We present a general parametrization of B ± → π ± K, π 0 K ± and B d → π 0 K, π ∓ K ± decays, taking into account both electroweak penguin and rescattering effects. This formalism allows -among other things -an improved implementation of the strategies that were recently proposed by Neubert and Rosner to probe the CKM angle γ with the help of B ± → π ± K, π 0 K ± decays. In particular, it allows us to investigate the sensitivity of the extracted value of γ to the basic assumptions of their approach. We find that certain SU (3)-breaking effects may have an important impact and emphasize that additional hadronic uncertainties are due to rescattering processes. The latter can be controlled by using SU (3) flavour symmetry arguments and additional experimental information provided by B ± → K ± K modes. We propose a new strategy to probe the angle γ with the help of the neutral decaysHere rescattering processes can be taken into account by just measuring the CP-violating observables of the decay B d → π 0 K S . Finally, we point out that an experimental analysis of B s → K + K − modes would also be very useful to probe the CKM angle γ, as well as electroweak penguins, and we critically compare the virtues and weaknesses of the various approaches discussed in this paper. As a by-product, we point out a strategy to include the electroweak penguins in the determination of the CKM angle α from B → ππ decays.

The presence of a sizable CP-violating phase in B s -B s mixing would be an unambiguous signal of physics beyond the standard model. We analyze various possibilities to detect such a new phase considering both tagged and untagged decays. The effects of a sizable width difference ⌬⌫ between the B s mass eigenstates, on which the untagged analyses rely, are included in all formulas. A novel method to find this phase from simple measurements of lifetimes and branching ratios in untagged decays is proposed. This method does not involve two-exponential fits, which require much larger statistics. For the tagged decays, an outstanding role is played by the observables of the time-dependent angular distribution of theWe list the formulas needed for the angular analysis in the presence of both a new CP-violating phase and a sizable ⌬⌫, and propose methods to remove a remaining discrete ambiguity in the new phase. This phase can therefore be determined in an unambiguous way.

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We have recently seen new upper bounds for B(s)(0)→μ(+)μ(-), a key decay to search for physics beyond the standard model. Furthermore a nonvanishing decay width difference ΔΓ(s) of the B(s) system has been measured. We show that ΔΓ(s) affects the extraction of the B(s)(0)→μ(+)μ(-) branching ratio and the resulting constraints on the new physics parameter space and give formulas for including this effect. Moreover, we point out that ΔΓ(s) provides a new observable, the effective B(s)(0)→μ(+)μ(-) lifetime τ(μ(+)μ(-)), which offers a theoretically clean probe for new physics searches that is complementary to the branching ratio. Should the B(s)(0)→μ(+)μ(-) branching ratio agree with the standard model, the measurement of τ(μ(+)μ(-)), which appears feasible at upgrades of the Large Hadron Collider experiments, may still reveal large new physics effects.