Photon Asymmetries in ${nd\rightarrow}$ ³ Hγ Using EFT(${/\!\!\!\pi}$) Approach

Abstract

The parity-violating Lagrangian of the weak nucleon-nucleon (NN) interaction in the pionless effective field theory (EFT(${/\!\!\!\pi}$)) approach contains five independent unknown low-energy coupling constants (LECs). The photon asymmetry with respect to neutron polarization in ${np\rightarrow d\gamma A_\gamma^{np}}$, the circular polarization of outgoing photon in ${np\rightarrow d\gamma P_\gamma^{np}}$, the neutron spin rotation in hydrogen ${\frac{1}{\rho}\frac{d\phi^{np}}{dl}}$ , the neutron spin rotation in deuterium ${\frac{1}{\rho}\frac{d\phi^{nd}}{dl}}$ and the circular polarization of γ-emission in ${nd\rightarrow}$ ³ Hγ ${P^{nd}_\gamma}$ are the parity-violating observables which have been recently calculated in terms of parity-violating LECs in the EFT(${/\!\!\!\pi}$) framework. We obtain the LECs by matching the parity-violating observables to the Desplanques, Donoghue, and Holstein (DDH) best value estimates. Then, we evaluate photon asymmetry with respect to the neutron polarization ${a^{nd}_\gamma}$ and the photon asymmetry in relation to deuteron polarization ${A^{nd}_\gamma}$ in ${nd\rightarrow}$ ³ Hγ process. We finally compare our EFT(${/\!\!\!\pi}$) photon asymmetries results with the experimental values and the previous calculations based on the DDH model.