New physics effects in tree-level decays and the precision in the determination of the quark mixing angleγ

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.