Theoretical Uncertainties in the Nuclear Matrix Elements of Neutrinoless Double Beta Decay: The Transition Operator

We explore the theoretical uncertainties related to the transition operator of neutrinoless double-beta (0 nu beta beta) decay. The transition operator used in standard calculations is a product of one-body currents, that can be obtained phenomenologically as in Tomoda [1] or Simkovic et al. [2]. However, corrections to the operator are hard to obtain in the phenomenological approach. Instead, we calculate the 0 nu beta beta decay operator in the framework of chiral effective theory (EFT), which gives a systematic order-by-order expansion of the transition currents. At leading orders in chiral EFT we reproduce the standard one-body currents of Refs. [1] and [2]. Corrections appear as two-body (2b) currents predicted by chiral EFT. We compute the effects of the leading 2b currents to the nuclear matrix elements of 0 nu beta beta decay for several transition candidates. The 2b current contributions are related to the quenching of Gamow-Teller transitions found in nuclear structure calculations.