Unlike QED, QCD in general can't be solved perturbatively because the coupling constant depends on the energy scale we are working in. Consequently, the perturbation expansion discussed in the context of QED, does not converge rapidly. At low-energy scales, the coupling constant of QCD is large; ∼ O(1). For this reason (low-energy) QCD processes are not calculable using traditional perturbation theory. At high energies, coupling constant becomes sufficiently small that perturbation theory can again be used. Secondly, meson (quark-antiquark combination) being colour neutral can exist freely in nature. Heavy quark charmonium and bottomonium bound states are observed as resonances in e+e− annihilation. The velocities of the heavy quarks in the charmonium and bottomonium states are relatively low, βc ∼ 0.3 and βb ∼ 0.1. In this case, the observed spectra of charmonium and bottomonium states, provide a probe of the QCD potential in the non-relativistic limit. In non-relativistic QCD (NRQCD), the interaction between two quarks (or between a quark and an antiquark) can be expressed as a static potential of the form V(r). V(r) = -a/r + b*r
Following code uses set of radially symmetric test functions to approximate the ground state wavefunction on quarkonium bound state.
This project is being supervised by Prof. Nilmani Mathur, TIFR Mumbai