Recent results and prospects from NA48/2: K± → π0l±ν and K± → π+π−e±ν,K± → π0π0e±ν decays

Cristina Lazzeroni∗

School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom

Abstract

In 2003-2004 the NA48/2 Collaboration at CERN collected a large sample of K± decays. Using data taken withminimal trigger conditions, a sample of 2.5 × 106 K± → π0μ±ν and 4.0 × 106 K± → π0e±ν events was recorded,and allows precise measurements of the decay form factors. This report describes the event selection and the fittingprocedure, and gives a preliminary result for the form factors in various parameterizations. In addition, with thefull data sample collected, more than one million K± → π+π−e±ν and about 45000 K± → π0π0e±ν decays hasbeen analysed. An improved determination of the branching ratio and high precision form factor measurements forK± → π+π−e±ν, and a preliminary result for the branching ratio of K± → π0π0e±ν are presented in this paper. Futureprospects include the observation of several thousands decays in similar muonic modes that will be studied at theNA62 experiment.

Keywords: NA48, Kaon, Semileptonic decays, Form factors, Branching ratio

1. Beam and detector

Simultaneous K+ and K− beams were produced by400 GeV/c primary protons delivered by the CERNSPS and impinging on a beryllium target. The NA48/2beamline selected kaons with a momentum range of(60 ± 3) GeV/c. A detailed description of the beamlineand of the detector is available in [1]. The momentumof charged particles from K± decays was measured by amagnetic spectrometer consisting of four drift chambers(DCH1-DCH4) and a dipole magnet between DCH2and DCH3. Each chamber has eight planes of sensewires, two horizontal, two vertical and two along eachof the orthogonal 45 degrees directions. The spectrom-eter is located in a tank filled with helium at atmo-spheric pressure and separated from the decay volumeby a Kevlar window. A 16 cm diameter alluminium vac-uum tube centred on the beam axis runs the length of thespectrometer through central holes in the window, drift

∗On behalf of the NA48 Collaboration

chambers and calorimeters. Charged particles are mag-netically deflected in the horizontal plane by an anglecorresponding to a transverse momentum kick of 120MeV/c. The momentum resolution of the spectrome-ter is σ(p)/p = 1.02% ⊕ 0.044%p (p in GeV/c). Themagnetic spectrometer is followed by a scintillator ho-doscope. A liquid Krypton calorimeter (LKr) is usedto measure the energy of electrons and photons. Thecalorimeter is 27 X0 thick and has an energy resolutionσ(E)/E = 0.032/

√E⊕0.09/E⊕0.0042 (E in GeV). The

space resolution for single electromagnetic showers canbe parameterised as σx = σy = 0.42/

√E ⊕ 0.06 cm

for each transverse coordinate x, y. For the selection ofmuons, a muon veto system (MUV) was essential to dis-tinguish muons from pions. It consisted of three planesof alternating horizontal and vertical scintillator strips.Each plane was shielded by a 80 cm thick iron wall. Theinefficiency of the system was at the level of one per milfor muons with momentum greater than 10 GeV/c andthe time resolution was below 1 ns.

Available online at www.sciencedirect.com

Nuclear Physics B (Proc. Suppl.) 233 (2012) 192–197

0920-5632/ © 2013 CERN. Published by Elsevier B.V. All rights reserved.

www.elsevier.com/locate/npbps

doi:10.1016/j.nuclphysbps.2012.12.076

© CERN for the benefit of the NA48 Collaboration.

2. The K± → π0 l±ν decays

Semileptonic kaon decays (denoted as Kl3 in the fol-lowing, with l = e, μ) provide the most accurate way andfree of theoretical uncertainties, to measure the CKMmatrix element |Vus| [2]. To extract |Vus|, the knowledgeof the decay form factors is crucial: since the form fac-tors determine the Dalitz plot structure, both the detec-tor acceptance (needed to measure the decay rate) andthe phase space integral (needed to derive |Vus| from thedecay rate) heavily depend on the form factors. Thehadronic matrix element of Kl3 decays is described bytwo dimensionless form factors f±(t), which depend onthe squared four-momentum t = (pK − pπ)2 transferredto the lepton system. The K± decays are usually de-scribed in terms of the vector form factor f+ and thescalar form factor f0 defined as [2]:

f0(t) = f+(t) +t

m2K − m2

π

f−(t).

The functions f+ and f0 are related to the vector(1−) and scalar (0+) exchange to the lepton system, re-spectively. The contribution of f− can be neglected inKe3 decays since it is proportional to the lepton masssquared. By construction f0(0) = f+(0). Since f+(0) isnot directly measurable, it is customary to normalise allform factors to this quantity, so that:

f̄+(t) =f+(t)f0(t)

; f̄−(t) =f−(t)f0(t).

To describe the form factors, two different parameteri-sations are used in this report. Widely known and mostused is the Taylor expansion, called quadratic parame-terisation in the following:

f̄+,0(t) = 1 + λ′+,0t

m2π

+12λ′′+,0

t2

m4π

where λ′ and λ′′ are the slope and the curvature ofthe form factors, respectively. The disadvantage of thisparameterisation is related to the strong correlations be-tween the parameters and the absence of a direct physi-cal interpretation. To reduce the number parameters andto add a physical motivation, the pole parameterisationis used:

f̄+(t) =M2

V

M2V − t

; f̄0(t) =M2

S

M2S − t

.

Here, the dominance of a single vector (V ) or scalar(S) resonance is assumed and the corresponding polemass MV or MS is the only free parameter.

The data used for the form factor analysis presentedhere were collected in 2004 during a dedicated runwith a special trigger setup which required one ormore tracks in the magnetic spectrometer and an en-ergy deposit of at least 10 GeV/c in the electromagneticcalorimeter. Besides, the intensity of the beam was low-ered and the momentum spread was reduced. The NA48detector measures only the charged lepton and the twophotons from the π0 decay, while the neutrino leaves thedetector unseen. To select the decay, one track in themagnetic spectrometer and at least two clusters in theelectromagnetic calorimeter were required. The trackhad to be inside the geometrical acceptance of the de-tector, and needed a good reconstructed decay vertex,proper timing and a momentum greater than 5 GeV/cin case of electrons. For muons the momentum neededto be greater than 10 GeV/c to ensure high MUV effi-ciency. To identify the track as a muon, an associatedhit in the MUV system and E/p < 0.2 was required,where E is the energy deposited in the LKr calorimeterand p is the track momentum. For electrons a range of0.95 < E/p < 1.05 and no associated hit in the MUVsystem were required. The neutral pions were recon-structed by two photon clusters in the LKr calorimeter,with an energy Eγ > 3 GeV/c, well isolated from anytrack hitting the calorimeter, and in time with the trackin the spectrometer. Finally, the missing mass squaredwas required to satisfy m2

miss < (10MeV/c2)2 under a K±hypothesis.

For K±e3, the only significant background is from

K± → π±π0. A cut in the transverse momentum of theevent reduces this background to less than 0.1% whilelosing only about 3% of the signal. For K±

μ3 the back-ground from K± → π±π0 with π± decaying in flight issuppressed by using a combined requirement on the in-variant mass m(π±π0) (under π± hypothesis) and on theπ0 transverse momentum. This cut reduces the contam-ination to 0.5%, but causes a loss of statistics of about24%. Another background source is K± → π±π0π0

events with π± decaying in flight and one π0 not recon-structed. Its contribution is estimated to be only about0.1% and therefore no specific cut was applied. To ex-tract the form factors, two-dimension fits to the Dalitzplot densities ρ(E∗

l , E∗π) are performed:

ρ(E∗l , E

∗π) =

d2N(E∗l , E

∗π)

dE∗l dE∗

π

≈ A f 2+ (t) + B f+(t)( f+(t) − f0(t))

m2K − m2

π

t

+C[( f+(t) − f0(t))m2

K − m2π

t]2

C. Lazzeroni / Nuclear Physics B (Proc. Suppl.) 233 (2012) 192–197 193

To obtain the lepton and pion energies E∗l and E∗

π inthe kaon rest frame, the reconstructed lepton and pionfour-momenta are boosted into the kaon rest frame. Thekaon energy is computed from the decay products, as-suming no transverse component of the momentum ofthe kaon. This leaves two solutions for the longitudinalcomponent of the neutrino momentum, from which theone closer to 60 GeV/c is used. In this way the energyresolution in the Dalitz plot, in particular for high pionenergies, is greatly improved. The reconstructed Dalitzplots are then corrected for remaining background, de-tector acceptance and distortions induced by radiativeeffects. The radiative effects are simulated by using aspecial Monte Carlo generator developed by the KLOEcollaboration[3]. This generator gives the same correc-tions as a recent calculation within Chiral PerturbationTheory with fully inclusive real photon emission[4]. Forthe purpose of the fit, the Dalitz plots were subdividedinto cells of 5 MeV × 5 MeV; cells which crossed orare outside the kinematical borders are not used in thefit. The fit results for the quadratic and the pole param-eterisations are listed in Tables 1 and 2. The systematicuncertainties are evaluated by changing the cuts defin-ing the vertex quality and the geometrical acceptanceby small amounts. In addition, variations to the reso-lutions of pion and muon energies in the kaon centreof mass system are applied; the pion decay backgroundis varied and the differences in the results of two inde-pendent analyses done in parallel are taken into account.For comparison the combined K±

l3 quadratic fit results asreported by recent experiments[2] are shown in Fig. 1.The 68% confidence level contours are displayed forboth neutral (KLOE, KTeV and NA48) and chargeddecays (ISTRA+ studied K− only). The preliminaryNA48/2 results presented here are the first high preci-sion measurements done with both K+ and K− mesons.The form factors are in good agreement with the mea-surements done by the other experiments (except theneutral channel from NA48[5]) and compatible with thecombined fit done by FlaviaNet[2].

λ′+[10−3] λ′′+[10−3] λ0+[10−3]

K±e3 27.2±0.7±1.1 0.7±0.3±0.4

K±μ3 26.3±3.0±2.2 1.2±1.1±1.1 15.7±1.4±1.0

tot 27.0±1.1 0.8±0.5 16.2±1.0

Table 1: Preliminary form factor fit results for the quadratic with sta-tistical and systematic uncertainties. For the combined (tot) resultboth uncertainties were combined.

MV [MeV/c2] MS [MeV/c2]K±

e3 879±3±7K±μ3 873±8±9 1183±31±16

tot 877±6 1176±31

Table 2: Preliminary form factor fit results for the pole parameteriza-tions with statistical and systematic uncertainties. For the combined(tot) result both uncertainties were combined.

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Figure 1: Combined quadratic fit results for Kl3 decays. The ellipsesare 68% confidence level contours. For comparison the combined fitfrom the FlaviaNet kaon working group is shown [2].

3. The K± → π+π−e±ν decays

The kinematics of the K± → π+π−e±ν decayis described by the five Cabibbo-Maksymowicz vari-ables [6]: the square of the di-pion invariant mass S π,the square of the di-lepton invariant mass S e, the an-gle θπ of the π± in the di-pion rest frame with respectto the flight direction of di-pion in the kaon rest frame,the angle θe of the e± in the di-lepton rest frame withrespect to the flight direction of di-lepton in the kaonrest frame, and the angle Φ between the di-pion and di-lepton planes in the kaon rest frame. The decay ampli-tude is the product of the leptonic weak current and thehadronic current. The hadronic current is described interms of three (F,G,R) axial- vector and one (H) vec-tor complex form factors. The sensitivity of the decaymatrix element to the form factor R is negligible due tothe small mass of the electron. These form factors maybe developed in a partial wave expansion with respectto the variable cosθπ:

F = Fseiδ fs + Fpeiδ fp cosθπ + Fdeiδ fd cos2θπ + ...

G = Gpeiδgp cosθπ +Gdeiδgd cos2θπ + ...

H = Hpeiδhp cosθπ + Hdeiδhd cos2θπ + ...

C. Lazzeroni / Nuclear Physics B (Proc. Suppl.) 233 (2012) 192–197194

Limiting the expansion to S- and P-waves and con-sidering a unique phase δp for all P-wave form factorsin absence of CP violating weak phases, one will obtainthe decay probability, that depends only on the form fac-tor magnitudes Fs, Fp, Gp, Hp, the single phase differ-ence δ = δs − δp and kinematic variables. The form fac-tors can be expressed as a series expansion of the dimen-sionless invariants q2 = (S π/4m2

π) − 1 and S e/4m2π [7].

Two slope and one curvature terms are sufficient to de-scribe the measured Fs form factor variation within theavailable statistics:

Fs/ fs = 1 + f ′s/ fsq2 + f ′′s / fsq4 + f ′e S e/ fs4m2π

while two terms are enough to describe the Gp form fac-tor:

Gp/ fs = gp/ fs + g′p/ fsq2

and two constants to describe the Fp and Hp form fac-tors. A high precision measurement of the normalisedform factor parameters (divided by fs as shown above)has been published by NA48/2 [8]. The measurementof their absolute values requires the measurement of thebranching fraction. Recently a new measurement of theK± → π+π−e±ν branching ratio by NA48/2 has beenpublished in [9]. Here only a summary description ofthe measurement is given.

The K± → π+π−e±ν rate is measured relative toK± → π±π+π− normalization channel. The two sam-ples were collected concurrently using the same trigger.The branching ratio (BR) is obtained as

BR(K±e4) =

Ns − Nb

Nn

AnεnAsεs

BR(K3π)

where Ns, Nb and Nn are the numbers of signal, back-ground and normalization candidates. As and εs are theacceptance and trigger efficiency for the signal sample,while An and εn are those for the normalization events.The signal and normalization data samples were se-lected if having three reconstructed charged tracks intime with the corresponding hodoscope signals. Thethree-track reconstructed vertex of the ±1 total chargewas required to lie within 5 cm of the beam axis, andits longitudinal position was required to be between 2m and 95 m downstream of the final collimator. Themaximum momentum sum was set at 70 GeV/c. Allvertex tracks were required to be within the spectrom-eter, hodoscope, LKr and muon veto acceptances. Thedistance between any two tracks at DCH1 was requiredto be larger than 2 cm, and the distance between anytrack and the beam mean position (monitored with aseparate sample of K± → π±π+π− decays) was largerthan 12 cm. The minimum distance between the track

impact at the LKr front face and the nearest LKr deadcell was required to be at least 2 cm. The track-to-track distance at the LKr front face had to be larger than20 cm to prevent shower overlaps. No in-time track-associated hits were allowed in two planes of the muonveto. The vertex with the lowest fit χ2 was selected. Atrack with p > 2.75 GeV and 0.9 < E/p < 1.1 was iden-tified as electron/positron, while the track with p > 5GeV and E/p < 0.8 was regarded as a pion. A cuton the value of a dedicated linear discriminant variablebased on shower properties has been applied, to rejectevents with one misidentified pion. Kaon candidateswere then selected among the vertices with a single elec-tron/positron candidate and a pair of opposite-chargedpions. To suppress the K± → π±π+π− background, thevertex invariant mass M3π in the π±π+π− hypothesis andits transverse momentum were required to be outsidean ellipse centred at the PDG kaon mass [10] and zerotransverse momentum, with semi-axes of 20 MeV/c2

and 35 MeV/c, respectively. The square missing massof K± → π±X decay was required to be larger than0.04 (Gev/c2)2 to reject π±π0 decays with a subsequentπ0 → e+e−γ process. The invariant mass of any pos-sible electron-positron system was required to be morethan 0.03 GeV/c2 in order to reject photon conversions.For K± → π+π−e±ν events, the reconstruction of thekaon momentum assuming a four-body decay with theundetected neutrino was implemented, and the solutioncloser to 60 GeV/c was chosen. For the normalizationchannel the vertex was required to be composed of threecharged pions. M3π and transverse momentum were re-quired to be inside an ellipse with semi-axes 12 MeV/c2

and 25 MeV/c, respectively. Events with reconstructedkaon momentum between 54 and 66 GeV/c were keptfor further analysis. A total sample of about 1.1 millioncandidates and about 19 millions of prescaled normal-ization candidates were selected from data recorded in2003-2004.

There are two main background sources: K± →π±π+π− decays with subsequent π→ eν decay or a pionmis-identified as an electron; and K± → π0(π0)π± withsubsequent π0 → e+e−γ decay with undetected photonsand an electron mis-identified as a pion. The back-ground contamination was estimated from the wrongsign events (two same sign pions), which can only bebackground. To estimate the right sign part of the back-ground in the selected sample, the number of wrong signevents were multiplied by 2, as the dominant contri-bution comes from K± → π±π+π− decays, as is con-firmed by Monte Carlo simulation. The total back-ground contribution is below 1%. A detailed GEANT3-based Monte Carlo simulation was used to take into ac-

C. Lazzeroni / Nuclear Physics B (Proc. Suppl.) 233 (2012) 192–197 195

count full detector geometry, DCH alignment, local in-efficiencies and beam properties. Sources of systematicuncertainties include acceptance stability, muon veto ef-ficiency, accidental activity in detectors, particle iden-tification, background estimate procedure, radiative ef-fects modelling, trigger efficiency and Monte Carlo sim-ulation statistical error.

The resulting branching fraction is measured to be 3times more precise than the current value [10]:

BR(K± → π+π−e±ν) =

(4.257 ± 0.004stat ± 0.016syst ± 0.031ext) × 10−5.

The external error, caused by the uncertainty of the nor-malization channel branching fraction, is the dominanterror of the measurement. The measured branchingfraction has been used to extract the normalization formfactor fs = 5.705±0.003stat±0.017syst±0.031ext and allthe absolute values of hadronic form factor parameter-ization constants are shown in Table 3. Normalizationerrors are fully correlated. A large anticorrelations existbetween f ′ and f ′′ (-0.954) as well as between gp andg′p (-0.914).

value Stat. Syst. Norm.f ′s 0.867 0.040 0.029 0.005f ′′s -0.416 0.040 0.034 0.003f ′e 0.388 0.034 0.040 0.002fp -0.274 0.017 0.023 0.002gp 4.952 0.057 0.057 0.031g′p 0.508 0.097 0.074 0.003hp -2.271 0.086 0.046 0.014

Table 3: Form factors with statistical, systematic and normalizationuncertainties, after using the measurement of fs.

4. The K± → π0π0e±ν decays

For K± → π0π0e±ν decays, due to restrictions ofsymmetry, the matrix element does not depend on θπand Φ angles, and it is parametrized just in terms ofthe only form factor Fs that in the general case maydepend on S π and S e. The rate is measured relativeto K± → π0π0π± normalization channel. These twosamples are collected with the same trigger of high ef-ficiency for the corresponding event topology. A com-mon event selection was considered as far as possible.Events with at least four γs detected by LKr, and at leastone track, reconstructed from spectrometer data, wereregarded as candidates. Every combination of two γ

pairs, detected by LKr, was considered as a pair of π0s.Reconstructed longitudinal positions of both π0 → γγdecay candidates were required to coincide within 500cm, and their average position Zn to be in the fiducialvolume. Decay longitudinal position Zch, assigned toevery track, was defined as the closest distance approachbetween the track and the beam axis. A combined ver-tex, composed of four LKr clusters and one chargedtrack, was required to have the difference between thesetwo measured longitudinal positions |Zn − Zch| less than800 cm. Pion and electron identification was the sameas in charged case.

The K± → π0π0e±ν and K± → π0π0π± decayswere discriminated by means of elliptic cuts in the(Mπ0π0π± , pt) plane, where Mπ0π0π± is the invariant massof the combined vertex in the 3π hypothesis, and pt

is the transverse momentum. The elliptic cut sepa-rates about 70 million normalization events from 45000K± → π0π0e±ν candidates. The residual fake-electronbackground is estimated to be about 1.3% of the signal.Background from K± → π0π0π± with the subsequentπ± → e±ν is only 0.1% of the signal. For the calcu-lation of the K± → π0π0π± acceptance, the NA48/2empirical parameterization of its Dalitz plot [11] hasbeen used. For the K± → π0π0e±ν decay mode, theNA48/2 result [12] for Fs parameterization has beenused, since it well describes also K± → π0π0e±ν decaysfor S π > (2mπ± )2.

Following the notation decsribed in the previoussection, and using the obtained acceptance valuesAs =1.77% and An= 4.11% and the value of the nor-malization channel branching fraction from [10], thepreliminary result has been obtained:

Br(K± → π0π0e±ν) =

(2.595 ± 0.012stat ± 0.024syst ± 0.032ext) × 10−5.

This measurement is 10 times more precise thanthe current PDG corresponding value [10]. System-atic errors include the contributions from backgrounduncertainty, simulation statistical error, sensitivity toform factors, radiative corrections, trigger efficiencyand beam geometry uncertainties. The external errorcomes from the uncertainty on the normalization chan-nel branching fraction.

5. Future prospects

The NA62 experiment, using the same beam line anddetector of NA48/2, collected data in 2007 to performtests of Lepton Flavour Universality. The collected datasample contain about 40 × 106 K+e3 and 20 × 106 K+μ3

C. Lazzeroni / Nuclear Physics B (Proc. Suppl.) 233 (2012) 192–197196

events, respectively. A special KL run was also taken,providing further K0

e3 and K+μ3 samples of about 4 × 106

events each. Therefore NA62 will be able to achievean higher statistical precision measurements of the formfactors of all Kl3 channels as available already today.

Improved measurements of K± → π+π−e±ν andK± → π0π0e±ν branching ratios have been presentedhere. The study of the form factors for the neutral chan-nel is in progress and will complete the high-precisionpicture of K± → ππe±ν decays. While the above anal-yses are published or close to completion and shouldappear shortly in final publications, future prospects in-clude the observation of several thousand decays in sim-ilar muonic modes: K± → π0π0μ±ν (never observed)and K± → π+π−μ±ν (7 events observed) [13]. Suchpoorly known modes could be studied also in the forth-coming NA62 experiment currently under construction.

References

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[10] Review of Particle Physics (RPP), Phys. Rev. D 86 (2012)010001.

[11] J. Batley et al., Phys. Lett. B 686 (2010) 101-108.[12] J. Batley et al., Eur. Phys. J. C 70 (2010) 635-657.[13] V. Bisi, R. Cester, A. Marzari-Chiesa, M. Vigone, Phys. Lett. B

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