Parity-violating two-pion exchange nucleon-nucleon interaction

Abstract

We calculate in chiral perturbation theory the parity-violating two-pion exchange nucleon-nucleon potentials at leading one-loop order. At a distance of r = m −1 π ≃ 1.4 fm they amount to about ±16% of the parity-violating 1π-exchange potential. We evaluate also the parity-violating effects arising from 2π-exchange with excitation of virtual ∆(1232)-isobars. These come out to be relatively small in comparison to those from diagrams with only nucleon intermediate states. The reason for this opposite behavior to the parity-conserving case is the blocking of the dominant isoscalar central channel by CP-invariance. Furthermore, we calculate the T-matrix related to the iteration of the parity-violating 1π-exchange with the parity-conserving one. The analytical results presented in this work can be easily implemented into calculations of parity-violating nuclear observables.PACS: 12.20.Ds, 12.38.Bx, 21.30.Cb.Nuclear parity violation is an important tool to study the standard model of strong and electroweak interactions [1,2]. In the two-nucleon system parity violation has been traditionally represented by parity-violating one-meson exchange where the strong and weak interactions are parametrized through parity-conserving and parity-violating meson-nucleon vertices. Due to CP-invariance, there exists no parity-violating coupling of neutral scalar or pseudoscalar mesons to nucleons (Barton's theorem). Therefore, standard parametrizations of the parity-violating NN-potential involve the exchange of charged pions (π ± ) as well as vector mesons (ρ ±,0 and ω). The pertinent parity-violating meson-nucleon coupling constants h

A study of the parity-odd nucleon-nucleon potential

“…[19], a more systematic approach based on chiral symmetry considerations has been investigated as well. This has lead to a derivation of the / P chiral NN potential [23,25,24] up to next-to-leading order. This potential consists of six LECs consisting of the pion-nucleon vertex h π and five NN contact terms.…”

“…We conclude that, apart from renormalization of LO LECs, the only corrections to the OPE potential are those in Eq. (25). Naively one might think that this potential should vanish in nucleon-nucleon scattering since it is proportional to p 2 − p 2 which is zero on-shell.…”

“…These diagrams involve LO vertices only, that is h π for the / P vertex and g A or the Weinberg-Tomazawa interaction for the P -conserving vertices. The relevant diagrams have been calculated several times [23,25] and here we give the results using spectral function regularization [39,26] …”

Parity nonconserving two-pion exchange in elastic proton-proton scattering

“…A comparison with the potential obtained from chiral perturbation theory [16] may be in order. That contains also the (reducible) box diagram and a triangle diagram with s-wave rescattering.…”

“…Closest comes the recent Ref. [16] in deriving PNC the two-pion potential in chiral perturbation theory. Our aim in the present paper is to calculate this potential including realistic form factors and extending the calculation to the observableĀ L .…”