[Paper Review] K+-(mu3) Form Factors Measurement at NA48/2

M. Veltri|arXiv (Cornell University)|Jan 26, 2011

Particle physics theoretical and experimental studies1 references3 citations

TL;DR

This paper presents a high-precision preliminary measurement of $K^{\pm}_{\mu 3}$ form factors using 3.4 million events from the NA48/2 experiment at CERN. By applying quadratic, pole, and dispersive parametrizations, the study reports a scalar form factor slope consistent with other measurements and theory, with improved statistical precision due to simultaneous use of $K^+$ and $K^-$ beams.

ABSTRACT

We report here a measurement of form factors of $K^{\pm}_{μ3}$ decay by the NA48/2 experiment at CERN. Using a sample of 3.4$ imes10^6$ events we provide preliminary form factor values according to various parametrizations. The slope of the scalar form factor is in agreement with other measurements and theory predictions.

Motivation & Objective

• To measure the $K^{\pm}_{\mu 3}$ form factors with high precision using a large event sample.
• To test the consistency of the scalar form factor slope with theoretical predictions and other experimental results.
• To reduce systematic uncertainties by using both $K^+$ and $K^-$ decays in the analysis.
• To provide input for the precise determination of $|V_{us}|$ and for testing lepton universality and CKM unitarity.
• To lay the groundwork for higher-precision $K_{e3}$ form factor measurements in the NA62 experiment.

Proposed method

• The analysis uses a sample of 3.4 × 10⁶ $K^{\pm}_{\mu 3}$ events collected by the NA48/2 experiment at CERN's SPS.
• Events are selected via a track in the drift chamber (DCH), two LKr clusters consistent with $\pi^0$ decay, and muon identification using the MUV system and $E/p < 0.2$.
• Kinematical constraints are applied, requiring the missing mass squared to be less than 10 MeV² in the muon hypothesis.
• Background suppression is achieved via cuts on $m_{\pi^\pm\pi^0}$ and $\pi^0$ transverse momentum, reducing contamination to 0.6%.
• A fit to the Dalitz plot density is performed in 5 × 5 MeV² cells, correcting for acceptance, resolution, and radiative effects.
• Three parametrizations are used: quadratic, pole, and dispersive, with the dispersive form incorporating physical constraints and dispersion relations.

Experimental results

Research questions

• RQ1 What are the precise values of the $K^{\pm}_{\mu 3}$ form factor parameters using a large, high-statistics sample?
• RQ2 How do the measured form factor slopes compare with theoretical predictions and previous experiments?
• RQ3 To what extent does the inclusion of both $K^+$ and $K^-$ decays improve the precision of the form factor determination?
• RQ4 Can the dispersive parametrization, which incorporates physical constraints, provide a better description of the form factors than the quadratic or pole forms?
• RQ5 What is the expected precision gain in $K_{e3}$ form factor measurements using the same data sample in the NA62 experiment?

Key findings

• The quadratic fit yields $\lambda'_{+} = 30.3 \pm 2.7 \pm 1.4$ × 10⁻³ and $\lambda''_{+} = 1.0 \pm 1.0 \pm 0.7$ × 10⁻³, with the quadratic term consistent with zero.
• The pole parametrization gives $m_V = 836 \pm 7 \pm 9$ MeV/c² and $m_S = 1210 \pm 25 \pm 10$ MeV/c² for the vector and scalar pole masses, respectively.
• The dispersive parametrization yields $\Lambda_{+} = 28.5 \pm 0.6 \pm 0.7 \pm 0.5$ × 10⁻³ and $\ln C = 188.8 \pm 7.1 \pm 3.7 \pm 5.0$, with theoretical uncertainty included.
• The scalar form factor slope is found to be larger than in the previous NA48 measurement and agrees with other experimental and theoretical results.
• The analysis demonstrates improved precision by using both $K^+$ and $K^-$ beams, reducing systematic uncertainties.
• The same data sample is expected to yield a $K_{e3}$ sample of 4.2 × 10⁶ events, enabling higher-precision form factor measurements due to reduced parameter correlations.