Philipp Frings (Karlsruhe Institute of Technology)
The CKM angle $\beta$ ($\beta_s$) is one of the key $CP$-violation parameters in the SM. It is best determined by the mixing-induced $CP$ asymmetry in the decay $B_d\to J/\psi K_S$ ($B_s \to J/\psi \phi$). However, the theoretical precision of this determination has been under discussion for a long time and the estimated uncertainties ranged from negligible to sizable. The possible corrections are due to penguin diagrams that are suppressed parametrically by CKM elements. Nonetheless, QCD long-distance effects may enhance these corrections considerably. In the past, mostly data-driven methods that exploit the $SU(3)$ flavor symmetry have been used to estimate the theoretical corrections. In contrast, we present a genuine first-principles calculation of the penguin pollution. Our approach is based on an operator product expansion (OPE) that exploits the heaviness of charmonia. We show that it is possible to separate long and short-distance effects in decays of $B$ mesons to charmonia. With our simplified Hamiltonian the number of non-perturbative matrix elements is small at leading order in the OPE, we then use $1/N_c$ counting to order these matrix elements. We conclude with predictions for the theoretical precision of $\beta$ and $\beta_s$ and the $CP$ violation observables $C_f$ and $S_f$ for various final states $f$ that consist of a charmonium and a light meson e.g. $J/\psi \pi^0,$ $J/\psi K_S,$ $J/\psi \rho$, or $J/\psi \phi$.
Based on: http://de.arxiv.org/abs/1503.00859