Ab initio Calculation of the $np\to d\gamma$ Radiative Capture Process

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 ${\gamma }^{(*)}d\to np$. 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 the amplitudes for these low-energy inelastic processes. At $m_{\pi }\sim 806\mathrm{MeV}$, using only lattice QCD inputs, a cross section ${\sigma }^{806\mathrm{MeV}}\sim 17\mathrm{mb}$ is found at an incident neutron speed of $v=2,200\mathrm{m}/\mathrm{s}$. Extrapolating the short-distance contribution to the physical pion mass and combining the result with phenomenological scattering information and one-body couplings, a cross section of ${\sigma }^{\text{lqcd}}(np\to d\gamma )=334.9(\begin{array}{c}+5.2\\ -5.4\end{array})\mathrm{mb}$ is obtained at the same incident neutron speed, consistent with the experimental value of ${\sigma }^{\text{expt}}(np\to d\gamma )=334.2(0.5)\mathrm{mb}$.

Figure 1

The double ratios of the two principal correlators are shown for $m_{\pi }\sim 450\mathrm{MeV}$ for the three magnetic field strengths. The bands correspond to the single-exponential fits to the correlator and the associated statistical uncertainty.

Figure 2

LQCD calculations of the energy-splittings between the two lowest-lying eigenstates, with the single-nucleon contributions removed, as a function of $\tilde{n}$, along with the associated fits. The lower (blue) set of points correspond to the $m_{\pi }\sim 450\mathrm{MeV}$ ensemble and the upper (green) points to $m_{\pi }\sim 806\mathrm{MeV}$. The slope of the sets of points is proportional to ${\overline{L}}_1$ at the appropriate pion mass.

Figure 3

The results of LQCD calculations of ${\overline{L}}_1$ (blue points). The blue (green) shaded regions show the linear (quadratic) in $m_{\pi }$ extrapolation of ${\overline{L}}_1$ to the physical pion mass (dashed line) in natural nuclear magnetons (nNM). The vertical (red) line indicates the physical pion mass.