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M. Imran Jamil

Publications and source records attributed to M. Imran Jamil.

4 recordsLinked to original sources
arXiv2020

J/$Ψ$-J/$Ψ$ scattering cross sections of Quadratic and Cornell Potentials

We study the scattering of J/$Ψ$-J/$Ψ$ mesons using Quadratic and Cornell potentials in our tetraquark ($c$$\bar{c}$$c$$\bar{c}$) system. The system's wavefunction in the restricted gluonic basis is written by utilizing adiabatic approximation and Hamiltonian is used via quark potential model. Resonating group technique is used to get the integral equations which are solved to get the unknown inter-cluster dependence of the total wavefunction of our tetraquark system. T-Matrix elements are calculated from the solutions and eventually the scattering cross sections are obtained using the two potentials respectively. We compare these cross sections and find that the magnitude of scattering cross sections of Quadratic potential are higher than Cornell potential.

hep-ph↗
arXiv2018

$ρJ/Ψ$ Scattering in an Improved Many Body Potential

We calculate the cross-sections for the processes $ρJ/ψ\rightarrow D^0\bar{D}^0$, $ρJ/ψ\rightarrow D^0\bar{D}^{0*}$ ($D^{0*}\bar{D}^{0}$) and $ρJ/ψ\rightarrow D^{0*}\bar{D}^{0*}$ using a QCD-motivated many-body overlap factor to modify the usual sum of two-body interaction model. The realistic Cornell potential has been used for pairwise interaction in the four quark Hamiltonian and noted to give lesser cross-sections as compared to the quadratic potential. The Resonating group method is employed along with the Born approximation which decouples its integral equations. It is pointed out that the additional QCD effect (a gluonic field ovelap factor) result in a significant suppression in the cross sections as compared to the more popular sum of two-body interaction.

hep-ph↗
arXiv2016

$\bar{D}^{0}D^{0*}$ $(D^{0}\bar{D}^{0*})$ System in QCD-Improved Many Body Potential

For a system of current interest (composed of charm, anticharm quarks and a pair of light ones), we show trends in phenomenological implications of QCD-based improvements to a simple quark model treatment. We employ resonating group method to render this difficult four-body problem manageable. We use a quadratic confinement so as to be able to improve beyond the Born approximation. We report the position of the pole corresponding to $\bar{D}^{0}D^{0*}$ molecule for the best fit of a model parameter to the relevant QCD simulations. We point out the interesting possibility that the pole can be shifted to $3872$ MeV by introducing another parameter $I_{0}$ that changes the strength of the interaction in this one component of $X(3872)$. The revised value of this second parameter can guide future trends in modeling of the full exotic meson $X(3872)$. We also report the changes with $I_{0}$ in the $S$-wave spin averaged cross sections for $\bar{D}^{0}D^{0*}\longrightarrowωJ/ψ$ and $\bar{D}^{0}D^{0*}\longrightarrowρJ/ψ$. These cross sections are important regarding the study of QGP (quark gluon plasma).

hep-ph↗
arXiv2011

Dynamical effects of QCD in $q^2 \bar{q}^{2}$ systems

We study the coupling of a tetraquark system to an exchanged meson-meson channel, using a pure gluonic theory based four-quark potential {\em matrix} model which is known to fit well a large number of data points for lattice simulations of different geometries of a four-quark system. We find that if this minimal-area-based potential matrix replaces the earlier used simple Gaussian form for the gluon field overlap factor $f$ in its off-diagonal terms, the resulting $T$-matrix and phase shifts develop an angle dependence whose partial wave analysis reveals $D$ wave and higher angular momentum components in it. In addition to the obvious implications of this result for the meson-meson scattering, this new feature indicates the possibility of orbital excitations influencing properties of meson-meson molecules through a polarization potential. We have used a formalism of the resonating group method, treated kinetic energy and overlap matrices on model of the potential matrix, but decoupled the resulting complicated integral equations through the Born approximation. In this exploratory study we have used a quadratic confinement and not included the spin-dependence; we also used the approximation of equal constituent quark masses.

hep-ph↗