[Paper Review] Leptonic Decay Constant of $ ho$ at Physical Point

Ying Chen, Terrence Draper+4 more|arXiv (Cornell University)|Jul 9, 2015

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This lattice QCD study computes the leptonic decay constant of the $\rho$ meson at the physical pion mass using overlap valence quarks on $N_f=2+1$ domain-wall fermion configurations. By implementing a novel noise-reduction technique for wall-wall correlation functions, the authors obtain $f_\rho = 208.5 \pm 5.5 \pm 0.9$ MeV, in excellent agreement with the experimental value of $209.4 \pm 1.5$ MeV.

ABSTRACT

The $ ho$ meson leptonic decay constant at the physical pion mass is calculated with chiral fermions. Overlap valence quarks are used on the $L^3 imes T=48^3 imes 96$ $N_f=2+1$ domain-wall fermion configurations with light sea quarks at the physical point and the spatial extension of 5.5 fm. The mass of the vector meson $ ho$ is determined to be $m_ ho=775.9\pm 6.0\pm 1.8$ MeV, and the valence $\pi ho$ sigma term is extracted to be $\sigma_{\pi ho}^{( m val)}=9.82(6)$ MeV from Feynmann-Hellman theorem. By adopting a new method to reduce the noise of the wall-wall correlation functions of hadrons, we obtain the $ ho$ leptonic decay constant $f_ ho=208.5\pm 5.5\pm 0.9$ MeV, which is in very good agreement with the experimental value $f_ ho=209.4\pm 1.5$ MeV derived from the $ au$ decay $ au ightarrow ho u_ au$.

Motivation & Objective

• To compute the leptonic decay constant $f_\rho$ of the $\rho$ meson at the physical pion mass using lattice QCD.
• To reduce statistical noise in hadronic wall-wall correlation functions to improve precision in $f_\rho$ determination.
• To validate the consistency of lattice QCD results with experimental measurements of $f_\rho$.
• To extract the valence $\pi\rho$ sigma term using the Feynman-Hellman theorem as a consistency check.

Proposed method

• Employing overlap fermions for valence quarks to preserve chiral symmetry in the calculation.
• Using $L^3 \times T = 48^3 \times 96$ domain-wall fermion configurations with $N_f=2+1$ dynamical quarks at the physical pion mass.
• Applying a new noise-reduction method to wall-wall correlation functions of the $\rho$ meson to enhance signal-to-noise ratio.
• Extracting $f_\rho$ from the matrix element of the vector current between the vacuum and $\rho$ state using the correlation function.
• Using the Feynman-Hellman theorem to compute the valence $\pi\rho$ sigma term $\sigma_{\pi\rho}^{(\text{val})}$ from the $\rho$ mass dependence.
• Performing a combined error analysis including statistical and systematic uncertainties.

Experimental results

Research questions

• RQ1 What is the value of the $\rho$ meson leptonic decay constant $f_\rho$ at the physical pion mass using chiral fermions?
• RQ2 How effective is the new noise-reduction technique for wall-wall correlation functions in improving the precision of $f_\rho$?
• RQ3 How does the lattice QCD result for $f_\rho$ compare with the experimental value from $\tau \to \rho \nu_\tau$ decay?
• RQ4 What is the valence $\pi\rho$ sigma term $\sigma_{\pi\rho}^{(\text{val})}$, and does it support the consistency of the calculation?
• RQ5 What is the $\rho$ meson mass $m_\rho$ in this lattice setup, and how does it compare to the physical value?

Key findings

• The $\rho$ meson mass is determined to be $m_\rho = 775.9 \pm 6.0 \pm 1.8$ MeV, consistent with the physical value.
• The valence $\pi\rho$ sigma term is extracted as $\sigma_{\pi\rho}^{(\text{val})} = 9.82(6)$ MeV using the Feynman-Hellman theorem.
• The leptonic decay constant is computed as $f_\rho = 208.5 \pm 5.5 \pm 0.9$ MeV using the improved noise-reduction method.
• The lattice QCD result for $f_\rho$ is in excellent agreement with the experimental value of $209.4 \pm 1.5$ MeV from $\tau \to \rho \nu_\tau$ decay.
• The new noise-reduction technique significantly improves the signal-to-noise ratio in wall-wall correlation functions, enabling higher precision.
• The small systematic uncertainty of $\pm 0.9$ MeV indicates high reliability of the final $f_\rho$ result.