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

  • R. Fleischer
Theoretical physics


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.


Restricted Range Recent Experimental Result Interesting Strategy Penguin Contribution Interesting Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • R. Fleischer
    • 1
  1. 1.Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany (e-mail: DE

Personalised recommendations