[Paper Review] Bs and Bc mesons in lattice QCD with exact chiral symmetry

Ting-Wai Chiu, Tung‐Han Hsieh|arXiv (Cornell University)|Apr 26, 2007

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This lattice QCD study computes the masses and decay constants of Bs and Bc mesons using exact chiral symmetry on a 32³×60 lattice with 100 gauge configurations at β = 7.2. It determines m_{Bs} = 5385(27)(17) MeV, f_{Bs} = 253(8)(7) MeV, m_{Bc} = 6278(6)(4) MeV, f_{Bc} = 489(4)(3) MeV, and vector meson masses m_{Bs^*} = 5424(28)(19) MeV and m_{Bc^*} = 6315(6)(5) MeV, providing precise predictions for heavy-flavor mesons with controlled systematic errors.

ABSTRACT

We determine the masses and decay constants of the pseudoscalar mesons Bs and Bc, and also the masses of the vector mesons Bs^* and Bc^*, in quenched lattice QCD with exact chiral symmetry. For 100 gauge configurations generated with single-plaquette action at beta = 7.2 on the 32^3 x 60 lattice, we compute point-to-point quark propagators for 33 quark masses in the range [0.01, 0.85], and measure the time-correlation functions of pseudoscalar and vector mesons. The inverse lattice spacing and the charm quark bare mass are determined using the mass and decay constant of eta_c(2980). The bare masses of s and b quarks are chosen such that the masses of the corresponding vector mesons are in good agreement with phi(1020), and Upsilon(9460) respectively. Our results are: m_{Bs} = 5385(27)(17) MeV, f_{Bs} = 253(8)(7) MeV, m_{Bc} = 6278(6)(4) MeV, f_{Bc} = 489(4)(3) MeV, m_{Bs^*} = 5424(28)(19) MeV, and m_{Bc^*} = 6315(6)(5) MeV.

Motivation & Objective

• To compute the masses and decay constants of the pseudoscalar and vector mesons Bs and Bc using lattice QCD with exact chiral symmetry.
• To achieve high-precision predictions for heavy-flavor mesons by controlling systematic errors through exact chiral symmetry and fine-tuned quark masses.
• To calibrate the bare quark masses using the ηc(2980) mass and decay constant, and to set the s and b quark masses by matching vector meson masses to experimental values.
• To provide benchmark results for theoretical and experimental comparisons in heavy quark physics.

Proposed method

• Using 100 quenched gauge configurations generated with a single-plaquette action at β = 7.2 on a 32³×60 lattice.
• Computing point-to-point quark propagators for 33 quark masses in the range [0.01, 0.85] to ensure sufficient control over chiral extrapolation.
• Measuring time-correlation functions for pseudoscalar and vector mesons to extract mass and decay constant information via standard two-point function analysis.
• Determining the inverse lattice spacing and charm quark bare mass by matching the ηc(2980) mass and decay constant to experiment.
• Setting the strange and bottom quark bare masses so that the vector meson masses reproduce the experimental values of φ(1020) and Υ(9460).
• Applying finite-volume and chiral extrapolation techniques to obtain physical results with controlled systematic uncertainties.

Experimental results

Research questions

• RQ1 What are the masses and decay constants of the Bs and Bc pseudoscalar mesons in lattice QCD with exact chiral symmetry?
• RQ2 How accurately can the vector meson masses Bs^* and Bc^* be predicted using this lattice setup and quark mass tuning?
• RQ3 To what extent does the use of exact chiral symmetry reduce systematic errors in heavy-flavor meson spectroscopy?
• RQ4 How well do the computed meson masses agree with experimental values when the s and b quark masses are tuned to reproduce φ(1020) and Υ(9460)?
• RQ5 What is the precision of the lattice QCD prediction for the Bc meson, a key system for testing heavy quark effective theory?

Key findings

• The mass of the Bs pseudoscalar meson is determined to be m_{Bs} = 5385(27)(17) MeV, with statistical and systematic uncertainties.
• The decay constant of the Bs meson is f_{Bs} = 253(8)(7) MeV, indicating a significant coupling to the weak current.
• The Bc pseudoscalar meson mass is computed as m_{Bc} = 6278(6)(4) MeV, consistent with expectations for a heavy quarkonium-like state.
• The Bc decay constant is found to be f_{Bc} = 489(4)(3) MeV, reflecting its unique quark content and weak decay properties.
• The vector meson masses are predicted with high precision: m_{Bs^*} = 5424(28)(19) MeV and m_{Bc^*} = 6315(6)(5) MeV.
• The results demonstrate that exact chiral symmetry enables reliable, high-precision calculations of heavy-flavor meson spectroscopy in quenched lattice QCD.