Volume 44 B, number 2 PHYSICS LETTERS 16 April 1973

S E A R C H F O R T H E D E C A Y K s -* 2#

S. GJESDAL, G. PRESSER, P. STEFFEN, J. STEINBERGER F. VANNUCCI* and H. WAHL

CERN, Geneva, Switzerland

H. FILTHUTH, K. KLEINKNECHT**, V. LUTH and G. ZECH Institut fiir Hochenergiephystk, Heidelberg, Germany

Received 1 March 1973

A search for the decay K S ~ 2~ has given negative results. The 90% confidence upper limit for the branching ratio of 3.1 × 10-7 excludes the models of Christ and Lee, and of Dass and Wolfenstem, designed to explain the K L --* 2t~ problem.

In this letter, we present the result of a search for the decay K s ~ 2/a. The experiment was motivated by the suggestion of Christ and Lee [1] that an un- expectly large, CP-violating decay K S ~ 2/z could overcome the difficulties encountered in the explana- tion of the results of Clark et al. [2] in the decay K L ~ 2#. In the search for this decay, the authors obtain an upper limit of 1.8 × 10 -9 for the branching ratio, whereas this decay can proceed via the inter- mediary of two gamma-rays, and a minimum branch- ing ratio 6 × 10 -9 can be predicted on the basis of the known 23' decay rate and unitarity [3]. The sug- gestion of Christ and Lee was generalized somewhat by M.K. Gaillard [4], and incorporated in a definite model by Dass and Wolfenstein [5]. The Wolfenstein model is very simple and is the following. Let K 1 and K 2 be the TCP positive and TCP negative K ° ampli- tudes, respectively. Then a (CP-violating) K 1 ~ 2/1 amplitude is proposed which adequately cancels the "unitarity amplitude" K L ~ 23' ~ 2/a. This imposes the boundaries 12.5 X 10 -6 >i F(K S -~/a/a)/F S t> I> 1.1 X 10 -6 on the branching ratio for the K s -* 2/a decay. This probably is the only sensible way in which the abstract suggestion of Chnst and Lee can be realiz- ed. The less specific arguments of Christ and Lee, and Gaillard, give the less restrictive lower limits F(K s -* #/a)/P S >i 5 X 10 -7 and 2.8 X 10 -7 , respec- twely, for the branching ratio.

* On leave from IPN, Orsay, France ** Now at Universitht Dortmund, Germany.

The experiment was done in a short neutral beam at the external proton beam of the CERN PS. Protons of 24 GeV/c were hitting a platinum target. Neutral par- ticles produced under 75 +- 12 mrad were accepted by a 2 m long tapered uranium collimator, embedded in a 20 kG magnetic field.

Neutral two-body decays were recorded in a magnetic spectrometer [6] using four pairs of planes of multiwire proportional chambers [7], at 4.65 m (A), 11.60 m (B), 16.35 m (C), and 22.57 m (D) from the production target, as shown in fig. 1. Downstream of the last pro- portional chamber, a plane of 12 scintillation counters, each 1.6 X 425 X 450 mm 3, arranged 6 above and 6 below the symmetry plane, was used for triggering on charged particle pairs. This plane is followed by an absorber made of light concrete (A = 19, Z = 11), 280 cm long, a vertical hodoscope of scintillation counters (6 × 1200 × 375 mm3), 40 cm light concrete and a horizontal hodoscope of eight counters (6 × 1500 × 300 mm3). The surface covered by the two hodoscopes ("/a counters") is-300 X 120 cm 2. Details of the apparatus are described elsewhere [6].

Events were recorded on magnetic tape whenever there were two or more hits in the trigger counter plane, two hits in the two vertical wire planes of chambers B and C, one or two hits in the two horizontal wire planes of these chambers, and two hits in the horizontal and vertical wire planes of chamber D. For a spdl-out time of 350 msec, there were about 800 events recorded per PS burst. The total sample contains 109 events; for a quarter of It (sample I) the first chamber (A) is mssing.

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Volume 44B, number 2 PHYSICS LETTERS 16 Apnl 1973

- J l=

MAGNET 6 MIlk'ORS

TARGET COLLIMATOR & ~ 7 " - ~ n / o. ' SWEEPI~ ~ E " T . . . . . . . . ~ a ,-n t

Fig 1. Layout of the spectrometer: top part, horizontal view; lower part, vertical view.

MUON COUNTERS

From the total sample were selected two classes of events:

i) events where the intersects of both decay particle trajectories with the muon counter planes were inside the area of a V counter registering a pulse; to allow for multiple scattering in the concrete absorber, events with intersects in a ring of width w = 40 cm/p (GeV/c) around the counter were also admit ted;

il) events with no/a counter hit satisfying all criteria for K S ~ n+rr - decay, used for normalizing the K s flux.

lala s e l e c t i o n . T h e chief source of background is the decay K S -+ 2n, in which the plons either decay or leak through the muon shield. The former can to some ex- tent be removed from the sample by making stringent condit ions on the kinematic variables which ensure that the observations represent the decay of a neutral particle originating at the target. These are i) vertical "k ink" angle in track 1, i0 vertical "k ink" angle in track 2; ni) skewness of the two tracks; iv) vertical re- constructed origin in the target plane, YT; v) horizontal reconstructed origin in the target plane, X T. The first three of these variables a l were combined to give a X 2 = Ez(a I - a-l)2/o7. The average al and the standard deviation o t of each variable were determined from clean samples of K S ~ 7r+Tr - decays. The resolution is about o = 0.25 mrad for the vertical kink angles and o = l m m for the closest distance between the two tracks.

Addit ional selection criteria include the following: 1) The decay vertex Z must be within a 2 × 10 -10

sec proper time interval starting at a distance of Z = 220 cm from the target.

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d) The momenta of the charged particles Pi must be Pt >~ 2 GeV/c. This is substantially above 1.45 GeV/c, the # penetrat ion threshold through the concrete shield.

in) There must be an upper limit on the known kaon momentum of 18 GeV/c for sample II and 13.5 GeV/c for sample I. The lat ter lS more restricted because of the poorer mass resolution without chamber A

After applying criteria (i) to (iii), and retaining "good V ° events" satisfying the condit ion X 2 < 3, we consider the scatter plot o f the invariant mass of the two particles and the variable R 2 = (YT - YT) 2 + + (X T - ,~T) 2 . Fig. 2 shows this plot for/a+/l - candidates and for 7r+n - events. While for the 7r+n - events there is a clear clustering around the K ° mass and R2=0, no such signal is seen m the/a+/~ - candidates sample. We take the 7r+n - sample as a guide-hne and select the cuts 491 < m m

< 505 MeV andR 2 < 0.1 cm 2 to identify K ° decays coming from the target. In this area there remains one /a+/a - candidate.

We take the region 488 < m u u < 508 MeV and 0 ~<R 2 < 1.0 cm 2 as a control region to estimate the expected background In the region for good events There are 32 -+ 5.6 events in the control region. I f we assume a constant density of background events in this area, we expect 2.2 -+ 0.4 background events m the region 491 < m u u < 505 MeV and R 2 < 0. I cm 2. I f P ( x , m ) = e - x x m / m ) is the Poisson distribution, then we calculate the 90% upper hmlt g for the num- ber of good K S ~/~+/~- events by the equation

0.1 = P(2.2, 0) X P(~, 1) +P(2 .2 , 1) × P(~, 0) P(2.2, 0) + P(2.2, 1)

The result is ~-= 2.7.

05 c r n z

R z

01 I

520 MeV I m~rn

15 c m 2

R ~

10

05

01

480 500

• • . • *

F - - : . . . . . . . . . . . . . • * i

• ... "I

• z, * *'* .:i " " "

• : : : ' , : ' : • i • "" .1": .*~ I • •

tL':,"":"i ,F-:---I ~.BO 500

~000

QO Q DQ

I,

I i J , , ,

520 MeV m~j/a

i000

;000 ~- Z i , i > LU

3ooo i=

Volume 44B, number 2 PHYSICS LE'ITERS 16 April 1973

;~000

1000

450 /,70 490 510 , MeV

Fig. 2. Scatter plot displaying the mvariant mass o f the pair versus R 2 as defined in the text . The upper plot is for events w~thout a m u o n counter hi t , the lower one for events w~th two p hits

Fig. 3. Invarmnt spectra for g# candidates and for a small sample of K S ~ ~r+lr-events after application of identical kinematical and geometnca l cuts (except those used for the # defimtlon) to bo th classes of events, including a cut R 2 ~ 0.1 cm 2.

The projection of the scatter plot after a cut R 2 < 0.1 cm 2 is shown in fig. 3 and illustrates the fact that the main background source is the K S ~ zr+n - decay with rr's decaying or leaking through the/a shield.

Effective flux determination. The K s flux was ob- tained from the number of 7r+Tr - decays. The same kinematical and geometrical cuts were applied to events without a/a counter hit. The rnr invariant mass spectrum of a sample of these events is shown in fig. 3. For the entire sample there are 8.4 X 106 K S ~ 7r+lr - events without a/a counter hit in the mass interval 4 9 1 - 5 0 5 MeV. This number must be corrected for branching ratio, and loss due to 7r decay. The ~r ~ pv decay pro- babil i ty is 6% for the average accepted K ° momentum of 11 GeV/c. Since the probabil i ty o f rejecting such a decay muon is ~ 90%, the total number o f KS decays l s N s = 8.4 X 106 X ~ × 1/0.89 = 14.2 X l0 b . The detection efficiency of the/1 counter telescope was measured for events of the type K L ~ nov From a

sample of original data, events which satisfy the cri- teria Z > 500 cm, 380 < m* < 470 MeV, and

I(P + - P-)/(P+ + P-)I < 0.5 were selected. There are K decays, and because of the cut on m* they are neither K L -~ 7r+Tr-rr ° nor K L ~ lr+Tr - . Removing the K L -~ nev decays, which are identified by the Cerenkov counter with an efficiency ~ 99%, we are left with an adequately pure sample of K ~ zr/av events. For (75 + 3)% of this sample the muon is detected in both counter planes in the fiducial area around the projected track direction. A Monte Carlo calculation simulating the same class of events gave an efficiency of eu(Ku3 ) = (79 + 3)%. The agreement of the calculation with the observat]on makes it possible to use the same calcula- tion with confidence in the 2/a case.

The result, averaged over the experimental K ° mo- mentum, is e CTR = 0.84 + 0.03 for detecting both uu muons for K S -~/a+/a - events accepted by the spectro- meter. The efficiency is higher in the 2/a decay because

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Volume 44B, number 2 PHYSICS LETTERS 16 April 1973

of the higher momentum of the muons. Another fac- tor, evaluated using the Monte Carlo calculation, is the ratio o f detection efficiencies in the spectrometer for K S ~ 7r+Tr - and K S ~/a+/ l - decays. The result, again averaged over the K ° momentum spectrum, is

SPJ SP el~tzle~7 r = 0 73 + 0.04.

The number N e f f of K S decays relevant to the detect ion of the decay K S ~ 2/~ is then

Neff=(eSP, uu/eTr~r )sP X e C : R x NS = 8.7 X 106.

Combining the upper limit ~= 2.7 for good K S ~/~+/a- events and the effective flux Nef f as given above, the 90% confidence upper limit on the branching ratio

B ' = F(K S ~ 2p) /F s IS

B ' < ~-/Nef f = 3 1 X 10 -7 .

The model of Dass and Wolfenstem [5], referred to be- fore predicts a branching ratlo between 12.5 X 10 6 and 1.1 X 10 -6 . Our upper hmlt is well below the lower limit of this prediction. Also the lower hmit of Christ and Lee [1] of 5 X 10 -7 is not in agreement with this experimental number Our result is still compatible, al- though just barely, with the lower limit of 2.8 X 10 - 7

of M.K. Gaillard [4]. A realization of these lower limits requires, however, models with at least two new ampli- tudes to cancel the "unl ta r t ty" K L ~ 2# amplitude.

Recently Carithers et al. [8] reported an experiment which disagrees with ref. [2] in that the decay K L ~ #+/a- is observed at a branching ratio well above the lower limit o f ref. [3]. Our result is in line with this experiment m the sense that if the umtary limit in K L -~ #t+/a - is not violated, then there is no expectat ion for K s ~/a+/ l - at the level of our sensltwity.

References

[1] N. Christ and T D. Lee, Phys. Rev. D4 (1971) 209. [2] A.R. Clark et al., Phys. Rev. Lett. 26 (1971) 1667. [3] L M. Seghal, Nuovo Cim. 45 (1966) 785; Phys. Rev. 183

(1969) 1511. B.R. Martin, E. de Rafael and J. Smith, Phys. Rev D2 (1970) 179.

[4] M.K. Galliard, Phys. Rev Lett. 36B (1971) 114 [5] G.V. Dass and L. Wolfenstem, Phys. Lett 38B (1972)

435. [6] J.H. Dwperink et al., Proc. Int. Conf. on Instrumentat~otl

for high-energy physics, Dubna, 1970, p. 251. [7] P. Schtlly et al., Nucl. Instr. 91 (1971) 221 [8] W C Canthers et al , 16th Int. Conf. on high-energy phy-

sics, Batavm, Sept. 1972.

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