Precision Upsilon Spectroscopy from Nonrelativistic Lattice QCD

TL;DR

The study uses nonrelativistic lattice QCD with a tadpole-improved action to compute the Upsilon heavy-quarkonium spectrum on quenched lattices, testing methods for extracting ground and excited state energies. Through multi-correlator, multi-exponential fits and two correlated approaches for spin splittings, the authors reproduce the 1S–3S spectrum and chi_b fine structure, and predict eta_b and D-state centers. They also compare nonperturbative dispersion masses with perturbative expectations, and examine the Upsilon mass via rest and kinetic energy methods, finding consistent results when relativistic corrections are included. The work demonstrates the viability of NRQCD on the lattice for heavy quarkonia, provides a framework for precise parameter determinations, and lays groundwork for unquenched calculations and future refinements in the b-quark sector.

Abstract

The spectrum of the Upsilon system is investigated using the Nonrelativistic Lattice QCD approach to heavy quarks and ignoring light quark vacuum polarization. We find good agreement with experiment for the Upsilon(1S), Upsilon(2S), Upsilon(3S) and for the center of mass and fine structure of the chi_b states. The lattice calculations predict b-bbar D-states with center of mass at (10.20 +/- 0.07 +/- 0.03)GeV. Fitting procedures aimed at extracting both ground and excited state energies are developed. We calculate a nonperturbative dispersion mass for the Upsilon(1S) and compare with tadpole-improved lattice perturbation theory.

Figures (6)

• Figure 1: NRQCD simulation results for the spectrum of the $\Upsilon$ system including radial excitations. Experimental values (dashed lines) are indicated for the triplet $S$-states, and for the spin-average of the triplet $P$-states. The energy zero from simulation results is adjusted to give the correct mass to the $\Upsilon(1{^3S}_1)$.
• Figure 2: Simulation results for the spin structure of the lowest lying $P$-wave states in the $\Upsilon$ family. The dashed lines are the experimental values for the triplet states. Energies are measured relative to the center of mass of the triplet states.
• Figure 3: $^1S_0$ Effective masses by (source, sink).
• Figure 4: $^1P_1$ Effective masses by (source, sink).
• Figure 5: $^3S_1$ Effective amplitudes $G(t)\;\cdot e^{E_1 \cdot t}$ from three-exponential fits with $t_{\rm min} = 5$, $t_{\rm max} = 24$.