Interpretation of near-threshold peaks using the method of independent S-matrix poles

Abstract

We propose a model-independent analysis of near-threshold enhancements using independent S-matrix poles. In this formulation, we constructed a Jost function with controllable zeros to ensure that no poles are generated on the physical Riemann sheet. We show that there is a possibility of misinterpreting the observed near-threshold signals if one utilized a limited parametrization and restrict the analysis to only one element of the S-matrix. Specifically, there is a possibility of the emergence of ambiguous pair of poles which are singularities of the full S-matrix but may not manifest in one of its elements. For a more concrete discussion, we focused on an effective two-channel scattering where the full S-matrix is a $2\times 2$ matrix. We apply our method to the coupled two-channel analysis of the $P_{\psi }^N(4312{)}^{+}$ and found that the compact pentaquark interpretation cannot be ruled out yet.

19 pages, 4 figures; Added references

References in corpus (16)

• Observation of a narrow pentaquark state, $P_c(4312{)}^{+}$, and of two-peak structure of the $P_c(4450{)}^{+}$
• Interpretation of the LHCb $P_c$ States as Hadronic Molecules and Hints of a Narrow $P_c(4380)$
• Interpretation of the Narrow $J/\psi p$ Peaks in ${\Lambda }_b\to J/\psi p{K}^{-}$ Decay in the Compact Diquark Model
• Towards a theory of hadron resonances
• Two-pole structures in QCD: Facts, not fantasy!
• Remarks on pole trajectories for resonances
• Measurement of the J/$\psi$ photoproduction cross section over the full near-threshold kinematic region
• Novel approaches in Hadron Spectroscopy
• Hadron mass scaling near the s-wave threshold
• Revealing the nature of hidden charm pentaquarks with machine learning
• Model independent analysis of coupled-channel scattering: a deep learning approach
• Deep Learning Exotic Hadrons
• Classifying near-threshold enhancement using deep neural network
• Near-threshold Spectrum from Uniformized Mittag-Leffler Expansion -Pole Structure of $Z(3900)$-
• Application of the Uniformized Mittag-Leffler Expansion to $\Lambda (1405)$
• Is two-poles' $\Lambda (1405)$ one state or two?

Cited by in corpus (1)

• Learning Pole Structures of Hadronic States using Predictive Uncertainty Estimation