Charmoniumlike channels $1^+$ with isospin 1 from lattice and effective field theory

Šadl, Mitja (author), Collins, Sara (author), Guo, Zhi-Hui (author), Padmanath, M. (author), Prelovšek, Saša (author), Yan, Lin-Wan (author)

Many exotic charmoniumlike mesons have already been discovered experimentally, of which the $Z_c$ mesons with isospin 1 are prominent examples. We investigate $J^{PC}=1^{+\pm}$ states with flavor $\bar{c}c\bar{q}q (q=u,d)$ in isospin 1 using lattice QCD. This is the first study of these mesons employing more than one volume and involving frames with nonzero total momentum. We utilize two $N_f=2+1$ CLS ensembles with $m_{\pi}\simeq 280~\mathrm{MeV}$ . The simulations are performed with unphysical light quark masses at a single lattice spacing of $a\simeq 0.086~\mathrm{fm}$ and omit $\psi(2S)\pi$, $\psi⁡(3770)\pi$ and three-particle decay channels, so our results provide only qualitative insights. Resulting eigenenergies are compatible or just slightly shifted down with respect to noninteracting energies, where the most significant shifts occur for certain $D\bar{D}^*$⁢ states. Both channels $1^{+\pm}$ have a virtual pole slightly below the threshold if $D\bar{D}^*$ is assumed to be decoupled from other channels. In addition, we perform a coupled channel analysis of $J/\psi \pi$ and $D\bar{D}^*$ scattering with $J^{PC}=1^{+-}$ within an effective field theory framework. The $J/\psi \pi$ and $D\bar{D}^*$⁢ invariant-mass distributions from BESIII and finite-volume energies from several lattice QCD simulations, including this work, are fitted simultaneously. All fits yield two poles relatively close to the $D\bar{D}^*$ threshold and reasonably reproduce the experimental $Z_c$ peaks. They also reproduce lattice energies up to slightly above the $D\bar{D}^*$ threshold, while reproduction at even higher energies is better for fits that put more weight on the lattice data. Our findings suggest that the employed effective field theory can reasonably reconcile the peaks in the experimental line shapes and the lattice energies, although those lie close to noninteracting energies. We also study $J/\psi \pi$ scattering in s wave and place upper bounds on the phase shift.

• Language: English
• Keywords: physics of elementary particles, hadrons, lattice QCD
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: Str. 054513-1-054513-36
• Numbering: Vol. 111, iss. 5
• PID: 20.500.12556/RUL-168061
• UDC: 539.120.811
• ISSN on article: 2470-0010
• DOI: 10.1103/PhysRevD.111.054513
• COBISS.SI-ID: 230409219
• Publication date in RUL: 27.03.2025

Record is a part of a journal

• Title: Physical review
• Shortened title: Phys. rev., D
• Publisher: American Physical Society
• ISSN: 2470-0010
• COBISS.SI-ID: 29757223

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: fizika osnovnih delcev, hadroni, kvantna kromodinamika na mreži