The exponent λ of the structure function F₂ ∼x^−λ is calculated using the solution of the DGLAP equation for gluon at lowx reported recently by the present authors. The quantity λ is calculated both as a function ofx at fixedQ² and as a function ofQ² at fixedx and compared with the most recent data from H1

The transversity distribution of quarks in a nucleon is one of the three fundamental distributions, that characterize nucleon's properties in hard scattering processes at leading twist (twist 2). It measures the distribution of quark transverse spin in a nucleon polarized transverse to its (infinite) momentum. It is a chiral-odd twist-two distribution function — gluons do not couple to it. Quarks in a nucleon/hadron are relativistically bound and transversity is a measure of the relativistic nature of bound quarks in a nucleon. In this work, we review some important aspects of this less familiar distribution function which has not been measured experimentally so far.

At lowx, an analytic solution of the DGLAP equation for gluon in the next-to-leading order (NLO) is obtained by applying the method of characteristics. Its compatibility with double leading logarithmic approximation (DLLA) asymptotics is discussed and comparison with the exact ones like GRV98NLO is made. The solution is then utilized to calculate the derivatives∂F₂ (x,Q²)/∂ lnQ²and ∂ lnF₂(x,Q²)/∂ ln (1/x) and compared with the recent HERA data. Our solution is found to reproduce most of the essential features of the data on the derivatives.

We used variationally improved perturbation theory (VIPT) in calculating the slope and curvature of Isgur–Wise (I–W) function with the Cornell potential $− \dfrac{4\alpha_{s}}{3r} br + c$ instead of the usual stationary state perturbation theory as done earlier. We used $−(4\alpha_{s} /3r)$, i.e. the Coulombic potential, as the parent and the linear one, i.e. $br +c$ as the perturbed potential in the theory and calculated the slope and curvature of Isgur–Wise function including three states in the summation involved in the first-order correction to wave function in the method.

We have recently reported the calculation of slope and curvature of Isgur–Wise function based on variationally improved perturbation theory (VIPT) in a quantum chromodynamics (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.

An analytical solution of the non-singlet polarized parton distribution $\Delta q^{NS} (x, Q^{2}) = (\Delta u(x, Q^{2}) − \Delta d(x, Q^{2}))$ is obtained by solving the DGLAP (Gribov and Lipatov, Sov. J. Nucl. Phys. 15, 438 (1972); Lipatov, ibid, 20, 94 (1975); Dokshitzer, Sov. Phys. JETP 46, 641 (1997); Altarelli and Parisi, Nucl. Phys. B126, 298 (1977)) equation by the method of characteristics. We then evaluate the non-singlet spin-dependent structure function $g^{NS}_{1}$ . The result is compared with the data from HERMES (Airapetian et al, Phys. Rev. D75, 012007 (2007)).

We modify the mesonic wave function by using a short distance scale $r_{0}$ in analogy with hydrogen atom and estimate the values of masses and decay constants of the open flavour charm mesons 𝐷, $D_{s}$ and $B_{c}$ within the framework of a QCD potential model. We also calculate leptonic decay widths of these mesons to study branching ratios and lifetime. The results are in good agreement with experimental and other theoretical values.

We use variationally improved perturbation theory (VIPT) for calculating the elastic form factors and charge radii of $D$, $D_{s}$, $B$, $B_{s}$ and $B_{c}$ mesons in a quantum chromodynamics (QCD)-inspired potential model. For that, we use linear-cum-Coulombic potential and opt the Coulombic part first as parent and then the linear part as parent. The results show that charge radii and form factors are quite small for the Coulombic parent compared to the linear parent. Also, the analysis leads to a lower as well as upper bounds on the four-momentum transfer $Q^{2}$, hinting at a workable range of $Q^{2}$ within this approach, which may be useful in future experimental analyses. Comparison of both the options shows that the linear parent is the better option.