Volume 45B, number 1 PHYSICS LETTERS 25 June 1973

S E A R C H F O R T H E D E C A Y 7r ° ~ 43, *

R.J. ABRAMS*, A.S. CARROLL, T.F. KYCIA, K.K. LI, D.N. MICHAEL, P.M. MOCKETT** and R. RUBINSTEIN Brookhaven National Laboratory, Upton, New York 11973, USA

Received 7 May 1973

We have searched for the decay ~r ° ~ 4"), using the decay K s ~ *rS*r ° as a source of kinematically defined #° 's . No events were observed, where one event would correspond to a branching ratio (,r ° ~ 43")/(*r ° --, 23') of 2 .7× 10 -s .

The decay rr ° ~ 43' is not forbidden by any known conservation laws, though no searches for it have been previously reported. It has been pointed out [ 1 ] that this decay could be a source of background in ex- periments searching for the C violating decay lr ° ~ 33' [ 2 - 5 ] . A first guess for the value of the ratio R = (Tr°~ 43')/(~r° ~ 23') might be " 0 t 2 ( 5 X 10-5); an early estimate [ 1 ] for R indicated that it could be ~ 10 -9 , while a recent calculation [6] gives values in the range 10 -13 to 10 -16 .

We have searched for this decay concurrently with an experiment [7] whose prime objective was to study K +- ~ ~r-%r°3'; kaon decays in flight were studied using a 1.8 GeV/c partially separated beam at the Brookhaven National Laboratory AGS. The incident kaon and its charged decay pion were recorded with a core readout wire chamber spectrometer. The conversion points of 3"s from the decay were recorded in a 3' detector [8] which consisted of eight layers of lead, optical spark chamber, and 32 element scintillator hodoscope. The trigger required an incident kaon, three or more 3"s in the 3' detector and a charged particle in a hodoscope at the end of the spectrometer. Approximately equal numbers of K ÷ and K - decays were recorded.

From the wire chamber information, the c.m. momentum of the charged secondary, assuming it to be a pion, was calculated for those events with a decay vertex within the fiducial volume. In fig. 1, this c.m. momentum spectrum is shown for those events

~' Work supported by the U.S. Atomic Energy Commission. * Present Adress: University of Illinois, Chicago, Illinois.

** Present Address: University of Washington, Seatle, Washington.

Z l.d

> 400

r n

~ 200 Z

w _>

_.J "' O(

I I I I

50 I O0 150 200 250

CENTER-OF-MASS MOMENTUM (MeV/c)

Fig. 1. Center-of-mass momentum spectrum of the charged secondary (assuming it to be a pion) obtained from the wire chamber information, for events where the 7 hodoscope indicated four 3"s. Events between 200 and 210 MeV/c were selected for scanning.

where the 3' hodoscope indicated four 3"s, with at least one hodoscope counter separating 3' showers. Most events with c.m. momentum below 135 MeV/c are due to K s ~ ¢rSTr°rr ° decays, while those near 250 MeV/c would be due to K ± ~ lrs,r°(Klr2) followed by lr ° ~ 43' if our trigger were perfect. In general, however, these latter events will be normal 7r ° ~ 23' decays where the 3' showers break up to trigger four non-adjacent groups of scintillators in the 3' detector. There will also be some K s ~ #£v and K s ~ lr+-Tr°3' events followed by shower breakup, and some acciden- tal coincidences of K +- -~ 7rSlr°rr ° decays with either another beam particle or another decay. The main problem, therefore, was to remove the background from the events in the region of c.m. momentum 205 MeV/c, to see if there are any lr ° ~ 43' candidates.

From our knowledge of the properties of the indicent kaon beam, the spectrometer, and the 3' hodoscope including the 3' detection efficiency as a

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Volume 45B, number 1 PHYSICS LETTERS 25 June 1973

function of 7 energy [8], we made a Monte Carlo study of KTr2, n ° ~ 47 decays in our apparatus, where we assume that the 7r ° ~ 43' decays have a phase space distribution. From this Monte Carlo study it was found that for Krr 2 decays in our fiducial volume, 1.2 X 10 -3 of all 7r ° ~ 43' would be detected. The number of real n ° ~ 47 events that would be lost by any cuts applied to the data could also be determined.

To search for rr ° ~ 43' events, all the 3' detector optical spark chamber photographs were scanned only for those triggers which had a charged pion with c.m. momentum between 200 and 210 MeV/c; there were a total of 16000 such candidates, for our sample of 1.7 X 1010 incident kaons. Of these, 1001 were found to have four visible showers (defined as two or more sparks not necessarily consecutive) in the scintillators that triggered the event. The conver- sion point of each 3' was measured, and using the decay vertex obtained from the wire chamber infor- mation, the four 7 directions were obtained.

The following procedure was followed in order to remove background from our sample.

1) The incident kaon and outgoing pion momenta were adjusted slightly to make the pion c.m. momen- tum for each event be 205 MeV/c the exact c.m. momentum for Kn 2 decay. The direction and momen- tum of each n ° is then known. From this and the four 3' directions, the four kinematic equations for 7r ° ~ 43' can be solved, giving the four 3' laboratory energies. Many of the solutions were non physical, giving one or more negative momentum photons, and these events were removed, leaving 63 candidates. The Monte Carlo generated events showed that be- cause of our known measurement uncertainties this procedure would lose 18% of real rr ° ~ 43' events.

(See fig. 2a) 2) Since we expect many events to be Krr 2,

rr ° -~ 23', followed by shower breakup, all remaining events were fit to this hypothesis, taking all combina- tions of two 3'% from the four found. A X 2 for this hypothesis was formed, and all events were eliminated that had a probability of 1% or greater of fitting to this decay mode. This reduced our sample to 10 candidates. The Monte Carlo generated events showed that only 15% of true 7r ° ~ 43' events would be lost by this cut. (See fig. 2b)

3) Another we can use to eliminate shower breakup events is the relative position of t h e vertices-

k.-

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:3 Z

2001 I I I r-: I

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0 I I I I ' " - - I00 - 5 0 0 5 0 I 0 0

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150

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EVENTS

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3 0 6 0 9 0

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t Fig. 2. In each of the figures, the solid histogram is our total data sample and the dotted histogram is the Monte Carlo study of K ± ~ 7r-+lr °, lr ° ~ 43' (using a phase space distribu- tion), normalized to the same total number of events. The arrows indicate the positions of the three cuts described in the text. a) Histogram of E3"mi n , the minimum of the four 3" laboratory energies for each event, b) Histogram of the

2 2 smallest value of X~rO.~2, r for each event; ×~rO._.2.r is the x 2 for the fit of any pair of the four 3"s to the decay K ± ~ 7r±~r °, 7r ° ~ 23'. The shaded events are those which survived the cut in a, above, c) Histogram of the smallest value of 03,3' for each event; 03,3, is the angle between the line joining the conversion points of two 3,'s, and the incident kaon direction. The crosses indicate those events which survived the cuts in a and b, above.

of two showers. In general, a subsidiary shower will appear close to the axis of a primary shower and deeper in the detector. To make this quantitative, we eliminated events where the line joining the

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Volume 45B, number 1 PHYSICS LETTERS 25 June 1973

conversion points of any two showers made an angle of less than 45 ° with the incident kaon direction. The Monte Carlo study showed that this cut would only loose 4% of true rr ° ~ 43' events, while our experimen- tal sample was reduced to three candidates after this cut. (See fig. 2c)

4) As shown in ref. [8], the length of a 3' shower in our detector can be predicted from the 3' energy to an accuracy of ~-+40%. Each of the surviving candidates was tested by comparing the measured shower lengths with those predicted from the 3' laboratory energies obtained in test 1). The three candidates all had probabilities of under 0.1% for the lr ° --> 43' hypothesis. We conclude that they are not zr ° ~ 43' decays, and that we have not observed any such events.

The Monte Carlo calculation (assuming a phase space distribution) of the detection efficiency for true KTr2, 7r ° ~ 43' events accepted by our apparatus, after the analysis cuts described above, is 7.8 X 10 -4 . In order to calculate an upper limit to the branching ratio, we use the number of incident kaons (1.7 × 1010), the fraction decaying in our fiducial volume (0.053) and the KTr 2 branching ratio

(0.21). We correct for the fraction of K~r2's with c.m. momentum between 200 and 210 MeV/c (0.62), scanning efficiency (0.79), wire chamber spark efficienty (0.94), wire chamber track reconstruction efficiency (0.89), experimentally measured Klr 2 rate (0.80) and other minor corrections (0.78).

The result is that one observed event would corre- spond to a branching ratio R = (n ° ~ 43,)/(7r ° ~ 23') of 2.7 X 10 -5 . Since we observe no events, we can place an upper limit to this decay mode of R < 6. t X 10 - 5 (90% confidence limit).

References

[1] A.V. Tarasov, Soviet J. Nucl. Phys. 5 (1967) 4~5. [2] R.P. Ely and D.H. Frisch, Phys. Rev. Lett. 3 (1959) 565. [3] D. Cline and R.M. Dowd, Phys. Rev. Lett. 14 (1965) 530. [4] J. Duclos et al., Phys. Lett. 19 (1965) 253. [5] V.M. Kut'in, V.I. Petrukhin and Yu.D. Prokoshkin,

JETP Lett. 2 (1965) 243. [6] R.L. Schult and B.L. Young, Phys. Rev. D6 (1972) 1988. [7] R.J. Abrams et al., Phys. Rex,. Lett. 29 (1972) 1118; 30

(1973) 500. [8] R.J. Abrams et al., BNL Report No. 17365 (1972) and

Nucl. Instr. and Methods 107 (1973) 569.

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