Longitudinal asymmetry and proton spin rotation in p⃗d scattering with pionless effective field theory

Abstract

The energy dependence of the longitudinal asymmetry $({A}_{L})$ and the spin rotation of the proton on the deuterium target in the $\stackrel{P\vec}{p}d$ scattering are presented using the pionless effective field theory formalism. The strong, weak, and Coulomb interactions have been introduced in the $\stackrel{P\vec}{p}d$ scattering. We have shown that in the presence of Coulomb interaction, the parity-conserving (PC) and the parity-violating (PV) sectors are modified. The PV two-body transitions diagrams have been evaluated with the inclusion of Coulomb interaction and consequently the PV observables are enhanced. The leading-order values of the ${A}_{L}$ and the spin rotation of the proton on the deuterium target are calculated at the proton laboratory energies above 0.7 MeV, in order to calculate the Coulomb effect perturbatively, up to 3 MeV where typical momenta is $Q\ensuremath{\ll}{m}_{\ensuremath{\pi}}$. With the lack of experimental data for the low-energy coupling constants (LECs), we have used two estimated sets for the five independent (PV) LECs of the weak $NN$ PV Lagrangian. The order of magnitude, of the PV observables with these two sets, is found to be ${10}^{\ensuremath{-}6}$ to ${10}^{\ensuremath{-}7}$ which indicates that the expected order is achieved in this energy range. The cutoff independent results support the validity of our approach.