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$$B^\pm \rightarrow DK^\pm $$$B^{\pm }\to D{K}^{\pm }$transitions are known to provide theoretically clean information about the CKM angle$$\gamma $$$\gamma$, with the most precise available methods exploiting the cascade decay of the neutralDintoCPself-conjugate states. Such analyses currently require binning in theDdecay Dalitz plot, while a recently proposed method replaces this binning with the truncation of a Fourier series expansion. In this paper, we present a proof of principle of a novel alternative to these two methods, in which no approximations at the level of the data representation are required. In particular, our new strategy makes no assumptions about the amplitude and strong phase variation over the Dalitz plot. This comes at the cost of a degree of ambiguity in the choice of test statistic quantifying the compatibility of the data with a given value of$$\gamma $$$\gamma$, with improved choices of test statistic yielding higher sensitivity. While our current proof-of-principle implementation does not demonstrate optimal sensitivity to$$\gamma $$$\gamma$, its conceptually novel approach opens the door to new strategies for$$\gamma $$$\gamma$extraction. More studies are required to see if these can be competitive with the existing methods.

 

A bstract We perform a systematic study of SU(2) flavor amplitude sum rules with particular emphasis on U -spin. This study reveals a rich mathematical structure underlying the sum rules that allows us to formulate an algorithm for deriving all U -spin amplitude sum rules to any order of the symmetry breaking. This novel approach to deriving the sum rules does not require one to explicitly compute the Clebsch-Gordan tables, and allows for simple diagrammatic interpretation. Several examples that demonstrate the application of our novel method to systems that can be probed experimentally are provided.