Proposal to detect a moving triangle singularity in $\psi(2S) \to \pi^+ \pi^- K^+ K^-$ process

TL;DR

This paper predicts a moving triangle singularity in the $ o o K^+K^-$ invariant mass spectrum of $ o o$ decay, which can be observed through specific experimental cuts, guiding future experimental verification.

Contribution

It introduces the concept of a moving triangle singularity in this decay process and proposes experimental conditions to observe it, which is a novel prediction in this context.

Findings

The triangle singularity position varies from 1.158 to 1.181 GeV.

Experimental cuts on $m_{ ext{pi+pi-}}$ can reveal the singularity.

The singularity's movement can be tracked by changing the cuts.

Abstract

In this work, we propose that there exists a moving triangle singularity in the $\psi(2S) \to \pi^+ \pi^- K^+ K^-$ process, whose position can vary from 1.158 to 1.181 GeV in the invariant mass spectrum of $K^+K^-$. After a precise analysis on this process, it turns out that after doing some cuts on $m_{\pi^+\pi^-}$, experiments do have the opportunity to observe this triangle singularity. In addition, when changing the cuts on $m_{\pi^+\pi^-}$, the movement of the predicted triangle singularity can also be observed. Thus, we suggest future experiments, especially Super Tau-Charm Facility (STCF), to do an anlysis on the $\psi(2S) \to \pi^+ \pi^- K^+ K^-$ process to verify our prediction.