Triangle singularity in $B^0\to \pi^- K^+ X(3872)$ via the $D_{s1}\bar{D} D^*$ loop and possible precise measurement of the $X(3872)$ mass

TL;DR

This paper proposes a method to precisely measure the $X(3872)$ mass using the triangle singularity effect in the decay $B^0 o \pi^- K^+ X(3872)$, which is highly sensitive to the $X(3872)$ mass near the $D^{ ext{*}0}ar{D}^0$ threshold.

Contribution

It introduces a novel approach leveraging the triangle singularity in the decay process to determine the $X(3872)$ mass with high precision.

Findings

The $K^+X(3872)$ line shape is highly sensitive to the $X(3872)$ mass near the threshold.

The narrow width of $D_{s1}(2536)$ enhances the triangle singularity effect.

Large $X(3872)$ width (around 1 MeV) can hinder the measurement accuracy.

Abstract

We investigate the $B^0\to \pi^- K^+ X(3872)$ decay via the $D_{s1}(2536)\bar{D} D^*$ rescattering diagram. The line shape of the $K^+X(3872)$ distribution curve around $D_{s1}(2536)\bar{D}$ threshold is very sensitive to the $X(3872)$ mass because the triangle singularity (TS) can be generated from the loop. By means of this characteristic, we can determine whether the $X(3872)$ mass is below or above the $D^{\ast 0}\bar{D}^0$ threshold with high precision. The narrowness of $D_{s1}(2536)$ in the loop is one of the key reasons why the TS mechanism of measuring the $X(3872)$ mass may work. The $X(3872)$ width impact on the $K^+X(3872)$ line shape is also crucial in the TS mechanism. If the width is as large as 1 MeV, the proposed method of measuring the $X(3872)$ mass would be ruined.