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In order to include the effect of high energy and topological parameters on black holes in $F(R)$ gravity, we consider two corrections to this gravity: energy-dependent spacetime with different topological constants, and a nonlinear electrodynamics field. In other words, we combine $F(R)$ gravity's rainbow with ModMax nonlinear electrodynamics theory to see the effects of high energy and topological parameters on the physics of black holes. For this purpose, we first extract topological black hole solutions in $F(R)$% -ModMax gravity's rainbow. Then, by considering black holes as thermodynamic systems, we obtain thermodynamic quantities and check the first law of thermodynamics. The effect of the topological parameter on the Hawking temperature and the total mass of black holes is obvious. We also discuss the thermodynamic topology of topological black holes in $F(R)$-ModMax gravity's rainbow using the off-shell free energy method. In this formalism, black holes are assumed to be equivalent to defects in their thermodynamic spaces. For our analysis, we consider two different types of thermodynamic ensembles. These are: fixed $q$ ensemble and fixed $\phi$ ensemble. We take into account all the different types of curvature hypersurfaces that can be constructed in these black holes. The local and global topology of these black holes are studied by computing the topological charges at the defects in their thermodynamic spaces. Finally, in accordance with their topological charges, we classify the black holes into three topological classes with total winding numbers corresponding to $-1, 0$, and $1$. We observe that the topological classes of these black holes are dependent on the value of the rainbow function, the sign of the scalar curvature, and the choice of ensembles., Comment: Accepted in Prog. Theor. Exp. Phys (2024)

Determination of the wave-function is very essential in the calculation of static and dynamic properties like masses,decay constants of pseudo-scalar mesons and masses of vector mesons.We use Dalgarno's perturbation theory and Variation-ally Improved Perturbation Theory (VIPT) to solve Schrodinger equation in a QCD inspired potential model wuth Cornell potential,which consists linear and coulomb potential.We use both the options like Columbic parent firstly and then linear parent while using the VIPT method. Comparison of both these methods and also with experimental results are done in the calculation of masses and decay constants., Comment: arXiv admin note: text overlap with arXiv:1902.02070

We employ the variational method to study the properties such as masses, decay constants, oscillation frequency and branching ratios of leptonic decays of heavy flavour mesons with linear cum coulomb Cornell potential. Gaussian function, Coulomb wave function and Airy function are taken as the trial wave-function of variational method in this study. Our analysis suggests that Gaussian trial wave-function provides results which are in close proximity with the experimental results. We also make a comparison with the results from QCD Sum rules and lattice QCD, as well as with recent PDG data.

We use WKB Approximation in the calculation of slope and curvature of Isgur-Wise function in a QCD inspired potential model.This work is an extension of the approximation methods to the QCD inspired potential model.The approach hints at an effective range of distance for the calculation of slope and curvature of Isgur-Wise function.Comparision is also made with those of Dalgarno and VIPT to see the advantages of using WKB Approximation.

We use VIPT in calculating the elastic form factors and charge radii of D, Ds, B, Bs and Bc mesons in a QCD inspired potential model. For that we use linear cum Coulombic potential and opt firstly the Coulombic part as parent and then linear part as parent.The results show that charge radii and form factors are quite small for Coulombic parent case than the linear parent. Also, the analysis leads to a lower as well as upper bound on the four momentum transfer Q2 hinting at a workable range of Q2 within this approach which may be useful in future for experimental analysis. Comparision of both the options prefer the linear parent., Comment: 6 figures

The QCD inspired potential model persued by us earlier has been recently modified to incorporate an additional factor 'c' in the linear cum Coulomb potential. While it felicitates the inclusion of standard confinement parameter b = 0.183GeV 2, unlike in previous work, it still falls short of explaining the Isgur-Wise function for the B mesons without adhoc adjustment of the strong coupling constant. In this work, we determine the factor 'c' from the experimental values of decay constants and masses and show that the reality constraint on 'c' yeilds bounds on the strong coupling constant as well on slope and curvature of Isgur-Wise function allowing more flexibility to the model., Comment: 5 figures

We have recently reported the calculation of slope and curvature of Isgur-Wise function based on Variationally Improved Perturbation Theory (VIPT) in a QCD inspired potential model. In that work, Coulombic potential was taken as the parent while the linear one as the perturbation.In this work, we choose the linear one as the parent with Coulombic one as the perturbation and see the consequences. Keywords: VIPT,Isgur-Wise function, charge radii and convexity pa- rameter.