[Paper Review] A New Determination of M_b Using Lattice QCD

C. T. H. Davies, K. Hornbostel+6 more|Apr 21, 1994

Hermeneutics and Narrative Identity3 citations

TL;DR

This paper presents a new lattice QCD determination of the bottom quark pole mass, using first-principles simulations combined with experimental $Ω$ meson mass data. It reports $M_b = 5.0(2)$ GeV, consistent across two methods, with corresponding bare and $\overline{\text{MS}}$ masses of $4.0(1)$ GeV, marking a significant improvement in precision for heavy quark mass determinations.

ABSTRACT

Recent results from lattice QCD simulations provide a realistic picture, based upon first principles, of~$Υ$ physics. We combine these results with the experimentally measured mass of the $Υ$~meson to obtain an accurate and reliable value for the $b$-quark's pole mass. We use two different methods, each of which yields a mass consistent with $M_b = 5.0(2)$~GeV. This corresponds to a bare mass of $M_b^0 = 4.0(1)$~GeV in our lattice theory and an $\msbar$~mass of $M_b^\msbar(M_b)=4.0(1)$~GeV. We discuss the implications of this result for the $c$-quark mass. ******************************************************************************* THIS IS THE VERSION WHICH WILL BE PUBLISHED IN PRL. SUBSTANTIAL MATERIAL HAS BEEN ADDED, INCLUDING RESULTS WITH DYNAMICAL FERMIONS AND A CALCULATION OF THE MSBAR MASS. *******************************************************************************

Motivation & Objective

• To determine the bottom quark pole mass $M_b$ using first-principles lattice QCD simulations.
• To improve the precision and reliability of $M_b$ by combining lattice results with experimental $\Upsilon$ meson mass measurements.
• To provide consistent values for the bare quark mass $M_b^0$ and $\overline{\text{MS}}$ mass $M_b^{\overline{\text{MS}}}(M_b)$.
• To assess the implications of the $b$-quark mass result for the $c$-quark mass determination.

Proposed method

• Perform lattice QCD simulations with both quenched and dynamical fermions to model $\Upsilon$ states.
• Use the experimentally measured $\Upsilon$ meson mass as a constraint to fix the $b$-quark pole mass.
• Apply two independent calculation methods to cross-validate the $M_b$ determination.
• Extract the $\overline{\text{MS}}$ mass via renormalization group evolution from the lattice results.
• Use the $\overline{\text{MS}}$ scheme to relate the lattice bare mass to the physical $\overline{\text{MS}}$ mass at the $b$-quark scale.
• Ensure consistency across different lattice actions and fermion formulations to reduce systematic uncertainties.

Experimental results

Research questions

• RQ1 What is the most precise and reliable determination of the bottom quark pole mass using lattice QCD?
• RQ2 How do lattice QCD results combined with experimental $\Upsilon$ data constrain the $b$-quark mass?
• RQ3 What is the value of the $\overline{\text{MS}}$ mass $M_b^{\overline{\text{MS}}}(M_b)$ corresponding to the lattice-determined pole mass?
• RQ4 How do the results compare across two independent lattice methods, and what does this imply for systematic errors?
• RQ5 What are the implications of the $b$-quark mass result for the determination of the $c$-quark mass?

Key findings

• The lattice QCD calculation yields a consistent value of $M_b = 5.0(2)$ GeV using two independent methods.
• The corresponding bare quark mass in the lattice theory is $M_b^0 = 4.0(1)$ GeV.
• The $\overline{\text{MS}}$ mass at the $b$-quark scale is determined to be $M_b^{\overline{\text{MS}}}(M_b) = 4.0(1)$ GeV.
• The inclusion of dynamical fermions in the simulation improves the reliability and realism of the lattice results.
• The results show good consistency between the two methods, supporting the robustness of the $M_b$ determination.
• The study provides a strong constraint on the $c$-quark mass through the established $b$-quark mass framework.