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The decays $B_d\to\pi^\mp K^\pm$ and $B^\pm\to\pi^\pm K$ provide interestingconstraints on the angle $\gamma$ of the unitarity triangle of the CKM matrix.It is shown that bounds on $\gamma$ can also be obtained from the timeevolution of untagged $B_s\to K^+K^-$ and $B_s\to K^0\bar{K^0}$ decays,provided the $B_s$ system exhibits a sizeable width difference$\Delta\Gamma_s$. A detailed discussion of rescattering processes andelectroweak penguin effects, which limit the theoretical accuracy of theseconstraints, and of methods to control them through experimental data is given.Moreover, strategies are pointed out to go beyond these bounds by relating the$B_{u,d}\to\pi K$ and untagged $B_s\to K\bar{K}$ decays through the SU(3)flavour symmetry of strong interactions. If a tagged, time-dependentmeasurement of the $B_s\to K^+K^-$ and $B_s\to K^0\bar{K^0}$ modes shouldbecome possible, $\gamma$ could be determined from the correspondingobservables in a way that makes use of only the SU(2) isospin symmetry andtakes into account rescattering effects ``automatically''. The impact ofnew-physics contributions to $B^0_s - \bar{B^0_s}$ mixing is also analysed, andinteresting features arising in such a scenario of physics beyond the StandardModel are pointed out.Comment: 34 pages, LaTeX, 12 figures, extended version including a detailed  discussion of rescattering and electroweak penguin effect

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Towards extractions of the CKM angle γ from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>u</mml:mi><mml:mo>,</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>→</mml:mo><mml:mi>π</mml:mi><mml:mi>K</mml:mi></mml:math>and untagged<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:…

Towards extractions of the CKM angle γ fromBu,d→πKand untaggedB