The double thresholds distort the lineshapes of the $P_{\psi s}^\Lambda(4338)^0$ resonance

TL;DR

This paper investigates how double threshold effects distort the lineshapes of the newly observed $P_{ extpsi s}^ extLambda(4338)^0$ resonance, challenging the adequacy of Breit-Wigner fits and emphasizing the need for refined analysis methods.

Contribution

It introduces a detailed analysis of threshold effects on the $P_{ extpsi s}^ extLambda(4338)^0$ lineshape using coupled-channel models and advocates for improved experimental analysis considering unitarity and analyticity.

Findings

The resonance peak may originate from poles on different Riemann sheets.

Breit-Wigner parameterization can be misleading for threshold-distorted lineshapes.

Threshold differences can produce novel lineshape features.

Abstract

Very recently, the LHCb Collaboration reported the first observation of the hidden charm pentaquark with strangeness, $P_{\psi s}^\Lambda(4338)^0$. Considering this state is very close to the $\Xi_c^0\bar{D}^0$ and $\Xi_c^+D^-$ thresholds, we explore the possible bias of the Breit-Wigner parameterization, with emphasis on the effect of its coupling to the double thresholds $\Xi_c^0\bar{D}^0$ and $\Xi_c^+D^-$. We first use a qualitative picture based on the ``uniformization" of the Riemann surface of the two-channel system to understand the positions of the enhancement. Then we use the Lippmann-Schwinger equation (LSE) formalism (equivalent to the $K$-matrix parameterization) with two models, the zero-range model and Flatt\'e model to investigate the $J/\psi \Lambda$ lineshapes. Our results show that the nominal peak of the $P_{\psi s}^\Lambda(4338)^0$ could arise either from the pole well above the $\Xi_c^+ D^-$ threshold on the $(-,+)$ sheet or from the pole well below the $\Xi_c^0 \bar{D}^0$ threshold on the $(-,-)$ sheet in the two-channel system. Using the Breit-Wigner distribution to depict the above two lineshapes could be misleading. We also find a novel type of lineshapes with the enhancement constrained by the threshold difference. We urge the LHCb collaboration to perform the refined experimental analysis considering the unitarity and analyticity, e.g. using the K-matrix parameterization. As a by-product, we obtain that the ratio of the isospin violating decay ${\Gamma_{P_{\psi s}^{\Lambda}\to J/\psi\Sigma}}/{\Gamma_{P_{\psi s}^{\Lambda}\to J/\psi\Lambda}}$ could be up to $10\%$.