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

R. Fleischer

doi:doi:10.1007/s100520050005

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2023 Impact factor 4.2

Particles and Fields

Eur. Phys. J. C 16, 87-95
DOI 10.1007/s100520000405

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

R. Fleischer

Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany (e-mail: Robert.Fleischer@desy.de)

Received: 1 March 2000 / Published online: 18 May 2000 - © Springer-Verlag 2000

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 B⁰_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.