Penguin Contributions to CP Phases in Bd,s Decays to Charmonium

The precision of the CP phases 2 beta and 2 beta(s) determined from the mixing-induced CP asymmetries in B-d -> J/psi K-S and B-s -> J/psi phi, respectively, is limited by the unknown long-distance contribution of a penguin diagram involving up quarks. The penguin contribution is expected to be comparable in size to the precision of the LHCb and Belle II experiments and, therefore, limits the sensitivity of the measured quantities to new physics. We analyze the infrared QCD structure of this contribution and find that all soft and collinear divergences either cancel between different diagrams or factorize into matrix elements of local four-quark operators up to terms suppressed by Lambda(QCD)/m(psi), where m(psi) denotes the J/psi mass. Our results, which are based on an operator product expansion, allow us to calculate the penguin-to-tree ratio P/T in terms of the matrix elements of these operators and to constrain the penguin contribution to the phase 2 beta as vertical bar Delta phi(d)vertical bar <= 0.68 degrees. The penguin contribution to 2 beta(s) is bounded as vertical bar Delta phi(0)(s)vertical bar <= 0.97 degrees, vertical bar Delta phi(parallel to)(s)vertical bar <= 1.22 degrees, and vertical bar Delta phi(perpendicular to)(s)vertical bar <= 0.99 degrees for the case of longitudinal, parallel, and perpendicular phi and J/psi polarizations, respectively. Further, we place bounds on vertical bar Delta phi(d)vertical bar for B-d -> psi(2S)K-S and the polarization amplitudes in B-d -> J/psi K*. In our approach, it is further possible to constrain P/T for decays in which P/T is Cabibbo unsuppressed, and we derive upper limits on the penguin contribution to the mixing-induced CP asymmetries in B-d -> J/psi pi(0), B-d -> J/psi rho(0), B-s -> J/psi K-S, and B-s -> J/psi K*. For all studied decay modes, we also constrain the sizes of the direct CP asymmetries.