An X(3872)-Like Peak in $B\rightarrow (J/\psi \pi ^+\pi ^-) K\pi$ Due to Triangle Singularity

Abstract

Triangle mechanisms for $B^0\rightarrow (J/\psi \pi ^+\pi ^-) K^+\pi ^-$ are studied. Experimentally, an X(3872) peak has been observed in this process. When the final $(J/\psi \pi ^+\pi ^-)\pi$ invariant mass is around the $D^*\bar{D}^*$ threshold, one of the triangle mechanisms causes a triangle singularity and generates a sharp X(3872)-like peak in the $J/\psi \pi ^+\pi ^-$ invariant mass distribution. The Breit–Wigner mass and width fitted to the spectrum are 3871.68 MeV (a few keV above the $D^{*0}\bar{D}^0$ threshold) and $\sim$ 0.4 MeV, respectively. These Breit-Wigner parameters hardly depend on a choice of the model parameters. Comparing with the precisely measured X(3872) mass and width, $3871.69\pm 0.17$ MeV and $< 1.2$ MeV, the agreement is remarkable. When studying the X(3872) signal from this process, this non-resonant contribution has to be understood in advance. We also study a charge analogous process $B^0\rightarrow (J/\psi \pi ^0\pi ^-) K^+\pi ^0$. A similar triangle singularity exists and generates an $X^-(3876)$-like peak.