We calculate the Isgur–Wise function of heavy light mesons and its derivatives — its slope and its curvature, in an improved version of our earlier QCD Inspired Quark Model with two-loop static potential.

No abstract

Momentum sum rule can be used as an inequality to estimate the lower and upper bounds of the momentum fractions of quarks and gluons in a model of proton valid in a limited x range. We compute such bounds in a self-similarity based model of proton structure function valid in the range 6.2 × 10 −7 ≤ x ≤ 10 −2 . The results conform to the asymptotic QCD expectations.

The Froissart bound implies that the total cross section (or, equivalently, the structure function) cannot rise faster than the logarithmic growth of $ \ln^{2} \left(\frac{1}{x} \right)$. In this work, we show that such a slow growth is not compatible with the notion of self-similarity. As a result, it calls for the modification of the defining transverse-momentum-dependent parton density function (TMD PDF) of a self-similarity based proton structure function $F_{2} \left(x,Q^{2} \right)$ at small \textit{x}. Using plausible assumptions, we obtain the Froissart saturation condition on this TMD PDF.Comment: 11 pages, 2 figures, 1 tabl

We study heavy light mesons in a QCD inspired quark model with the Cornell potential [Formula: see text]. Here we consider the linear term br as the parent and [Formula: see text], i.e. the Coloumbic part as the perturbation. The linear parent leads to Airy function as the unperturbed wave function. We then use the Dalgarno method of perturbation theory to obtain the total wave function corrected up to first order with Coulombic piece as the perturbation. With these wave functions, we study the Isgur–Wise function and calculate its slope and curvature.

Considering the Cornell potential V (r) = − 4αs 3r + br + c, we have revisited the Dalgarno's method of perturbation by incorporating two scales r short and r long as integration limit so that the perturbative procedure can be improved in a potential model. With the improved version of the wave function the ground state masses of the heavy-light mesons D, D s , B, B s and B c are computed. The slopes and curvatures of the form factors of semi-leptonic decays of heavy-light mesons in both HQET limit and finite mass limit are calculated and compared with the available data.

We summarize the results of the Isgur–Wise function investigated within a QCD inspired quark model. We estimate the slope and the convexity parameter of the function.

In this paper, we use momentum sum rule to compute the fractions of momentum carried by quarks and gluons in a self-similarity based model of proton. Comparison of the results with the prediction of QCD asymptotics is also made.