Constraints on the CKM angle $\gamma$ and strong phases from $B\to\pi K$ decays

A.J. Buras; R. Fleischer

doi:doi:10.1007/s100520050006

2022 Impact factor 4.4

Particles and Fields

Eur. Phys. J. C 16, 97-104
DOI 10.1007/s100520000409

Constraints on the CKM angle $\gamma$
and strong phases from $B\to\pi K$ decays

A.J. Buras¹ - R. Fleischer²

¹ Technische Universität München, Physik Department, 85748 Garching, Germany
² Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany

Received: 31 March 2000 / Published online: 18 May 2000 - © Springer-Verlag 2000

Abstract
As we pointed out recently, the neutral decays $B_d\to\pi^\mp K^\pm$ and $B_d\to\pi^0K$ may provide non-trivial bounds on the CKM angle $\gamma$ . In this paper, we reconsider this approach in the light of recent CLEO data, which look very interesting. In particular, the results for the corresponding CP-averaged branching ratios are in favour of strong constraints on $\gamma$ , where the second quadrant is preferred. Such a situation would be in conflict with the standard analysis of the unitarity triangle. Moreover, constraints on a CP-conserving strong phase $\delta_{\rm n}$ are in favour of a negative value of $\cos\delta_{\rm n}$ , which would be in conflict with the factorization expectation. In addition, there seems to be an interesting discrepancy with the bounds that are implied by the charged $B\to\pi K$ system: whereas these decays favour a range for $\gamma$ that is similar to that of the neutral modes, they point towards a positive value of $\cos\delta_{\rm c}$ , which would be in conflict with the expectation of equal signs for $\cos\delta_{\rm n}$ and $\cos\delta_{\rm c}$ . If future data should confirm this ``puzzle'', it may be an indication for new-physics contributions to the electroweak penguin sector, or a manifestation of large non-factorizable SU(3)-breaking effects.