Manifestly Lorentz invariant formulation of chiral effective field theory for neutrinoless double beta decay

The neutrinoless double beta decay process of two neutrons, $nn\rightarrow ppee$, is studied in the manifestly Lorentz invariant formulation of chiral effective field theory. Due to the better ultraviolet behavior of the relativistic scattering equation, the $nn\rightarrow ppee$ contact term is not needed for renormalization at leading order, in contrast to the nonrelativistic case. The predicted $nn\rightarrow ppee$ amplitude is consistent with the previous result from the generalized Cottingham formula at 10% level. The present approach is validated by reproducing the charge symmetry breaking and charge independence breaking in the nucleon-nucleon ($NN$) scattering length.