Abstract
We employ a non-relativistic version of QCD (NRQCD) to study heavy q q bound states in the lowest approximation without fine structure. We use gluon configurations on a 6 3×48 lattice at β=6.2 from the UKQCD Collaboration. For a bare quark mass near that of the b-quark ( Ma=1.6) we obtain the bound state masses for the S-, P- and both types of D-waves. We also detect signals for two types of hybriges ( q qg states). The results are sufficiently accurate to confirm that the values of the D-wave mass from both D-waves coincide thus indicating that the cubical invariance of the lattice is restored to full rotational invariance to a good approximation. We also study S- and P-wave masses for values of the range of bare quark mass Ma=1.0, 1.3, 1.6 and 1.9. The results confirm the idea that the S/P-splitting is relatively insensitive to the value of the bare quark mass.
Highlights
Heavy quark bound states (J/ψ, Υ) are intrinsically interesting but because of the nearly non-relativistic motion of the constituent quarks, offer the prospect of numerical calculations considerably more tractable than the standard calculations for light quarks [1, 2, 3, 4, 5]
For quark masses M ≫ ΛQCD, the quark velocity v ≪ 1, so that its dynamics are well modelled by an effective field theory, nonrelativistic QCD (NRQCD), in which the kinetic energy term is nonrelativistic [3, 6]
This approximation will only be valid for momenta very much less than some cut-off Λ = a−1 of the order of the heavy quark mass M
Summary
Heavy quark bound states (J/ψ, Υ) are intrinsically interesting but because of the nearly non-relativistic motion of the constituent quarks, offer the prospect of numerical calculations considerably more tractable than the standard calculations for light quarks [1, 2, 3, 4, 5]. For quark masses M ≫ ΛQCD, the quark velocity v ≪ 1, so that its dynamics are well modelled by an effective field theory, nonrelativistic QCD (NRQCD), in which the kinetic energy term is nonrelativistic [3, 6] This approximation will only be valid for momenta very much less than some cut-off Λ = a−1 (a is the lattice spacing) of the order of the heavy quark mass M. The effective action will contain correction terms which serve both to implement relativistic effects such as the hyperfine structure splitting and to compensate for the effects of the high momentum states which have been removed from the theory These may be reorganised into a power series in the characteristic quark velocity determined by the dynamics. We intend to explore these and other questions in future work
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