CPLEAR Results on the CP Parameters of Neutral Kaons Decaying to Π+Π−Π0 R

Home , CPLEAR experiment

CPLEAR results on the CP parameters of neutral kaons decaying to π+π−π0 R. Adler, A. Angelopoulos, A. Apostolakis, E. Aslanides, G. Backenstoss, P. Bargassa, C P. Bee, O. Behnke, A. Benelli, V. Bertin, et al.

To cite this version:

R. Adler, A. Angelopoulos, A. Apostolakis, E. Aslanides, G. Backenstoss, et al.. CPLEAR results on the CP parameters of neutral kaons decaying to π+π−π0. Physics Letters B, Elsevier, 1997, 407, pp.193-200. in2p3-00000063

HAL Id: in2p3-00000063 http://hal.in2p3.fr/in2p3-00000063 Submitted on 16 Nov 1998

HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

CERN–PPE/97–54

12 May 1997

+ 0

CPLEAR results on the CP parameters of neutral kaons decaying to

The CPLEAR Collaboration

1 1 11 2

R. Adler 2 , A. Angelopoulos , A. Apostolakis ,E.Aslanides , G. Backenstoss ,

9 17 9 11 7;13

P. Bargassa13 ,C.P.Bee,O.Behnke ,A.Benelli ,V.Bertin ,F.Blanc ,

15 9 5 9 16

P. Bloch 4 ,P.Carlson ,M.Carroll,J.Carvalho,E.Cawley, S. Charalambous ,

3 9 15 14 14

G. Chardin 14 , M.B. Chertok , A. Cody , M. Danielsson , M. Dejardin , J. Derre ,

2 16 8 7 11

A. Ealet 11 ,B.Eckart ,C.Eleftheriadis ,I.Evangelou ,L.Faravel ,P.Fassnacht ,

5 17 4 10

C. Felder2 , R. Ferreira-Marques ,W.Fetscher , M. Fidecaro , A. Filipˇciˇc ,

9 9 9 14 17

D. Francis 3 ,J.Fry, E. Gabathuler , R. Gamet ,D.Garreta ,H.-J.Gerber ,

14 9 9 11

A. Go 14 , C. Guyot ,A.Haselden,P.J.Hayman, F. Henry-Couannier ,

11 15 13 14

R.W. Hollander6 ,E.Hubert ,K.Jon-And , P.-R. Kettle , C. Kochowski ,

6;13 11 2 16 5

P. Kokkas 4 ,R.Kreuger ,R.LeGac , F. Leimgruber , A. Liolios , E. Machado ,

8 14 10 3 11

I. Mandi´c10 ,N.Manthos,G.Marel ,M.Mikuˇz , J. Miller ,F.Montanet ,

13 17 16 2

A. Muller14 ,T.Nakada, B. Pagels , I. Papadopoulos , P. Pavlopoulos ,

5 2 2 3

J. Pinto da Cunha5 , A. Policarpo , G. Polivka ,R.Rickenbach, B.L. Roberts ,

1 9 2 17 7

T. Ruf 4 ,L.Sakeliou,P.Sanders,C.Santoni,M.Sch¨afer , L.A. Schaller ,

4 14 14 2 12

T. Schietinger2 , A. Schopper , P. Schune ,A.Soares ,L.Tauscher , C. Thibault ,

4 8 5 6

F. Touchard 11 , C. Touramanis , F. Triantis ,E.VanBeveren, C.W.E. Van Eijk ,

17 13 17 14 10 S. Vlachos2 ,P.Weber , O. Wigger , M. Wolter ,C.Yeche ,D.Zavrtanik and

D. Zimmerman 3

Abstract

0 K

The CPLEAR experiment measured time-dependent decay-rate asymmetries of K and

+ 0 0

decaying to in order to study the interference between the decay amplitudes of

S 0

— either CP-violating or CP-conserving — and the CP-conserving K decay amplitude.

From the analysis of the complete data set we ﬁnd for the CP-violating parameter + ,

+4 +2

Re( ) = 2 7 10 ; Im( ) = 2 9

0 +0

+ stat. syst. stat. syst.

1 1

3 3

10 Re() = ( +28 7 3 ) 10 ;

and for the CP-conserving parameter , stat. syst.

)=(10 8 2 ) 10 :

Im( stat. syst. From the latter, the branching ratio of the CP-

+1:3 +0:5

0 + 0 7

! B= 2:5 stat: syst: 10 :

conserving K decay is deduced to be

1:0 0:6 S

(Submitted to Physics Letters B)

1 Introduction 0

The CPLEAR experiment at the Low Energy Antiproton Ring at CERN uses tagged K 0

and K to study CP, T and CPT symmetries in the neutral kaon system. In previous CPLEAR

publications, the measurements of the CP-violating parameter + [1] and the value of the CP-

+ 0

conserving parameter [2], obtained from the analysis of neutral kaons decaying into ,

0 were reported for a 25% data sample. In this letter, new measurements of + and based on

our complete data set are presented.

0 + 0

Interest in the search of the CP-violating amplitude of K extends beyond

S 0

the search for CP violation in the K decays. Firstly, increasing experimental precision in the

+ measurement of the phase, + , of the CP-violating parameter can be fully exploited for an indirect CPT test, only if the precision of the CP-violating parameters of neutral kaons decaying

to three pions is improved substantially [3]. Secondly, the measurement of the CP-conserving

0 + 0

K amplitude allows the results to be cross-checked with the phenomenological S global ﬁts to all known neutral- and charged-kaon decay rates and to be compared with the

predictions of chiral perturbation theories [4–8].

+ 0 l +1

(1) l

The CP eigenvalue for the ﬁnal state is given by where is the relative

0 +

angular momentum between the two charged pions (or between the and the pair).

As the sum of the masses of the three pions is close to the kaon mass, the pions have a low

E ( ) l > 0

kinetic energy CM in the kaon rest-frame, and the states with are suppressed by the

0 + 0

! A centrifugal barrier. This implies two contributions to the K decay amplitude :

S S

+ 0

=+1

one from the decay to a state with CP (kinematics-suppressed and CP-allowed),

and the other from the decay to a CP = state (kinematics-favoured but CP-suppressed). The

0 + 0

! A l = 0 K decay is dominated by the CP-allowed decay amplitude with and

L L

CP = .

0 0

A K

The K decay amplitude interferes with both the CP-conserving decay ampli- S

L L

3 ( =+1) 3 ( =1)

CP 0 CP

K A tude A and the CP-violating decay amplitude . These amplitudes depend

S S S

2 +

X Y X ' (2m =m )(E ( ) CM

on the Dalitz variables and [2], which can be estimated to be K

2 0

E ( )) Y ' (2m =m )(m =3 E ( ))

K K CM

CM and . The former interference term is antisym-

X > 0 X < 0 metric in X , and is observed by separating the events with and . We deﬁne the

CP-conserving parameter as

R R

( =+1) 3( =+1)

3 CP CP

dX d Y A dX d Y A (X; Y ) A (X; Y ) (X; Y ) A (X; Y )

X<0 0

X> L S L S

R R

= : =

(1)

2 2

dX d Y jA (X; Y )j dX d Y jA (X; Y )j

0 X<0 X> L L

1) University of Athens, Greece

2) University of Basle, Switzerland

3) Boston University, USA

4) CERN, Geneva, Switzerland

5) LIP and University of Coimbra, Portugal

6) Delft University of Technology, Netherlands

7) University of Fribourg, Switzerland

8) University of Ioannina, Greece

9) University of Liverpool, UK

10) J. Stefan Inst. and Phys. Dep., University of Ljubljana, Slovenia

11) CPPM, IN2P3-CNRS et Universit´e d’Aix-Marseille II, Marseille, France

12) CSNSM, IN2P3-CNRS, Orsay, France

13) Paul-Scherrer-Institut(PSI), Villigen, Switzerland

14) CEA, DSM/DAPNIA CE-Saclay, France

15) KTH-Stockholm, Sweden

16) University of Thessaloniki, Greece

17) ETH-IPP Z¨urich, Switzerland

1 This contribution vanishes when data are integrated over the whole phase space, allowing the

observation of the latter interference term through the measurement of the CP-violating param-

eter + given by

( =1)

3 CP

(X; Y ) A (X; Y )

dX d Y AL S

= :

jA (X; Y )j

dX d Y L

0 + 0

K R ( ) R ( )

We deﬁne the decay rates for an initial decaying to to be + and

> 0 X < 0

for X and respectively, where is the decay eigentime. Similarly the decay rates

K R ( ) R ( ) for an initial are deﬁned as + and . The time-dependent asymmetry integrated

over the whole phase space,

h i

R ( )+R () [R ()+R ()]

+ +

h i

A ( ) =

+ (2)

R ( )+R () +[R ()+R ()]

+ +

= 2 (") 2 e [ ( ) cos (m) ( ) sin (m)] ;

0 +0

Re Re + Im

0 0 0 0

m K K K K "

where is the – mass difference, the – decay-width difference and the CP-

L S S L

K K

violation parameter in the – mixing, is used to extract the CP-violation parameter + .

> 0 X < 0

The two asymmetries obtained by separating the rates for X and ,

R ( ) R ( )

A ( ) =

(3)

R ( )+R ()

= 2 (") 2 e [ ( ) cos (m) ( ) sin(m)] ;

0 +0 Re Re + Im

are used to determine the CP-conserving parameter .

2 Data selection

The CPLEAR method and detector have been described elsewhere [9]. In this experiment,

0 K

initial K and are produced in the reactions

+ + 0

p ! K K pp ! K K ; p (at rest) and (at rest) where the strangeness of the neutral kaon is identified on an event-by-event basis. The results reported in the present paper are based on the complete data set recorded by CPLEAR. The selection criteria are mostly identical to those described in our previous papers [1, 2]. The differences are due to upgrades of our detector in 1994 and 1995. During the 1994 data-taking, the spherical target (radius 7 cm) was replaced by a cylindrical one with a radius of 1.1 cm, filled with gaseous hydrogen at a pressure of 27 bar. In 1995, a cylindrical proportional chamber with a radius of 1.5 cm was added around the new target. This chamber, located close to the annihilation vertex, was used in the first stage of the trigger to reject more efficiently the annihilation background, resulting in a smaller dead time and in an increase in the rate of recorded signal events by a factor of two.

In addition, an improvement of the selection criteria was possible by requiring in the

pp new chamber a hit on each of the K tracks coming from the annihilation vertex, and

no hit associated with the secondary particles from the neutral-kaon decay. This new condition

p !

allowed the release of some selection cuts used in the previous analysis in order to reject p

+ + 0 +

K pp ! K K K and (or c.c.) background. This leads to a substantial increase (about 30%) in the signal acceptance at short decay time.

However, the increased material around the interaction region enhanced the background

n ! (1115) ! p due to K hyperon production followed by decay. Such events only appear

2 0 in the K data set, simulating CP-violation asymmetry. This background is strongly reduced by

using time-of-ﬂight to identify the protons.

> 0:25

The ﬁnal data sample contains a total of 508 000 events with a decay time S ,

0 0

K K K

where S is the mean life. The decay-time distributions of initial and are denoted by

( ) N ( ) N ( )+N ( )

N and respectively. Figure 1 shows the measured decay-time distribution

0 !

of the full data set, together with the simulated decay-time distribution which includes K

+ 0

events and the contribution from semileptonic decays. The simulated distribution is normalized to the real data for decay-times above 6 S , where semileptonic decays are the only

source of background, by ﬁtting a constant to the ratio of these two decay-time distributions.

( )

The total-background fraction distribution , deﬁned in [1] as the relative difference

+ 0

between the data and the simulated events, is parametrized by

( ) = exp ((0:2+4:1)) 0:008+0:006 :

The linear part describes the semileptonic contribution which amounts to 4.15% of the selected

events. The exponential part accounts for the background at short decay time (0.16%, possibly

+ + 0 + 0 0 0

K K K K

resulting from K and (or c.c.) events, decays into followedbya

(1115) ! p Dalitz decay, and decays).

3 Decay asymmetries and ﬁtting

We followed the procedure described in Ref. [1], taking into account normalization (i.e.

0 K the tagging efﬁciency of K relative to ), regeneration and acceptance effects, to compute the

measured asymmetry

N ( ) N ( )

exp

A ( ) =

N ( )+N()

4[1 ( )] 1

+ A ();

+ (4)

( +1)

A ( ) K K

where + is given by Eq. (2) and is the average / normalization factor. The param-

eter + and the normalization factor are left free when ﬁtting Eq. (4) to the data. The current

m Re " L world average values are used for and S [10] , and and ( ) [11].

The ﬁt yields

Re( ) = (2 7 ) 10

+ stat.

Im( ) = (2 9 ) 10

+ stat. (5)

= 1:116 0:004

( ) ( )

0 +0 with a statistical correlation coefﬁcient of the parameters Re + and Im of 68%. Fig- ure 2 shows the measured asymmetry and the results of the ﬁt.

In an analogous way, we followed the procedure of Ref. [2] to compute the measured

> 0 X < 0

decay-rate asymmetries for X and :

N ( ) N ( )

exp

A ( ) =

N ( )+N ()

1 4[1 ( )]

+ A (); =

(6)

+1 ( +1)

A ( )

where are the asymmetries given by Eq. (3). We ﬁrst performed a six-parameter ﬁt for

0 the variables + , , and the normalization factors for events with positive and negative ,

0 X<0 +0

X> and respectively. This ﬁt gives for values consistent with those of Eq. (5) and

0 X<0

not correlated with . It also gives values of X> and which are statistically compatible.

= =

0 X<0

We therefore assumed X> , and, in order to improve the determination of the

0 +

normalization factor ,weﬁxed + [11]. Simultaneous ﬁts of the two asymmetries

exp

A ( )

were then performed allowing only and to vary. The ﬁt gives

) = (+28 7 ) 10

Re( stat.

) = (10 8 ) 10

Im( stat.

= 1:116 0:003

) Im()

with a statistical correlation coefﬁcient of the parameters Re( and of 68% and a negligible correlation between and . Figure 3 shows the measured asymmetries and the result of the ﬁt.

4 Systematic errors

Tables 1 and 2 summarize the sources of systematic errors which may affect the deter-

mination of + and .

Table 1: Summary of systematic errors on the real and imaginary parts of +

+3 +3

( ) 10 ( ) 10

0 +0 Source of systematic error Re + Im +1.5 +0.7 Amount and normalization of the background –0.7 –0.2

(1115) background +4.1 +1.9 0

CP-conserving K decay amplitude –0.1 –

0:3 0:4

Decay-time dependence of normalization

0:2 0:2

Decay-time resolution

0:1 < 0:1

Regeneration <

m L , S and – –

Error determination limited by Monte Carlo statistics.

Table 2: Summary of systematic errors on the real and imaginary parts of

+3 +3

) 10 () 10 Source of systematic error Re ( Im +1.3 +0.5

Amount of background and background asymmetry in X –1.4 –0.3

+0.7 +0.2 X (1115) background and asymmetry in

–2.3 –0.8

0:2 0:2 Decay-time dependence of normalization

Decay-time resolution +1.1 +0.7

0:1 < 0:1 Regeneration <

+0.1

m 0:1 L , S and

–0.2

2:0 1:8 Acceptance

Error determination limited by Monte Carlo statistics.

4 Amount of background The amount and shape of the background at short decay time are estimated by comparing the decay-time distributions of real data and of simulated events. This determination is limited by the accuracy of our simulation. By comparing evaluations performed either on the decay-time or on the decay-radius distributions, and by varying the region where

the simulated data are normalized to the real data, the total-background fraction at short

10 decay time is estimated with an error of +2 .

Normalization of background

0 K The K / normalization factor for background events at short decay time may be differ-

ent to signal events. This contribution to the systematic error was estimated by using the

+ + 0 +

K K K normalization either of the rejected K events or of the rejected (or

c.c.) events for the maximum amount of background computed at short decay time. X

Background asymmetry in

K X

The K / normalization factor for background events may depend on the variable .

0 +

K K This is the case for the (or c.c.) background where the inversion of the pri-

mary pion with the same-sign secondary pion introduces a systematic shift of X which is

0 0

0 0 +

K K K positive for a K –tagged event and negative for a event. From the rejected

(or c.c.) events we estimated that the difference between the normalization factors for

> 0 X < 0 background events at X and was less than 20%. The resulting systematic error was determined by applying this normalization asymmetry to the estimated maximum

amount of background at short decay time.

The (1115) background

! p K The remaining (1115) component, which only contributes to the data set,

may be asymmetric in X because of the misidentiﬁcation of the proton as a pion. These

events were estimated to be less than 0.019% of the selected events and have a positive

(40 20)%

X in of the cases.

0 K

CP-conserving decay amplitude

0 + 0

The CP-conserving K decay amplitude does not cancel in the CP-violating

A ( )

asymmetry + if there is any difference in the detector acceptance for the phase-

> 0 X < 0 space regions X and . The asymmetry of the acceptance was estimated by

comparing the Dalitz plot distribution of real events with the one computed from the

3 (CP=+1)

(X; Y ) A (X; Y )

theoretical parametrization of the decay amplitudes A and

L S

0 [7]. The systematic error on + from this source is negligible.

Decay-time dependence of normalization

0 K The error introduced by the statistical uncertainties in the K / normalization correction was taken into account. Although data were corrected for any time dependence of the normalization, a search for a residual effect due to different event topologies was carried out and found to lead to a small error.

Decay-time resolution The systematic errors due to ﬁnite decay-time resolution, bin size, and the lower limit of the decay-time interval used in ﬁtting the asymmetries, were determined using simulated events.

Regeneration The effect of neutral kaon regeneration is expected to be negligible at short decay time,

where the asymmetries are maximal. This uncertainty was found to be less than a few

10 when changing the regeneration amplitudes within the uncertainties of the values

13% 9 extrapolated from higher energy data ( for the modulus and for the phase

[12]).

m L

, S and

m L

The experimental uncertainties on the values of , S and used in the ﬁt have a " negligible impact on the results, which are also insensitive to the input value of Re( ), see Ref. [1].

Acceptance Owing to the separate integration over the phase space in the different parts of Eq. (1), the

acceptance does not cancel in the expression for . Simulated data were used to determine

Y the effect of the acceptance as a function of X , and .

5 Final results and conclusions

Our ﬁnal result for + , shown in Fig. 4, is

10 ( )= 27

Re + stat. syst.

10 : ( )= 29

Im + stat. syst.

j j < 0:017

0 Assuming no correlation between the systematic errors, we obtain + at the 90%

conﬁdence level. Currently, this is the most precise determination of the real and imaginary

0 parts of + .

Our ﬁnal result for , shown in Fig. 5, is

) = (+28 7 3 ) 10

Re ( stat. syst.

)= (10 8 2 ) 10 :

Im ( stat. syst.

)

We do not ﬁx Im( to zero, in order to take into account strong-interaction phase-shift differ-

= 2 I =1

ences between the I and components of the decay amplitudes. The branching ratio

0 + 0 0

! Re() K

for the CP-conserving K decay is estimated from and the decay param-

S L

eters [2, 4]. Neglecting second-order terms in the strong-interaction phase-shift differences, we !

obtained

+0:5 +1:3

10 ; = 2:5

B + stat. syst. 0

K ! ( =+1)

0:6 1:0

S 0

where the systematic errors also include a contribution from the uncertainty on the K decay L

parameters. Currently, these results are the most precise determination of the CP-conserving

0 + 0

parameters for K decays into . These measurements are in good agreement with the S values predicted both by phenomenological ﬁts to all known kaon decay rates [4, 7] and by chiral perturbation theories [5–8].

Acknowledgements We would like to thank the CERN LEAR staff as well as the technical and engineering

staff of our institutes for their support and co-operation. This work was supported by the fol- e

lowing institutions: the French CNRS/Institut National de Physique Nuclaire et de Physique a des Particules, the French Commissariat l’Energie Atomique, the Greek General Secretariat of Research and Technology, the Netherlands Foundation for Fundamental Research on Mat- ter (FOM), the Portuguese JNICT, the Ministry of Science and Technology of the Republic of Slovenia, the Swedish Natural Science Research Council, the Swiss National Science Founda- tion, the UK Particle Physics and Astronomy Research Council (PPARC), and the US National Science Foundation.

6 References [1] R. Adler et al., Phys. Lett. B 370 (1996) 167 [2] R. Adler et al., Phys. Lett. B 374 (1996) 313 [3] R. Adler et al., CERN-PPE/96-189, 1996, to be published in Proc. Workshop on K Physics, Orsay, 1996 [4] T.J. Devlin and J.O. Dickey, Rev. Mod. Phys. 51 (1979) 237 [5] S. Fajfer and J.-M. G´erard,Z. Phys. C 42 (1989) 425 [6] H.-Y. Cheng, Phys. Lett. B 238 (1990) 399 [7] J. Kambor et al., Phys. Lett. B 261 (1991) 496 [8] G. D’Ambrosio et al., Phys. Rev. D 50 (1994) 5767; ibidem D 51 (1995) 3975 [9] R. Adler et al., Nucl. Instr. and Meth. A 379 (1996) 76 [10] R. Adler at al., Phys. Lett. B 369 (1996) 367; updated with CPLEAR full statistics, to be published. [11] R.H. Barnett et al., Phys. Rev. D 54 (1996) 1 [12] R. Adler et al., Phys. Lett. B 363 (1995) 243 [13] Y. Zou et al., Phys. Lett. B 329 (1994) 519 [14] Y. Zou et al., Phys. Lett. B 369 (1996) 362

7 S Data 22500 MC sum MC πlν

20000

17500

Number of events/0.5 τ 15000

12500

10000

7500

5000

2500

0 2468101214161820 [τ ]

Neutral kaon decay time S

0 + 0

Figure 1: The decay-time distribution of initial K and decaying into for real (+) and

+ 0

simulated (–) data. The simulated distribution (MC sum) results from and semileptonic decays of neutral kaons and is normalized to the real data set above 6 S . The background contribution from semileptonic events is given by the shaded area.

8 0.2 exp τ 0.18 A+-0 ( )

0.16

0.14

0.12

0.1

0.08

0.06

0.04

0.02

0 24681012141618 [τ ]

Neutral kaon decay time S

Figure 2: The measured CP-violating decay-rate asymmetry between 0.25 and 19.75 S .The

solid line is obtained by ﬁtting Eq. (4) to the data. The broken line shows the asymmetry ex-

0 + pected when assuming + .

9 0.2 0.18 Aexp(τ) 0.16 + 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 24681012141618 [τ ] Neutral kaon decay time S 0.2 0.18 Aexp(τ) 0.16 - 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 24681012141618 [τ ]

Neutral kaon decay time S

> 0 X < 0

Figure 3: The measured decay rate asymmetries for X and between 0.25 and

19.75 S . The solid curves are the result of the simultaneous ﬁt of Eq. (6) to the data, assuming

0 + common and . In this determination, we ﬁxed + = .

10 +3 40 )x10 +-0 30 σ Im( η 3

20 2σ

10 1σ

-10

-20

-30

-40

-30 -20 -10 0 10 20 30 η +3

Re( +-0)x10

()

0 Figure 4: The real and the imaginary parts of + : the central value with statistical and

total uncertainties, and the statistical contour plot; this paper. For comparison, the result of Zou

" (4)

0 +0 et al. [13] on Im( + ) obtained by ﬁxing Re( )=Re( )isalsoshown .

11 +3

20 Im( λ )x10 3σ

10 2σ

0 1σ

-10

-20

-30

-40

0 102030405060

Re(λ)x10+3

() Figure 5: The real and the imaginary parts of : the central value with statistical and total

uncertainties, and the statistical contour plot; this paper. For comparison, the result of Zou et al.

4) [14] is also shown ( .