Harmonic oscillator force between heavy quarks

الأصل · EN

A renormalization group procedure for effective particles is applied to quantum chromodynamics of one flavor of quarks with large mass m in order to calculate light-front Hamiltonians for heavy quarkonia, Hₗambda, using perturbative expansion in the coupling constant alphaₗambda. lambda is the renormalization group parameter with the interpretation of an inverse of the spatial size of the color charge distribution in the effective quarks and gluons. The eigenvalue equation for Hₗambda couples quark-anti-quark states with sectors of a larger number of constituents. The coupling to states with more than one effective gluon, and interactions in the quark-anti-quark-gluon sector, are removed at the price of introducing an ansatz for the gluon mass, mu². The simplified equation is used to evaluate a new Hamiltonian of order alphaₗambda that acts only in the effective quark-anti-quark sector and in the non-relativistic limit turns out to contain the Coulomb term with Breit-Fermi orrections and spin-independent harmonic oscillator term with frequency omega = [(4/3)(alphaₗambda/pi)]¹/2 lambda (lambda/m)² (pi/1152)¹/4. The latter originates from the hole excavated in the overlapping quark self-interaction gluon clouds by the exchange of effective gluons between the quarks. The new term is largely independent of the details of mu² and in principle can fit into the ball park of phenomenology. The first approximation can be improved by including more terms in Hₗambda and solving the eigenvalue equations numerically.