Penguin Contributions to CP Phases in B(d,s) Decays to Charmonium.

The precision of the CP phases 2β and 2β(s) determined from the mixing-induced CP asymmetries in B(d)→J/ψK(S) and B(s)→J/ψϕ, 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 Λ(QCD)/m(ψ), where m(ψ) denotes the J/ψ mass.