Virtual states in the coupled-channel problems with an improved complex scaling method

Abstract

We improve the complex scaling method (CSM) to obtain virtual states, which were previously challenging in the conventional CSM. Our approach solves the Schrödinger equation in the momentum space as an eigenvalue problem by choosing the flexible contours. It proves to be highly effective in identifying the poles across the different Riemann sheets in the multichannel scatterings. It is more straightforward and efficient than searching for the zeros of the Fredholm determinant of the Lippmann-Schwinger equation using the root-finding algorithms. This advancement significantly extends the capabilities of the CSM in accurately characterizing the resonances and virtual states in quantum systems.

arXiv comment12 pages, 14 figures, 2 tables. Version accepted by PRD

References in corpus (38)

• Observation of a New Narrow Charmonium State in Exclusive B+-->K+ pi+pi- J/psi Decays
• Observation of a narrow charmonium-like state in exclusive B+ -> K+ pi+pi- J/psi decays
• Construction of high-quality Nucleon-Nucleon potential models
• Hadronic molecules
• The hidden-charm pentaquark and tetraquark states
• Observation of $J/\psi p$ resonances consistent with pentaquark states in ${\Lambda }_b^0\to J/\psi K^{-}p$ decays
• The $XYZ$ states: experimental and theoretical status and perspectives
• Pentaquark and Tetraquark states
• Observation of a narrow pentaquark state, $P_c(4312{)}^{+}$, and of two-peak structure of the $P_c(4450{)}^{+}$
• An updated review of the new hadron states
• Nuclear effective field theory: status and perspectives
• Observation of an exotic narrow doubly charmed tetraquark
• Study of the doubly charmed tetraquark $T_{cc}^{+}$
• Threshold cusps and triangle singularities in hadronic reactions
• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Effective field theory description of halo nuclei
• Observation of a $J/\psi \Lambda$ resonance consistent with a strange pentaquark candidate in $B^{-}\to J/\psi \Lambda \bar{p}$ decays
• Coupled-channel approach to $T_{cc}^{+}$ including three-body effects
• Coupled-channel analysis of the possible $D^{(\ast )}{D}^{(\ast )}$, ${\bar{B}}^{(\ast )}{\bar{B}}^{(\ast )}$ and $D^{(\ast )}{\bar{B}}^{(\ast )}$ molecular states
• Explaining the Many Threshold Structures in the Heavy-Quark Hadron Spectrum
• Probing the long-range structure of the $T_{cc}^{+}$ with the strong and electromagnetic decays
• Doubly Charmed Tetraquark $T_{cc}^{+}$ from Lattice QCD near Physical Point
• $T_{cc}^{+}$ and its partners
• Bound state techniques to solve the multiparticle scattering problem
• Complex scaling : physics of unbound light nuclei and perspective
• Revisiting the $D{D}^{\ast }$ chiral interactions with the local momentum-space regularization up to the third order and the nature of $T_{cc}^{+}$
• Double-charm tetraquark under the complex scaling method
• $S$-wave fully charmed tetraquark resonant states
• Nature of the doubly-charmed tetraquark $T_{cc}^{+}$ in a constituent quark model
• Predicting the ${\bar{D}}_s^{(\ast )}{D}_s^{(\ast )}$ bound states as the partners of $X(3872)$
• Fully-charm and -bottom pentaquarks in a Lattice-QCD inspired quark model
• Comprehensive application of a coupled-channel complex scaling method to the KbarN-piY system
• Relativistic chiral description of the ${}^1{S}_0$ nucleon-nucleon scattering
• ^1S_0 pairing correlations in relativistic nuclear matter and the two-nucleon virtual state
• Complex Scaled Spectrum Completeness for Coupled Channels
• $P_c$ states and their open-charm decays with the complex scaling method
• Resonance in the $Y_{c}N$ potential model
• Nucleon-nucleon scattering with the Complex Scaling Method and realistic interactions

Cited by in corpus (7)

• Fully strange tetraquark resonant states as the cousins of $X(6900)$
• Probing exotic $J^{PC}$ resonances from deeply bound charmoniumlike molecules: Insights for identifying exotic hadrons
• Trilepton and tetralepton bound and resonant states: the QED counterpart of multiquark states
• Constraining the $DD{D}^{\ast }$ three-body bound state via the $Z_c(3900)$ pole
• The $\varphi NN,J/\psi NN,{\eta }_{c}NN$ systems based on HAL QCD interactions
• Investigation on the bottom analogs of the $T_{cc}^{+}$
• Bound and Resonant States of Muonic Few-Body Coulomb Systems: Extended Stochastic Variational Approach