# Model independent determination of the CKM phase *γ* using input from \( {D}^0\hbox{-} {\overline{D}}^0 \) mixing

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## Abstract

We present a new, amplitude model-independent method to measure the *CP* violation parameter *γ* in *B* ^{−} → *DK* ^{−} and related decays. Information on charm interference parameters, usually obtained from charm threshold data, is obtained from charm mixing. By splitting the phase space of the *D* meson decay into several bins, enough information can be gained to measure *γ* without input from the charm threshold. We demonstrate the feasibility of this approach with a simulation study of *B* ^{−} → *DK* ^{−} with *D* → *K* ^{+} *π* ^{−} *π* ^{+} *π* ^{−}. We compare the performance of our novel approach to that of a previously proposed binned analysis which uses charm interference parameters obtained from threshold data. While both methods provide useful constraints, the combination of the two by far outperforms either of them applied on their own. Such an analysis would provide a highly competitive measurement of *γ*. Our simulation studies indicate, subject to assumptions about data yields and the amplitude structure of *D* ^{0} → *K* ^{+} *π* ^{−} *π* ^{+} *π* ^{−}, a statistical uncertainty on *γ* of ~ 12° with existing data and ~ 4° for the LHCb-upgrade.

## Keywords

CKM angle gamma CP violation Charm physics B physics Hadron-Hadron Scattering## Notes

### **Open Access**

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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