Ab initio calculation of the $np\to d\gamma$ radiative capture process

Abstract

Lattice QCD calculations of two-nucleon systems are used to isolate the short-distance two-body electromagnetic contributions to the radiative capture process $np\to d\gamma$, and the photo-disintegration processes ${\gamma }^{(\ast )}d\to np$. In nuclear potential models, such contributions are described by phenomenological meson-exchange currents, while in the present work, they are determined directly from the quark and gluon interactions of QCD. Calculations of neutron-proton energy levels in multiple background magnetic fields are performed at two values of the quark masses, corresponding to pion masses of $m_{\pi }\sim 450$ and 806 MeV, and are combined with pionless nuclear effective field theory to determine these low-energy inelastic processes. Extrapolating to the physical pion mass, a cross section of ${\sigma }^{lqcd}(np\to d\gamma )=332.4(\begin{array}{l}+5.4\\ -4.7\end{array})mb$ is obtained at an incident neutron speed of $v=2,200m/s$, consistent with the experimental value of ${\sigma }^{expt}(np\to d\gamma )=334.2(0.5)mb$.