M1 Radiative and spin-nonflip $\pi \pi$ transitions of $B_c$ states in the Cornell potential model

In this paper, we mainly predict the rates of $M$1 radiative and spin-nonflip $\pi \pi$ transitions of the $B_c$-meson under the nonrelativistic Cornell potential model with a screening potential effect. We employ the numerical wave function to determine the $M$1 radiative transition widths of $B_c$ excited states and utilize the Kuang-Yan proposed method for the spin-nonflip $\pi \pi$ transitions among $B_c$ states. Our theoretical results are valuable for studying the $M$1 radiative and spin-nonflip $\pi \pi$ transition processes of $B_c$ states in experiments.