Energy dependence of the parity-violating asymmetry of circularly polarized photons in $d\vec{\gamma }\to np$ in pionless effective field theory

We calculate the energy dependence of the asymmetry in the cross sections for circularly polarized photons on an unpolarized deuteron target in $d\vec{\gamma }\to np$ in pionless effective field theory. By matching the parity-violating low-energy constants to different sets of corresponding model parameters we obtain estimates for the asymmetry. In addition we calculate two possible figures of merit for the asymmetry in order to assess the preferred photon energy at which to perform a possible future experiment at a high-intensity photon source.

Figure 1

Diagram contributing to the $E{1}_v$ amplitude. The thick solid line denotes a dibaryon propagator, the thin lines with arrows nucleon lines, and the wavy line a photon. The photon is minimally coupled and the cross denotes an insertion of the deuteron wave-function renormalization.

Figure 2

Diagrams contributing to the amplitude $Y$. Here the small open circle denotes a coupling to the nucleon magnetic moment. The green diamond represents an insertion of $L_1$.

Figure 3

NLO diagram contributing to the amplitude $X$. The orange circle represents an insertion of $L_2$.

Figure 4

LO diagrams contributing to the PV amplitudes $W$ and $V$. The blue box represents an insertion of a PV operator.

Figure 5

LO diagrams contributing to the PV amplitudes $U_1$, $U_2$, and $U_3$. The blue box represents an insertion of a PV operator.

Figure 6

NLO diagrams contributing to the PV amplitudes $U_1$, $U_2$, and $U_3$. The blue box represents an insertion of a PV operator. The green diamond represents an insertion of $L_1$ and the orange circle an insertion of $L_2$.

Figure 7

The PV asymmetry $A_L^{\gamma }$, as a function of the photon energy. The lowest photon energy on the plot is the breakup threshold value corresponding to the deuteron binding energy. The thin lines are $Z$-parametrization calculations and the thick lines resummed ERE calculations.

Figure 8

The PV asymmetry $A_L^{\gamma }$, as a function of the photon energy. The lowest photon energy on the plot is the breakup threshold value corresponding to the deuteron binding energy. The thin lines are $Z$-parametrization calculations and the thick lines resummed ERE calculations.

Figure 9

The figure of merit ${\left(A_L^{\gamma }\right)}^2\times \sigma$ as a function of photon energy. The lowest photon energy on the plot is the breakup threshold value corresponding to the deuteron binding energy. The thin lines are $Z$-parametrization calculations and the thick lines resummed ERE calculations.

Figure 10

The figure of merit $A_L^{\gamma }\times \sigma$ as a function of photon energy. The lowest photon energy on the plot is the breakup threshold value corresponding to the deuteron binding energy. The thin lines are $Z$-parametrization calculations and the thick lines resummed ERE calculations.