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Parity violating (PV) contributions due to interference between $gamma$ and $Z^0$ exchange are calculated for pion electroproduction off the nucleon. A phenomenological model with effective Lagrangians is used to determine the resulting asymmetry for the energy region between threshold and $Delta(1232)$ resonance. The $Delta$ resonance is treated as a Rarita-Schwinger field with phenomenological $N Delta$ transition currents. The background contributions are given by the usual Born terms using the pseudovector $pi N$ Lagrangian. Numerical results for the asymmetry are presented.
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A theory of two-pion photo- and electroproduction off the nucleon is derived considering all explicit three-body mechanisms of the interacting $pipi N$ system. The full three-body dynamics of the interacting $pipi N$ system is accounted for by the Faddeev-type ordering structure of the Alt-Grassberger-Sandhas equations. The formulation is valid for hadronic two-point and three-point functions dressed by arbitrary internal mechanisms provided all associated electromagnetic currents are constructed to satisfy their respective (generalized) Ward-Takahashi identities. It is shown that coupling the photon to the Faddeev structure of the underlying hadronic two-pion production mechanisms results in a natural expansion of the full two-pion photoproduction current $M_{pipi}^mu$ in terms of multiple dressed loops involving two-body subsystem scattering amplitudes of the $pipi N$ system that preserves gauge invariance as a matter of course order by order in the number of (dressed) loops. A closed-form expression is presented for the entire gauge-invariant current $M_{pipi}^mu$ with complete three-body dynamics. Individually gauge-invariant truncations of the full dynamics most relevant for practical applications at the no-loop, one-loop, and two-loop levels are discussed in detail. An approximation scheme to the full two-pion amplitude for calculational purposes is also presented. It approximates, systematically, the full amplitude to any desired order of expansion in the underlying hadronic two-body amplitude. Moreover, it allows for the approximate incorporation of all neglected higher-order mechanisms in terms of a phenomenological remainder current. The effect and phenomenological usefulness of this remainder current is assessed in a tree-level calculation of the $gamma N to K K Xi$ reaction.
Two-pion exchange parity-violating nucleon-nucleon interactions from recent effective field theories and earlier fully covariant approaches are investigated. The potentials are compared with the idea to obtain better insight on the role of low-energy constants appearing in the effective field theory approach and the convergence of this one in terms of a perturbative series. The results are illustrated by considering the longitudinal asymmetry of polarized protons scattering off protons, $vec{p}+p -> p+p$, and the asymmetry of the photon emission in radiative capture of polarized neutrons by protons, $vec{n}+p -> d+gamma$.
Several experimental investigations have observed parity violation in nuclear systems-a consequence of the weak force between quarks. We apply the $1/N_c$ expansion of QCD to the P-violating T-conserving component of the nucleon-nucleon (NN) potential. We show there are two leading-order operators, both of which affect $vec{p}p$ scattering at order $N_c$. We find an additional four operators at $O(N_c^0 sin^2 theta_W)$ and six at $O(1/N_c)$. Pion exchange in the PV NN force is suppressed by $1/N_c$ and $sin^2 theta_W$, providing a quantitative explanation for its non-observation up to this time. The large-$N_c$ hierarchy of other PV NN force mechanisms is consistent with estimates of the couplings in phenomenological models. The PV observed in $vec{p}p$ scattering data is compatible with natural values for the strong and weak coupling constants: there is no evidence of fine tuning.
[Background] Above the nucleon resonance region, the $N(e,epi^pm)N$ data cannot be explained by conventional hadronic models. For example, the observed magnitude of the transverse cross section is significantly underestimated in a framework with Reggeized background amplitudes. [Purpose] Develop a phenomenological framework for the $N(e,epi^pm)N$ reaction at high invariant mass $W$ and deep photon virtuality $Q^2$. [Method] Building on the work of Kaskulov and Mosel, a gauged pion-exchange current is introduced with a running cutoff energy for the proton electromagnetic transition form factor. A new transition form factor is proposed. It respects the correct on-shell limit, has a simple physical interpretation and reduces the number of free parameters by one. [Results] A study of the $W$ dependence of the $N(e,epi^pm)N$ lends support for the newly proposed transition form factor. In addition, an improved description of the separated and unseparated cross sections at $-t lesssim 0.5 ;text{GeV}^2$ is obtained. The predictions overshoot the measured unseparated cross sections for $-t > 0.5 ;text{GeV}^2$. Introducing a strong hadronic form factor in the Reggeized background amplitudes brings the calculations considerably closer to the high $-t$ data. [Conclusions] Hadronic models corrected for resonance/parton duality describe the separated pion electroproduction cross sections above the resonance region reasonably well at low $-t$. In order to validate the applicability of these models at high $-t$, separated cross sections are needed. These are expected to provide a more profound insight into the relevant reaction mechanisms.
We discuss the extended on-mass-shell scheme for manifestly Lorentz-invariant baryon chiral perturbation theory. We present a calculation of pion photo- and electroproduction up to and including order $q^4$. The low-energy constants have been fixed by fitting experimental data in all available reaction channels. Our results can be accessed via a web interface, the so-called chiral MAID (http://www.kph.uni-mainz.de/MAID/chiralmaid/).
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