EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

CERN{PPE/95{18914 December 1995

Search for CP violation in the decay of neutral kaons to �+���0

The CPLEAR Collaboration

R. Adler2), T. Alhalel11), A. Angelopoulos1), A. Apostolakis1), E. Aslanides11),G. Backenstoss2), C.P. Bee9), O. Behnke17), A. Benelli9), J. Bennet9), V. Bertin11),J.K. Bienlein17), F. Blanc7;13), P. Bloch4), C. Bula13), P. Carlson15), M. Carroll9),J. Carvalho5), E. Cawley9), S. Charalambous16), M. Chardalas16), G. Chardin14),M.B. Chertok3), A. Cody9), M. Danielsson15), S. Dedoussis16), M. Dejardin14),

J. Derre14), M. Dodgson9), J. Duclos14), A. Ealet11), B. Eckart2), C. Eleftheriadis16),I. Evangelou8), L. Faravel7), P. Fassnacht11), J.L. Faure14), C. Felder2),

R. Ferreira-Marques5), W. Fetscher17), M. Fidecaro4), A. Filip�ci�c10), D. Francis3),J. Fry9), C. Fuglesang15), E. Gabathuler9), R. Gamet9), D. Garreta14), T. Geralis13),

H.-J. Gerber17), A. Go3;15), P. Gumplinger17), C. Guyot14), P.F. Harrison9),A. Haselden9), P.J. Hayman9), F. Henry-Couannier11), W.G. Heyes4), R.W. Hollander6),

E. Hubert11), K. Jansson15), H.U. Johner7), K. Jon-And15), P.-R. Kettle13),C. Kochowski14), P. Kokkas2), R. Kreuger6), T. Lawry3), R. Le Gac11), F. Leimgruber2),

A. Liolios16), E. Machado5), P. Maley9), I. Mandi�c10), N. Manthos8), G. Marel14),M. Miku�z10), J. Miller3), F. Montanet11), T. Nakada13), A. Onofre5), B. Pagels17),

I. Papadopoulos16), P. Pavlopoulos2), F. Pelucchi11), J. Pinto da Cunha5), A. Policarpo5),G. Polivka2), H. Postma6), R. Rickenbach2), B.L. Roberts3), E. Rozaki1), T. Ruf4),L. Sacks9), L. Sakeliou1), P. Sanders9), C. Santoni2), K. Sarigiannis1), M. Sch�afer17),

L.A. Schaller7), T. Schietinger2), A. Schopper4), P. Schune14), A. Soares14), L. Tauscher2),C. Thibault12), F. Touchard11), C. Touramanis4), F. Triantis8), D.A. Tr�oster2), E. VanBeveren5), C.W.E. Van Eijk6), G. Varner3), S. Vlachos2), P. Weber17), O. Wigger13),

C. Witzig17), M. Wolter17), C. Yeche14), D. Zavrtanik10) and D. Zimmerman3).

Abstract

The time-dependent rate asymmetry of initial K0 and K0 decaying into �+���0 wasmeasured in order to reveal the CP-violating amplitude of the KS ! �+���0 decay.For the real and the imaginary parts of �+�0, we �nd Re(�+�0) = (6 � 13stat. �1syst.)� 10�3 and Im(�+�0) = (�2� 18stat.� 3syst.)� 10�3 which correspond toj�+�0j < 0:037 with 90% CL.

(Submitted to Physics Letters B)

1 Introduction

In this paper, results are presented on the CP-violating KS ! �+���0 decay studiedby the CPLEAR experiment at the Low Energy Antiproton Ring (LEAR) at CERN, wherethe decay rates of the initial K0 and K0 into the three-pion �nal state are measured.

The motivations for a search for the CP-violating amplitude of KS ! �+���0 decayextend beyond the search for CP violation in the KS decays of the neutral kaon system. Itis also an important experimental input to the best indirect test of CPT symmetry, basedon the Bell{Steinberger relation [1]. The increasing experimental precision in measuringthe �+� phase has renewed interest in a purely experimental test of CPT. For this, theprecision in measuring the amplitudes of the transitions to the three-body �nal states is alimiting factor. Our measurement substantially reduces the experimental uncertainty dueto the �+���0 �nal state, making it negligible compared with the experimental uncer-tainty of the other parameters contributing to the limit to CPT invariance.

The search for the CP-violating amplitude in the decay to �+���0 is di�erent tothat in the more familiar two-pion channels. The two-pion �nal states and the �0�0�0

state each have a well-de�ned CP eigenvalue. In contrast, the CP eigenvalue of a �+���0

state with zero total angular momentum is given by (�1)l+1, where l is the relative an-gular momentum between �+ and ��. Since the sum of the masses of the three pionsis close to the kaon mass, the decays of K0 and K0 into three-pion states with l > 0are suppressed by kinematics. Therefore, the process KL ! �+���0 is dominated by theCP-allowed decay amplitude A�+���0

L with l = 0 and CP=�1. The KS may decay intothe kinematics-suppressed and CP-allowed �nal state with l = 1 and CP=+1, or into thekinematics-favoured but CP-forbidden �nal state with l = 0 and CP=�1. This results ina Dalitz plot population which is symmetric with respect to the �+ and the �� for theKS ! �+���0 CP-violating amplitude and anti-symmetric for the KS ! �+���0 CP-allowed amplitude. Thus, in the KL{KS interference term, the CP-allowed contribution ofKS decays vanishes when the decay amplitude is integrated over the phase space of theneutral kaon decays [2]. Therefore the parameter �+�0, de�ned as

�+�0 =

RdA�+���0

S A�+���0

L�

Rd

���A�+���0

L

���2; (1)

1) University of Athens, GR-10680 Athens, Greece2) University of Basle, CH-4056 Basle, Switzerland3) Boston University, Boston, MA 02215, USA4) CERN, CH-1211 Geneva 23, Switzerland5) LIP and University of Coimbra, P-3000 Coimbra, Portugal6) Delft University of Technology, 2629 JB Delft, Netherlands7) University of Fribourg, CH-1700 Fribourg, Switzerland8) University of Ioannina, GR-45110 Ioannina, Greece9) University of Liverpool, Liverpool L69 3BX, UK10) J. Stefan Inst. and Phys. Dep., University of Ljubljana, SI-61111 Ljubljana, Slovenia11) CPPM, IN2P3-CNRS et Universit�e d'Aix-Marseille II, F-13288 Marseille, France12) CSNSM, IN2P3-CNRS, F-91405 Orsay, France13) Paul-Scherrer-Institut(PSI), CH-5232 Villigen, Switzerland14) CEA, DSM/DAPNIA, CE-Saclay, F-91191 Gif-sur-Yvette, France15) Royal Institute of Technology, S-10405 Stockholm, Sweden16) University of Thessaloniki, GR-54006 Thessaloniki, Greece17) ETH-IPP Z�urich, CH-8093 Z�urich, Switzerland

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where the integration is over the entire phase space of the K0 ! �+���0 decay, dependsonly on the CP-violating part of the amplitude A�+���0

S for the decay KS ! �+���0.

2 Experimental method

In the CPLEAR experiment, the parameter �+�0 is determined from the time-dependent K0{K0 decay rate asymmetry, which is a direct measurement of the KS{KL

interference term. This asymmetry A+�0(� ) is prominent in the early decay-time regionand is given as

A+�0(� ) =R+�0(� )�R+�0(� )

R+�0(� ) +R+�0(� )

= 2Re(")� 2 [Re(�+�0) cos (�m� )� Im(�+�0) sin (�m� )] e�1

2(�S��L)�

(2)

where R+�0(� ) and R+�0(� ) are the K0 and K0 decay rates, �m is the KL{KS massdi�erence, �L and �S (= 1=�S) are the KL and KS decay widths, respectively, and " is theCP violation parameter in the K0{K0 mixing.

The initial K0 and K0 are produced in the reactions

pp(at rest)! K��+K0 and pp(at rest)! K+��K0

each with a branching ratio of approximately 2 � 10�3. The strangeness of the neutralkaon is tagged by the sign of the associated charged kaon. The 200 MeV/c antiprotonsfrom LEAR are stopped in a target of gaseous hydrogen (16 bar) at a rate of 106 s�1.The detector [3] has a cylindrical symmetry and is placed inside a solenoid providinga magnetic �eld of 0.44 T. Charged particles are tracked using 2 layers of proportionalchambers (PC), 6 layers of drift chambers and 2 layers of streamer tubes. A scintillator-�Cerenkov-scintillator sandwich provides input to a kaon fast identi�cation system basedon energy loss, time of ight and �Cerenkov light measurements. Photons are detected inan electromagnetic calorimeter with 18 layers of lead converters and tubes working in alimited-streamer mode. Each of these layers is equipped with two layers of pickup strips,allowing a three-dimensional reconstruction of electromagnetic showers. Fast and e�cientevent selection is performed online using a hardwired multilevel trigger system.

3 Data selection

The results reported in the present paper are based on the analysis of data takenduring 1992 and 1993. The events selected contain four charged-particle tracks, withzero total charge and one or more electromagnetic showers in the calorimeter, whichare well away from any charged track. The latter requirement considerably reduces thebackground from pp annihilations to K+K��+�� and also from �+�� and semileptonicdecays of neutral kaons. The pp-annihilation vertex, reconstructed from the charged kaonand a pion of opposite charge (primary pion), is required to be within 20 mm of thebeam axis and well within the target along the beam axis. The neutral-kaon decay vertexis reconstructed from the remaining �+ and �� tracks (secondary pions). The distancebetween the two vertices in the transverse plane is required to be greater than 1.2 cm.The opening angle of the secondary pions has to be larger than 8o in order to remove e+e�

pairs from conversions or �0 Dalitz decays, and smaller than 172o in order to removeevents with particles back-scattered from the detector's outer components.

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Events are then selected using constrained �ts to satisfy either pp(at rest) !

K+��K0�K0 ! �+���0

�or the charge conjugate (c.c.) process, with the following re-

quirements:

{ conservation of energy and momentum with the constraints that the missing massat the primary vertex is the mass of the neutral-kaon, and the total missing massis the �0 mass.

{ colinearity of the neutral-kaon momentum vector and the vector connecting theprimary and decay vertices, both in the transverse plane.

About 250 000 events satisfy this �rst set of selection criteria. Analysis of the possiblebackground events contained in this sample is performed using both real data and MonteCarlo simulation.

Mainly due to the e�ectiveness of the constrained �ts, the background resulting fromK+��K0

�K0 ! �+��

�or the c.c. process is reduced to a negligible amount (� 0:02%).

The same holds for many other annihilation channels, such as multi-pion �nal states,whose contribution is at most 0.002%. The possible systematic error caused by this isincluded in the �rst and second entries of Table 1.

The contribution from neutral kaons decaying into semileptonic �nal states canbe determined from Monte Carlo simulation and from the relative branching ratios. Itamounts to� 4% of the signal events and is found to be strongly suppressed at short decay-times, where the decay particles which hit the PCs have better momentum resolution,resulting in a more e�cient rejection by the constrained �ts (Fig. 1). Due to its decay-time distribution this contribution has very little e�ect on the result.

At short decay-times, the remaining background contributions are the following:

(a) pp ! �0K+��K0 (or c.c.) events, where a KS decays into �+��, but where theprimary charged-pion is taken as a secondary pion and vice versa, even though thevertex resolution in the transverse plane is of the order of 1.5 mm. This results in`combinatorial' background mainly at very short decay-times.

(b) pp ! K+K��+�� events satisfying the selection criteria due to a badly recon-structed track.

(c) pp! K+��K0 (or c.c.) events with a KS decaying to �0�0, followed by a �0 Dalitzdecay to e+e� .

Background events of type (a) are rejected if they ful�l invariant mass assignmentand vertex alignment consistent with the pp! �0K+��K0 (KS ! �+��) or c.c. hypoth-esis. These cuts have very little e�ect on genuine three-pion events.

Events of type (b) are further reduced by discarding events where a four- or three-track vertex-�t probability is high, and where the total missing momentum is low. Inaddition the time-of- ight information of the charged particles is used to con�rm theprimary K� and secondary �� hypothesis.

The Dalitz decays in type (c) events are further eliminated using invariant massand time-of- ight techniques.

After these additional cuts a total of 137 000 events remain. The decay-time distri-butions are denoted by N(� ) and N(� ) for K0 and K0, respectively. The decay-time � iscalculated using the neutral-kaon momentum, improved by the constrained �ts mentionedabove.

Figure 1 shows the measured decay-time distribution N(� ) + N(� ), together withthe simulated decay-time distribution, which includes K0 and K0 ! �+���0 decays andthe predicted contribution from semileptonic decays. The simulated data are normalized

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to the real data for decay-times above 6 �S, where semileptonic events are the only sourceof background. The contribution of the semileptonic events is shown in the shaded area.

Figure 2 shows the total-background fraction distribution �(� ), given by

�(� ) =(N(� ) +N(� ))� (N 3�(� ) +N3�(� ))

N(� ) +N(� )(3)

where N3�(� ) + N3�(� ) is the normalized number of Monte Carlo events for K0 and K0

decaying to �+���0. This total-background fraction is taken into account when �ttingthe asymmetry and evaluating the systematic errors by using a parameterization of �(� ),which includes the semileptonic contribution and a small residual background, observedat very short decay-times (Fig. 1).

The determination of �(� ) is limited by the precision to which the Monte Carlo simu-lation can reproduce the detector and selection acceptances. This precision was determinedto be better than 1% by comparing the decay-time distributions from a background-freesub-sample of real events with the Monte Carlo distributions. This sub-sample consists ofsignal events with a �0 ! reconstructed using the calorimeter information and is toosmall to be used on its own for a measurement of �+�0.

4 Decay asymmetries and �tting

In order to obtain the time-dependent CP-asymmetry de�ned in Eq. 2 from themeasured rates N(� ) and N(� ), their relative normalization has to be taken into accountas discussed in [4], and it is necessary to consider the K0 and K0 tagging e�ciencies. Thesee�ciencies �(K0) and �(K0) are not identical due to the di�erent strong interaction cross-sections of K+ and K�, and of �+ and ��, in the detector. A normalization factor � isde�ned as �(K+; ��)=�(K�; �+), which depends on the momenta of the primary charged-kaon and pion, and is independent of the decay mode.

The momentum distributions are related to the radial distance of the secondaryvertex of the neutral kaons, resulting in a small dependence of � on the decay-time.A look-up table (LUT) has been constructed, using the K0 and K0 decays to �+�� atvery short decay-times [4], in order to map � with good precision as a function of themomenta of the primary charged-kaon and pion, �( ~pK ; ~p�). The decay-time dependenceof � is corrected on an event-by-event basis using this LUT. The overall average value of� is then determined as a free parameter in the �t of the asymmetry.

Di�erent decay-track topologies may have di�erent acceptances. One should how-ever notice that the acceptance of events with di�erent topologies cancels in the K0{K0

asymmetry and that track lengths and momentum resolution of the secondary (decay)tracks have no in uence on the normalization, which is determined by the primary K���

tracks.Figure 3 shows the measured asymmetry

Aexp+�0(� ) =

N (� )�N(� )

N (� ) +N(� )

�=� � 1

� + 1+4 �[1 � �(� )]

(� + 1)2A+�0(� ) (4)

where A+�0(� ) is given by Eq. 2. The parameter �+�0, as well as the normalization factor�, were left free in �tting Eq. 4 to the data. The numerical values for Re(�), �S and �L are

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taken from [5]. One should note that in Eq. 4 the �rst term in � is adding to 2Re(") in Eq.2 and that the � dependence of the second term is weak. Thus one cannot di�erentiatein this �t between normalization e�ects and the value of Re(") . The �t result is alsovery weakly sensitive to the choice of the value of �m, which we take from our recentpublication [6].

The �t yields

Re(�+�0) = (6� 13stat.)� 10�3

Im(�+�0) = (�2� 18stat.)� 10�3

� = 1:127 � 0:007:

The statistical correlation coe�cient of the parameters Re(�+�0) and Im(�+�0) is 66%.The solid line in Fig. 3 represents the result of the �t. For comparison, the broken

line is obtained assuming �+�0 = �+�.

5 Systematic errors

The following systematic errors were investigated:{ The systematic error introduced by uncertainty in the total-background fraction�(� ) was found to be 0:4� 10�3 for Re(�+�0) and 0:5� 10�3 for Im(�+�0). A studyof rejected events showed that one possible background, namely K+K��+�� events,could appear to have a normalization di�erent from signal events. Taking this as anextreme case and varying the background normalization within the correspondinglimits resulted in systematic errors of 0:5 � 10�3 for Re(�+�0) and 1:1 � 10�3 forIm(�+�0).

{ The assumption that the contribution from CP-allowed KS ! �+���0 decays can-cels in the asymmetry does not hold if there is any di�erence in the detector accep-tance for the phase-space regions ECM(�+)><ECM(��). Studies using both real andsimulated data, for selected phase space regions, where no asymmetry caused byCP-allowed KS decays is expected, showed no di�erence in acceptance within thepresent statistical accuracy (< 2 � 10�3). This statistical limit translates into anerror of 0:1�10�3 for Re(�+�0). There is no e�ect for Im(�+�0) since the CP-alloweddecay amplitude contributes only through the cosine term of the interference.

{ The error introduced by the LUT was determined by changing the values in the LUTwithin their statistical errors. Although data were corrected for any time dependenceof the normalization, a search for a residual e�ect due to di�erent event topologieshas been carried out using a detailed Monte Carlo simulation. The accuracy onthe determination of the normalization time dependence, currently limited by theMonte Carlo statistics, leads to a systematic error of 0:7 � 10�3 for Re(�+�0) and2:8� 10�3 for Im(�+�0).

{ The systematic error due to �nite decay-time resolution and bin size, as well as tothe lower limit of the decay-time interval used in �tting the asymmetry, was studiedusing Monte Carlo events. The total uncertainty is less than 0:3�10�3 for Re(�+�0)and less than 0:4� 10�3 for Im(�+�0).

{ The e�ect of neutral kaon regeneration is expected to be negligible at short decay-times, where the asymmetry is sensitive to CP violation. Its uncertainty was foundto be less than 0:1� 10�3 for Im(�+�0) when changing the regeneration amplitudesby �13% and the regeneration phases by �9o [4], i.e. within the errors extrapolatedfrom higher energy data.

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{ The experimental uncertainties of the values of �m and �S used in the �t accountfor systematic errors of less than 0:2 � 10�3 for both the real and imaginary partsof �+�0.

Table 1 summarizes the systematic errors which may a�ect the determination of �+�0.

Source of systematic error Re(�+�0)� 10�3 Im(�+�0)� 10�3

Amount of background 0.4 0.5Normalization of background 0.5 1.1CP-allowed KS decay amplitude � 0.1 {Decay-time dependence of normalization � 0.7 2.8Decay-time resolution 0.3 0.4Regeneration { 0.1�m and �S 0.1 0.2� Error determination currently limited by statistics.

Table 1: Summary of systematic errors

6 Final results and conclusions

Our �nal result is

Re(�+�0) = (6� 13stat. � 1syst.)� 10�3

Im(�+�0) = (�2� 18stat. � 3syst.)� 10�3:

Assuming no correlation between the systematic errors, we obtain j�+�0j < 0:037 at the90% con�dence level.

This is the �rst determination of �+�0 using the method of measuring the rate asym-metry of tagged K0 and K0 decaying to �+���0. We have obtained the best sensitivityfor �+�0 compared to all previous measurements [5], and also to the recent measurement[7], as shown in Fig. 4.

Our measurement reduces the contribution of the error of �+�0 to a negligible levelin a test of CPT invariance based on the Bell{Steinberger relation [8, 9].

Acknowledgments

We would like to thank the CERN LEAR sta� for their support and co-operationas well as the technical and engineering sta� of our institutes. This work was supportedby the following institutions: the French CNRS/Institut National de Physique Nucl�eaireet de Physique des Particules, the French Commissariat �a l'Energie Atomique, the GreekGeneral Secretariat of Research and Technology, the Netherlands Foundation for Fun-damental Research on Matter (FOM), the Portuguese JNICT and INIC, the Ministry ofScience and Technology of the Republic of Slovenia, the Swedish Natural Science ResearchCouncil, the Swiss National Science Foundation, the UK Particle Physics and AstronomyResearch Council (PPARC), and the US National Science Foundation.

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References

[1] J.S. Bell and J. Steinberger, Proc. 1965 Oxford Int. Conf. on Elementary Particles(Oxford, 1966) p. 165.

[2] The CPLEAR Collaboration, Observation of the CP-conserving KS ! �+���0 decay

amplitude, in preparation.[3] The CPLEAR Collaboration, The CPLEAR detector at CERN, in preparation.[4] R. Adler at al., Phys. Lett. B363 (1995) 243.[5] Particle Data Group, Phys. Rev. D50 (1994) 1173.[6] R. Adler at al., Phys. Lett. B363 (1995) 237.[7] Y. Zou et al., Phys. Lett. B329 (1994) 519.[8] G.B. Thomson and Y. Zou, Phys. Rev. D51 (1995) 1412.[9] The CPLEAR Collaboration, An improved determination of the K0�K0 mass di�er-

ence: a test of CPT symmetry, in preparation.

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s

Figure 1: The decay-time distribution of initial K0 and K0 decaying into �+���0 for real(+) and simulated ({) data. The simulated distribution (MC sum) results from �+���0

and semileptonic decays of neutral kaons and is normalized to the real data above 6 �S.The contribution to background from semileptonic events is given by the shaded area.

s

s

Figure 2: The total-background fraction �(� ). The solid line is obtained by a parame-terization of the di�erence between decay-time distributions of real data and simulatedneutral kaons decaying to �+���0 (normalized above 6 �S).

8

s

Figure 3: The measured time-dependent CP-asymmetry between 0.5 and 20 �S. The solidline is obtained by �tting Eq. 4 to the data. The broken line shows the asymmetry expectedwhen assuming �+�0 = �+�.

Figure 4: The contour plot for Re(�+�0) and Im(�+�0) obtained in the present work.For comparison, the recent result of Zou et al. [7] is also shown. In the absence of thestatistical correlation coe�cients of [7], the error bars for both experiments represent totaluncertainties, i.e. statistical and systematic uncertainties added in quadrature.

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