The NA48/2 experiment at the CERN SPS collected in 2003 and 2004 large
samples of the decays K+- -> pi+ pi- e+- nu (Ke4+-), K+- -> pi0 pi0 e+- nu
(Ke400) and K+- -> pi0 pi0 pi+-. From the Ke4+- form factors and from the cusp
in the M00^2 distribution of the K+- -> pi0 pi0 pi+- events, the pi-pi
scattering lengths a00 and a20 could be extracted. This measurement is a
fundamental test of Chiral Perturbation Theory (ChPT). The branching fraction
and form factors of the Ke400 decay were precisely measured, using a much
larger data sample than in previous experiments. An improved measurement of the
slope parameters for the decay K+- -> pi0 pi0 pi+- showed evidence for a
non-zero value of k.Comment: Contribution to the proceedings of HQL06, Munich, October 16th-20th
  200

Masetti, L.

English

arXiv

The NA48/2 experiment at the CERN SPS collected in 2003 and 2004 large samples of the decays K+- -> pi+ pi- e+- nu (Ke4+-), K+- -> pi0 pi0 e+- nu (Ke400) and K+- -> pi0 pi0 pi+-. From the Ke4+- form factors and from the cusp in the M00^2 distribution of the K+- -> pi0 pi0 pi+- events, the pi-pi scattering lengths a00 and a20 could be extracted. This measurement is a fundamental test of Chiral Perturbation Theory (ChPT). The branching fraction and form factors of the Ke400 decay were precisely measured, using a much larger data sample than in previous experiments. An improved measurement of the slope parameters for the decay K+- -> pi0 pi0 pi+- showed evidence for a non-zero value of k.The NA48/2 experiment at the CERN SPS collected in 2003 and 2004 large samples of the decays K+- -> pi+ pi- e+- nu (Ke4+-), K+- -> pi0 pi0 e+- nu (Ke400) and K+- -> pi0 pi0 pi+-. From the Ke4+- form factors and from the cusp in the M00^2 distribution of the K+- -> pi0 pi0 pi+- events, the pi-pi scattering lengths a00 and a20 could be extracted. This measurement is a fundamental test of Chiral Perturbation Theory (ChPT). The branching fraction and form factors of the Ke400 decay were precisely measured, using a much larger data sample than in previous experiments. An improved measurement of the slope parameters for the decay K+- -> pi0 pi0 pi+- showed evidence for a non-zero value of k

Masetti, Lucia

CERN Document Server

Ke4 decays and Wigner cuspContribution to the proceedings of HQL06,Munich, October 16th-20th 2006Lucia Masetti1Institut fu¨r PhysikUniversita¨t MainzD-55099 Mainz, GERMANY1 IntroductionThe single-flavour quark condensate 〈0 |qq| 0〉 is a fundamental parameter of χPT ,determining the relative size of mass and momentum terms in the expansion. Sinceit can not be predicted theoretically, its value must be determined experimentally,e.g. by measuring the pipi scattering lengths, whose values are predicted very preciselywithin the framework of χPT , assuming a big quark condensate [1], or of generalisedχPT , where the quark condensate is a free parameter [2].The K+−e4 decay is a very clean environment for the measurement of pipi scatteringlengths, since the two pions are the only hadrons and they are produced close tothreshold. The only theoretical uncertainty enters through the constraint [3] betweenthe scattering lengths a20 and a00. In the K± → pi0pi0pi± decay a cusp-like structurecan be observed at M200 = 4m2pi+ , due to re-scattering from K± → pi+pi−pi±. Thescattering lengths can be extracted from a fit of the M200 distribution around thediscontinuity.2 Experimental setupSimultaneous K+ and K− beams were produced by 400 GeV energy protons from theCERN SPS, impinging on a beryllium target. The kaons were deflected in a front-end achromat in order to select the momentum band of (60± 3) GeV/c and focusedat the beginning of the detector, about 200 m downstream. For the measurementspresented here, the most important detector components are the magnet spectrom-eter, consisting of two drift chambers before and two after a dipole magnet and thequasi-homogeneous liquid krypton electromagnetic calorimeter. The momentum of1Present address: Physikalisches Institut, Universita¨t Bonn, D-53012 Bonn, GERMANY1arXiv:0704.1307v1  [hep-ex]  10 Apr 2007the charged particles and the energy of the photons are measured with a relativeuncertainty of 1% at 20 GeV. A detailed description of the NA48/2 detector can befound in Ref. [4].3 K± → pi+pi−e±νeThe K+−e4 selection consisted of geometrical criteria, like the requirement of havingthree tracks within the detector acceptance and building a good vertex; particle iden-tification requirements, based mainly on the different fraction of energy depositedby pions and electrons in the electromagnetic calorimeter; kinematical cuts for back-ground rejection, like an elliptical cut in the (pT ,M3pi) plane centered at (0,MK). Inorder to improve the pion rejection, the electron identification also included a LinearDiscriminant Analysis combining the three quantities with the highest discriminatingpower. Two reconstruction strategies can be applied to the K+−e4 events: either im-posing the kaon mass and extracting the kaon momentum from a quadratic equation,or imposing the kaon momentum to be the mean beam momentum (60 GeV/c alongthe beam axis) and extracting the kaon mass from a linear equation (see Fig. 1).10 210 310 450 52 54 56 58 60 62 64 66 68 70pK(GeV/c) )2 (GeV/ce4Km0.3 0.4 0.5 0.6 0.7 0.82Entries per 0.005 GeV/c110210310410510  datae4K MCe4KBackgroundFigure 1: Kaon momentum (left) and mass (right) of the K+−e4 events reconstructedwith a quadratic or a linear equation, respectively. The data (crosses) are comparedto signal MC (open histogram) plus background (yellow).Analysing part of the 2003 data, 3.7× 105 K+−e4 events were selected with a back-ground contamination below 1%. The background level was estimated from data,using the so-called “wrong sign” events, i.e. with the signature pi±pi±e∓νe, that, atthe present statistical level, can only be background, since the corresponding kaondecay violates the ∆S = ∆Q rule and is therefore strongly suppressed [5]. The mainbackground contributions are due to K± → pi+pi−pi± events with pi → eν or a pionmis-identified as an electron. The background estimate from data was cross-checkedusing Monte Carlo simulation (MC).23.1 Form factorsθθφνpipi+−K+e+pieFigure 2: Topology of the Ke4 decay.The form factors of the K+−e4 decay are parametrised as a function of five kinematicvariables [6] (see Fig. 2): the invariant masses Mpipi and Meν and the angles θpi, θeand φ. The matrix elementT =GF√2V ∗usu(pν)γµ(1− γ5)v(pe)(V µ − Aµ)contains a hadronic part, that can be described using two axial (F and G) and onevector (H) form factors [7]. After expanding them into partial waves and into a Taylorseries in q2 = M2pipi/4m2pi+ − 1, the following parametrisation was used to determinethe form factors from the experimental data [8, 9]:F = (fs + f′sq2 + f ′′s q4)eiδ00(q2) + fp cos θpieiδ11(q2)G = (gp + g′pq2)eiδ11(q2)H = hpeiδ11(q2).In a first step, ten independent five-parameter fits were performed for each bin inMpipi, comparing data and MC in four-dimensional histograms in Meν , cos θpi, cos θeand φ, with 1500 equal population bins each. The second step consisted in a fit of thedistributions in Mpipi (see Figs. 3,4), to extract the (constant) form factor parameters.The polynomial expansion in q2 was truncated according to the experimentalsensitivity. The dependence on Meν and the D-wave were found to be negligiblewithin the total uncertainty and the corresponding parameters were therefore set tozero. The δ = δ00 − δ11 distribution was fitted with a one-parameter function given bythe numerical solution of the Roy equations [3], in order to determine a00, while a20was constrained to lie on the centre of the universal band. The following preliminaryresult was obtained:f ′s/fs = 0.169± 0.009stat ± 0.034syst30.90.9511.051.11.151.21.250.28 0.3 0.32 0.34 0.36 0.38 0.4NA48/2 Ke4 PRELIMINARY statistical errors only’ ’ ’0.70.80.911.11.21.30.28 0.3 0.32 0.34 0.36 0.38 0.4NA48/2 Ke4 PRELIMINARY statistical errors only’-0.15-0.1-0.0500.050.10.28 0.3 0.32 0.34 0.36 0.38 0.4NA48/2 Ke4 PRELIMINARY statistical errors only-0.9-0.6-0.300.30.60.28 0.3 0.32 0.34 0.36 0.38 0.4NA48/2 Ke4 PRELIMINARY statistical errors onlyFigure 3: F , G and H dependence on Mpipi. The points represent the results of thefirst-step fits, the lines are fitted in the second step.f ′′s /fs = −0.091± 0.009stat ± 0.031systfp/fs = −0.047± 0.006stat ± 0.008systgp/fs = 0.891± 0.019stat ± 0.020systg′p/fs = 0.111± 0.031stat ± 0.032systhp/fs = −0.411± 0.027stat ± 0.038systa00 = 0.256± 0.008stat ± 0.007syst ± 0.018theor,where the systematic uncertainty was determined by comparing two independentanalyses and taking into account the effect of reconstruction method, acceptance, fitmethod, uncertainty on background estimate, electron-ID efficiency, radiative correc-tions and bias due to the neglected Meν dependence. The form factors are measuredrelative to fs, which is related to the decay rate. The obtained value for a00 is compat-ible with the χPT prediction a00 = 0.220±0.005 [10] and with previous measurements[11, 12].4 K± → pi0pi0e±νeAbout 10,000 K00e4 events were selected from the 2003 data and about 30,000 fromthe 2004 data with a background contamination of 3% and 2%, respectively. The400.10.20.30.40.50.28 0.3 0.32 0.34 0.36 0.38 0.4NA48/2 Ke4 PRELIMINARY Universal Band fit statistical errors onlyFigure 4: δ = δ00 − δ11 distribution as a function of Mpipi. The points represent theresults of the first-step fits, the line is fitted in the second step.selection criteria were similar to the ones used for the K+−e4 events, apart from therequirement of containing one track and 4 photons compatible with two pi0s at thesame vertex. The electron identification was based on the fraction of energy depositedin the electromagnetic calorimeter and on the width of the corresponding shower. Thebackground level was estimated from data by reversing some of the selection criteriaand was found to be mainly due to K± → pi0pi0pi± events with a pion mis-identifiedas an electron (see Fig. 5).2 in GeV/cKm0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.72Entries / 5 MeV/c110210310Signal MC00e4Kpi3K)γe3(KFigure 5: Invariant mass distribution in logarithmic scale of the K00e4 events selectedfrom the 2003 data (crosses) compared to the signal MC (red) plus physical (yellow)and accidental (blue) background.The branching fraction was measured, as a preliminary result from the 2003 data5only, normalised to K± → pi0pi0pi±:BR(K00e4 ) = (2.587± 0.026stat ± 0.019syst ± 0.029ext)× 10−5,where the systematic uncertainty takes into account the effect of acceptance, triggerefficiency and energy measurement of the calorimeter, while the external uncertaintyis due to the uncertainty on the K± → pi0pi0pi± branching fraction. This result isabout eight times more precise than the best previous measurement [13].For the form factors the same formalism is used as in K+−e4 , but, due to thesymmetry of the pi0pi0 system, the P -wave is missing and only two parameters areleft: f ′s/fs and f′′s /fs. Using the full data sample, the following preliminary resultwas obtained:f ′s/fs = 0.129± 0.036stat ± 0.020systf ′′s /fs = −0.040± 0.034stat ± 0.020syst,which is compatible with the K+−e4 result (see Fig. 6).s/fsf’0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22s/f sf’’-0.14-0.12-0.1-0.08-0.06-0.04-0.0200.02totσ 1e400K 68%e400Ktotσ 1e4+-K 68%e4+-KFigure 6: Comparison of the f ′s/fs and f′′s /fs measurements in K+−e4 and K00e4 .5 K± → pi0pi0pi±From 2003 data, about 23 million K± → pi0pi0pi± events were selected, with negligiblebackground. The squared invariant mass of the pi0pi0 system (M200) was computedimposing the mean vertex of the pi0s, in order to improve its resolution close tothreshold. At M200 = 4m2pi+ , the distribution shows evidence for a cusp-like structure(see Fig. 7, left) due to pipi re-scattering.602004006008001000120014001600x 10 20.08 0.09 0.1 0.11 0.12 0.132500030000350004000045000500000.076 0.077 0.078 0.079 0.08350036003700380039004000410042004300x 10 2-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8Figure 7: Left: M200 of the selection K± → pi0pi0pi± data events. The arrow indicatesthe position of the cusp. Right: angle between the pi± and the pi0 in the pi0pi0 centreof mass system. The points represent the data, the three curves, the MC distributionfor different values of k′Fitting the distribution with the theoretical model presented in Ref. [14] and usingthe unperturbed matrix elementM0 = A0(1 +12g0u+12h′u2 + 12k′v2),the following result was obtained [15], assuming k′ = 0 [16]:g0 = 0.645± 0.004stat ± 0.009systh′ = −0.047± 0.012stat ± 0.011systa2 = −0.041± 0.022stat ± 0.014systa0 − a2 = 0.268± 0.010stat ± 0.004syst ± 0.013theor,where the a0 − a2 measurement is dominated by the uncertainty on the theoreticalmodel.In a further analysis, the value of k′ was obtained from a fit above the cusp in theplane cos θ vs M200, where θ is the angle between the pi+ and the pi0 in the pi0pi0 centreof mass system. Evidence was found for a non-zero value of k′ (see Fig. 7, right):k′ = 0.0097± 0.0003stat ± 0.0008syst,where the systematic uncertainty takes into account the effect of acceptance andtrigger efficiency. Reweighting the MC with the obtained value of k′, the standard fitof the M200 distribution with the Cabibbo-Isidori model was performed to obtain thecusp parameters, that were found to be compatible with the published values.7References[1] G. Colangelo AIP Conf. Proc. 756, 60 (2005).[2] M. Knecht et al. Nucl. Phys. B 457, 513 (1995).[3] B. Ananthanarayan et al. Phys. Rept. 353, 207 (2001).[4] J. R. Batley et al. Phys. Lett. B 634, 474 (2006).[5] P. Bloch et al. Phys. Lett. B 60, 393 (1976).[6] N. Cabibbo and A. Maksymowicz Phys. Rev. 137, B438 (1965); Ibid. 168, 1926(1968).[7] J. Bijnens et al. 2nd DAΦNE Phisics Handbook, 315 (1995).[8] A. Pais and S. B. Treiman Phys. Rev. 168, 1858 (1968).[9] G. Amoros and J. Bijnens J. Phys. G 25, 1607 (1999).[10] G. Colangelo et al. Nucl. Phys. B 603, 125 (2001).[11] L. Rosselet et al. Phys. Rev. D 15, 574 (1977).[12] S. Pislak et al. Phys. Rev. D 67, 072004 (2003).[13] S. Shimizu et al. Phys. Rev. D 70, 037101 (2004).[14] N. Cabibbo and G. 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Ke4 decays and Wigner cusp

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