Rencontres de Moriond 2008

NEW RESULTS ON KAON DECAYS FROM NA48/2

CRISTINA MORALES MORALES" Institut fiir Physik. JohannP.s GntrnhP.r_g- Uni11P.rsitiit, 5.'i0.9.9 Mainz, GP.rmn.ny

E-mn.il: r:moralP.s@mail. r.P.rn .. r.h

Recent results from the NA~8/2 experiment are presented. The 71"11' scattering lengths ag and a~ have been extracted from the cusp in lhe i\,JJ0 distribution of K± __. 71'±71'

071'

0 decays and from the K± -> 71' 171'- e±u phase shift o. Branching ratios and form fat"tors have been measured for K± ---> 11'=."'f"'f, K± -+ 'll'±"'f e 1 e- and K± -> 1T±e 1 e- decays and arr. also summarized hcrl'.

1 Introduction

During 2003 and 2004, the NA48/2 experiment at CERN SPS has collected the world largest amount of charged kaon decays. The main goal of NA48/2 was the search for direct CP violation in K:r. decays into three pions. However, given the high statistics achieved, many other physics topics were also covered including the study of the rrrr interaction at low energy, radiative decays, the measurement of V11 •• from semileptonic decays, etc .. In the following sections. recent results on ChPT parameters obtained by the NA48/2 Collaboration wili be presented.

2 The NA48/2 experiment

Simultaneous K+ and K- beams were produced by 400 GeV protons from the CERN SPS, impinging on a Be target. Kaons were deflected in a front-end achromat to select a momentum band of 60 ± 3 GeV /c and then focused such that they converge about 200 m downstream at. the beginning of the detector. A description of the detector can be found in 1. For the measurements presented here, the most important detector components are the magnet spectrometer, consisting of two drift chambers before and two after a dipole magnet, and the quasi-homogeneous liquid krypton calorimeter. The momentum of the charged particles and the energy of the photons are measured with a relative uncertainty of 13 at 20 GeV. The trigger was mainly designed to select events with three charged tracks (charged trigger) and K±--> rr±rr0 rr0 events (neutral trigger).

"On behalf of the l\A-18/2 Collaboration.

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Figure I: (Left) Invariant 7ru7ru mass sqnarcrl of K= _, 7r =7r0 7r0 candidates. '.'\olc the rrcsP.ncr. of a cusp for M'5o = 4m~- (arrow). (Right) Variation of phase shift in K± _, 11"-+11"-e=v decays with 7r-7r- invariant mass

3 Measurement of 7r7r scattering lengths

The quark condensate (Olqq!O) is a fundamental parameter of ChPT. Its value must be deter­mined experimentally, e.g. by measuring the 7r7r scattering lengths a8 and a6, which arc predicted very precisely within the framework of ChPT 2 .

NA48/2 has reported two new measurements of the 71"71" scattering lengths using K= ---+ 7r±7ro7ro

and K± ---+ 71"-'-71"- e± z; decays. A cusp observed in the Mrrorro distribution of K± -+ rr±rr0 rr0

decays at MJ0 = 4m;= (Fig. 1 (left)) can be explained by 71"-71"- re-scattering terms 3.4 and provides a measurement of a8 and a6 from a fit of the MJ0 distribution around the cusp discon­tinuity. A sample of about 59.6 x 106 decays from 2003 and 2004 data has been used for this analysis, and the preliminary results from the fit of the Cabibbo-Isidori model 5 are:

(a8 - a6)mrr+ a6mrr+

0.261 ± 0.006stal ± 0.003syst ± O.ODlext ± 0.013theory · -0.037 ± 0.013stat ± 0.009syst ± 0.002exh

(1)

where the theoretical uncertainty is due to neglected O(an and radiative corrections. Alternative fits are being performed following the approach by 0 .

In K± -+ rr+rr-e±v decays, the pions are produced close to threshold. The decay amplitude depends on the complex phases 60 and 61 (the Sand P waves 71"71" phase shifts for isospin I= 0). The difference 8 = 80 - 81 can be measured as a function of the invariant mass of the two pions, Mrrrr· NA48/2 has performed a combined fit to the decay form factors and the phase shift difference as a function of Mn in a sample of 670000 signal candidates with 0.5% background 7 .

The results arc shown in Fig. 1 (right) together with two earllcr cxperimcnts 8·9 . From the phase shift measurements, the 7r7r scattering lengths can be extracted using dispersion relations 10 .

At the center of the "C"niversal Band 11 , a6 is related to ag. A one paramater fit gives a8 =

0.256±0.006stat ±0.002.sy.st ~g gi~ext, which implies a6 = -0.0312±0.0011.,tat ±0.0004.sy.st :::g:gn~ext. The external error reflects the width of the Universal Band. From a two parameters fit , the results a.re:

0.233 ± 0.016stat ± 0.001syst: -0.047 ± O.Ollstat ± 0.004syst:

(2)

with p = 0.967. Theoretical work including isospin symmetry breaking effects 12suggests that ag could decrease by ~ 0.02 for and a6 by ~ 0.004, bringing this measurement in agreement with other measurements and ChPT predictions 7 .

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Figure 2: (Left) Pion trac:k energy of K± - ,,.±1l"n normalization data (bla< k) and MC events (red. blue) without and with trigger efficiency correction, respectively. (Right) .lln invariant. m&~s of Kl. - 1TJ.1'1' candidates.

The contributions of the chiral lagrangian to this decay 13 appear at O(p4 ). At this order, only the t::.I = 1/2 invariant amplitudes A(z) and C(z) with z = A/~1/Mkt contribute. A(z) con­tains the O(p4 ) loop diagram contributions and the t.re.e level cmml.e.rterm.s absorbed in unknown parameter c predicted to be positive and of 0(1) 14 . The loop leads to a characteristic signature in the invariant. mass .l'vf"Y1 distribution, which is favoured to he above 2m,,. ~ and exhibits a cusp at 2m"+ threshold. The parameter i: fixes the value of the branching ratio and the MT1

spectrum shape. C(z) contains pole.s and tadpole.s 13•15 effects. O(p6 ) studies concluded 16 that 1mitarity correction effects could in('rease the BR between 30% - 403, while vector meson ex­change contributions would be negligible. NA48/2 has analyzed about 403 of its data, finding 1164 signal candidates with 3.33 back­ground ( 40 times more statistic::. than previous experiments 17). This decay and its normalization channel (K± --> rr±7r0 ) were collected through the neutral trigger chain intended for the collec­tion of K± ----> 7r±7ro7ro decays and therefore suffered from a very low trigger efficiency (~ 50%). Elaborate studies were performed to measure these efficiencies and correct for them (see Fig. 2 (left)). The reconstructed M-n spectrum can be seen in Fig. 2 for selected candidates (crosses), signal MC (yellow) and background (red). The model dependent branching ratio of K± --> 7r±'Y'Y has been measured, assuming the va­lidity of the O(p6

) ChPT as presented in 16 and taking c = 2 ". The preliminary result is BR(K± ----> 7r±'Y'Y) = (1.07 ± 0.04,,1,,t ± 0.08,.yst) x 10-6 . A model independent BR measurement is in prep;iration, together with the ext.met.ion of i: from a fit to M-.n and BR.

This decay is similar to K± ----> 7l'±'Y'Y with one photon internally converting into a pair of electrons. NA48/2 has reported the first observation of the decay K± ----> 7r±'Y e+ e- using the full 2003 and 2004 data sample18

. 120 candidates with 7.3±1.7 estimated background events have been selected in the accessible region with M-yee > 0.26 Ge V / c2 invariant mass. The candidates are o;hown in Fig. 3 (left). Uo;ing K± --> 7r±7r7i as normalization channel, the branching ratio has been determined in a model independent way to be BR = (1.19 ± 0.12stal ± 0.04sysi) x 10-R for M-,ec > 0.26 Ge V / c2

. The parameter c has also been measured assuming the validity of O(p6 ) l!I

and found to be c = 0.90 ± 0.45.

nThis is a realistic assumption based on previous results by 17 which obtained c = 1.8 ± 0.6.

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Figure :l: (Left) M~ . - .- invariant mass of K± ~ r.± 'l" 1 <: - canditlates. Cros.<;<.'S am signal anti colored histograms background. (Right) K'= ~ r.±e+ e- differential decay rate and different fit results from the considered models.

The FCNC process K=-> r.±e-e- can be described in ChPT 20 . ~A48/2 has collected 7146 can­didates with 0.6<;{ background. The decay rate ha.<; heen mea.<;ured using K± -> r.±r.9J as norma­lization. A preliminary model independent. mea<;11rement for;; = A1?1 P.- /."Vfj,± > 0.08 gave BR =

(2.26 ± 0.03stat ± 0.03syst ± 0.06ext) x 10-1. l\Iodel dependent. fits to the z-spedrnm have heen

performed (Fig. 3 (right)), 9bt.aining the correspouding form factor:; and BR. Tht-> preliminary average BR in the full kinematic range is: BR= (3.08 ± 0.045 tat ± 0.08cxt ± 0.07modd) x 10-7 _

Comparison of re~<;ults with previous experiments and theoretical predictions can he found in 2:i _

References

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