QCD-improved limits from neutrinoless double beta decay

We analyze the impact of QCD corrections on limits derived from neutrinoless double beta decay ($0\nu\beta\beta$). As demonstrated previously, the effect of the color-mismatch arising from loops with gluons linking the quarks from different color-singlet currents participating in the effective operators has a dramatic impact on the predictions for some particular Wilson coefficients. Here, we consider all possible contributions from heavy particle exchange, i.e. the so-called short-range mechanism of $0\nu\beta\beta$ decay. All high-scale models (HSM) in this class match at some scale around a $\sim$ few TeV with the corresponding effective theory, containing a certain set of effective dimension-9 operators. Many of these HSM receive contributions from more than one of the basic operators and we calculate limits on these models using the latest experimental data. We also show with one non-trivial example, how to derive limits on more complicated models, in which many different Feynman diagrams contribute to $0\nu\beta\beta$ decay, using our general method.