[Paper Review] SU(3) breaking effects in hyperon beta decay from lattice QCD

Shoichi Sasaki, Takeshi Yamazaki|ArXiv.org|Oct 13, 2006

Particle physics theoretical and experimental studies3 citations

TL;DR

This lattice QCD study investigates SU(3) flavor symmetry breaking in hyperon beta decay using domain wall fermions, focusing on the $Ω^0 \to \Sigma^+$ decay. It finds non-zero second-class form factors $f_3$ and $g_2$, providing direct evidence of SU(3) breaking, and determines $f_1(0) = 0.953(24)$, indicating a negative second-order correction, leading to $|V_{us}| = 0.219(27)$, consistent with $K_{l3}$ decays and CKM unitarity.

ABSTRACT

We present results of an exploratory study of flavor SU(3) breaking effects in hyperon beta decays using domain wall fermions. From phenomenological point of view, the significance of this subject is twofold: (1) to extract the element $V_{us}$ of the Cabibbo-Kabayashi-Maskawa mixing matrix from the $ΔS=1$ decay process, and (2) to provide vital information to analysis of the strange quark fraction of the proton spin with the polarized deep inelastic scattering data. In this study, we explore the $Ξ^0 o Σ^+$ beta decay, which is highly sensitive to the SU(3) breaking since this decay corresponds to the direct analogue of neutron beta decay under an exchange between the down quark and the strange quark. We expose the SU(3) breaking effect on $g_A/g_V=g_1(0)/f_1(0)$ up to the first order in breaking. The second-class form factors $g_2$ and $f_3$, of which non-zero values are the direct signals of the SU(3) breaking effect, are also measured. Finally, we estimate $f_1(0)$ up to the second-order correction and then evaluate $|V_{us}|$ combined with the KTeV experiment.

Motivation & Objective

• To investigate SU(3) flavor symmetry breaking effects in hyperon beta decays using first-principles lattice QCD calculations.
• To extract the $SU(3)$-breaking corrections to the axial-vector to vector current ratio $g_A/g_V$ in the $Ω^0 \to \Sigma^+$ decay.
• To measure second-class form factors $f_3$ and $g_2$ as direct signals of $SU(3)$ breaking.
• To estimate the second-order correction to $f_1(0)$ and determine $|V_{us}|$ using KTeV experimental data.
• To resolve the theoretical controversy over the sign of the second-order correction to $f_1(0)$.

Proposed method

• Lattice QCD simulations with domain wall fermions in the quenched approximation at $N_f=2$ with $m_{ud}=0.05$, $m_s=0.08$.
• Computation of three-point correlation functions for vector and axial-vector currents with finite momentum transfer.
• Extraction of form factors via simultaneous linear equations from projected correlation functions using momentum projectors $\mathcal{P}^4$ and $\mathcal{P}^3_5$.
• Linear $q^2$ extrapolation of form factors to $q^2=0$ using mild $q^2$ dependence.
• Extrapolation of $f_3(0)/f_1(0)$ and $g_2(0)/g_1(0)$ to the physical point $\delta=0.0954$ using five simulated $\delta$ values.
• Fitting $f_1(0)$ as a function of $\delta$ using $f_1(0) = 1 + c_2\delta^2$ to extract the second-order correction.

Experimental results

Research questions

• RQ1 What is the magnitude and sign of the $SU(3)$-breaking correction to $f_1(0)$ in the $Ω^0 \to \Sigma^+$ decay?
• RQ2 Are the second-class form factors $f_3$ and $g_2$ non-zero, providing direct evidence of $SU(3)$ breaking?
• RQ3 How does the $g_A/g_V$ ratio in $Ω^0 \to \Sigma^+$ compare to neutron beta decay, and what does this imply for $SU(3)$ breaking?
• RQ4 Does the second-order correction to $f_1(0)$ favor the Ademollo-Gatto theorem and reconcile $|V_{us}|$ with $K_{l3}$ decays?
• RQ5 Is the lattice QCD result consistent with heavy baryon chiral perturbation theory and large $N_c$ analysis?

Key findings

• The second-class form factor $f_3(0)/f_1(0)$ is measured as $+0.250(22)$, providing direct evidence of $SU(3)$ breaking.
• The second-class form factor $g_2(0)/g_1(0)$ is measured as $-0.588(39)$, confirming non-zero $SU(3)$-breaking effects.
• The second-order correction to $f_1(0)$ is negative, with $f_1(0) = 0.953(24)$ at the physical point.
• The value of $|V_{us}|$ is determined as $0.219(27)_{\rm exp}(5)_{\rm theory}$, consistent with $K_{l3}$ decays and CKM unitarity.
• The lattice result contradicts predictions from both heavy baryon chiral perturbation theory and large $N_c$ analysis, which predict a positive second-order correction.