Abstract
The recent observation by the D$\O$ collaboration of the first tetraquark candidate with four different quark flavors $(u, d, s$ and $ b)$ in the $B^0_s\pi^{\pm}$ channel having a narrow structure, has still not been confirmed by other collaborations. Further independent experiments are required either to confirm the $X(5568)$ state or to set limits on its production. Though quantum numbers are not exactly clear, the results existing in the literature indicate that it is probably an axial-vector or scalar state candidate. In this study, mass and pole residue of the $X(5568)$ resonance assuming as a tightly bound diquark, with spin-parity both $J^{P}=1^{+}$ or $J^{PC}=0^{++}$ are calculated using two-point Thermal SVZ sum rules technique by including condensates up to dimension six. Moreover, its partner in the charm sector is also discussed. Investigations defining the thermal properties of $X(5568)$ and its charmed partner may provide valuable hints and information for the upcoming experiments such as CMS, LHCb and PANDA.
Highlights
A central issue of elementary particle physics is the description of quark dynamics
Choosing the effective potential given by Eq (4), the dynamical breaking of magnetic symmetry generally leads to the condensation of magnetic monopoles and impart color confining properties to the SU(3) dual quantum chromodynamics (QCD)
The variation of the temperature-dependent quark potential including color screening effects for several values of c with αs = 0.25, αs = 0.24 and αs = 0.23 coupling in SU(3) dual QCD vacuum has been depicted in Fig. 4 which is in agreement with the recent lattice studies [55, 56]
Summary
The two length scales, i.e. the penetration depth and coherence length are defined to demonstrate the scaling nature of the QCD vacuum, and their ratio defines the Ginzburg–Landau parameter indicating the border of type-I and type-II dual superconductor. The existence of these two length scales describes the intrinsic shape of the confining flux tube and is a characteristic of the dual superconductor model of confinement in QCD. Finite temperature quark confining potential and the associated string tension has been extracted which demonstrates a considerable reduction in the vicinity of critical temperature showing agreement with the recent lattice studies
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