3) v M B,ππN for the non-resonant M B → ππN transitions, and (4) v ππN,ππN for the non-resonant ππN → ππN interactions. By applying the projection operator techniques, we derive a set of coupled-channel equations which satisfy the unitarity conditions within the channel space spanned by the considered two-particle M B states and the three-particle ππN state. The resulting amplitudes are written as a sum of non-resonant and resonant amplitudes such that the meson cloud effects on the N * decay can be explicitly calculated for interpreting the extracted N * parameters in terms of hadron structure calculations. We present and explain in detail a numerical method based on a spline-function expansion for solving the resulting coupled-channel equations which contain logarithmically divergent one-particle-exchange driving terms Z (E) M B,M ′ B ′ resulted from the ππN unitarity cut. This method is convenient, and perhaps more practical and accurate than the commonly employed methods of contour rotation/deformation, for calculating the two-pion production observables. For completeness in explaining our numerical procedures, we also present explicitly the formula for efficient calculations of a very large number of partial-wave matrix elements which are the input to the coupled-channel equations. Results for two pion photo-production are presented to illustrate the dynamical consequence of the one-particle-exchange driving term Z (E) M B,M ′ B ′ of the coupled-channel equations. We show that this mechanism, which contains the effects due to ππN unitarity cut, can generate rapidly varying structure in the reaction amplitudes associated with the unstable particle channels π∆, ρN , and σN , in agreement with the analysis of Aaron and Amado [Phys. Rev. D13, 2581(1976]. It also has large effects in determining the two-pion production cross sections. Our results indicate that cautions must be taken to interpret the N * parameters extracted from using models which do not include ππN cut effects. Strategies for performing a complete dynamical coupled-channel analysis of all of available data of meson photo-production and electro-production are discussed.

show abstract

Unitarity and the Bethe-Salpeter equation

Cited by 12 publications

References 29 publications

Dynamically generated open-charm baryons beyond the zero-range approximation

Dynamically generated open-charm baryons beyond the zero-range approximation

Nucleon resonances with hidden charm in coupled-channels models

Dynamical coupled-channel model of meson production reactions in the nucleon resonance region

Contact Info

Product

Resources

About