Volume 63B, number 3 PHYSICS LETTERS 2 August 1976
NEW MEASUREMENTS OF THE RADIAT IVE DECAY MODES OF THE ~-MESON
G. COSME, A. COURAU, B. DUDELZAK, B. GRELAUD, B. JEAN-MARIE, S. JULLIAN, D. LALANNE, F. LAPLANCHE, G. PARROUR, R. RISKALLA, Ph. ROY and G. SZKLARZ
Universit( Paris-Sud, Centre d'Orsay Laboratoire de l'AcceT(rateur Lin(aire, 91405 Orsay, France
Received 6 May 1976
The radiative decay modes of the 0-meson have been studied: e+e - --- 0 --' ~ ~ 33'; e+e - ~ 0 ~ n'[ ~ 37. Cross sections o0-~7~37 and o0-}no7..,37 have been measured at five energies in the 0-meson energy region and clearly show the 0-resonance in the r/7 -~ 33' mode as well as in the no3" -., 33" mode. From a Breit-Wigner fit to the experi- mental data the values of the branching ratios are deduced: BO..~3 , = (1.5 0.4) 10-2;Bo~no3" = (1.4 0.5) 10 -3.
Introduction. In the last experiment using the ORSAY storage ring and the experimental apparatus based on optical spark chambers [1 ], various modes of the @meson disintegration have been studied. In this paper the analysis of the two radiative decay modes of the @meson is described:
e+e - -* ~ n7 -~ 33'.
The aim was to improve the accuracy of the corre- sponding branching ratios and to check for the mode -~ r/7 the discrepancy between the two published values [2, 3].
Photon showers are observed in a sandwich made of 11 lead sheets (0.5 radiation length each) inter- spaced between spark chambers. Because of the low spurious sparking rate it was possible to identify a photon by two close sparks in two gaps. A 33' event was selected if at least one of the photon had 4 sparks (or more) and such an event was conserved in the pro- cess of analysis if the potential direction of each pho- ton could reach the 9th chamber at least. Energy con- servation and shower apex position define for an e+e - --* 33' event the energy of each photon. Data have been taken at 5 energies 2E(MeV): 1015.25, 1016.85, 1019.25, 1021.85 and 1023.25. The energy calibra- tion of the machine has been achieved through the
o o (K~-~ -* KLK S zr+lr - ) channel studied in the same experiment. At all the energies the monitor reaction was the Bhabba scattering e+e - ~ e+e - .
Backgrounds and signal extraction criteria. The ra-
diative decay modes of the C-meson being rare modes, the difficulty was to extract from about 1400 events selected as 33' events in the process of scanning about 106 photographs (integrated luminosity L = 65 nb- 1), the small amount due to the reactions studied.
The 33' events are mainly due to 4 sources:
o o o _~ 27r o ._} 33' seen e+e - .-} ~ KLK s, K s
33' (by electromagnetic annihilation)
-~ ~ frO7 ~ 37.
To extract the signal due to each of the last two re- actions three criteria are at our disposal.
1. The zone criterion. The reactions ~ 77 (~r7) 33' possess the property of having the momentum of
one of the three photons (the one opposite to the pseudoscalar meson) constant. This property, which results from kinematics, is our main criterion for sig- nal extraction since the two background reactions do not have it. On a Dalitz-plot (due to the sixfold sym- metry, the Dalitz-plot was reduced to a sextant by or- dering the three photon momenta) a 37 event will ap- pear as a point somewhere on the plot and the events due to the reaction -~ r/7 --> 33' on a line correspond- ing to a momentum of 362 MeV, while those due to the reaction 0 "* rr7 ~ 33' on a line corresponding to a momentum of 501 MeV. Due to angular imprecision in shower apex determination, the r/7 and n7 events are spread out in zones on each side of the initial lines.
Volume 63B, number 3 PHYSICS LETTERS 2 August 1976
qb- - IT*~"-.. 3~"
"~. 10 0 ';.
Me ~ 3 ~ [
10 0 ~)....it
e+ e -~ 3~'(E M) M
' : I . . "
2 . " "
.~ . . , , o
Fig. 1. Dalitz-plots: Monte-Carlo and data distributions.
The imprecision was estimated to be A) = A0 = 1.4 and confirmed through the channel --, 7r+rr-Tr
rr+lr-77. Using such a standard error in the apex po- sition of each photon, one gets a realistic prediction of the experimental distribution of these events on the Dalitz-plot by a Monte-Carlo generation including a shower program. Fig. 1 a and 1 b show respectively the generated r/7 and 7r? events. Fig. lc shows the gen- erated events for the background reaction 4) ~ KLKs ,o o K~ -+ 27r ~ 37 seen. By far, the most important con- tribution to the counting rate (about 80%) is due to this reaction, but the density of these events is very low for/'max < 430 MeV and/'max > 480 MeV, most of them being concentrated in the region 430 < Pmax < 480 MeV. Therefore, in order to deal with events not too contaminated with background, the phase- space was reduced to the higher half of the Dalitz-plot (/'max < 430 MeV, Pmin > 220 MeV) in the case of the ~) ~ 773, reaction (fig. la) and to the lower narrow region of the Dalitz-plot (/'max > 480 MeV, Pmin > 100 MeV) in the case of the 4)~ no') ' reaction (fig. 1 b). In the case of the ~ 7)7 reaction the first cut (Pmax < 430 MeV) reduces the signal counting rate by a factor of 2, while the second (Pmin > 220 MeV) pro- duces a supplementary reduction in background and practically no loss of signal events. In the case of the
--, 7r7 reaction the first cut (Pmax > 480 MeV) has no effect on the signal events, while the second (Pmin > 1 O0 MeV), which is necessary in order to eliminate
photons of too low energy difficult to deal with, re- duces the signal counting rate by 30%. Fig. ld shows the generated events for the reaction e+e - ~ 3"), (by electromagnetic annihilation) for Pmin > 100 MeV. The contribution of this source of background is only about 7% of the initial counting rate, but these events are almost uniformly distributed on the Dalitz-plot and remain, in the regions of interest, an important source of background for the r/7 reaction and especially for the 7r7 reaction. Therefore one has checked for this source of background the agreement between the Monte-Carlo predictions and the experimental data be- low the ~b energy at 915 and 990 MeV .
Fig. 2a and 2b show in the regions of interest the experimental momentum distribution of the photon opposite to the pseudoscalar meson respectively for the 4) ~ 7)7 and 4) ~ 7r'), modes The signal due to the corresponding reaction is seen clearly. Background sub- traction under the peak gives a first and correct estima- tion of the total number of events for each mode. Nevertheless, in this way all the information is not used and a better separation signal-background has been achieved by working directly on the Dalitz-plot.
In each of the regions of interest (Pmax < 430 MeV, Pm~a > 220 MeV for the reaction rD' and Pmax > 480 MeV, Pmin > 100 MeV for the reaction n7) one is looking for the number of experimental events inside the r/7 (rr7) zone and outside the r/7 (7r7) zone. Two methods of background subtraction have been used.
Volume 63B, number 3 PHYSICS LETTERS 2 August 1976
- u'~ 30
qb - ' L r
f 362 i 300 350
qb ' ---- 1T*'
i li ,,~ /.90 500 0 (MeV)
Fig. 2a. Experimental momentum distribution of the photon opposite to the n (in the region Pmax < 430 MeV, Pmin > 220 MeV). b) Experimental momentum distribution of the photon opposite to the no (in the region Pmax > 480 MeV, Pmin > 100 MeV).
The first consists of subtracting from the experimental counting rate inside the r~3' 0r3') zone the normalized backgrounds inside the same zone as given by the Monte-Carlo distributions (fig. lc and fig. ld). (It is worth remarking that the reaction r/7 (fig. 1 a) appears as a background reaction for the zt3' reaction and its contribution in the rt3' zone had to be subtracted). In the second method one is interested only in the experi- mental counting rate outside the r/7 Or7) zone which is mainly background. The reasonable assumption that the background distribution does not go suddenly through a maximum when crossing the 7/7 0r3') zone and continuity considerations allowed us to deduce its contribution inside the r/7 (rr3') zone. These two methods have been applied using first a wide r/7 (n7) zone (confidence level 98%), then again using a narrow zone (confidence level 91%). The final results of back- ground subtraction all agree within 5 to 10%.
2. The energy criterion. This criterion is equivalent to a rough measurement of the total energy of the three photons.
By calculating for each photon the ratio of the num- ber of gaps having sparks to the total number of gaps along the photon direction counted from the conver- sion point and summing up the 3 ratios (Y~Ri) a differ- ence can be expected between a signal coming from a
reaction such as @ --' r/7 (rr?) -+ 33' where the three photons have about 1 GeV to share and a background reaction such as ~ vo vo vo -,Lr~ S , v~ S ~ 2n ~ 33' seen where the three photons have less than 0.5 GeV to share. Suppressing the lower energy events by setting ~R i > 2 one barely affects the counting rate efficiency of the signal events (about 1%), while rejecting 60% of the initial K~ --,33' seen background events. It should be noted that this criterion is of no use for rejecting background events due to the reaction e+e - -* 33' (by electromagnetic annihilation) which have the same ,Y_,R i distribution as the signal events.
3. The coplanarity criterion. For a 33' event due to the @ --' r/3' (rr7) --, 33' reaction, the three photons are necessarily in the same plane (momentum conservation) which is the reaction plane and is defined by the 3 con- version points. For each 33' event one calculates the angle a between the reaction plane and the measured direction of the best developed photon. Requiring a < 15 one estimates (through the study of the e+e -
23' and --, rr+rr-rr -+ 7r+lr- y'/reactions) a loss in signal efficiency of 3% while rejecting 25% of the ini. tial K~ -+ 3"), seen background. Indeed, for this reac- tion the plane defined by the 3 conversion points is not the reaction plane, since one is dealing here with a 43' reaction (one of the photons not being seen by the apparatus) and, therefore, tx can have any value. Again, this criterion is of no help for rejecting the e+e- -+ 33' (by electromagnetic annihilation) background events which are equally coplanar.
It is important to emphasize that using a limited phase-space as explained, the zone criterion alone is sufficient to get the cross section after background subtraction (see above). The addition of the energy or coplanarity criteria or both should only reduce the background level without significantly affecting the signal events. Within 5 to 10% this is exactly what one finds.
Results. Fig. le shows all our 33' data on a Dalitz- plot and table 1 shows our results in terms of counting rates and experimental cross sections as a function of energy respectively for the @ -" r/7 and @ --, lr3' reac- tions. The values B = P(~ ~ 23')/F(r/~ total) = 0.38 and B = F0r - ' 23')/F0r -'- total) = 0.99 have been used . Our overall efficiency was 8% in the case of the rD' reaction and 19% in the case of the 7r7 reac- tion.
Fig. 3a and fig. 3b show the corresponding excita-
Volume 63B, number 3 PHYSICS LETTERS
Table 1 Data as a function of energy for the reactions e+e - --* q~ --* r}3, and e+e - .* ~ .* no'y.
2 August 1976
Energy (MeV) 1015.25 1016.85 1019.25 1021.85 1023.25 IgE
L (nb-I) 10.2 13.5 21.3 10.5 9.7
N~ + Nbackgroun d 4 8 39 11 6 68 Nbackground 0 2.2 10.6 0.7 0 13.5 (Oexp)~._,n3,(nb) 13.7 6.8 13.0 8.0 43.7 11.4 31.6 11.0 22.1 9.1
Nno + Nbackgroun d 3 8 19 7 3 40 Nbackground 1 2 2 2 1 8 (Oexp)C,.*no 7 1.06 +- 1.06 2.41 1.28 4.09 1.15 2.59 1.55 1.09 1.09
A / '0 ,,D r-
o= ~3 U3
1014 1016 10111 1020 1022 102/,
tion curves. The experimental cross sections exp-* ~7 and Oexp. . "7 are fitted by a convolution of a Breit- Wigner resonance (without any interference) and radia- tive corrections. The radiative corrections being re- moved, the results of these fits at 2E =M~ = 1019.7 MeV are:
%__,nT=66nb (+25%), %__, ,o~/=6.2nb (+30%).
Taking the average world value:
o~ total = 4.4/ab ( - 10%)
Bev__,n, r = (1.5 - 0.4) X 10 -2,
B~__,,o 7 =(1.4 -+ 0.5) X 10 -3.
The quoted errors are the total errors, the statistical error being 17% in the case of the -* r17 reaction and 22% in the case of the --, n7 reaction.
The previously published values are: for the mode -~ r~ 7
Bq,.*n, r =(7.3 -+ 1.8) 10 .-2 (ref. ),
B,.*~ =(2.6 -+ 0.7) 10 -2 (ref. ).
for the mode ~ ~ rr7
B~_ , ,%
Volume 63B, number 3 PHYSICS LE'ITERS 2 August 1976
the new value of the --> r~7 branching ratio through the channel:
-+ 7)7 ~ n+Tr -n7 ~ nn77"Y .
Among the 75 events having 2 charged tracks and three photons within our cuts (detection efficiency
5%) there are about a dozen which have the right kinematics. For each of these events it is possible to choose two out of the three photons having an equiva- lent mass near the lr mass, the 3 pion system corre- sponding to an equivalent mass close to the 77 mass. Using B : F ( r /~ rr+rr-Tr)/F(r/-+ total) = 0.24 (4), one finds the following upper limit:
Bg,__, n, r < 2.4 X 10 -2 with 95% C.L.
This upper limit deduced from a completely differ- ent analysis is in good agreement with the value given above using ~ -+ r/7 -~ 37.
Added to the other measured radiative transitions V ~ P7 (03 ~ lr7, p - ~ 7r-7, K * ~ K7), our results seem to increase the difficulties of the non-relativistic quark model as well as of the restricted vector meson dominance model [7 -9 ] . Various attempts to explain the data have been made recently but it appears that if the 03-~ mixing angle 0 v is kept close to its ideal value sin 0 v = l /x/3, the quark model even with free parameters for the quark magnetic moments or alter- natively broken SU 3 symmetry cannot fit all the data [9, 10]. However a solution is given in paper 
which will fit all the available data on V ~ P7 if one uses 0 v as a free parameter. The best value 0 v = 24 is very close to the predictions of the current mixing formalism, but is in trouble with the vector meson- photon couplings as predicted by SU 3.
We are indebted to the late Professor A. Lagarrigue for his constant support. It is a pleasure to thank Dr. F.M. Renard for fruitful discussions. We are grate- ful to the Orsay Storage Ring Group, headed by Dr. P. Marin, for their help and advice in operating ACO. Technical support by J. Brugnon and G. Lissilour is acknowledged.
 G. Cosme et al., Nucl. Instr. 99 (1972) 599.  M. Basile et al., Phys. Lett. 38B (1972) 117.  D. Benaksas et al., Phys. Lett. 42B (1972) 511.  G. Cosme et al., Phys. Lett. 63B (1976) 349.  N. Barash-Schmidt et al., Review of particle properties
(April 1974).  C...