Radiative Corrections to Two-Neutrino Double-Beta Decay

We use heavy-nucleus effective field theory to compute radiative corrections to two-neutrino double-β decay (2νββ). Our main result is the first derivation of a universal radiative-correction factor for double-weak decays-the analog of the Sirlin function in single-β decay-independent of nuclear matrix elements and excitation energies. This "double-weak Sirlin function" depends on the individual electron energies as well as their relative angle and differs significantly from the approximation obtained by summing two single-β decay Sirlin functions. In addition, we calculate the nuclear-structure-dependent component of the radiative corrections and find that they can still be neglected at current experimental sensitivities. On the other hand, the double-weak Sirlin function induces distortions of the electron energies and angular spectra that are comparable in size to the leading nuclear-structure correction parametrized by the ratio of nuclear matrix elements, ξ_{31}. Our results indicate that extractions of nuclear-structure information and tests of the standard model from high-precision 2νββ measurements must include double-weak radiative corrections, implying that recent extractions of ξ_{31} should be revisited.