# Higher Order Corrections to Nonleptonic and Rare Decays

**Principal Investigator:** Tobias Huber (Siegen)

**Participating Researchers: ** Guido Bell (Siegen), Björn O. Lange (Siegen), Thomas Mannel (Siegen)

Nonleptonic and rare decays of heavy flavors are one of the most important testing grounds for the flavour part of the Standard Model (SM) and are generally assumed to have a strong sensitivity for effects beyond the SM (BSM). In particular, charmless nonleptonic decays are important for CP violation measurements, since the largest direct CP asymmetries can be observed in these decays, at least within the SM.

For this reason, a large part of the experimental effort at currently running and planned flavour experiments is concentrated in this field. Over the next few years, the data accumulated at LHC as well as the data to be expected from Belle II will allow measurements of decay rates of charmless nonleptonic and rare decays at an unprecedented level of precision, forcing us to significantly improve the theoretical predictions.

The purpose of this project is to push the theoretical frontier in this area. The methodology employed is QCD factorization (QCDF), which is an effective field theory method allowing us to split off perturbative contributions (related to short distance physics) from nonperturbative pieces (related to long distances). While the latter need to be either extracted from data or - in the less favorable case - from a model, the perturbative part can be calculated and systematically improved.

Thus the strategy for this project is on the one hand to improve on the perturbative side by driving the calculations to the next-to-next-to leading order (NNLO) level and using these results for a global analysis of the data. On the other hand, the nonperturbative input (such as the one or two pion light-cone distribution amplitude) also has to be improved by extracting it with sufficient precision from other sources.

While two-body decays have been investigated already in detail, exclusive decays with more than two particle final states have only recently been studied in a model independent framework such as QCD factorization. The large amount of data expected also for e.g. three-body nonleptonic decays will allow many more cross checks of theoretical predictions through studies of their Dalitz distributions. Thus one other goal of this project is to improve the QCD based approaches to multi-body decays.

Finally, to reach the ultimate goal of precision to be expected from the NNLO QCD calculations, also effects from quantum electrodynamics (QED) need to be taken into account. This can be done in perturbation theory, thus the methodology is the same as in the perturbative QCD calculations. However, there is a crucial conceptual difference: Once QED is take into account, one has to fromulate factorization properly in a first step, since photons are colour-neutral particles.