[Paper Review] B-physics from lattice QCD...with a twist

N. Carrasco, P. Dimopoulos+12 more|arXiv (Cornell University)|Dec 3, 2012

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper presents a precise lattice QCD determination of the b-quark mass, B- and Bs-meson decay constants, and bag parameters using the ratio method with improved interpolating operators and Wilson twisted mass fermions. The results, obtained across four lattice spacings and extrapolated to the continuum limit, yield $\overline{m}_b(\overline{m}_b) = 4.35(12)\,\text{GeV}$, $f_B = 197(10)\,\text{MeV}$, $f_{B_s} = 234(6)\,\text{MeV}$, $B_{B_s}^{\overline{MS}} = 0.90(5)$, and $B_{B_d}^{\overline{MS}} = 0.87(5)$, with uncertainties dominated by systematic effects.

ABSTRACT

We present a precise lattice QCD determination of the b-quark mass, of the B and Bs decay constants and first results for the B-meson bag parameters. For our computation we employ the so-called ratio method and our results benefit from the use of improved interpolating operators for the B-mesons. QCD calculations are performed with Nf = 2 dynamical light-quarks at four values of the lattice spacing and the results are extrapolated to the continuum limit. The preliminary results are mb(mb) = 4.35(12) GeV for the MSbar b-quark mass, fBs = 234(6) MeV and fB = 197(10) MeV for the B-meson decay constants, BBs(mb) = 0.90(5) and BB(mb) = 0.87(5) for the B-meson bag parameters.

Motivation & Objective

• To reduce uncertainties in B-physics hadronic parameters to the 1% level required for testing the Standard Model and searching for New Physics.
• To improve the projection onto the ground state in heavy-light meson correlators by optimizing interpolating operators using Gaussian smearing.
• To extend the range of heavy-quark masses in lattice QCD simulations to $\sim 2.5m_c$ for better extrapolation to the b-quark limit.
• To apply the ratio method to achieve high-precision results for the $b$-quark mass, decay constants, and bag parameters with controlled systematic errors.
• To provide preliminary estimates of $B_{B_s}^{\overline{MS}}$, $B_{B_d}^{\overline{MS}}$, and the ratio $\xi = f_{B_s}\sqrt{B_{B_s}}/(f_B\sqrt{B_{B_d}})$ with uncertainties in the 5% range.

Proposed method

• The ratio method is employed to compute the $b$-quark mass and decay constants, using ratios of heavy-light meson masses and matrix elements at different heavy-quark masses to cancel systematic uncertainties.
• Improved interpolating operators based on Gaussian smearing are used to enhance the overlap with the ground state and reduce noise in correlation functions at short Euclidean time separations.
• Simulations are performed with $N_f=2$ dynamical light quarks on four lattice spacings, with the continuum limit achieved via extrapolation.
• The $b$-quark mass is determined by extrapolating the ratio $M_{hl}/\mu_h^{\text{pole}}$ to the static limit using the ratio method, ensuring asymptotic freedom and smooth convergence.
• Bag parameters are computed via the ratio method applied to $\Delta B = 2$ matrix elements, with $1/\overline{m}_b$ corrections included using tree-level HQET matching.
• Chiral and continuum extrapolations are performed using linear fits in the light-quark mass, with the double-ratio $\zeta$ used to control the $f_{B_s}/f_B$ ratio and reduce systematic errors.

Experimental results

Research questions

• RQ1 What is the precise value of the $\overline{\text{MS}}$ $b$-quark mass at the $b$-quark scale, with uncertainties below 3%?
• RQ2 How accurately can the $B$- and $B_s$-meson decay constants be computed using improved interpolating operators and the ratio method?
• RQ3 What are the values of the $B$-meson bag parameters $B_{B_s}^{\overline{MS}}$ and $B_{B_d}^{\overline{MS}}$ with controlled systematic errors?
• RQ4 How well do the $B$-meson bag parameters extrapolate to the $b$-quark limit, and what is the impact of $1/\overline{m}_b$ corrections?
• RQ5 What is the value of the ratio $\xi = f_{B_s}\sqrt{B_{B_s}}/(f_B\sqrt{B_{B_d}})$, which is crucial for unitarity triangle analysis?

Key findings

• The $\overline{\text{MS}}$ $b$-quark mass is determined as $\overline{m}_b(\overline{m}_b) = 4.35(12)\,\text{GeV}$, with a relative uncertainty of about 2.7%.
• The $B$-meson decay constant is found to be $f_B = 197(10)\,\text{MeV}$, and the $B_s$-meson decay constant is $f_{B_s} = 234(6)\,\text{MeV}$, with a ratio $f_{B_s}/f_B = 1.19(5)$.
• The $B$-meson bag parameter for the $B_s$ system is $B_{B_s}^{\overline{MS}}(\overline{m}_b) = 0.90(5)$, and for the $B_d$ system it is $B_{B_d}^{\overline{MS}}(\overline{m}_b) = 0.87(5)$.
• The ratio $B_{B_s}/B_{B_d} = 1.03(2)$ is obtained, indicating consistency with the Standard Model prediction for $\Delta B = 2$ transitions.
• The parameter $\xi = f_{B_s}\sqrt{B_{B_s}}/(f_B\sqrt{B_{B_d}})$ is estimated as $1.21(6)$, with uncertainties dominated by statistical and systematic effects.
• The analysis confirms that $1/\overline{m}_b$ corrections are at the level of one standard deviation, validating the use of the ratio method with tree-level HQET matching.