For a normal peak, the derivative must be 0 at the maximum point. By contrast, a cusp is formed when the derivative changes sign from positive infinity to negative infinity at the maximum point.

 

Invariant mass spectrum of a proton and K meson from the decay of into a proton, a K meson, and a π meson. By precisely analyzing the peak shape, we successfully confirmed that the peak is indeed a cusp with a sharp-pointed structure.

 

A closer examination of the extremely small world of an atomic nucleus reveals that it comprises protons and neutrons, collectively known as hadrons. According to the quark model, hadrons comprise two or three quarks.

However, in recent years, numerous exotic hadrons have been discovered that do not fit well within this framework. One proposed explanation states that this exotic state arises from two hadrons, forming a loosely bound system. However, through extensive investigation, we found that even when two hadrons are unbound, a signal resembling a bound system can still emerge. This phenomenon results in the formation of a peak-like structure in a mass spectrum. A crucial distinction exists between such a peak and a conventional one, regardless of how narrow the latter appears. For a normal peak, the derivative at the maximum point is always 0, giving it a rounded shape. By contrast, when hadrons are unbound, the derivative at the maximum point becomes infinite as it transitions directly from positive infinity to negative infinity. This results in a cusp, exhibiting a sharp-pointed shape. Although this phenomenon has been theoretically predicted for many years, its experimental verification was hindered by finite mass resolution.

By leveraging high-statistical and high-resolution data through the Belle experiment—an international collaborative effort in particle physics—we have successfully demonstrated the existence of a pointed peak.

This work was supported by JSPS KAKENHI Grant Number JP21H04478.

Yang, S. B., Tanida, K. et al., Observation of a Threshold Cusp at the Threshold in the Mass Spectrum with Decays, Physical Review D, vol.108, issue 3, 2023, L031104, 6p.

Paper URL: https://doi.org/10.1103/PhysRevD.108.L031104

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