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Two-loop anomalous dimensions and one-loop renormalization scheme matching factors are calculated for six-quark operators responsible for neutron-antineutron transitions. When combined with lattice QCD determinations of the matrix elements of these operators, our results can be used to reliably predict the neutron-antineutron vacuum transition time, ₍₍, in terms of basic parameters of baryon-number-violating beyond-the-Standard-Model theories. The operators are classified by their chiral transformation properties, and a basis in which there is no operator mixing due to strong interactions is identified. Operator projectors that are required for nonperturbative renormalization of the corresponding lattice QCD six-quark operator matrix elements are constructed. A complete calculation of =1/₍₍ in a particular beyond-the-Standard-Model theory is presented as an example to demonstrate how operator renormalization and results from lattice QCD are combined with experimental bounds on to constrain the scale of new baryon-number-violating physics. At the present computationally accessible lattice QCD matching scale of 2 GeV, the next-to-next-to-leading-order effects calculated in this work correct the leading-order plus next-to-leading-order predictions of beyond-the-Standard-Model theories by <26%. Next-to-next-to-next-to-leading-order effects provide additional unknown corrections to predictions of that are estimated to be <7%.
Buchoff et al. (2016) studied this question.