# Constraining penguin contributions and the CKM angle \(\gamma\) through \(B_d\to\pi^+\pi^-\)

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## Abstract.

The decays \(B_d\to\pi^+\pi^-\) and \(B_s\to K^+K^-\) provide an interesting strategy to extract the CKM angle \(\gamma\) at “second-generation”*B*-physics experiments of the LHC era. A variant for “first-generation” experiments can be obtained, if \(B_s\to K^+K^-\) is replaced by \(B_d\to\pi^\mp K^\pm\). We show that the most recent experimental results for the CP-averaged \(B_d\to\pi^+\pi^-\) and \(B_d\to\pi^\mp K^\pm\) branching ratios imply a rather restricted range for the corresponding penguin parameters, and upper bounds on the direct CP asymmetries \({\cal A}_{\rm CP}^{\rm dir}(B_d\to\pi^+\pi^-)\) and \({\cal A}_{\rm CP}^{\rm dir}(B_d\to\pi^\mp K^\pm)\). Moreover, we point out that interesting constraints on \(\gamma\) can be obtained from the CP-averaged \(B_d\to\pi^+\pi^-\) and \(B_d\to\pi^\mp K^\pm\) branching ratios, if in addition mixing-induced CP violation in the former decay is measured, and the \(B^0_d\)–\(\overline{B^0_d}\) mixing phase is fixed through \(B_d\to J/\psi K_{\rm S}\). An extraction of \(\gamma\) becomes possible, if furthermore direct CP violation in \(B_d\to\pi^+\pi^-\) or \(B_d\to\pi^\mp K^\pm\) is observed.

## Keywords

Restricted Range Recent Experimental Result Interesting Strategy Penguin Contribution Interesting Constraint## Preview

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