Prediction of the Omega_bbb mass from lattice QCD

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Abstract

The mass of the triply heavy baryon Omega_bbb is calculated in lattice QCD with 2+1 flavors of light sea quarks. The b quark is implemented with improved lattice NRQCD. Gauge field ensembles from both the RBC/UKQCD and MILC collaborations with lattice spacings in the range from 0.08 fm to 0.12 fm are used. The final result for the Omega_bbb mass, which includes an electrostatic correction, is 14.371+-0.004(stat)+-0.011(syst)+-0.001(exp) GeV. The hyperfine splitting between the physical J=3/2 state and a fictitious J=1/2 state is also calculated.

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G. Lepage, P. Mackenzie (1992)

In this paper we show that the apparent failure of QCD lattice perturbation theory to account for Monte Carlo measurements of perturbative quantities results from choosing the bare lattice coupling constant as the expansion parameter. Using instead ``renormalized'' coupling constants defined in terms of physical quantities, like the heavy-quark potential, greatly enhances the predictive power of lattice perturbation theory. The quality of these predictions is further enhanced by a method for automatically determining the coupling-constant scale most appropriate to a particular quantity. We present a mean-field analysis that explains the large renormalizations relating lattice quantities, like the coupling constant, to their continuum analogues. This suggests a new prescription for designing lattice operators that are more continuum-like than conventional operators. Finally, we provide evidence that the scaling of physical quantities is asymptotic or perturbative already at \(\beta\)'s as low as 5.7, provided the evolution from scale to scale is analyzed using renormalized perturbation theory. This result indicates that reliable simulations of (quenched) QCD are possible at these same low \(\beta\)'s.

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Heavy-quark bound states in lattice QCD

B. Thacker, G. Lepage (1991)

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Massive Fermions in Lattice Gauge Theory

Paul Mackenzie, Andreas S. Kronfeld, Aida X. El-Khadra (1996)

This paper presents a formulation of lattice fermions applicable to all quark masses, large and small. We incorporate interactions from previous light-fermion and heavy-fermion methods, and thus ensure a smooth connection to these limiting cases. The couplings in improved actions are evaluated for arbitrary fermion mass~\(m_q\), without expansions around small- or large-mass limits. We treat both the action and external currents. By interpreting on-shell improvement criteria through the lattice theory's Hamiltonian, one finds that cutoff artifacts factorize into the form \(b_n(m_qa)[\vek{p}a]^{s_n}\), where \(\vek{p}\) is a momentum characteristic of the system under study, \(s_n\) is related to the dimension of the \(n\)th interaction, and \(b_n(m_qa)\) is a bounded function, numerically always~\(\order(1)\) or less. In heavy-quark systems \(\vek{p}\) is typically rather smaller than the fermion mass~\(m_q\). Therefore, artifacts of order \((m_qa)^s\) do not arise, even when \(m_qa\gsim1\). An important by-product of our analysis is an interpretation of the Wilson and Sheikholeslami-Wohlert actions applied to nonrelativistic fermions.