Erratum: Elementary1H(p,p′π+

Abstract

A detailed study of the elementary p(p,p ′ π + )n reaction is presented using the delta isobar model. In this model, in the first step one of the two protons in the initial state gets excited to ∆. This, in the second step, decays into a nucleon and a pion. For the pp→N∆ step the parametrized form of the DWBA t-matrix of Jain and Santra, which reproduces most of the available data on pp→n∆ ++ , is used. The cross-sections studied include the outgoing proton momentum spectra in coincidence with the pion, the outgoing pion momentum spectra and the integrated total cross-section. We find that all the calculated numbers are in good agreement with the corresponding measured cross sections. PACS number(s): 25.40.Ve, 13.75.-n, 25.55.-e 1

Role of the resonance in the reaction

“…Here a quite severe cutoff Λ ∆ π is needed to reproduce data, in consistent with the previous study [23] of pp → n∆ ++ reactions.…”

“…Previous calculations used Λ ∆ π = 0.65 GeV [23] and 0.63 GeV [53]. Whereas they included only the ∆ resonance to reproduce the total cross sections for the pp → pnπ + reaction, we need to reduce it to 0.59 GeV to allow contributions from the off-shell nucleon pole and the Roper resonance for the best description of the total cross section.…”

“…But their contributions are included in actual calculations. In addition to the ∆(1232) and the off-shell nucleon pole included in previous works [22,23,24,25], the Roper resonance is added in our calculation. For the production of the Roper resonance and the intermediate virtual nucleon, the π 0 and σ-meson exchanges are included while the ρ-meson exchange is found to give negligible contribution and is dropped.…”

“…For the production of the ∆(1232) resonance, we only include π-meson exchange since iso-scalar meson exchanges cannot contribute and according to Ref. [23] any attempt to include the ρ-meson exchange worsens the agreement with experiments of pp → n∆ ++ reactions. A Lorentz covariant orbital-spin(L-S) scheme [26] are used for the effective ∆πN, N * σN, and N * πN vertices.…”

“…While the ISI factor with pp → ppη reaction near threshold is relatively simple with 3 P 0 pp initial state dominant, it becomes technically more complicated for pp → NNπ with several important initial partial waves even at energies very close to the threshold. In practice, for the pion production reactions, the ISI dumping effect is not included explicitly in previous calculations [22,23] and is done by adjusting the vertex form factors to reproduce the total cross sections. Since how to treat this dumping factor does not influence our main conclusion here, we follow the simple practical approach as these previous calculations [22,23] on the same reaction, although the ISI could be taken into account by some more complicated approaches, such as by including the partial wave ISI factors [42,43] or distortions of wave functions [44,45,46].…”