New physics effects in tree-level decays and the precision in the determination of the quark mixing angle γ.

We critically review the assumption that no new physics is acting in tree-level B-meson decays and study the consequences for the ultimate precision in the direct determination of the Cabibbo-Kobayashi-Maskawa (CKM) angle γ. In our exploratory study we find that sizeable universal new physics contributions, ΔC1,2, to the tree-level Wilson coefficients C1,2 of the effective Hamiltonian describing weak decays of the b quark are currently not excluded by experimental data. In particular, we find that ImΔC1 and ImΔC2 can easily be of order ±10% without violating any constraints from data. Such a size of new physics effects in C1 and C2 corresponds to an intrinsic uncertainty in the CKM angle γ of the order of |δγ|≈4°, which is slightly below the current experimental precision. The accuracy in the determination of γ can be improved by putting stronger constraints on the tree-level Wilson coefficients, in particular C1. To this end we suggest a more refined theoretical study as well as more precise measurements of the observables that currently provide the strongest bounds on hypothetical new weak phases in C1 and C2. We note that the semileptonic CP asymmetries seem to have the best prospect for improving the bound on the weak phase in C1