Contributions from the color-octet matrix elements to the $\overline{B}$ $\to$ $\ddot{I}€\ddot{I}€$ decays with QCD factorization approach

Abstract

Motivated by the $\ddot{I}€\ddot{I}€$ puzzle in nonleptonic $B$ decays in the time of high-precision and huge-data for particle physics, we restudy the $\overline{B}$ $\to$ $\ddot{I}€\ddot{I}€$ decays with QCD factorization approach. An additional contributions from the color-octet current matrix elements (COCME) which are unnoticed in almost all the previous calculation, are taken into consideration and parameterized by $X$. It is found that (1) form factor $F_0^{B\ddot{I}€}$ $\approx$ $0.22$ is favored by the available latest measurements. (2) The COCME contributions are helpful to interpret the experimental data on branching ratios rather than $CP$ asymmetries for the $\overline{B}$ $\to$ $\ddot{I}€\ddot{I}€$ decays.

20 pages