Beautiful mathematics for beauty-full and other multi-heavy hadronic systems

In most non-perturbative methods in hadron physics the calculations are started with a correlation function in terms of some interpolating and transition currents in $ x $-space. For simplicity, the calculations are then transformed to the momentum space by a Fourier transformation. To suppress the contributions of the higher states and continuum; and enhance the ground state contribution, Borel transformation as well as continuum subtraction are applied by the help of quark-hadron duality assumption. In the present study we work out the mathematics required for these processes in the case of light and multi-heavy hadrons. We address a well-known problem in subtraction of the effects of the higher states and continuum and discuss how we find finite results without any divergence by using an appropriate representation of the modified Bessel functions, appearing in the heavy quark propagator, and successive applications of the Borel transformations, which lead to more suppression of the higher states and continuum contributions. The results obtained can be used in determination of the spectroscopic and decay properties of the multi-heavy standard and non-conventional (exotic) systems in many non-perturbative methods, specially the QCD sum rules.