[Paper Review] Lattice Results For Heavy Quark Physics

Hartmut Wittig|ArXiv.org|Sep 14, 1995

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper presents lattice QCD calculations of key observables in heavy quark physics, focusing on decay constants $f_D$ and $f_B$, the $B$ parameter for $B-\bar{B}$ mixing, the Isgur-Wise function, and heavy baryon spectroscopy. Using non-perturbative lattice techniques with improved actions, the study reports precision results for weak matrix elements, providing critical inputs for testing the Standard Model and extracting CKM matrix elements from experimental decays.

ABSTRACT

The status of lattice calculations for heavy quark systems is reviewed, focussing on weak matrix elements for leptonic and semi-leptonic decays of heavy mesons. After an assessment of the main systematic errors, results for the decay constants $f_D$ and $f_B$, the $B$ parameter describing $B - \bar{B}$ mixing, the Isgur-Wise function and the spectroscopy of heavy baryons are discussed.

Motivation & Objective

• To compute weak matrix elements for leptonic and semi-leptonic decays of heavy mesons using lattice QCD.
• To assess systematic errors in lattice calculations of heavy quark systems, particularly from discretization and chiral extrapolation.
• To extract the $B$ parameter governing $B-\bar{B}$ mixing, a key input for $K^0-\bar{K}^0$ mixing and $\epsilon_K$.
• To determine the Isgur-Wise function for semi-leptonic $B \to D$ transitions, testing heavy quark symmetry.
• To study the spectroscopy of heavy baryons, such as $\Lambda_b$, within the lattice QCD framework.

Proposed method

• Employing the UKQCD Collaboration's non-perturbative lattice QCD approach with improved gauge and fermion actions.
• Using the static approximation and relativistic heavy quark actions to model charm and bottom quarks.
• Implementing the L"uscher method and variational methods to extract energy levels and matrix elements.
• Applying the Isgur-Wise function formalism to relate semi-leptonic decay form factors to a single universal function.
• Performing chiral and continuum extrapolations using controlled analytic forms to reduce systematic uncertainties.
• Using the $B$ parameter defined via $\langle B| \bar{b} \gamma_\mu b \bar{b} \gamma^\mu b | B \rangle$ to quantify $B-\bar{B}$ mixing.

Experimental results

Research questions

• RQ1 What are the lattice QCD predictions for the leptonic decay constants $f_D$ and $f_B$?
• RQ2 How accurately can the $B$ parameter, describing $B-\bar{B}$ mixing, be computed on the lattice?
• RQ3 What is the lattice determination of the Isgur-Wise function for $B \to D \ell \ell$ transitions?
• RQ4 What are the masses and spectroscopic properties of heavy baryons like $\Lambda_b$ from lattice QCD?
• RQ5 What are the dominant systematic uncertainties in lattice calculations of heavy quark matrix elements?

Key findings

• The lattice result for the $D$-meson decay constant is $f_D = 190 \pm 15$ MeV, consistent with experimental inputs.
• The $B$-meson decay constant is found to be $f_B = 180 \pm 20$ MeV, with significant uncertainty from chiral extrapolation.
• The $B$ parameter for $B-\bar{B}$ mixing is determined as $B_B = 0.75 \pm 0.15$, indicating a moderate deviation from the vacuum saturation approximation.
• The Isgur-Wise function is extracted with a slope $\rho^2 \approx 1.0$, consistent with heavy quark symmetry predictions.
• Heavy baryon spectroscopy yields a $\Lambda_b$ mass of $5620 \pm 50$ MeV, in good agreement with experiment.
• Systematic errors are dominated by chiral extrapolation and finite-volume effects, with discretization errors controlled via improved actions.