Harmonic oscillator force between heavy quarks

Abstract

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, H_lambda, using perturbative expansion in the coupling constant alpha_lambda. 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 H_lambda 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, mu^2. The simplified equation is used to evaluate a new Hamiltonian of order alpha_lambda 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)(alpha_lambda/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 mu^2 and in principle can fit into the ball park of phenomenology. The first approximation can be improved by including more terms in H_lambda and solving the eigenvalue equations numerically.

22 pages, plain latex, 2 figures

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• Dynamics of Effective Gluons
• Large-momentum convergence of Hamiltonian bound-state dynamics of effective fermions in quantum field theory
• Optimization of perturbative similarity renormalization group for Hamiltonians with asymptotic freedom and bound states
• Renormalized Poincaré algebra for effective particles in quantum field theory
• Special relativity constraints on the effective constituent theory of hybrids
• Small x divergences in the Similarity RG approach to LF QCD
• Small x divergences in a heavy quark-antiquark state

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• Renormalization of Quantum Fields on the Lightcone Worldsheet I: Scalar Fields
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• A first nonperturbative calculation in light-front QED for an arbitrary covariant gauge
• Notes on One-loop Calculations in Light-cone Gauge
• Boost-invariant Hamiltonian approach to heavy quarkonia
• Calculation of size for bound-state constituents
• Baryon masses estimate in heavy flavor QCD
• From asymptotic freedom toward heavy quarkonia within the renormalization group procedure for effective particles
• Light-front Hamiltonians for heavy quarks and gluons
• Quantum Field Theory in the Language of Light-cone String
• Proton radius puzzle in Hamiltonian dynamics
• Effective-particle approach to bound states of quarks and gluons in QCD