  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 $np\rightarrow$
$d\gamma$ $A^{np}_\gamma$, the circular polarization of outgoing photon in
$np\rightarrow$ $d\gamma$ $P^{np}_\gamma$, 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 $\gamma$-emission in $nd\rightarrow$ $^3H\gamma$ $P^{nd}_\gamma$ 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 $nd\rightarrow$
$^3H\gamma$ process. We finally compare our EFT($//!/!/!/pi$) photon
asymmetries results with the experimental values and the previous calculations
based on the DDH model.
