Lüscher's finite size method with twisted boundary conditions: an application to $J/\psi$-$\varphi$ system to search for narrow resonance

Abstract

We investigate an application of twisted boundary conditions for study of low-energy hadron-hadron interactions with Lüshcer's finite size method. It allows us to calculate the phase shifts for elastic scattering of two hadrons at any small value of the scattering momentum even in a finite volume. We then can extract model independent information of low-energy scattering parameters such as the scattering length, the effective range and the effective volume from the $S$-wave and $P$-wave scattering phase shifts through the effective range expansion. This approach also enables us to examine the existence of near-threshold and narrow resonance states, of which characteristic is observed in many of newly discovered charmonium-like $XYZ$ mesons. As a simple example, we demonstrate our method for low-energy $J/\psi$-$\varphi$ scatterings to search for Y(4140) resonance using 2+1 flavor PACS-CS gauge configurations at the lightest pion mass, $m_{\pi }=156$ MeV.

15 pages, 8 figures; v2: version published in Phys. Rev. D

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• The $XYZ$ states: experimental and theoretical status and perspectives
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• Two-particle multichannel systems in a finite volume with arbitrary spin
• Multichannel one-to-two transition amplitudes in a finite volume
• Excited and exotic charmonium, $D_s$ and $D$ meson spectra for two light quark masses from lattice QCD
• X(3872) and Y(4140) using diquark-antidiquark operators with lattice QCD
• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• Low-energy Scattering of $(D{\bar{D}}^{\ast }{)}^{\pm }$ System And the Resonance-like Structure $Z_c(3900)$
• Two-Baryon Systems with Twisted Boundary Conditions
• Hidden charm molecules in finite volume
• Nuclear Reactions from Lattice QCD
• Partial twisting for scalar mesons
• Low-energy Scattering of $(D^{\ast }{\bar{D}}^{\ast }{)}^{\pm }$ System and the Resonance-like Structure $Z_c(4025)$
• Two Photon Decays of ${\eta }_c$ from Lattice QCD
• Bound states on the lattice with partially twisted boundary conditions
• A Lattice Study of $({\bar{D}}_1{D}^{\ast }{)}^{\pm }$ Near-threshold Scattering
• On tetraquarks with hidden charm and strangeness as phi-psi(2S) hadrocharmonium
• Compositeness of hadron resonances in finite volume
• Lattice QCD review of charmonium and open-charm spectroscopy
• Renormalization of a Contact Interaction on a Lattice
• Lattice study of scattering phase shifts for $D{D}^{\ast }$ and $B{B}^{\ast }$ systems using twisted boundary conditions: Search for bound state formation
• The strong coupling $g_{XJ/\psi \varphi }$ of $X(4700)\to J/\psi \varphi$ in the light-cone sum rules
• Decoding the near-threshold $X_{0,1}(4140)$ and $X_1(4685)$ states via OZI-suppressed coupled-channel scattering
• Formal Developments for Lattice QCD with Applications to Hadronic Systems