Modern Physics Letters A

The issue of texture specific fermion mass matrices have been examined briefly from the “bottom-up” perspective. In case no conditions are imposed, the texture ansatze leads to a large number of viable possibilities. However, besides textures, if in case one incorporates the ideas of “natural mass matrices” and uses the facility of Weak Basis Transformations, then one is able to arrive at a minimal finite set of viable mass matrices in the case of quarks.

We have analyzed the available midrapidity $(|y|<0.5)$ transverse momentum spectra of identified particles such as protons $(p)$, kaons $(k)$, $k_s^0$, $\Lambda$, $\Omega$ and $\Xi$ for different centralities of Pb+Pb collisions at the LHC energy $\sqrt{s_{NN}}=2.76\mathrm{\text{TeV}}$. We have used our earlier proposed unified statistical thermal freeze-out model. The model incorporates the effect of nuclear transparency in such energetic collisions and the resulting asymmetry in the collective-flow profile along the longitudinal and the transverse directions. Our calculated results are found to be in good agreement with the experimental data measured by the ALICE experiment. The model calculation fits the experimental data for different particle species which provide thermal freeze-out conditions in terms of temperature and collective-flow parameters. The analysis shows a rise in the thermal freeze-out temperature and a mild decrease in the transverse collective-flow velocity as we go from central to the peripheral collisions. The baryon chemical potential is assumed to be nearly zero for the bulk of the matter $({\mu }_B\approx 0)$, a situation expected in the heavy ion collisions at LHC energies in the Bjorken approach owing to nearly complete nuclear transparency. The contributions from the decay of the heavier resonances are also taken into account in our calculations.

We investigate the conditions on the additional constant $\mu$ in the so-called $R+{\mu }^4/R$ theory of gravity, due to existence of different kinds of space-like surfaces in both weak field and strong field limits, and their possible correspondence to black hole event horizons. Adopting a Schwarzschild limit, we probe the behavior of $\mu$ in different contexts of radial and radial–rotational congruence of null geodesics. We show that these cases serve as correspondents to black hole horizons in some peculiar cases of study.

We present black hole solutions in (2+1)-dimensional Einstein’s theory of gravity coupled with Born–Infeld (BI) nonlinear electrodynamic and a massless self-interacting scalar field. The model has five free parameters: mass $M$, cosmological constant $\ell$, electric $q$ and scalar $r_0$ charges and BI parameter $\beta$. To attain exact solution for such a highly nonlinear system we adjust, i.e. finely tune, the parameters of the theory with the integration constants. In the limit $\beta \to 0$, we recover the results of Einstein–Maxwell–Scalar theory, obtained before. The self-interacting potential admits finite minima apt for the vacuum contribution. Hawking temperature of the model is investigated versus properly tuned parameters. By employing this tuned-solution as basis, we obtain also a dynamic solution which in the proper limit admits the known solution in Einstein gravity coupled with self-interacting scalar field. Finally, we establish the equations of a general scalar–tensor field coupled to nonlinear electrodynamics (NED) field in 2+1 dimensions without searching for exact solutions.

We present commutation relations depending on the rainbow functions which are slightly different from the well-known results. However, the advantage of these new commutation relations are compatible with the calculation of the Hawking temperature in the rainbow Schwarzschild black hole.

We construct explicitly the constants of motion for geodesics in the five-dimensional Sasaki–Einstein spaces $Y^{p,q}$. To carry out this task, we use the knowledge of the complete set of Killing vectors and Killing–Yano tensors on these spaces. In spite of the fact that we generate a multitude of constants of motion, only five of them are functionally independent implying the complete integrability of geodesic flow on $Y^{p,q}$ spaces. In the particular case of the homogeneous Sasaki–Einstein manifold $T^{1,1}$ the integrals of motion have simpler forms and the relations between them are described in detail.

Contrary to almost standard opinion that the $X(3872$) resonance is the $D^{\ast 0}{\bar{D}}^0+\mathrm{\text{c.c.}}$ molecule or the $qc\bar{q}\bar{c}$ four-quark state, we discuss the scenario where the $X(3872)$ resonance is the $c\bar{c}={\chi }_{c1}(2P)$ charmonium which “sits on” the $D^{\ast 0}{\bar{D}}^0$ threshold.

We explain the shift of the mass of the $X(3872)$ resonance with respect to the prediction of a potential model for the mass of the ${\chi }_{c1}(2P)$ charmonium by the contribution of the virtual $D^{\ast }\bar{D}+\mathrm{\text{c.c.}}$ intermediate states into the self energy of the $X(3872)$ resonance. This allows us to estimate the coupling constant of the $X(7872)$ resonance with the $D^{\ast 0}{\bar{D}}^0$ channel, the branching ratio of the $X(3872)\to D^{\ast 0}{\bar{D}}^0+\mathrm{\text{c.c.}}$ decay, and the branching ratio of the $X(3872)$ decay into all non-$D^{\ast 0}{\bar{D}}^0+\mathrm{\text{c.c.}}$ states. We predict a significant number of unknown decays of $X(3872)$ via two gluon: $X(3872)\to \text{gluon gluon}\to \text{hadrons}$.

We suggest a physically clear program of experimental researches for verification of our assumption.