RECENT QCD-RELATED RESULTS FROM KAON PHYSICS AT CERN (NA48/2 AND NA62) ∗

The NA48/2 experiment presents a preliminary result of K ± l decays form factors measurement based on the 4 . 28 × 10 6 K ± e 3 and 2 . 91 × 10 6 K ± µ 3 selected decays collected in 2004. The result is competetive with other measurements in K ± µ 3 mode and has a smallest uncertainty for K ± e 3 , that leads to the most precise combined K ± l 3 result and allows to reduce the form factor uncertainty of | V US | . The NA62 experiment collected a large sample of charged kaon decays with a highly eﬃcient trigger for decays into electrons in 2007. A ﬁnal result of a new measurement of the electromagnetic transition form factor slope of the neutral pion in the time-like momentum region from the 1 . 11 × 10 6 fully reconstructed π 0 Dalitz decays is presented in the second part of this article.


Introduction
The main purpose of the NA48/2 experiment at the CERN SPS was a search for the direct CP violation in K ± decay to three pions [1].The experiment used simultaneous K + and K − beams with momenta of 60 GeV/c propagating through the detector along the same beam line.
The main components of the NA48/2 detector were a magnetic spectrometer, composed by four drift chambers and a dipole magnet deflecting the charged particles in the horizontal plane, and a liquid krypton electromagnetic calorimeter (LKr) with an energy resolution of about 1% for 20 GeV photons and electrons.For the selection of K ± µ3 decays, a muon veto system (MUV) was essential to distinguish muons from pions.
The data used for the form factors (FF) analysis were collected in 2004 during a dedicated run with a special trigger setup which required one or more tracks in the magnetic spectrometer and an energy deposit of at least 10 GeV/c in the electromagnetic calorimeter.
The NA62 experiment collected data during 2007, using the NA48/2 detector, aiming at measuring the ratio R K of the rates of the leptonic kaon decays.The experiment used modified beam central momentum of 74 GeV/c and different trigger conditions optimized to collect electrons.

K l3 form factors
Semileptonic kaon decays K ± → π 0 l ± ν (K l3 ) offer the most precise determination of the CKM matrix element |V US | [2] that require both a branching ratio and a FF experimental measurement.K l3 precision FF measurement results based on the NA48/2 data analysis are presented here.
The K l3 decay width in the absence of electromagnetic effects can be represented by the Dalitz plot density depending on the lepton and pion energies in the kaon rest frame E l and E π respectively [3] where t = (P Here, f + (t) and f 0 (t) are the so-called vector and scalar K l3 FF, respectively.m K is a mass of K + , m π is a mass of π 0 and m π + is a mass of π + .Definitions of the implemented parameterizations are shown in Table I: the quadratic [4] parameterization (fit parameters λ + , λ + , λ 0 ), the pole [5] (fit parameters M V , M S ) and the dispersive [6] one (fit parameters Λ + , ln[C]).

K l3 events reconstruction and selection
The data selection requires one track in the magnetic spectrometer and a time coincidence with at least two clusters in the LKr from a π 0 decay.The track had to be inside the geometrical acceptance of the detector, and needed a proper timing and a momentum p > 5 GeV/c in the case of electrons.For muons, the momentum needed to be greater than 10 GeV/c to ensure a proper efficiency of the MUV system.To identify a track as an electron, we require 2.0 > E/p > 0.9, where E is the energy deposited in the LKr and p is the momentum measured in the spectrometer, and no signal in the MUV system.To identify the track as a muon, we require an associated hit in the MUV system and E/p < 0.9.
Longitudinal K l3 decay position Z n (neutral vertex Z coordinate) is defined as a longitudinal position of a π 0 decay reconstructed from LKr data assuming the PDG [7] value for π 0 mass.The transverse neutral vertex coordinates (X n , Y n ) are calculated as the impact point position of the reconstructed charged track on the Z n plane.
For a kaon momentum (P K ) measurement, we direct the Z axis along the beam average position in space, measured from K ± → π ± π + π − data.In the assumptions of m(ν) = 0 and kaon flight along the beam axis, two solutions of quadratic equation for P K exist, and the closest to average beam momentum value is chosen.
The background contribution has been estimated by means of the Monte Carlo simulation (MC).For K e3 , the background from K ± → π ± π 0 (2π) significantly contributes to the selected sample.A cut on the neutrino transverse momentum P t (ν) ≥ 0.03 GeV/c is reducing this background below 0.027%.
The total statistics of selected data is 4.28 × 10 6 events for K e3 , and 2.91 × 10 6 events for K µ3 selection.

Fit procedure and preliminary K l3 form factor results
To extract FF, an events-weighting fit is performed for the Dalitz plots defined with 5×5 MeV cells of E π 0 versus E l energies in the kaon rest frame.The K e3 and K µ3 Dalitz plots were fitted simultaneously with a common set of the fit parameters.MINUIT [8] package and ROOT [9] interface were used to minimize χ 2 by means of the FF parameters variation, and in such a way the resulting parameter central values, their errors (Table II) and correlation coefficients (Table III) were found.The largest contributions to the systematic uncertaity are related to the beam shape and LKr measurement precision.The fit quality is defined by the following values of χ 2 /n.d.f.: 1004.6/1073 for the quadratic parameterization, 1001.1/1074 for the pole and 998.3/1074 for the dispersive one.

π 0 transition form factor
The decay π 0 D → e + e − γ with a branching fraction of Br = (1.174± 0.035)% [7] proceeds through a π 0 → γγ * process with an off-shell photon converting into an e + e − pair.The π 0 electromagnetic transition form factor (TFF) describes the deviation of this transition from a point-like interaction.
Kinematic variables x and y, commonly used to describe the Dalitz decay kinematics, are defined in terms of particle four-momenta The limits on the variables are given by: r ≤ x ≤ 1, −β ≤ y ≤ β, where x .The normalised π 0 D differential decay width reads where F (x) stands for the π 0 electromagnetic TFF, and δ(x, y) represents radiative corrections to the π 0 D decay.The form factor F (x) is expected to vary slowly in the allowed kinematic region and is parametrised by a linear expression F (x) = 1 + ax, where a is the so-called TFF slope parameter.

Final result of the π 0 TFF slope
The extraction of the π 0 TFF slope from the selected data sample is based on a comparison between the data distribution of the reconstructed x variable, and MC distributions corresponding to different TFF slope values used at the MC generator level.The fit result corresponds to the MC distribution with the best data/MC agreement.Both MC simulation samples (K 2πD and K µ3D ) are included in the MC distribution, since they both contain genuine π 0 Dalitz decays.Selected events were divided into equipopulous bins and a χ 2 test was used for the data/MC histogram comparison.The fit result was then obtained by the χ 2 minimisation.
The most important systematic uncertainties originate from an imprecise simulation of the beam momentum spectrum width, and from the result sensitivity to the spectrometer momentum scale calibration.The NA62 final result for the π 0 TFF slope reads [10] a = (3.68 ± 0.51 stat ± 0.25 syst ) × 10 −2 = (3.68 ± 0.57) × 10 −2 , with χ 2 /n.d.f.= 54.8/49, and a p-value of 0.26.The result improves the precision on the π 0 TFF in the time-like momentum region.

Conclusion
K l3 form factors measurement is performed by NA48/2 experiment on the basis of 4.28 × 10 6 K ± e3 and 2.91 × 10 6 K ± µ3 events selected from 2004 run data.Result is competetive with the other ones in K ± µ3 mode, and a smallest error in K ± e3 has been reached that gives us also the combined result with the smallest error.
The π 0 transition form factor slope parameter is measured using the NA62 experiment data set from 2007.About 1.11 million fully reconstructed π 0 Dalitz decays were selected and studied.The obtained result a = (3.68 ± 0.57) × 10 −2 confirms a positive π 0 TFF slope value with a significance exceeding 6σ.The measured value is compatible with the theoretical predictions.