Pionic content of ϱNN and ϱNΔ vertex functions

Composite vertices that lead to soft form factors

“…A similar analysis applies to the appearance of soft composite ρ-baryon-baryon vertices in Ref. [15].…”

“…Smaller cutoffs are also advocated by an earlier theoretical investigation [14] which demonstrates that the boson nature of the pion requires a cut-off parameter much smaller than 1 GeV. Small Λ ρN N and Λ ρN ∆ have also been obtained by Haider and Liu [15] and by Deister et al [16] when composite models are used for the ρNN and ρN∆ vertices.…”

“…However, under this circumstance, it will be necessary to iterate the calculations so as to obtain a convergent solution of Λ. Such self-consistent calculations are indeed possible, as has been demonstrated in the study of composite ρNN and ρN∆ vertices by Deister et al [16] and by Haider and Liu [15], where a set of coupled integral equations of the composite vertex functions is established and iterated to all orders.…”

“…Furthermore, propagators of particles having spins higher than 1/2 will also introduce higher powers of momenta. In these latter cases, higher-order multipole form factors (n > 2) need to be used to ensure the convergence of the integration [15]. Although this complication introduces more tedious angular momentum algebra, it will not alter the qualitative conclusion obtained with the present s-wave study (see Section IV.…”

Δ decay in the nuclear medium

“…This means that either the strength of the ρN∆ coupling, f ρN ∆ , is considerably weaker than what is usually assumed, or some additional amplitude tends to cancel the contribution from the rho. A recent theoretical study on the microscopic analysis of the ρN∆ vertex due to Liu and Haider [12], in fact, suggests that the value of f ρN ∆ is much smaller.…”