Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · hep-lat/9610026

A calculation of the $B_{B}$ parameter in the static limit

Joseph Christensen·Terrence Draper·Craig McNeile
View original source ↗Read source document ↗Export metadata ↓

Abstract

We calculate the $B_{B}$ parameter, relevant for $\overline{B}^0$ -- $B^0$ mixing, from a lattice gauge theory simulation at $β= 6.0$. The bottom quarks are simulated in the static theory, the light quarks with Wilson fermions. Improved smearing functions produced by a variational technique, MOST, are used to reduce statistical errors and minimize excited-state contamination of the ground-state signal. We obtain $B_B(4.33 GeV) = 0.98^{+4}_{-4}$ (statistical) $^{+3}_{-18}$ (systematic) which corresponds to $\widehat{B}_B = 1.40^{+6}_{-6}$ (statistical) $^{+4}_{-26}$ (systematic) for the one-loop renormalization-scheme-independent parameter. The systematic errors include the uncertainty due to alternative (less favored) treatments of the perturbatively-calculated mixing coefficients; this uncertainty is at least as large as residual differences between Wilson-static and clover-static results. Our result agrees with extrapolations of results from relativistic (Wilson) heavy quark simulations.

Explore related subjects

hep-lathep-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Joseph Christensen, Terrence Draper, Craig McNeile. 1998-02-06. A calculation of the $B_{B}$ parameter in the static limit. https://doi.org/10.1103/physrevd.56.6993

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Efficient Quantum Simulations of Yang-Mills theory with Maximal-tree Gauge

We develop a quantum algorithmic framework for the efficient simulation of Yang--Mills theories, including the $\mathrm{SU}(3)$ gauge theory in Quantum Chromodynamics (QCD). The framework uses maximal-tree gauge in terms of gauge field variables that removes all local gauge redundancies. In the resulting gauge-fixed formulation and digitization in the field-amplitude basis, we show that Hamiltonian time evolution admits an efficient implementation based on quantum singular value transformation (QSVT). We derive upper bounds on the total number of qubits and gate complexity, finding polynomial scaling with the inverse simulation precision $1/\varepsilon_s$, lattice volume $\mathcal{V}$, gauge coupling $g$, and target energy scale $E$. Our results provide a rigorous complexity-theoretic demonstration that non-Abelian Yang--Mills theories can be simulated efficiently on quantum computers, paving the way toward first-principles quantum simulations of non-perturbative QCD dynamics.

hep-lat↗
arXiv2026

Accurate Sampling from Diffusion Models

A new proposal called DM-SMC (Diffusion Model - Sequential Monte Carlo) is investigated, which samples ensembles defined in terms of an action, using diffusion models trained on samples from the ensemble. The SMC setup allows for accurate sampling in spite of an approximate diffusion model and the finite stepsize used in the numerical solution of the stochastic process. Improved update strategies are also investigated. Results are presented for a $Z_2$ symmetric scalar field theory in 2 dimensions near its 2nd order phase transition.

hep-lat↗
arXiv2026

Decomposition of the axial-vector current in a finite box

We consider the matrix element of the axial-vector current between two nucleon states in a finite box. Starting from the chiral Lagrangian density with nucleon and Delta-isobar degrees of freedom, we study the finite-volume effects at the one-loop level. We show that the standard decomposition into the axial-vector and pseudoscalar form factor is incomplete in a finite box. We derive expressions for the complete set of in-box form factors at one loop, and demonstrate how to extract the full set from lattice correlation functions. We verify that the axial Ward identity holds in the chiral limit. We derive the one-loop expressions for the pseudoscalar form factor and verify that the in-box axial Ward identity away from the chiral limit is fulfilled also. Selected numerical results are shown for two flavor-SU(2) lattice ensembles. Sizable finite-volume effects are observed, with an important role for the Delta-isobar. We discuss the implications of our results for lattice studies of the axial-vector current. We conclude that full finite-box results are crucial for a precise determination of the form factors.

hep-lat↗