Determining<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>γ</mml:mi></mml:math>using<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mo>±</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mo>→</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>DK</mml:mi></mml:mrow><mml:mrow><mml:mo>±</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>with multibody<i>D</i>decays

Abstract

We propose a method for determining $\ensuremath{\gamma}$ using ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{\mathrm{DK}}^{\ifmmode\pm\else\textpm\fi{}}$ decays followed by a multibody D decay, such as $\stackrel{\ensuremath{\rightarrow}}{D}{K}_{S}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+},$ $\stackrel{\ensuremath{\rightarrow}}{D}{K}_{S}{K}^{\ensuremath{-}}{K}^{+},$ and $\stackrel{\ensuremath{\rightarrow}}{D}{K}_{S}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}.$ The main advantages of the method are that it uses only Cabibbo allowed D decays, and that large strong phases are expected due to the presence of resonances. Since no knowledge about the resonance structure is needed, $\ensuremath{\gamma}$ can be extracted without any hadronic uncertainty.

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