Thermonuclear reaction rate of the deuteron alpha capture reaction in cluster effective field theory

In this work, we calculate the thermonuclear reaction rate of the \(d(\alpha ,\gamma )^{6}\textrm{Li}\) radiative capture process within the framework of cluster effective field theory (CEFT). The deuteron and the alpha particle are treated as effective degrees of freedom, enabling a systematic description of the low-energy dynamics relevant to primordial nucleosynthesis. The capture cross section is calculated by including the E 1 and E 2 electromagnetic transition amplitudes, while Coulomb interactions are treated nonperturbatively. The thermonuclear reaction rate is then evaluated at next-to-leading order over the temperature range \(10^6 \textrm{K} \le T\le 10^{10} \textrm{K}\) relevant to astrophysical applications. The scattering sector low-energy constants were previously constrained by experimental \(d-\alpha \) phase shifts, while the electromagnetic low-energy constants \(L_{E1}^R\) and \(L_{E2}^R\) were constrained by the experimental astrophysical S-factor. These parameters are used in the present calculation without any further refitting. The resulting CEFT reaction rate is compared with previous theoretical calculations, the LUNA reaction rate, and the NACRE II reaction rate. The CEFT result follows the overall temperature dependence of the NACRE II rate over a substantial part of the considered temperature range, while showing a more pronounced deviation from the LUNA rate. The present calculation provides an additional consistency test of the previously constrained CEFT capture description at a temperature-dependent astrophysical observable and provides a useful CEFT based reaction rate input for studies of primordial \(^{6}\textrm{Li}\) production.