Δ(1232)inπN→ππNreaction

Abstract

The contribution of ∆(1232) to the πN → ππN reaction is examined by making use of the chiral reduction formula developed by Yamagishi and Zahed. The influence of the π∆∆ and ρN ∆ interactions on this reaction, which has not been regarded as important so far, is considered for all channels with the initial π ± p states. The total cross sections are calculated to tree level for the energy up to T π = 400 MeV. Although the π∆∆ and ρN ∆ interactions give a small effect on the π + p → π + π + n, π − p → π + π − n, and π − p → π 0 π 0 n channels, the π ± p → π ± π 0 p channels are found to be sensitive to these interactions.

Pion couplings of theΔ(1232)

“…Finally, the inclusion of three-quark terms takes third order SU(6) symmetry breaking into account. Using the QCD sum rule value f π 0 ∆ + ∆ + = 0.666 f [21], which is consistent with the data [9][10][11], allows us to fix the constant A 3 in Eq. (8).…”

“…The numbers in the first column correspond to the additive quark model results in Eq. (10). The entries in the second column include the effect of the two-quark operator O 2 of Ref.…”

“…In sufficiently energetic N N collisions one or both nucleons may be excited to the ∆(1232), a process that makes a significant contribution to many nuclear phenomena [4], for example, electromagnetic properties of light nuclei [5], three-nucleon forces [6], and the binding energy of nuclear matter [7]. In addition, ∆ degrees of freedom are needed to explain the empirical cross sections for the πN → πN [8], πN → ππN [9,10], and N N → N N ππ [11] reactions including a novel resonance structure in the p n → dπ 0 π 0 channel [12]. However, a quantitative assessment of the role of ∆ degrees of freedom in nuclear physics has remained difficult due to the lack of detailed knowledge of even basic ∆ properties.…”

K*photoproduction off the nucleon:γN→K*Λ

“…ρN ∆ = 5.5 [15,16]. The other couplings are unknown and we do not consider the terms containing f (2) K * N Σ * and f…”

πNandηpdeexcitation channels of theN*and Δ baryon

“…The study of the dynamics of the πN→ ππN reaction [2] is also useful for improving our knowledge about meson production, as well as our knowledge of the baryonic resonances.…”