[Paper Review] KLOE results on kaon decays and summary status of Vus

T. Spadaro|ArXiv.org|Mar 19, 2007

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper presents high-precision KLOE measurements of kaon semileptonic decays to extract the CKM matrix element $V_{us}$, achieving a world-leading precision of $|V_{us}| = 0.2247(19)$, and confirms consistency with CKM unitarity ($\Delta = (-13 \pm 10) \times 10^{-4}$). The results are based on $2.5~\text{fb}^{-1}$ of data from the DA\PhiNE $\phi$-factory, using $K_{L}$, $K_{S}$, and $K^{\pm}$ decays to determine branching ratios, form factor slopes, and lifetimes with sub-percent accuracy.

ABSTRACT

Recent KLOE measurements allowing the extraction of the Vus element of the CKM matrix are here briefly described. The status of the resulting value of Vus is summarized. The perspectives for the completion of ongoing analyses are discussed, with particular emphasis on the measurements of scalar form factor slopes from study of KLmu3 and of Vus from the decay width of K+-l3.

Motivation & Objective

• To extract $V_{us}$ with high precision from semileptonic kaon decays using data from the KLOE experiment at DA\PhiNE.
• To test the unitarity of the CKM matrix by comparing $|V_{ud}|^2 + |V_{us}|^2 + |V_{ub}|^2$ to 1, with $|V_{ud}|$ from super-allowed beta decays.
• To resolve the long-standing discrepancy in $V_{us}$ values from $K_{e3}$ and $K_{\mu 3}$ decays by measuring form factor slopes and branching ratios with high accuracy.
• To assess $e/\mu$ universality in weak decays by comparing $G^2(\mu 3)/G^2(e3)$ ratios from $K_{L}$ and $K^{\pm}$ decays.
• To contribute to the determination of $|V_{us}/V_{ud}|$ via $K^{+} \to \pi^{+} \nu$ branching ratio measurements, improving the global CKM unitarity test.

Proposed method

• Measure absolute branching ratios of $K_{L} \to \pi^{-} \ell^{+} \nu$ and $K^{\pm} \to \pi^{0} \ell^{+} \nu$ using $K_{S}$ and $K_{L}$ tagging via $K_{S} \to \pi^{+} \pi^{-}$ and $K^{\pm}$ decays to $\mu\nu$ or $\pi\pi^{0}$.
• Use time-of-flight (TOF) and energy resolution of the EMC to reconstruct $K_{L}$ and $K^{\pm}$ decay vertices with sub-100 ps timing and ~1 MeV momentum resolution.
• Extract form factor slopes $\lambda_{+}$ and $\lambda_{0}$ from Dalitz plot distributions of $K_{L\mu 3}$ and $K_{Le3}$ decays using kinematic reconstruction.
• Determine $K_{L}$ and $K^{\pm}$ lifetimes from photon cluster timing in the EMC, with $\tau_{L} = 51.66(11)$ ns and $\tau_{+} = 12.367(44)(65)$ ns.
• Apply theoretical corrections: $S_{\rm EW}$ for electroweak effects and $\delta_{e3,\mu 3}$ for long-distance radiative corrections at the few-per-mil level.
• Use the Leutwyler-Roos value $f_{+}(0) = 0.961(8)$ to extract $|V_{us}|$ from $f_{+} \times |V_{us}|$ measurements.

Experimental results

Research questions

• RQ1 What is the precise value of $V_{us}$ extracted from KLOE's measurements of $K_{L}$ and $K^{\pm}$ semileptonic decays?
• RQ2 How do the form factor slopes $\lambda_{+}$ and $\lambda_{0}$ from $K_{L\mu 3}$ and $K_{Le3}$ decays affect the $V_{us}$ determination?
• RQ3 Is the $e/\mu$ universality of weak couplings confirmed by the ratio $G^2(\mu 3)/G^2(e3)$ in $K_{L}$ and $K^{\pm}$ decays?
• RQ4 Does the measured $|V_{us}/V_{ud}|$ from $K^{+} \to \pi^{+} \nu$ branching ratio agree with the world average and CKM unitarity?
• RQ5 What is the current status of the $V_{us}$ puzzle, and does KLOE's data resolve the discrepancy between $K_{e3}$ and $K_{\mu 3}$ determinations?

Key findings

• The KLOE experiment measures $|V_{us}| = 0.2247(19)$ from $f_{+} \times |V_{us}|$ values, with a relative uncertainty of 0.30% from $K_{Le3}$ and 0.36% from $K_{L\mu 3}$.
• The average $f_{+} \times |V_{us}| = 0.21595(50)$ is consistent with the world average and yields $\Delta = (-13 \pm 10) \times 10^{-4}$, indicating no significant deviation from CKM unitarity.
• The $e/\mu$ universality test yields $G^2(\mu 3)/G^2(e3) = 1.0059(83)$ for $K_{L}$ and $0.981(25)$ for $K^{\pm}$, both consistent with unity at the 1% level.
• The $K^{+} \to \pi^{+} \nu$ branching ratio is measured as $63.66(9)_{\rm st}(15)_{\rm sy}\%$, leading to $|V_{us}/V_{ud}| = 0.2286(^{+27}_{-15})$.
• A global fit combining $V_{ud} = 0.97377(27)$, $V_{us}$ from KLOE, and $|V_{us}/V_{ud}|$ yields $V_{us} = 0.2240(16)$ and $\Delta = 1.60(89) \times 10^{-3}$ with a $\chi^2$ probability of 53%, confirming consistency.
• The KLOE results reduce the $V_{us}$ puzzle: the discrepancy with the 2004 PDG value ($\Delta = -35 \pm 15 \times 10^{-4}$) is now only $1.3\sigma$, indicating improved agreement.