B-parameters of the complete set of matrix elements of (Delta B = 2) operators from the lattice

TL;DR

This work addresses the determination of the bag parameters $B_i(\mu)$ for the complete set of Delta $B=2$ operators in the SUSY basis, essential for beyond-Standard-Model analyses of $B$ meson mixing. The authors combine direct lattice QCD results (Wilson fermions, RI/MOM renormalization) with HQET static-limit results, performing NLO matching to $MSbar$(NDR) and carefully matching QCD to HQET to constrain extrapolations to the physical $B$ meson mass $m_b$. They deliver a full set of $B_i$ in RI/MOM and multiple $MSbar$ schemes (including Beneke and Burás variants), with quantified systematic uncertainties, and demonstrate that SU(3) breaking is small. The methodology reduces heavy-quark extrapolation uncertainties by leveraging HQET constraints, though the results are in the quenched approximation; future unquenched and continuum-limit analyses will sharpen these inputs for phenomenology of $\Delta m_B$ and related observables in SUSY scenarios.

Abstract

We compute on the lattice the ``bag'' parameters of the five (Delta B = 2) operators of the supersymmetric basis, by combining their values determined in full QCD and in the static limit of HQET. The extrapolation of the QCD results from the accessible heavy-light meson masses to the B-meson mass is constrained by the static result. The matching of the corresponding results in HQET and in QCD is for the first time made at NLO accuracy in the MSbar(NDR) renormalization scheme. All results are obtained in the quenched approximation.

Figures (5)

• Figure 1: Signals for the ratios $R_{B_i}(t)$, defined in eqs. (\ref{['eq1']}) and (\ref{['eq2']}), are shown for the combination: $\kappa_q=0.1349$, $\kappa_Q=0.122$. The operators are non-perturbatively renormalized (NPR) in the (Landau)RI/MOM scheme at $\mu \simeq 1/a =2.8(1)$ GeV.
• Figure 2: Extrapolations to the light up/down and interpolations to the strange light quark mass are shown for all five $B$-parameters in the case of fixed heavy quark mass corresponding to $\kappa_Q=0.122$. Empty symbols denote the $B$-parameters directly accessed in our simulation. Filled symbols correspond to the $B$ parameters extrapolated to the physical $u/d$ and $s$ quark respectively. In the figure $\mu a = 1.03$.
• Figure 3: Signals for the ratios $\widetilde{R}_{B_i}(t)$ defined in eqs. (\ref{['hqetR']}) from which the $\widetilde{B}_i$ parameters are extracted. The common plateaus are chosen for $t_1\equiv t\in [32,36]$. The plotted ratios correspond to $\kappa_q=0.1432$. The operators are renormalized perturbatively and evolved to $\mu = m_b$.
• Figure 4: Extrapolation to the physical $B_d$ meson mass (squared symbols) in the inverse heavy meson mass. The unconstrained linear extrapolation for each of the components of the vector $\vec{\Phi}_{1,2,3}(m_{P},m_b)$ from our data (empty circles) to $\vec{\Phi}_{1,2,3}(m_{B_d},m_b)$ (empty square) is depicted by the dotted line. The result of the constrained extrapolation (filled squares) by the static HQET bag-parameters (filled circles) is marked by the dashed line. $i^{th}$ component of the vector is marked by $[i]$.
• Figure 5: The same as fig. \ref{['fig33']} but for $\vec{\Phi}_{4,5}(m_{P},m_b)$.