Magnetic dipole transition in proton-deuteron radiative capture at BBN energies within potential model

The $pd$ radiative capture reaction plays a vital role in Big Bang nucleosynthesis and stellar proton-proton chain. The study of the low-energy reaction is challenging in both experiments and theories. Using the framework of potential model, we analyze $pd$ radiative capture below 1 MeV for both electric dipole ($E1$) and magnetic dipole ($M1$) transitions. The obtained astrophysical $S$ factors agree well with recent results, especially at energies relevant to sensitive deuterium abundance. The calculated reaction rate shows good agreement, with less than a 5\% difference compared to recent works. The extrapolated value for $S(0)$ including both transitions is determined to be $0.211 \pm 0.016$ eV b. A comparison with experimental data using the $\chi^2$ test reveals the sensitivity of the $M1$ cross section at low energies to the scattering potential depth.