Semileptonic Hyperon Decays

TL;DR

Hyperon semileptonic decays are analyzed within the Cabibbo SU(3) framework to determine the CKM element $V_{us}$ and test unitarity. Theoretical treatment focuses on vector and axial form factors, with the Ademollo-Gatto theorem constraining $f_1(0)$ corrections to SU(3) breaking, enabling a robust extraction of $V_{us} f_1(0)$. A global fit to four hyperon decays yields $V_{us}=0.2250\pm0.0027$, and neutron data fix $F+D=1.2670\pm0.0030$, indicating excellent agreement with CKM unitarity and minimal observed SU(3) breaking. The study highlights the need for lattice QCD to quantify SU(3) breaking and calls for further experiments to resolve residual tensions with $K_{l3}$ determinations, strengthening the overall test of the Standard Model flavor sector.

Abstract

We review the status of hyperon semileptonic decays. The central issue is the $V_{us}$ element of the CKM matrix, where we obtain $V_{us}=0.2250 (27)$. This value is of similar precision, but higher, than the one derived from $K_{l3}$, and in better agreement with the unitarity requirement, $|V_{ud}|^2+|V_{us}|^2+|V_{ub}|^2=1$. We find that the Cabibbo model gives an excellent fit of the existing form factor data on baryon beta decays ($χ^{2} = 2.96$ for 3 degrees of freedom) with $F + D = 1.2670 \pm 0.0030$, $F - D = -0.341 \pm 0.016$, and no indication of flavour-SU(3)-breaking effects. We indicate the need of more experimental and theoretical work, both on hyperon beta decays and on $K_{l3}$ decays.

Figures (8)

• Figure 1: Plan view of the E715 apparatus, with typical particle trajectories. The incident proton-beam angle corresponds to a positive targeting angle in the horizontal plane. Note that the X and Z scales are different.
• Figure 2: The KTeV Detector
• Figure 3: The $\Sigma^{+} \rightarrow p\, \pi^{0}$ mass peak, after all selection criteria have been applied. The background to the left of the peak is due to $\Xi^{0} \rightarrow \Lambda\, \pi^{0}$ decays ( followed by $\Lambda \rightarrow p\, \pi^{-}$ or $\Lambda \rightarrow p e^{-}\overline{\nu}_e$ ). Since $\Xi^{0} \rightarrow \Sigma^{+}\, e^{-}\, \overline{\nu}_{e}\,\,$ is the only source of $\Sigma^{+}\,$ in the beam ($\Xi^{0} \rightarrow \Sigma^{+} \, \pi^{-}\,$ is kinematically forbidden), signal events are identified by having a $p$-$\pi^{0}\,$ mass within 15 $\mathrm{MeV}$ of the nominal $\Sigma^{+}\,$ mass.
• Figure 4: The three variables used to fit $g_1 / f_1\,$ and $g_2 / f_1\,$, and the energy spectrum of the electron in the $\Sigma^{+}\,$ frame (used to determine $f_2 / f_1\,$ ). The points are data and the histogram is a Monte Carlo simulation with $g_1 / f_1\,$$= 1.27$ and $\hbox{$g_2 / f_1\,$} = 0.$
• Figure 5: Confidence interval plot for $f_1$ and $g_1$. The inverted triangle is exact SU(3) symmetry; the star indicates the KTeV value. Solid circles and squares are SU(3) breaking fits from ratand Flores-Mendieta:1998ii respectively.