ELSEVIER Nuclcar Physics A626 (1997) 157c 165c

N U C L E A R PHYSICS A

Measurement of CP,T and C P T violation parameters in the Neutral Kaon system at CPLEAR

Michael Carroll

()liver Lodge Laboratory. Dept. of Physics, University of Liverpool, P.().Box 147, Liverpool, L69 3BX, England P'or th~ C P L E A R Col labora t ion ~

The, CPLEA1R exper iment at. CEIR, N measures the t ime dependent decay rate asym-

metries of ini t ia l ly pure t( ° and ~o states to s tudy CP,T and C P T symmetr ies in the neutral kaon system. The latest results on ~+ , A m and x are reported, as well as direct

tests of T violat ion and C P T violat ion in K ° - ~ oscillations. Our results are consistent with C P T invar iance and allow for an improved l imit on the K°-K ° mass difference. Fur- ther, a possible loss of q u a n t u m coherence of the neutral kaon system has been tested to a level near the Planck scale.

! . I N T R O D U C T I O N

The C P L E A R experiment[ l ] investigates CP, T and C P T symmetr ies in the neutra l kaon system. Unlike previous exper iments which have used KL and Ks beams to investigate CP violat ion in various channels[2] (e.g.~r+rr - , rr+rr-rc°,~r%r °) C P L E A R uses ini t ia l ly pure K °

and ~o states. The rates of their decays to a number of final states are measured, allowing

~The CPLEAR Collaboration [t. Adler 2, T. Alhale111, A. Angelopoulos 1, A. Apostolakis 1, E. Aslanides 11, G. Backenstoss 2, P. Bargassa 13, C.P. Bee 9, O. Behnke 17, A. Benelli 9, V. Bertin ll, F. Blanc 7'13, P. Bloch 4, P. Carlson 1~, M. Carroll 9, J. Carvalho 5, E. Cawley 9, S. Charalambous 16, G. Chardin 14, M.B. Chertok 3, A. Cody 9, M. Danielsson 15, M. Dejardin 14, J. Derre 14, A. Ealet 11, B. Eckart 2, C. Eleftheriadis 16, I. Evangelou s, L. Faravel z, p. Fassnacht11, C. Felder 2, R. Ferreira-Marques 5, W. Fetscher 17, M. Fidecaxo 4, A. Filipei~ 1°, D. Francis 3, J. Pry 9, E. Gabathuler 9, R. Garnet 9, D. Garreta 14, H.- J. Gerber iv, A. Go &~5, C. Guyot 14, A. Haselden 9, P.J. Hayman 9, F. Henry-Couannier 11, R.W. Hollander 6, E. Hubert H, K. Jon-And is, P.-IR. Kettle 13, C. Kochowski 14, P. Kokkas 2, R. Kreuger 6'13, R. Le Gac H , F. Leimgruber 2, A. Liolios 16, E. Machado s, I. Mandid l°, N. Manthos s, G. Mare114, M. Miku~ 1°, J. Miller 3, F. Montanet 11 , T. Nakada 13 , B. Pagels lr, I. Papadopoulos 16, P. Pavlopoulos 2, J. Pinto da Cunha 5, A. Policarpo 5, G. Polivka 2, IR Rickenbach 2, B.L. Roberts 3, T. Ruf 4, L. Sakeliou 1, P. Sanders 9, C. Santoni 2, M. Schfifer 17, L.A Schaller 7, T. Schietinger 2, A. Schopper 4, P. Schune 14, A. Soares 14, L. Tauscher 2, C. Thibault 12, F. Touchard 11, C. Touramanis 4, F. Triantis s, E. Van Beveren s, C.W.E. Van Eijk ~, S. Vlachos 2, P. Weber 17, O. Wigger 13, M. Wolter 17, C. Yeche 14, D. Zavrtanik ~° and D. Zimmerman 3

l tlniversity of Athens, 2University of Basel, 3Boston University, 4CERN, 5LIP and University of Coimbra, ~Delff University of Technology, rUniversity of Fribourg, SUniversity of Ioannina, 9Univer- sity ()f Liverpool, loj. Stefan Inst. and Phys. Dep., University of Ljubljana, 11CPPM, IN2P3-CNRS et Universit~ d'Aix-Marseille II, 12CSNSM, IN2P3-CNRS, Orsay, 13paul-Scherrer-Institut(PSI), 14CEA, DSM/DAPNIA, CE-Saclay, 15KTH Stockhohn, 16University of Thessaloniki, lrETH-IPP Ziirich

0375-9474/98/$19.00 ¢_~ [998 Elsevier Science B.M All rights reserved. Pll S0375-9474(97)00532-0

158c R. Adler et al. /Nuclear Physics A626 (1997) 157c 165c

CP.T and CPT violation parameters to be extracted from time dependent asymmetries of the form:

A I ( r ) = /{FJ_~7(w) - REO~/(r) (1)

The CPLEAR experiment makes precise measurements of the CP violation parameter ~+_ [3] for ,7+7r decays and of the KL-Ks mass difference Am [4] from semileptonic decays. Other measurements include the determination of T and CPT violation parameters from semileptonic decays, and of the parameter z (to test the validity of the AS = AQ rule). The CP violation parameters in the 7r+~r-7~ ° [5] and 7r°7r ° [6] systems are also measured. The most sensitive indirect test of CPT invariance, based on the comparison between 0+ ~ the phase of rl+ , to 0sw, the superweak phase, is improved by using several of the CPLEA1R results.

2. THE CPLEAR EXPERIMENT

The K ° and ~o mesons are produced in equal amounts in pp annihilations at rest, through the channels:

pi5 ~ t(-Tr+K ° (2)

p~ ~ I<+~r-~ (3)

each one with a branching ratio of ~ 2 x 10 -3. The strangeness of the neutral kaon t<°(~ ~) at r = 0 is defined by the associated charged kaon K-(K~).

The detector[7] has a cylindrical geometry and is mounted inside a solenoid magnet of 3.6 m length and 1 m radius, producing a field of 0.44 T. It allows the detection of neutral kaon decays for the eigentime range 0 < r < 20 rs (rs is the Ks mean life). The 200 MeV/c antiprotons from the Low Energy Antiproton Ring (LEAR) of CERN at a rate ~ 106 s -t stop and annihilate inside a gaseous hydrogen target (16 bar pressure) at the centre of the detector. Charged particle tracking is performed by two multiwire proportional chambers, six drift chambers and two layers of streamer tubes. A scintillator(S~)-Cerenkov(C)- scintillator(S2) sandwich (PID) provides kaon/pion separation online and electron/Don separation otttine. The threshold for producing light in the Cerenkov is 300 MeV/c for pions and 700 MeV/c for kaons, allowing identification of the associated charged kaon by S~CS2 signals from the PID. Finally, an 18 layer lead-gas sampling electromagnetic calorimeter (X0 ~ 6.0) is used to detect photons.

A multi-level trigger system, including custom-made hardwired processors, provides a fast event selection. The trigger is based on particle identification, kinematical selection and shower counting, and provides a rejection factor of ~ 1000 in less than 34 ~s.

3. K ° ( K ° ) ~ n + n - DECAY MODE

The rates for initially pure K ° and ~0 decaying into the 7r+Tr - final state, R(T) and R(T) respectively, can be expressed as a function of the decay' eigentime r by:

1 T 2ReCe)[e_rs , + irl+_l u e_r , , + 2 I~+-I e ~(r,+rL>, cos(Am~ - 0+-)1 (4) R(T), ~(T) o~ 2

R. Adler et al./Nuclear Pt~vsics A626 (1997) 157c 165c I59c

where ~ describes CP violation in the kaon mixing matr ix and ['s.c are the decay widths of the Ks and KL, given by F.s.c = 1/%.L respectively. The I'll - t(s interfl'renc{~ term is

isolated by forming tile a symmet ry of tile observed rmmber of K c) and ~1 de('ays t(~ 7 " 7 - . N ( r ) and N ( r ) , as a function of tD' decay time:

- - l,-,. ~> cos(.Xmr O. ) .',- (.,-) - o, ~ ; ( 7- ) I,/+ I ~ :

1 +!r]+

The acceptances common to K ° and ]~' cancel in tile asymmetry, thus reducing the

systematic uncertaint ies . The K ° and I7 ° tagging efiqciences are not equal due to the difl'erent s t rong interact ion cross-seclions of K + and K , and of ~+ and 7r-, in t, he det('ctor material . Therefore the normal iza t ion factor (~ includes the tagging efficiency ~ of t,2 °

r('lative to I,, . (:~ _~ [[ + 4Rc(c)] × (. and is determined from the da ta together with the' CP violation parameters )t~ I and o , .

~" .o~ i ~,

,0 4

1o .~

:0 ~

\

6 8 10 12 14 16 18

Ii/$s

404 F

I

0.2

~,I i ~,.

/ 0.1 /~

-0.1 ! 0.02[

-0.2

-0.,3

-0.4

-0.0

0

2 i i

2 4 6 8 ~0 12 14 }6 18 20 T / 7 S

Figure 1. Summed K ° and ~o decay rates to v+Tr-, normal ised and acceptance cor- rected, and the background contr ibut ion from semileptonic decays.

Figure 2: A+_ asymmetry as a funct ion of decay time. The line is a result of our fit.

160c R. Adler et al./Nuclear Physics A626 (1997) 157c-165c

In this analysis we used a kinematical and geometrical fit with nine constraints. The fit improves the signal to-background ratio and the decay' time resolution. The onlv remaining background source consists of semileptonic decays. The amount of background

can be determined by summing the K ° and R ° decay time distributions, in which the Ks - KL interference cancels, and fitting the expected kaon decay rate and background shape, leaving the Ks lifetime and background level as free parameters, fig 1.

A total of 7 x 107 K°(K -~) -+ rc+rr - events in the time interval between 1 rs and 20 <s' are selected in this analysis. Figure 2 shows the asymmetry A+_ (7).

Using the value :Am = (530.7 ± 1.3) × 107hs -~ [81, and all data the preliminary result is:

Ir/+-I = ( 2 . 3 1 6 ± 0.025=t~t ± 0.028sy=t i 0.011e~t) × 10 3 (6)

o , 4 3 . 5 ° ± o :t= o ± o = 0.5=t~t 0.5=yst 0 4 ~ t (7)

Our systematic errors result mainly from the uncertainty on the value of Arn and the present uncertainty on the difference between the forward scattering ampli tudes of K ° and ~o due to the absence of da ta in our energy region. We have used the values calculated recently by Eberhard and Uchiyama [9] in order to correct for coherent regeneration on an event-by-event basis.

In 1996 a dedicated measurement of the difference between the K ° - ~o forward scattering ampli tudes in carbon at low momentum was carried out with the CPLEAR detector. This was done by inserting a 2.5 cm piece of carbon over a azimuthal angle of 120 ° at a radius of 6.5 cm to enhance the regeneration effect.

Figure 3 is a preliminary plot of the effect of the carbon regenerator on the K° /K° ratio compared with no regenerator, and the predicted effect using the Eberhard and Uchiyama values. After this measurement the systematic error on ~+_ due to regeneration effects is expected to decrease to less than 0.2 ° .

4. D E T E R M I N A T I O N O F A m A N D x F R O M K ° ( K °) --> n e v D E C A Y S

The C P L E A R experiment is able to tag the strangeness of the neutral kaons both at their production and at their decays. Therefore we are able to measure four decay rates B, as a function of the decay eigentime r of the kaon, depending on the strangeness of the

neutral kaon (K ° or ~0) at the production time, r = 0, and on the charge of the decay lepton (e + or e - ) . Such information means that a direct measurement of T violation can be made, as well as a direct test of CPT invariance.

R+(r) =_ R[K°(T=o) -+ e+~-u](r) R-(r) - R[K°(¢:o) -+ e-~+~](r) (8)

R (7) - R[K°{T=0) -~ e-~+~](T) R+(~) - R[~°{T=0) -+ e+~-~](T) (9)

The KL -- Ks mass difference Am, is obtained from the asymmetry

R. Adler et al./Nuclear Physics A626 (1997) 157c-165c 161c

i.6

1.5

14

13

12

I 1

i

0.9

0.8

• With Reqener<

a Without Regel

c: Prediction

0 2 4

I

[G r

erator

, * , i , I , , , I , , , I , , , I , , , I ,

8 IO 12 14 In 18 Transverse Rod[us (cm)

Figure 3. K°/K° ratio as a function of decay radius a) without regenerator b) with regenerator (measured) c) with regenerator (predicted).

[R+(T) + ~-(T)] - [~+(~) + R-(~)] A A ~ ( ~ ) = [R+(~) + ~ - ( ~ ) ] + [~+(T) + R-(~)] =

= 2 cos(Amw)e-½ (rs+rL)~ (10) (1 + 2 Re (X))e-FsT + (1 -- 2 Re (X))e-FL~

where a possible violation of the AS = AQ rule is taken into account by the parameter Re (x)[2].

The effect of the strangeness normalisation and the semileptonic channel identification is particularly small due to the manner of construction of the asymmetry A A m (Eq. 10)

which compares two sets of data containing both K ° and ~-0 and also e + and e-. Similarly, the rates entering A A m do not need to be corrected for regeneration in the detector material, since in the construction of A A m all terms linear in the regeneration amplitude cancel.

The semileptonic event selection includes the separation of electrons from pions by neural networks using information from the PID. Further event selection techniques in- clude the use of constrained fits using kinematical and geometrical information(6 con- straints) which provide significant reduction in the ~+~- background at low lifetimes. The decay time resolution after all selection cuts is better than 0.1 Ts. The data sample contains ~ 1.8 × 106 (K °,~-° ~ Trey) events collected up to mid 1995.

162c R. Adler et al. /Nuclear Physics A626 (1997) 157c-165c

>, 0,8

0.7

o~ [3

0,5

0.'*

0.3

0,2

0.1

-0 ,1 " ,~a ,¢ ' .

2 4 6 8 I0 12 14 16 18 20

Tff Ts

Figure 4. Tile time dependent AAm asymmetry. The line is the result of our fit.

The background is determined from a Monte Carlo simulation and consists mainly of residual neutral kaon decays to rr+~r - and is concentrated at short decay times. Our prel iminary result for all da ta is, fig. 4,

Arn = (0.5292 + 0 . 0 0 1 8 s t a t -I- 0.0005syst ) × 101°hs 1 (11)

which does not depend on the value of ¢+_ and is the most precise value obtained using semileptonic final states[2]. The value obtained for Re (z) is consistent with zero.

5. D I R E C T M E A S U R E M E N T OF T V I O L A T I O N

Since weak interactions do not conserve strangeness, a K ° meson can transform itself into a ~o meson in the course of time, and vice versa. Time reversal invariance demands that the two processes should proceed at exactly the same rates.

By using the tagging information at the production and decay of the neutral kaon, and assuming the validity of the A S = AQ rule, we are able to measure the rate of K0 --+ ~o transit ions, and vice versa. We are then able to compare the two transit ion rates by forming the following asymmetry:

~+(t) - R - (-,-) (12 )

R. Adler et al. /Nuclear Physics A626 (1997) 157c-165c 163c

where the parameter 2" is assumed to be zero and ~7' describes CP and T v io la t ion . . \ preliminary fit to this asymmetry using 25(;4 ̀ of available data gives:

.4r = (6.3 ± 2.1,t,t ± 1.8,v.~¢) × 1 0 - 3 (1:~)

where we note t, hat the expected value o{ A'v assuming CPT symmetry is 6.52 × l 0 The effect of T violation is expected at level of 10 a since CP is known to be violat,(,d at this degree and CPT invariance is believed to be exact.

6. D I R E C T T E S T O F C P T I N V A R I A N C E IN T H E K ° KO M I X I N G

CPT invariance implies, independel~t of T mvariance, that the mass and decay widths of

Ill,! I< ~) and I~ } , I~ ) are equal. By using >= C P T i K ° > within an arbitrary phase it ('an t)c prov( ' l l t h a t t i le a , symlne t ry . \ c p l :

/~ - R + A('r,r(m) - ~ 4 He (6cpr) (14)

R +R +

is sensitive to CPT violation when r >> rs. This is because CPT invariance requires .--;0.,

that the fraction of K°'s which survive as K ° is exactly equal to that of K s which remain

t~ '). .\ fit to ACpT(r) for large lifetimes using 25% of available data gives for Re(ace.r) a preliminary value compatible with zero,

R~ (6C'PT) = (0 .07 ± 0.53~t~L ± 0.45,v,t) X 10 -a ( t 5 )

7. I N D I R E C T C P T T E S T

The best limit on CPT violation is obtained by comparing the phase of r/+_ with the superweak angle ¢Ssw = t a r z - ~ ( 2 A m / A P ) , where AF = F s. - Fl,. The equation that relates 7;+ and ST is:

rl+- = CT + 6± + Z~O + C' (16)

where CT ticks a phase Csw and 5± describes the component of the CPT violation parameter 6CPT perpendicular to Cr,

i A F - 2Am -,S± _= 4Am2 + AF 2 (M>, - 3,1Ko) (17)

where Mgo and MKo are the ~o and K ° masses respectively and CPT conservation in the decay amplitude is assumed. The term c' describes the CP violation in the decay amplitude and can be neglected since ld I < 10-s[2]. The term ¢50 is derived to be:

d)o ~ ~[2BR(K,.. -+ ~lu)Im(:r) + BR(KL -+ 3~)Im.(r13~ 'l+ )] (18)

164c R. Adler "et al./Nuclear Physics A626 (1997) 157c-165c '

Equation (16) can be written as

d± = (cp+_ - ¢ sw) Ir/+-[ - ¢oCOSCsw (19)

Using preliminary CPLEAR measurements of Im(rl+ o) = ( - 4 :t: 10,~at :t: 4,u~t ) x 10 -3 and 1re(x) = (0.5 + 2.4sta, + 0.6sust) x 10 -3, we find ¢ocosCsw/}~7+-I = 0.02°± 0.15 °, compared with -0 .2 ° + 2.3 ° using PDG values [2].

This gives, together with our measurements of 8+- and Am, and AF from [2], a value

for the K°-K -° mass difference of:

[ :rt[~° --~'[l<° 10 -19 (90%C.L.) (20) :~IK I < 7.2 ×

8. T E S T O F Q U A N T U M M E C H A N I C S

()n a macroscopic level, Hawking [10] suggested that information is lost across 'horizons' (Black Hole radiance theory). On a microscopic level, due to quantum fluctuations this would entail space-time having a 'foamy' structure from creation of black holes on the Planck scale ('microhorizons'). Loss of information due to the microhorizons would res- ult in the loss of quantum coherence, allowing pure states to mix and necessarily CPT violation.

In this framework the modified quantum Liouville equation becomes [11]

/5 = z[p,H] + ~ H p (21)

where p is the energy density and ¢/Hp is the term which introduces the loss of quantum coherence, which in the proposed model [11] is expected to first order to be (9 (m2K/Mpt ,~ 2 x 10 -2° GeV).

The description of the open system in eqn. (21) introduces three energy conserving, CPT violating parameters (c~, fl, 7). The parameters must obey the conditions c~, 7 > 0 and c~ 7 > f12.

By fitting CPLEAR data for 7r+Tr - and 7reu simultaneously, plus using long-lifetime data from other experiments [12] for added constraints we find the following limits:

c~ < 4 .0 x 1 0 - 1 7 G e V [fll < 2.3 x 1 0 - 1 9 G e V 7 < 3.7 x 1 0 - 2 ~ G e V (22)

where we note that these limits approach the range of interest for testing the ideas based on quantum gravity.

9. S U M M A R Y

We have reported precise measurements of ¢+_ and Am from the CPLEAR experiment, where the Am measurement is the best by any single experiment. Further, a measurement in 1996 of regeneration parameters in our energy region will help to reduce our systematic error on 6+- to less than 0.2 °, making it the best single measurement of ¢+_.

By using these results with other CPLEAR measurements we have compared ¢+_ with the superweak phase 6 s w to provide the most sensitive indirect test of CPT invariance.

R, Adler et al./Nuclear Physics A626 (1997) 157c-165c 165c

We have also made direct tests of T and CPT symmetries and will provide improved measurements on these parameters in the future.

Also, we have provided limits on possible loss of quantum coherence due to quantum gravity.

R E F E R E N C E S

1. E. Gabathuler and P. Pavlopoulos, Strong and weak CP violation at LEAR, Proc- eedings of the Workshop on physics at LEAR with low energy cooled antiprotons, ed. U. Gastaldi and R. Klapisch, Plenum publisher, p.747 (1982).

2. Review of Particle Properties, Phys. Rev. D50 (1994) 1173.

3. CPLEAR Collaboration Phys. Lett. B363 (1995) 243.

4. CPLEAR Collaboration Phys. Lett. B363 (1995) 237.

5. CPLEAR Collaboration Phys. Lett. B370 (1996) 167.

6. CPLEAR Collaboration Zeit. Physik C70, (1996) 211.

7. CPLEAR Collaboration, Nucl. Instr. and Methods A, A379 (1996) 76.

8. CPLEAR Collaboration, Phys. Lett. B369 (1996) 367.

9. P.H.Eberhard and F. Uehiyama, Nucl. Instr. and Methods A350 (1994) 144.

10. S.Hawking, Comm. Math. Phys. 87 (1982) 395.

11. J.Ellis, J.S. Hagelin, D.V. Nanopoulos and M.Srednicki, Nucl. Phys. B241 (1984) 381.

12. C.Geweniger et al.,Phys. Lett. B48 (1974) 487.