abstract

The mechanism of color confinement has been studied in the framework of SU(3) color gauge theory in terms of Abelian fields and monopoles extracted by adopting magnetic symmetry. The existence of the mechanism of color confinement corresponds to the dual Meissner effect caused by monopoles. 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. As a result, the quark confining potential has been computed and the resulting expression of string tension has been constructed in the infrared sector of SU(3) dual QCD formulation. Moreover, with the introduction of dynamical quarks, the flux tube breaks and leads to the creation of quark–anti-quark pairs. Finite temperature quark confining potential and the associated string tension has also been extracted which demonstrates a considerable reduction in the vicinity of critical temperature showing agreement with the recent lattice studies.

abstract

The recent observation by the D\(\emptyset \) 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 assumed 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.

abstract

We report microscopic calculation of key \(\beta \)-decay properties for some of the crucial waiting-point species having neutron closed magic shells 50 and 82. Our calculation bears astrophysical significance vis-à-vis speeding of the r-process. The \(\beta \)-decay properties include electron emission weak rates, half-lives, energy rates of \(\beta \)-delayed neutrons and their emission probabilities, both under terrestrial and stellar conditions. We perform a \(pn\)-QRPA calculation with a separable multi-shell interaction and include both allowed and unique first-forbidden transitions in our calculation. We compare our results with previous calculations and measured data. Our calculation is in good agreement with the experimental data. For certain cases, we noted a significant decrease in the half-life calculation once the contribution of unique first-forbidden transitions was added. Our results are not in agreement with the shell model study where only for \(N=126\) waiting-point nuclei the forbidden transitions were reported to significantly reduce the calculated half-lives. Our model fulfills the Ikeda sum rule for even–even cases. For odd-\(A\) cases, the rule is violated by up to 0.7% for \(^{81}\)Ga.

abstract

Elastic scattering data for \(p + ^9\)Be, recently obtained in inverse kinematics, together with data from the literature measured in direct kinematics, were previously considered and evaluated via a Coupled Reaction Channels approach (CRC). This set of data for energies between 1.7 and 15 MeV/nucleon, free from normalization inconsistencies, is analyzed in this work using the microscopic approach of the Jeukenne, Lejeune and Mahaux interaction (JLM). The results show that even at these low energies the data can be well-described within this framework.

abstract

The Tolman–Bondi–Lemaître-type of inhomogeneous spacetime with generalised Chaplygin gas equation of state given by \(p = -\frac {A}{\rho ^{\alpha }}\), where \( \alpha \) is a constant, is investigated. We get an inhomogeneous spacetime at early stage but at the late stage of the universe, the inhomogeneity disappears with suitable radial co-ordinate transformation. For the large scale factor our model behaves like \(\Lambda \)CDM type which is in accord with the recent WMAP studies. We have calculated \(\frac {\partial \rho }{\partial r}\) and it is found to be negative for \(\alpha \gt 0\) which is in agreement with the observational analysis. A striking difference with Chaplygin gas (\(\alpha = 1\)) lies in the fact that with any suitable co-ordinate transformation, our metric cannot be reduced to the Einstein–de Sitter type of homogeneous spacetime in dust distribution as it is possible for the Chaplygin gas. We have also studied the effective deceleration parameter and find that the desired feature of flip occurs at the late universe. It is seen that the flip time depends explicitly on \(\alpha \). We also find that flip is not synchronous occurring earlier at the outer shells, thus offering a natural path against occurrence of the well-known shell crossing singularity. This is unlike the Tolman–Bondi case with perfect gas, where one has to impose stringent external conditions to avoid this type of singularity. We further observe that if we adopt separation of variables method to solve the field equations, the inhomogeneity in matter distribution disappears. The whole situation is later discussed with the help of Raychaudhury equation and the results are compared with previous cases. This work is the generalisation of our previous article, where we have taken \(\alpha =1\).