Boost-invariant Hamiltonian approach to heavy quarkonia

Abstract

Light-front Hamiltonian formulation of QCD with only one flavor of quarks is used in its simplest approximate version to calculate masses and boost-invariant wave functions of c-anti-c or b-anti-b mesons. It is shown that in the Hamiltonian approach in its simplest version the strong coupling constant alpha and quark mass m (for suitable values of the renormalization group parameter lambda that is used in the calculation), can be adjusted so that a) masses of 12 lightest well-established b-anti-b mesons are reproduced with accuracy better than 0.5 percent for all of them, which means 50 MeV in a few worst cases and on the order of 10 MeV in other cases, or b) masses of 11 lightest c-anti-c mesons are reproduced with accuracy better than 3 percent for all of them, which means better than 100 MeV in a few worst cases and on the order of 10 MeV in the other cases, while the parameters alpha and m are near the values expected in the cases a) and b) by analogy with other approaches. A 4th-order study in the same Hamiltonian scheme will be required to explicitly include renormalization group running of the parameters alpha and m from the scale set by masses of bosons W and Z down to the values of lambda that are suitable in the bound-state calculations. In principle, one can use the Hamiltonian approach to describe the structure, decay, production, and scattering of heavy quarkonia in all kinds of motion, including velocities arbitrarily close to the speed of light. This work is devoted exclusively to a pilot study of masses of the quarkonia in the simplest version of the approach.