Abstract. The dominant mechanism to produce hadronic bound states with large transverse momentum is fragmentation, that is the splitting of a high energy parton into a hadronic state and other partons. We review the present schemes to calculate the heavy quark fragmentation functions (FFs) and drive an exact analytical expression of FF which includes most of the kinematical and dynamical properties of the process. Using the perturbative QCD, we calculate the FF for c-quark to split into S-wave D + meson to leading order in the QCD coupling constant. Our result is compared with the current well-known phenomenological models which are obtained through a global fit to e + e − data from SLAC SLC and CERN LEP1 and we also compare the FF with experimental data form BELLE and CLEO. Specifically, we study the effect of outgoing meson mass on the pQCD FF. Meson masses are responsible for the low-z threshold, where z is the scaled energy variable.
In this paper, our main aim is to obtain the transmission (T) and the reflection (R) coefficients for one-dimensional scattering state of the spin-[Formula: see text] particles in an interaction with a special nuclear potential. For this reason, at first, we consider Dirac equation and then obtain the Milne’s nonlinear differential equation due to minimal length from Schrödinger-like equation and then calculate the T- and R-coefficients using one-dimensional Woods–Saxon potential on the basis of the generalized uncertainty principle. Finally, we will check the validity and the correctness of our results.
Using an analytical solution for the relativistic equation of single [Formula: see text]-hypernuclei in the presence of Woods–Saxon (WS) potential we present, for the first time, an analytical form for the excited state binding energies of 1p, 1d, 1f and 1g shells of a number of hypernuclei. Based on phenomenological analysis of the [Formula: see text] binding energies in a set of [Formula: see text]-hypernuclei, the WS potential parameters are obtained phenomenologically for the set of [Formula: see text]-hypernuclei. Systematic study of the energy levels of single [Formula: see text]-hypernuclei enables us to extract more detailed information about the [Formula: see text]-nucleon interaction. We also study the root mean square (RMS) radii of the [Formula: see text] orbits in the hypernuclear ground states. Our results are presented for several hypernuclei and it is shown that our results for the binding energies are in good agreement with experimental data.
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