International Journal of Modern Physics A

The persistent homology analysis is applied to the effective Polyakov-line model on a rectangular lattice to investigate the confinement–deconfinement nature. The lattice data are mapped onto the complex Polyakov-line plane without taking the spatial average and then the plane is divided into three domains. This study is based on previous studies for the clusters and the percolation properties in lattice QCD, but the mathematical method of the analyses are different. The spatial distribution of the data in the individual domain is analyzed by using the persistent homology to obtain information of the multiscale structure of center clusters. In the confined phase, the data in the three domains show the same topological tendency characterized by the birth and death times of the holes which are estimated via the filtration of the alpha complexes in the data space, but do not in the deconfined phase. By considering the configuration averaged ratio of the birth and death times of holes, we can construct the nonlocal order parameter of the confinement–deconfinement transition from the multiscale topological properties of center clusters.

The Bose–Einstein correlation (BEC) in forward region $(2.0<\eta <4.8)$ measured at 7 TeV in the Large Hadron Collider (LHC) by the LHCb collaboration is analyzed using two conventional formulas of different types named CF${}_{\text{I}}$ and CF${}_{\text{II}}$. The first formula is well known and contains the degree of coherence $(\lambda )$ and the exchange function $E_{\text{BE}}^2$ from the BE statistics. The second formula is an extended formula (CF${}_{\text{II}}$) that contains the second degree of coherence ${\lambda }_2$ and the second exchange function $E_{{\text{BE}}_2}^2$ in addition to CF${}_{\mathrm{\text{I}}}$. To examine the physical meaning of the parameters estimated by CF${}_{\mathrm{\text{II}}}$, we analyze the LHCb BEC data by using a stochastic approach of the three-negative binomial distribution and the three-generalized Glauber–Lachs formula. Our results reveal that the BEC at 7 TeV consisted of three activity intervals defined by the multiplicity $n$ ([8, 18], [19, 35], and [36, 96]) can be well explained by CF${}_{\mathrm{\text{II}}}$.

The time evolution of total entropy including the entropy associated with horizon and entropy of matter inside the horizon in homogeneous and isotropic Jordan frame (dilatonic) Brans–Dicke cosmologies is examined. We show that the bouncing Brans–Dicke cosmologies do not satisfy the generalized second law of thermodynamics during the contracting phase of evolution.

Normed division and Clifford algebras have been extensively used in the past as a mathematical framework to accommodate the structures of the Standard Model and grand unified theories. Less discussed has been the question of why such algebraic structures appear in Nature. One possibility could be an intrinsic complex, quaternionic or octonionic nature of the space–time manifold. Then, an obvious question is why space–time appears nevertheless to be simply parametrized by the real numbers. How the real slices of an higher-dimensional space–time manifold might be almost independent from each other is discussed here. This comes about as a result of the different nature of the representations of the real kinematical groups and those of the extended spaces. Some of the internal symmetry transformations might however appear as representations on homogeneous spaces of the extended group transformations that cannot be implemented on the elementary states.

Masses and decay width for some heavy baryons are studied within Isgur–Wise formalism. The extended Cornell potential is employed. The hyper-radial Schrödinger equation with extended Cornell potential is solved to obtain eigenvalues of energy and baryonic wave function by using the extended iteration method. Masses and the rate of decay width for some heavy baryons are calculated. The present results are improved in comparison with other recent works and are in a good agreement with experimental data.

A phenomenological study of the exclusive vector meson photoproduction within the discrete BFKL approach is performed. We estimate the BFKL amplitude in terms of a discrete set of eigenfunctions and use the HERA $F_2$ data to constrain the free parameters of the model. As a consequence, we derive a parameter free prediction of the energy dependence of the exclusive vector meson cross section. We demonstrate that the HERA and LHCb data for the exclusive $J/\mathrm{\Psi }$ and $\mathrm{{\rm Y}}$ photoproduction are quite well describe in a large energy range. However, the model overestimates the precise LHCb data for the smallest values of $x$, which can be interpreted as an indication of the onset of nonlinear (saturation) effects in the QCD dynamics.