[Paper Review] The B-meson mass splitting from non-perturbative quenched lattice QCD

Andrey Grozin, Damiano Guazzini+5 more|arXiv (Cornell University)|Oct 2, 2007

Quantum Chromodynamics and Particle Interactions3 references3 citations

TL;DR

This paper presents a non-perturbative, quenched lattice QCD computation of the B-meson spin-splitting using three-loop matching and non-perturbative renormalization of the chromo-magnetic operator in Heavy Quark Effective Theory. It achieves a significant improvement in accuracy by reducing perturbative uncertainties, bringing the theoretical prediction for the B_s-meson mass splitting much closer to experiment, with a 1% relative error on the matching coefficient C_spin.

ABSTRACT

We perform the non-perturbative (quenched) renormalization of the chromo-magnetic operator in Heavy Quark Effective Theory and its three-loop matching to QCD. At order 1/m of the expansion, the operator is responsible for the mass splitting between the pseudoscalar and vector B-mesons. These new computed factors are affected by an uncertainty negligible in comparison to the known bare matrix element of the operator between B-states. Furthermore, they push the quenched determination of the spin splitting for the Bs-meson much closer to its experimental value than the previous perturbatively renormalized computations. The renormalization factor for three commonly used heavy quark actions and the Wilson gauge action and useful parametrizations of the matching coefficient are provided.

Motivation & Objective

• To compute the B-meson spin-splitting (M_V^2 - M_PS^2) with improved precision using non-perturbative renormalization in quenched lattice QCD.
• To reduce uncertainties in the matching coefficient C_spin between QCD and Heavy Quark Effective Theory by computing it at three-loop order.
• To provide non-perturbative renormalization factors Z_spin^RGI for three common heavy quark actions and the Wilson gauge action.
• To improve agreement between lattice QCD predictions and experimental values for the B_s-meson spin-splitting by correcting for perturbative renormalization errors.

Proposed method

• Non-perturbative renormalization of the chromo-magnetic operator using the Schr"odinger functional scheme with finite-volume boundary conditions.
• Computation of the renormalization factor Z_spin^RGI in the pure gauge theory (N_f=0) to avoid light quark effects.
• Three-loop matching of the HQET chromo-magnetic operator to full QCD, with anomalous dimension and beta-function coefficients computed to three-loop order.
• Use of the RGI (renormalization group invariant) parameter λ_2^RGI to eliminate scheme dependence and improve accuracy.
• Parametrization of the matching coefficient C_spin(M/Λ) in terms of x = 1 / ln(M/Λ) for practical use in B-physics applications.
• Application of the new matching and renormalization factors to existing quenched lattice data for the bare λ_2 matrix element.

Experimental results

Research questions

• RQ1 How does non-perturbative renormalization of the chromo-magnetic operator in HQET improve the accuracy of B-meson mass splitting predictions in quenched lattice QCD?
• RQ2 What is the impact of three-loop matching on the uncertainty of the C_spin matching coefficient, and how does it compare to lower-order perturbative estimates?
• RQ3 To what extent does the new non-perturbative Z_spin^RGI reduce the discrepancy between quenched lattice QCD predictions and experimental values for the B_s-meson spin-splitting?
• RQ4 Can the improved matching and renormalization procedure bring theoretical predictions for the B-meson mass splitting into closer agreement with experiment, despite the quenched approximation?

Key findings

• The three-loop matching coefficient C_spin exhibits very small higher-order corrections, with a difference of only about 10^-2 between two- and three-loop results at the b-quark mass scale.
• The uncertainty in the matching coefficient C_spin is estimated at about 1% relative error when using the three-loop anomalous dimension, which is negligible compared to other uncertainties in the mass splitting.
• The non-perturbative renormalization factor Z_spin^RGI leads to a significant shift in the predicted B-meson mass splitting, bringing it much closer to the experimental value of 0.497 GeV^2.
• For the quenched lattice data at β=6.0, the corrected mass splitting increases from 0.28(6) GeV^2 (perturbative) to 0.38(7) GeV^2 (non-perturbative), and from 0.36(4) GeV^2 to 0.53(6) GeV^2, respectively, improving agreement with experiment.
• The results demonstrate that non-perturbative renormalization effects are substantial at low energies, with significant deviations from perturbative scale evolution observed in the Schr"odinger functional framework.
• The method is applicable to other spin-dependent potentials in heavy quark physics, extending the utility of the non-perturbative renormalization programme beyond the B-meson splitting.