[Paper Review] Matrix Elements for $D$- and $B$-Mixing from 2+1 Flavor Lattice QCD

C. C. Chang, C. Bérnard+7 more|arXiv (Cornell University)|Nov 26, 2013

Particle physics theoretical and experimental studies5 references4 citations

TL;DR

This paper presents precise lattice QCD calculations of hadronic matrix elements for $D$- and $B$-meson mixing using $2+1$ flavor asqtad fermions and the Fermilab interpretation of the Sheikholeslami-Wohlert action for heavy quarks. The study computes the complete set of five local four-quark operators relevant for both Standard Model and Beyond Standard Model physics, achieving final correlator fits for $B$-meson mixing and preliminary results for $D$-meson mixing with controlled chiral and continuum extrapolations.

ABSTRACT

We present the status of our calculation of hadronic matrix elements for $D$- and $B$-meson mixing. We use a large set of the MILC collaboration's $N_f=2+1$ asqtad ensembles, which includes lattice spacings in the range $a\approx0.12$-0.045 fm, and up/down to strange quark mass ratios as low as 0.05. The asqtad action is also employed for the light valence quarks. For the heavy quarks we use the Sheikholeslami-Wohlert action with the Fermilab interpretation. Our calculation covers the complete set of five local operators needed to describe $B$-meson mixing in the Standard Model and Beyond. In the charm sector, our calculation of local mixing matrix elements may be used to constrain new physics models. We present final correlator fit results on the full data set for the $B$-meson mixing project and preliminary fit results for the $D$-meson mixing project.

Motivation & Objective

• To compute the hadronic matrix elements of the five local four-quark operators responsible for $B$- and $D$-meson mixing in the Standard Model and beyond.
• To reduce theoretical uncertainties in $B$-meson mixing by achieving high-precision lattice QCD calculations with fine lattice spacing and light sea quark masses.
• To enable stringent tests of CKM unitarity and constraints on new physics models through precise matrix element determinations.
• To implement a consistent chiral-continuum extrapolation using partially-quenched heavy-meson staggered chiral perturbation theory (PQHMSχPT) to handle taste-symmetry violations and operator mixing.

Proposed method

• Uses $N_f=2+1$ asqtad ensembles with lattice spacings from $a \approx 0.12$ to $0.045$ fm and light sea quark masses as low as $m_s/20$.
• Employs the Fermilab interpretation of the Sheikholeslami-Wohlert action for valence charm and bottom quarks to reduce discretization errors.
• Computes two- and three-point correlation functions to extract matrix elements of the five $ riangleq h=2$ four-quark operators.
• Applies renormalization in the $ m{ar{MS}-NDR}$ scheme at the scale of the heavy quark mass using non-perturbative renormalization techniques.
• Performs chiral-continuum extrapolation using partially-quenched heavy-meson staggered chiral perturbation theory (PQHMSχPT), including both leading-order and next-to-leading-order terms.
• Uses simultaneous fits to $\langle \mathcal{O}_1, \mathcal{O}_2, \mathcal{O}_3 \rangle$ and $\langle \mathcal{O}_4, \mathcal{O}_5 \rangle$ to handle operator mixing and improve systematic control.

Experimental results

Research questions

• RQ1 What are the precise hadronic matrix elements of the five local four-quark operators governing $B$- and $D$-meson mixing in lattice QCD with $2+1$ flavor asqtad fermions?
• RQ2 How do taste-symmetry violations and operator mixing affect the chiral-continuum extrapolation of $B$-meson mixing matrix elements?
• RQ3 To what extent can lattice QCD reduce theoretical uncertainties in $B$-meson mixing compared to current phenomenological estimates?
• RQ4 What is the impact of including finer lattice spacings and lighter sea quark masses on the final error budget for $B$-mixing matrix elements?
• RQ5 How do the matrix elements of the $\mathcal{O}_4$ and $\mathcal{O}_5$ operators—relevant for new physics—behave in the $D$-meson system?

Key findings

• Final correlator fits have been completed for all five matrix elements in the $B$-meson mixing project, with consistent results from fan- and square-shaped correlators for $\mathcal{O}_3$ serving as a cross-check.
• Preliminary correlator fits for the $D$-meson mixing project are available, with renormalization and matching of BSM operators still in progress.
• The chiral-continuum extrapolation for $B$-meson mixing is being finalized using PQHMSχPT, which accounts for taste violations and mixing among $\mathcal{O}_1$, $\mathcal{O}_2$, $\mathcal{O}_3$ and separately among $\mathcal{O}_4$, $\mathcal{O}_5$.
• The inclusion of finer lattices and lighter sea quark masses is expected to reduce dominant systematic errors, particularly from wrong-spin operator contributions.
• The final error budget for $B$-mixing is expected to be consistent with expectations from prior studies, with no significant impact from mixing with wrong-spin terms.
• Results for $\langle \mathcal{O}_1 \rangle$ are shown as a function of light valence-quark mass in Figures 3 and 4, demonstrating the chiral extrapolation behavior across the ensemble set.