Determining the unitarity triangle angle ${\hat{I}}^3$ with a four-body amplitude analysis of ${\mathrm{B}}^{\pm }\to ({\mathrm{K}}^{+}{\mathrm{K}}^{-}\ddot{\mathrm{I}}{€}^{+}\ddot{\mathrm{I}}{€}^{-}{)}_{\mathrm{D}}{\mathrm{K}}^{\pm }$ decays

Abstract

We explain how a four-body amplitude analysis of the $\mathrm{D}$ decay products in the mode ${\mathrm{B}}^{\pm }\to ({\mathrm{K}}^{+}{\mathrm{K}}^{-}\ddot{\mathrm{I}}{€}^{+}\ddot{\mathrm{I}}{€}^{-}{)}_{\mathrm{D}}{\mathrm{K}}^{\pm }$ is sensitive to the unitarity triangle angle ${\hat{I}}^3$. We present results from simulation studies which show that a precision on ${\hat{I}}^3$ of $15^{\circ }$ is achievable with 1000 events and assuming a value of 0.10 for the parameter $r_B$.

8 pages, 3 figures. (This version has bug in equation 4 fixed, and minor modification to references.)