Nuclear Physics B (Proc Suppl.) 8 (1989) 393-396 393 North-Holland, Amsterdam

CP -VIOLATION IN THE COHERENT DECAY OF K°-K ° PRODUCED

~-p ANNIHILATION

JeSLlS ROLDAN,Jose BERNABEU andFranc lscoJ. BOTELLA

Departament de Flslca Tebrlca, Unlversltat de Valencia and

IF]C, Centre Mlxte Univ. Val~ncta-CS[C, E-46100 Burjassot, Valencia,

FROM

Spain

We study novel ways to measure the CP violating parameter ¢ ' /¢ by using the

method of the K°-K ° coherent decays.

1. INTRODUCTION

CP violation In K-* 27[ IS controlled by two complex parameters :

< ~ + ~ - I KL> < ~ °~° l KL> 11÷_ - ; % 0 = (1)

< KS> < ~°~°1K S)

From the theoret ical point of view It IS more Interesting to consider e and e ' given

by Yl+_ = 8+8 'and Tloo = e- 2e ' . e describes the contamination of CPvlolatlng terms In the

K°-K ° mass matr ix . e ' describes "d i rect" CP violation In the decay amplitudes

through possible d i f ferences betwen ~+~¢- and ~o~o channels. This IS the fundamental

parameter to test d i f ferent models of CP violation. Only recent ly a non vanishing value

for 6 ' / ¢ has been reported by the NA-31 Collaboration at CERN 1 and the E731

Collaboration at Fermi-Lab I :

[ ( 3.3 * 1.1 )10 -3 (CERN) E (2) t ( 3.2 + 2 . 8 ) 1 0 -3 (Fermi -Lab)

In all these experiments one has to prepare a K S beam, a non trivial task. This Implies the

dif f iculty to control huge systematic uncertaint ies.

2. COHERENT DECAY OF THE C=(-) STATE OF K ° ~o

We want to study here coherent decays of the K°-K ° system, Instead of having

to compare K S or K L "beam-decays". Suppose one Initial state corresponding to the

decay ~ -~ K ° ~-o or to s-wave anlhllatlon In the antlprotonlc atom ( ~p )s -* K° ~o If we

denote by A(Xl(t 1),X2(t2)) the decay amplitude corresponding to the apearance of final

states X 1 at t ime t 1 and X 2 at time t 2 ,we can construct the following rate :

N(XI 'X2)= I~ ! t l I~dlt2 IA(x l ( t l ) ,X2( t2 ) )J 2 (3)

394 J. Roldan et al. / CP-violation in the coherent dec,~y of K ° K °

which gwes :

N(X1 , x 2 ) __ (1+1=12) 2 1 12 12 81=12 £LrS I <Xl lKs> I <X21Ks>

{ rqll2 + Frl212 ) - 2C 2 Re('q 11 ) }

(4)

where < X I IKL> 1+~

~11 -= I = 1,2 and ~ - - - < X I I K s > 1 - e

and C1, 2 (1;1,1; 2) are tmme- lnterval dependent f a c t o r s .( see re fe rence 2 ). In pa r t i cu la r , fo r ~1=0 and ~2-* OO we have Cl(O,0o) = 1 and C2(O,o0) = 3.14 10 - 3 .

One can see tha t , fo r all expe r imen ta l t ime i n t e r v a l s m which 1:2 > 1 5 / r S , the

value of C 1 Is at least one order of magni tude l a rge r than C 2 It IS C 1 that

con t ro ls the to ta l number of events . The dominant decays f rom the (C =-) s ta te

cor respond to X 1 running over the leading modes of K L ( x x x , x / v ) and X 2 running

over the leading modes of K S ( x x ) and v l ceversa . The to ta l decay ra te IS given by

R = ~, N(XI ,X2) ( 1+1(xl2)2 I < a l I I K L > I 2 I<al l lKs>12

Xl,X 2 -~ 41el~'- rE £S C 1 -- C 1 (5)

We are In te res ted In the CP-v lo la t l ng decay of the K ° - ~-o sys tem to { 2~, 2~ }.

The cor respond ing branching ra t io Is

B r ( X I ' X 2 ) = N(XI'X~)R = Br( K s - - * Xl) B r ( K s - - * X 2) ~£rL •

{(l'qll 2+ I'I}212) -2 C2 Re(.q1~ ) } C1

(6)

w h l c h l s o f t h e o rder ( r s / [ ' L ) l e l 2 - 10 -3 .

3. MEASUREMENT OF e ' / e

Suppose the K ° - ~o sys tem to be In the de f in i te ( C = - ) s ta te , co r respond ing to a

re la t i ve angular momentum L=odd. Measure the number of coherent decay events

when both K ° 's decay to two plons In a given t ime in te rva l , and cons t ruc t

the fo l lowing quant i t y 3

N ( X I , X 2 ) Q(X1, X 2) ~ (7)

Br( K s --~ X 1) Br( K s ~ X 2)

J. Roldan et al. / CP-violation in the coherent decay of K° -~ "° 395

where Br is the corresponding K S branching rat io. The comparison of the

d i f fe rent decay channels gives 10 . 2 e f fec t In the ra t ios

~(1[ *1[ - ,~ +1[ -)

~(1[o .~o ,.~ o 1[ o)

0(~ +1[-,~ o 11o)

= 1 + 6 R e ( ¢ ' / ¢ )

= 1 + 3Re(¢ '/E)

(8)

which are independent of the chosen t ime in te rva l .

Assuming C1~, 1, one would need around 105-106 (K ° ~o) In the (C =-)

s tate to dist inguish a value of Re (e ' /e) around 10 -3

An Important point Is that , to the desired level of accuracy, the ra t io of K S

branching ra t ios IS provided in the same exper iment by the ra t io of branching

ra t ios of coherent decays f rom the (C=-) s ta te Into (2~) + X L , where X L Is a

dominant decay mode of K L (111[~,~Iv) :

B r ( K s - - ~ + ~ t - ) B r ( 1 [ + ~ - , X L )

Br (Ks - - ) 1[o ~o ) Br(1[o ~o. XL )

(9)

These are very good news to reduce sys temat ic e r ro r s .

These resu l ts are d i rec t ly applicable to ~ - f a c t o r l e s . In the preparat ion

of the K °- ~-o system through the ant lp ro ton-pro ton annihi lat ion ~-p -> K ° ~o at LEAR,

unless coincidence exper iments are planned, one expects to have an incoherent m lx tu re

of C even and odd e lgenstates of K°- ~o.

I f the Incoherent m ix tu re of (C=-) and (C=+) s ta tes of the K °- ~-o system Is

descr ibed by p= N u m b e r o f ( C = + ) s t a t e s / N u m b e r o f ( C = - ) s t a t e s , the observables are

now modif ied to g ive, for Instance

t3(~ +~- ,~ +1[ - ) { D l r L ] - I = 1 + 3 R e ( ~ ' / e ) 1+ 2 ( C l _ C 2 ) l ¢ l Z r s p + 0(10 -8) (10) ~o )

(D 1 Is a t ime- In te rva l dependent fac tor which appears In the (C=+) case,see re f .2 )

As long as p<<lO -3 , the contaminat ion of (C=+) s ta tes can be forgot ten.

On the cont rary , when p approaches the value 10 -3 or bigger, one needs to control

p In order to get Re(c ' / s ) . Notice that the e f fec t becomes now dependent on the

chosen t ime Interval (~1,~2), so a pr ior i a two parameter f i t to that dependence could

provide the two values Re(¢ ' /¢) and p independently. I f p aproaches 1, this separat ion

Is impossible. Of course, an Independent determinat ion of p can be obtained by noting

that the dominant decay channels of the (C=+) and (C =-) s ta tes of the K ° - ~o

system are completely d i f fe ren t . For Instance, f rom the ra tes of the dominant decay

396 J. Roldaa et a l . / CP-violation in the coherent decay of K°-K °

modes we get

Z N ( x s . X s ) p - 2 C1 xs, xs'

- - (11) D1 Z N(Xs'XL)

XsX L

This expression IS obtained under the approximation that only a (C=+) state

decays to the (Xs,X S) channels, and that a (C =-) state Is the only one decaying

to a (Xs,X L) channel. It Is of Interest to point out the non trivial time dependence

of the measured rates which has to be cancelled with the theoretical

predictions for C 1 and D 1 to produce a value of p independent of the time

Interval ('{1, t2)"

4. CONCLUSIONS

We have considered the coherent decays of the (C=-) state of the K °- ~o system

to { ~ , ~ } channels In a given time Interval . The comparison of (~ (see Eqs.(7),(8)) for

the d i f ferent channels gives directly e f fects of the order ¢ ' /¢ and It of fers a beautiful

method to determine this Important CP -violation parameter. The main advantages

of the method are the Independence of the chosen time Interval In the time Integrated

rates and the possible reduction of systematic er rors because we don' t need distinguish

K S and K L decays.

ACKNOWLEDGEMENT

J.R. IS Indebted to Generalltat Valenclana for a fellowship. This work has been

supported In part by CICYT under Grant AE-O021.

REFERENCES

1) H.Wahl, Tests of CP and CPT Invarlance, this volume

H.Burkhrardt et al., CERN-Dortmund-Edlnburgh-Malnz-Orsay-Plsa- Slegen

Collaboration, Phys. Letters 206B , 169 (1988)

CERN Experiment No. NA-31 Chlcago-Fermllab-Prlnceton-Saclay Collaboration (E731 at Fermllab)

2) J.Bernab6u, F.J.Botella, J.Rold&n, Phys. Let ters 211B , 226 (1988)

3) J.Rold&n, Master Thesis, University of Valencia (1988)