- Email: [email protected]
c
Nuclear Physics B150 (1979) 326-344 © North-Holland Publishing Company
SINGLE DIRECT PHOTON PRODUCTION IN pp COLLISIONS AT x/s = 53.2 GeV IN THE Pt INTERVAL 2.3 TO 5.7 GeV/c E. AMALDI, M. BENEVENTANO, B. BORGIA, A. CAPONE, F. DE NOTARISTEFANI, U. DORE, F. FERRONI, E. LONGO, L. LUMINARI, P. PISTILLI and I. SESTILLI Istituto di Fisica "G. Marconi" dell 'UniversitY, Roma, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Rorna, Italy G.F. DELL * and L.C.L. YUAN * Brookhaven National Laboratory, Upton, New York, USA G. KANTARDJIAN CERN, Gendva, Switzerland J. DOOHER * Adelphi University, Garden City, New York, USA Received 23 October 1978
We report the results of an experiment made at the CERN ISR to investigate the possible direct production of single photons in pp collisions at ~/s = 53.2 GeV at 90° and in the Pt itaterval 2.3 to 5.7 GeV/c. The value of the ratio R = n3,/nnO is compatible with zero for low Pt <~3 GeV/c but, in spite of the large error, shows a trend to increase for larger Pt.
1. Introduction Direct production of single photons at large Pt was foreseen years ago from a few theoretical models developed for describing high-energy collisions. The thermodynamic approach leads to direct gamma and dilepton production as was shown by Russian authors, in particular by Feinberg [I] ** The production of single photons has been considered also in the frame of par* Research supported by the US National Aeronautics and Space Administration and US Department of Energy. ** An extensive bibliography of precedent publications is given in this paper. 326
E. Amaldi et al. / Photon production
327
ton models of the nucleon [ 2 - 8 ] . If in the model the partons are identified with the quarks and gluons of QCD, the ratio R = nT/nno is expected to increase from negligible values at Pt 2 - 3 GeV/c, to a sizeable amount at Pt around 5 - 6 GeV/c [5-8]. In this paper we report in detail the results of an experiment made at the CERN ISR for x/s = 53.2 GeV, only part of which have been already published [9]. The experiment is based on the detection of photons produced either directly or in the decay of particles, mainly n o and 7?. Our main results are: (a) an upper limit for the ratio R for 2.2 ~< Pt ~ 3.4 GeV/c of about 5%, in disagreement with the conclusions reached by the Aachen-CERNHeidelberg-Dubna collaboration [ 10] which find for the same Pt interval a ratio R of the order of 20%; (b) an indication, in spite of the large statistical error, for R to increase at larger values o f p t . A BNL-Caltech-LBL collaboration [11 ] working at x/s = 19 GeV finds values of R compatible with a few per cent. A similar result is obtained by a FNAL-John Hopkins University collaboration [12] at x/s = 27 GeV and 2.5 ~
2. Experimental set-up and data collection The photon detector consists of a matrix of 9 X 15 lead glass counters 10 X 10 cm 2 in area and 35 cm long [9] placed behind two matrices of scintillation counters (1 cm thick) which allow the rejection of charged particles (fig. 1). The whole detector was mounted on a chariot moving on horizontal rails placed outside the storage rings perpendicular to the bisectrix of the two colliding beams. Such an arrangement allows the change, from the control room, of the distance r between the center of the interaction region and the front face of the lead glass array. The most delicate points in the search for single direct gamma ray emission are of two different types. The first is the danger of interpreting a gamma produced in the decay of a rr° or ~7as a single gamma ray, either because its companion is not observed in the solid angle of the apparatus above the energy threshold of the counters, or because the two gamma rays are not geometrically resolved. The second delicate problem is the background due to antineutrons annihilating in the lead glass with a large fraction of the energy emitted as lr°'s.
328
E. Amaldi et al. / Photon production (b)
50 cm
A
J 5x2
(a)
_!
-
I
~
9x15
Ilrflllllllllll
Fig. 1. Experimental layout. A and B are scintiilator hodoscopes for rejecting charged particles. C is a lead glass counter matrix. The distance r was different for different triggers. (a) Top view. (b) Front view of various sets of counters. In order to deal with the first difficulty we have collected the data under two geometrical configurations characterized by different values of the distance r. At large distance all n°'s of energy not greater than a certain value can be geometrically resolved by the lead glass counters but a large fraction of them give only one gamma ray within the detector. The opposite is true at the shorter distance provided an appropriate trigger is adopted. For the two gamma decay o f the r/meson, at large distance only one o f the two photons enters the detectors, and this is true also at short distance for a large fraction of them. For separating the fraction o f events due to antineutrons from those due to photons, we have measured the absorption in lead o f the neutral radiation incident on the detector. In this material the antineutrons have an interaction mean free path (Lco u ~-- 7 cm) much longer than the radiation length (Lrad "" 0.56 cm). The determination of the ratio R = nv/n~o is also affected by other instrumental effects, the most important o f which is the non-linearity of the energy response of the lead glass, and, to a much less extent, the absolute calibration o f the photon energy (k) scale. These points will be further discussed below. The data were collected under three different conditions: (i) the trigger Dma x is defined by the following recipe: (a) the distance r between O and I (fig. 1) is r = 4.70 m; (b) the lead glass counters are grouped in 15 submatrices of 3 × 3 = 9 counters connected in parallel, and we require that at least one of them shows a deposited energy greater than an electronic threshold eth = 1.25 GeV.
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(ii) The trigger D2~ is defined by: (a) the distance between O and I is reduced to r = 1.47 m; (b) the output of any one of the 15 (=5 horizontal × 3 vertical) central lead glass counters shows a deposited energy greater than an electronic threshold eth = 0.5 GeV. The trigger submatrix is identified in fig. l b b y the shaded area. (iii) The trigger D2h is defined as D2~ except for the value of the electronic threshold that was eth = 1.25 GeV. At both distances we collected data also with lead layers of various thicknesses in front of the whole detector in order to separate high-energy photons from antineutrons. Besides the pulse height of the single lead glass counters and the time of flight from the scintillation and lead glass counters, we always recorded the time of flight from a set of downstream counters of the CERN-Holland-Manchester collaboration experiment, placed in the same interaction region *. About 80% o f our events were in coincidence with signals o f at least one of these counters. The coincidences allowed the rejection o f events not coming from the interaction region. The luminosity was monitored by the same CHM counters. The lead glass counters were calibrated in electron beams, part at DESY (Hamburg) part at CERN PS, before and after the data collection for the experiments described in previous letters **. Thus the second calibration was made immediately before the data taking of the measurements described in the present paper. From the measurements taken between 0.5 and 4.0 GeV we found that the calibration curves never deviated from linearity by more than 15% and in any case very little from one counter to the other. Therefore, we used corrections by averaging the calibration curves observed in each counter. This is well-represented by the expression (fig. 2) k = kobs(1 - - y ) ,
(1)
where y =a+b
e-Ckobs ,
with kob s denoting the energy observed in the lead glass counter, k the corresponding corrected value, and a = 0.126,
b = 0.564,
c = 1.51 GeV -1 .
A check of the calibrations was made during the data analysis by reconstructing the 7r° mass spectrum obtained with each individual lead glass counter. From these measurements we found that the calibrations did not change appreciably during the whole data taking of this experiment. This was due, at least in great part, to the pos* We thank the members of this group (J. Armitage, P. Benz, G.J. Bobbink, F.C. Ern6, P. Kooijman, F.K. Loebinger, H.E. Montgomery, P.G. Murphy, J. Poorthuis, J.C. Sens, D. Stork and J. Timmer) in particualr Drs. F.C. Ern6 and J.C. Sens. ** A few more details can be found in ref. [14].
330
E. Amaldi et aL / Photon production
.5/
1,5
2n
I
2.5
I
3.0
t
3.5
I
4.0 k(GeV)
_&,
Fig. 2. Linearity correction of lead glass counters: y is defined by eq. (1). sibility of displacing the chariot carrying the lead glass array far away from the interaction region whenever danger of blackening of the glasses from stray radiation was expected. While no systematic effect from blackening was observed, we had to introduce small corrections (only exceptionally up to 10%) to the equivalent energy of single lead glass counters. After the application of these corrections we obtained a distributoin of the reconstructed mass of the n o for each of the 135 lead glass counters very similar to each other. The distribution of the corresponding 135 mean values shows a fullwidth half maxirrium of less than 4% (-+3 MeV). This result is satisfactory from the point of view of the relative calibration, while for the absolute calibration we checked the histogram of the reconstructed rr° mass spectrum obtained with the Dma x configuration with the result of a Monte Carlo calculation (fig. 3a) based on an energy resolution (FWHM) A k / k = 0.17k-1/2 GeV. We find that the uncertainty of the absolute calibration is less than -+3%. This comparison is made for the Dmax configuration because in this case the resolution is mainly determined by the energy resolution and only very slightly from the angular indetermination due to the transverse dimensions of the glass blocks. 3. Analysis of the data 3.1. Operational definitions and general remarks We have used the following operational definitions of cluster, single photon and reconstructed 7r° as in previous papers [9].
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E. AmaMi et al. / Photon production
Events/lOMeV
a)
150
100
l
I 200
t
300 M~,IMoV) Fig. 3. Mass distribution of reconstructed neutral pions. Full line resolution computed oy Monte Carlo calculation superimposed to background (dashed line) estimated from pairs of photons due to different decays; (a) for trigger Dmax, (b) for trigger D2~. loo
(a) Any lead glass counter which shows a maximum deposited energy with respect to adjacent counters defines an energy cluster whose energy is the sum o f the energies deposited in the involved counters. Only counters with a deposited energy >50 MeV are considered. The analysis thresholds for the energy o f the leading cluster
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E. Amaldi et al. / Photon production
are Eth = 2.2 GeV for Dma x ,
Eth = 1.0 GeV for D2Q,
Eth = 2.0 GeV for D2h . For other clusters: Eth = 0.05 GeV. (b) We define as a single photon a neutral cluster (i.e., a cluster without a signal from the corresponding scintillation counters) included in any set of 2 X 2 lead glass counters. This bperational definition is justified by the fact that, in the Dma x configuration, it is fulfilled by 98% of the pairs of separated clusters involved in the reconstructed 7r°'s. In addition no photon pair from unresolved go can give a 2 X 2 pattern in the D 2 configurations for Pt < 3.0 GeV/c and in the Dma x configuration for Pt ~< 6.0 GeV/c. We found that the loss of single photons due to the overlap of another uncorrelated cluster is negligible in the case ofDma x and amounts to 4% for Dz. (c) A neutral cluster not satisfying the previous condition is considered an "unresolved 7r°'', whenever it is kinematically compatible with a ~o decay. (d) We define as "reconstructed 7r°'' all pairs of clusters with an invariant mass in a convenient interval around the n ° mass after subtraction of the background (fig. 3). In the Dma x configuration (fig. 3a) the background is obtained by smooth interpolation between the observed data outside the n ° peak. In the D2~ configuration (fig. 3b) the background is obtained from the observed 3-cluster events, by combining the leading cluster of the n°'s with the third cluster. By this procedure the n°4r ° correlations are taken into account. Two corrections have been applied to the neutral clusters: (i) the conversion of photons into electrons in the material in front of the lead glass; (ii) the accidental pulses in the scintillators due to charged secondary particles crossing the matrices A and B (fig. 1) at the same time as the neutral secondaries triggering the lead glass. These two effects were measurea together by suppressing the anticoincidence requirement for one or both decay photons of the same neutral pion. By this procedure we found a global correction for (i) + (ii) of (+9 -+ 2)% to be applied to all neutral clusters. Two final remarks are in order. The first one is that in the following we consider only events with one or two clusters in the lead glass matrix C (fig. 1), and we look for single emitted photons only in one-cluster events. Therefore, we neglect single emitted photons accompanied by a second photon (due to the decay of a 7r° or 77). Since we throw away also three-cluster events, we also reject n ° accompanied by photons of any origin. It can be easily shown that in the absence of correlations, these two effects cancel each other. We will come back to this point in the discussion of systematic errors (sect. 4). To obtain from the observed number of single photons the direct photon contribution and the ratio R, we have to subtract the following effects:
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E. Amaldi et al. /Photon production
(l) gammas from 7r° (C1) and ~ (C2) whenever the other decay photon is either outside the matrix or below the minimum energy required to detect a cluster. (2) Antineutron annihilations (C3) in lead glass satisfying the requirement (b). The computation of R involves the differential invariant cross section for inclusive production of ~o around 90 °. Its determination from our data is discussed in subsect. 3.2. Subsect. 3.3 contains the determination of the C2 and C3 contributions. In subsect. 3.4 we present the determination of R. 3. 2. D i f f eran tial p t d i s t r i b u t i o n o f 7r° 's
Fig. 4 shows the invariant cross section E d 3 o / d p a obtained (around 90 °) from our data, part in the Dmax, part in the D2~ configurations. The corresponding numerical values are given in table 1.
EdS~ dp3
(cn~
1(?
o [}~x
103~
1~) 3:
2.5
3.0
L
J
3.5
4.0
4.5 pt(Ge~5.O
Fig. 4. Invariant cross section for ~T0 inclusive p r o d u c t i o n at 90 °.
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334
Table 1 Invariant cross section for 7r0 production (cm 2 - c 3 • GeV - 2 at x/s = 53.2 and 0 = 90 °) Pt
D2~
Dmax
(GeV/c) 2.1 2.3 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9 4.1 4.3 4.5 4.7 4.9 5.1
(9.2 (4.7 (2.1 (1.0 (5.8 (2.8 (1.6
-~ 0.7) -+0.5) +- 0.2) -+ 0.1) -+ 1.1) ± 0.4) ± 0.3)
-
30 30 30 30 31 31 31
(5.8 (2.8 (1.7 (8.9 (4.7 (3.3 (2.1 (1.2 (8.7 (4.8 (3.4 (2.0
± 0.6) -+0.3) ± 0.2) ± 0.9) ± 0.5) ± 0.4) ± 0.3) ± 0.2) ± 1.6) ± 1.1) ± 0.9) -+ 0.7)
-31 --31 -31 32 -
-
3 2
32 -32 32 -32 -33 -33 -33 -
-
The open circles represent the results for configuration Dma x. They are obtained from the reconstructed n°'s, corrected for their detection efficiency (fig. 5a). The closed circles represent the results for configuration D2~. They are o b t a i n e d from the "reconstructed + unresolved n ° ' ' with an efficiency correction given in fig. 5b. The absolute values o f the Dma x points have been decreased b y 10% in order to o b t a i n the overlap shown in fig. 5. This correction is an indication of the u n c e r t a i n t y of our normalization. The curve shown in fig. 4 represents the best fit of the data to an expression d3o 1 E ~ p 3 = A p-~ exp{ - b P t }
cm 2" c 3 / ( G e V ) 2 ,
(2)
w i t h A = (8.78 -+ 1.50) × 10 -27, n = 7.8 -+ 1.0 and b = 0.51 -+ 0.34 (GeV/c) - 1 in good agreement with the values given in ref. [15] and in fair agreement with ref. [10]. The absolute value of the cross section agrees within 30% with that o f ref. [15]. If this discrepancy is a t t r i b u t e d completely to differences in the absolute calib r a t i o n of the energy scale, our energies would be overestimated b y 3%.
3.3. Contribution to the observed single photons due to known processes The c o n t r i b u t i o n to the single observed p h o t o n s due to the 7r° decay, Cl(k), is obtained from the relation no k Cl(k ) = (~)MC
(nlrO)obs ,
(3)
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335
100 ~b)
80
6O
I
I
I
I
I
I
/ . - ~a) ----
0
I
2.5 3J] 35 4.0 4.5 5.0 k(6eVk) Fig. 5. Efficiency for ~r0 detection for 45 ° ~<0 < 135°; 0° < ~o< 360°; (a) in configuration Dma x, (b) in configuration D2~.
where (HTrO)obs is the number of observed n ° according to the definition given in frO subsect. 3.2, and (n 7 (k)/n~o)Mc is the ratio computed from a Monte Carlo calculation of the number of single photons of energy k seen in the detector, to the total number of detected nO's. In this computation we have used the expression (2) for the Pt distribution of the produced nO's. The contribution C1 (k) should not depend on the threshold adopted for the secondary cluster, if the Monte Carlo represents the data correctly. This effect has been studied by repeating the analysis with various cuts (between 50 and 500 MeV). We found that Cd (k) is independent of the cut's value. The ratio (n~ (k)/n~o)Mc is small and slowly varying in the D2~ configuration.
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E. Amaldi et al. / Photon production
Integrated over the whole k interval it amounts to 0.07. It is large (~5) in the Dma x configuration. This different behaviour is due in part to the fact that in D2 the trigg6r is provided only by the central part of the matrix so that the solid angle covered by lead glasses for the other photon of the same decay is much larger than it is in the Dma x case. In the most part however, it originates from the difference in the values of the thresholds for the leading cluster: in the case of D2~ the threshold (1 GeV) allows the detection of neutral pions in all decay configurations, while in the D m a x case the requirement of at least one photon with k > 2.2 GeV gives a detection efficiency different from zero only for asymmetric decay configurations. The situation described above is clearly expressed by the efficiency curves of fig. 5. The contribution C2, i.e., the observed single photons originating from the decay, has been computed by a very similar procedure: its value is given by C2(k)=(n'~(k)l
(n~O)obs ,
(4)
\ nTr0 ]MC
and has been computed under the assumption that the Pt distribution of the ~'s follows the same law (2) as do the 7r°'s [15] but using the value o n XB07 ~ 23')
=
0.19 + 0.03.
(5)
Ozr0
This value is obtained in the D2h configuration in which we collected a statistically significant sample of r/'s, as shown in fig. 6 where we have plotted the twocluster invariant-mass distribution. The value (5) is in satisfactory agreement, with the result 0.22 -+ 0.02 given in ref. [15]. The contribution C 3 due to antineutron annihilation is derived by the following procedure. A semilogarithmic plot of the absorption curves of the neutral secondaries, obtained with the trigger D2~ by placing lead absorbers of various thicknesses a in front of the whole detector are shown in fig. 7: the open circles refer to the "single observed photons", and the closed circles to the photons belonging to reconstructed neutral pions. These are well-represented by a straight line as expected for a pure sample of photons. The different behaviour of the data represented by circles is due to their composite nature, photons and antineutrons. The dashed curve represents a fit obtained by adding a constant background (B~, due to antineutrons), to an exponential distribution with the same slope as that of the full line. Using a constant antineutron background is justified by the large value of the interaction length for antineutrons. A correct estimate of this length involves the knowledge of the antineutron spectrum and of their detection efficiency, but it is not needed because of the smallness of the effect. The value of B~ integrated over k > 2 GeV amounts to 2% of the number of produced lr°. In conclusion we write
c3(k) =Bn(k). L. ~(D),
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Evmts/40 MeV
100 500
I
[
I
I
[
200
400
600
800
1000
600 (MeV) 700
MT~ IMeV)
Fig. 6. Invariant-mass distribution of the ~. The insertion shows the same points after subtraction of the background. The curve is the resolution obtained by a Monte Carlo computation. where B~ is referred to one unit of luminosity and solid angle, L is the integrated luminosity of the data under consideration, and co(D) the solid angle covered by the detector with the trigger D. 3.4. Determination o f R = nv/n.o The interval of values of k in which we can measure the ratio R is different in the three configurations. In the configuration Dma x we have 2.2 ~< k ~< 5.7 G e V / c , where the upper limit is determined by the statistics. For D2~ and D2h we have 2.0 ~< k < 3.0 G e V / c , with the upper limit determined by the single gamma definition: see subsect. 3.1. Table 2 shows the results of the analysis.
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' E. A m a l d i et al. / Photon production
N~nts (a.u.)
10C
~
'-~.~
10-
1
I
10
15
I 20
mm Pb
Fig. 7. Absorption curve of neutral radiation, photon + antineutrons: (a) absorption curve of single observed photons; (b) absorption curve of photons belonging to reconstructed rr0. The total number of 7r°'s produced in the phase space of the apparatus to be compared with direct single photons is given by nrro = @/nO)reconstructed + (nnO)unresolve d + (nnO)undetecte d , where the last term is the number of rr°'s with both photons below threshold computed from the Monte Carlo. In the configuration D2h we can not rely on the reconstructed lr ° for the normalization because the threshold in deposited energy is large (2.0 GeV), and therefore most of the observed pions are unresolved and affected by a small but unknown background. For this reason the normalization in the D2h configuration is based on the reconstructed ~'s, with the result that the errors are dominated by the uncertainty on the value (5) of (~n ×B(r~ ~ 27)/o7ro.
E. AmaMi et aL/ Photon production
339
Table 2 Experimental determination and upper limit on R for 2.3 ~
Dma x
D2~
D2h
Integrated luminosity (cm -2) Pt interval (GeV/c)
82. 1035
1.5. 1035
219. 1035
2.5-3.4
2.3-3.4
2.3-3.4
(1) reconstructed n o (2) unresolved n 0 (3) single observed photon from decay (C1) (4) undetected n 0 (A) total number of n ~ produced in the phase space of apparatus (1+2+3+4)
770 ± 30 0 3590 ± 160
560 ± 25 252 ± 16 73 ± 6
(18.1 ± 2) - 103 (22.5 ± 2) - 103
0 885 ± 30
(99 ± 10) • 103
(1) single photons (2) contributions to single photons C1 C2 C3 C 1 + C2 + C 3 (B) direct photons (1-2)
4957 _+ 70
156 ± 13
17900 ± 135
3590± 160 780±120 364± 55 4734 ± 210 223 ± 220
73-+ 6 49± 7 19± 3 141 ± 10 15 ± 16
7800-+800 6800±700 2800±400 (17.4 ± 1.1) • 103 (500 ± 1100)
(1.0 ± 1.0) • 10 - 2
(1.7 ± 1.8) • 10 - 2
0.5 • 10 - 3
~<2.7%
~<4.7%
<2.3%
direct photons total produced upper limit at 95% C.L.
R =
a) Quoted errors include all uncertainties of statistical nature. Here we consider errors due to statistics plus the u n c e r t a i n t y on the b a c k g r o u n d subtracted f r o m the ~? invariant-mass distribution. The total n u m b e r o f n o shown in table 2 for the D2h configuration, is c o m p u t e d f r o m the values o b t a i n e d with the o t h e r configurations by taking into a c c o u n t the corresponding integrated luminosities. A shown in table 2 we obtain in all three configurations in the Pt region 2 . 3 3.7 G e V / c a value for the total n u m b e r o f direct p h o t o n s consistent with zero, and an upper limit for the ratio R = n~t/nno o f 4% with 95% confidence level taking into account only the statistical errors. These results c o n f i r m our previous conclusion [ 9 ] The configuration Dma x allows the extension o f the Pt interval towards higher values and thus provides the possibility o f studying the behaviour o f R versus Pt. Table 3 and figs. 8, 9 show our results. Fig. 8 represents the energy s p e c t r u m o f observed single p h o t o n s after subtraction o f 7/and ff contributions. The curve is the e x p e c t e d s p e c t r u m ( c o m p u t e d by the Monte Carlo m e t h o d ) o f single p h o t o n s due to 7r° decay n o r m a l i z e d to the observed n u m b e r o f reconstructed 7r°. Fig. 9 shows, as a
3872-+ 62 10 85+ - 33 360_+19 74 + 9 29,+ 6 10 -+ 4
2.50-2.96 2.96-3.42 3.42-4.00 4.00-4.55 4.55 5.13 5.13-5.70
2683 727 240 57.8 16.3 4.7
± 130 -+ 33 ÷ 11 _+ 2.6 ,+ 1.0 ,+ 0.2
605 171 56 12 4 1.3
Co nt ri but ion due to no ~
+- 81 -+26 -+ 8 ,+ 2 -+ 1 -+ 0.2
292 70 19 3.4 0.5 0.1
ff
-+ 44 -+ 10 -+ 3 ,+ 1 _+ 1 -+ 1
110 ± 170 117 -+ 54 45 _+ 24 1 ,+ 9 82 + 6 3.9,+ 4
Direct photons
17100 5400 1360 486 150 57
no _+10%
0.7 -+ 1 2.2÷ 1 3.3_+ 1.8 0.2 ,+ 1.8 5.4 ,+ 4 6.8,+ 7
R
2.4 3.8 6.3 3.2 12.0 18.0
Upper limit 95% C.L.
a) The numbers of single photons given here are the measured numbers after subtraction of accidental background. This was appreciable only in the last two bins.
Single photons a)
Pt interval
Table 3 Determination of R in the D ma x configuration for 2.5 < Pt <~ 5.7 GeV/c
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lOOd Events/tO0MeV
10Q
I 311
i 411
I 511
kIGeV/cl Fig. 8. Spectrum of observed single photons after subtraction of ~ and fi contributions. The continuous curve is the result of a Monte Carlo computation of the ~0 contribution.
function o f p t , the ratio R ---nT/n~o. The quoted errors are statistical. Our points indicate a very small value, consistent with zero, for Pt less than ~3 GeV/e and in spite of the large statistical error a trend to increase with Pt reaching values of the order o f 10% for Pt around 5 GeV. This behaviour is what is expected from the theoretical prediction given in ref. [8] and represented by the full line in fig. 9.
4. Systematic errors The most important source of systematic errors is the energy dependence of the response of the lead glass blocks. Since we compare the nuhabers of single photons with the number o f 7r° of m o m e n t u m given by the composition of two photons of lower momenta, a deviation from linearity, combined with the steep dependence of
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E. Arnaldi et al. / Photon production
J~E
a0
6.0
0t tat~)
Fig. 9. Ratio R = nT/nTrO versus Pt. The curve represents the results of the QCD prediction given by Field [8]. the 7r° invariant cross section on Pt, can produce an appreciable change in R. The uncertainty in the linearity correction affects mainly the D2Q results bringing the corresponding upper limit from 4% to 6%. The reason is that with this trigger we include all decay configurations of the n ° and therefore the energy of single photons is about one half of that of the n°'s. Furthermore, we fall in an energy region where the linearity corrections vary very fast with energy (fig. 2). On the contrary, in the Dma x configuration the effect of this uncertainty is negligible in the region of low Pt values (~<3 GeV/c), because the majority of the resolved 7r°'s are in asymmetric configurations so that the single photons and the 7r°'s fall in about the same momentum region. In this case the upper limit for R found in sect. 3 remains practically unchanged and equal to 4%. Also for large Pt (~3 GeV/c) the effect of uncertainties in the linearity corrections is negligible because we fall in the energy region where the linearity correction varies very slowly with energy (fig. 2). As a further test of the reliability of the value of the contribution C1 (k), we have repeated its computation by changing by one unit the exponent n in expression (2). Its value did not change appreciably. Some further consideration is in order about the use of only one- and two-cluster
E. Amaldi et al. /Photon production
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events in the derivation o f R (subsect. 3.1). This procedure is certainly correct under the assumption of no strong correlations between directly produced photons and other particles. The limited influence of correlations o f this type on our results has been checked by comparing the values o f two ratios, r I and r2, which should be equal under our assumption, rt is the ratio of the numbers of reconstructed ~°'s + one uncorrelated photon (i.e., three-cluster events) to the number of reconstructed ~°'s. r2 is the ratio o f two-cluster events not due to reconstructed zr°'s to one-cluster events. We found for the Dma x and Dz~ configurations: r I -- 10% and 35%, r2 = 10% and 32%. In conclusion, an overall estimate of systematic errors gives +0.02 almost independent from Pt. The contributions of co and other radiative decays have been estimated to be smaller than the systematic error.
5. Conclusions Our main conclusions are summarized in tables 2 and 3 and figs. 8, 9. In the region 2.3 ~
References [1] E.L. Feinberg, Nuovo Cim. 34A (1976) 391. [2] C.O. Escobar, Nucl. Phys. B98 (1975) 173. [3] G.S. Farrar and S.C..Frautschi, Phys. Rev. Lett. 36 (1976) 1017; G.S. Farrar, Phys. Lett. 67B (1977) 337. [4] R.D. Field and R.P. Feynman, Phys. Rev. D15 (1977) 2590; Nucl. Phys. B136 (1978) 1. [5] F. Halzen and D.M. Scott, Phys. Rev. Lett. 40 (1978) 1117. [6] R.P. Feynman, R.D. Field and G.C. Fox, Nucl. Phys. B128 (1977) 1. [7] R. Riickl, S.J. Brodsky and J.F. Gun/on, Slac-Pub-2115 (May,1978). [8] R.D. Field, Rapporteur talk at 19th Int. Conf. on High-energy physics, Tokyo, August 1978.
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[9] E. Amaldi, M. Beneventano, B. Borgia, A. Capone, D. De Notaristefani, U. Dore, F. Ferroni, E. Longo, L. Luminari, P. Pistilli, I. Sestili, G.F. Dell and L.C.L. Yuan, Phys. Lett. 77B (1978) 240. [10] P. Darriulat, P. Dittmann, K. Eggert, M. Holder, K.T. Mc Donald, T. Modis, F.L. Navarria, A. Seiden, J. Strauss, G. Vesztergombi and E.G.H. Williams, Nucl. Phys. B110 (1976) 365. [ 11 ] R. Walker, presented at the Chicago Meeting of the American Physical Society, 1976. [12] J. Cronin, presented at 1977 Int. Symp. on Lepton and photon interactions at high energies (Hamburg) 1977. [13] A.J. Lankford, Measurements of vector meson production in pp at the ISR, CERN, internal report 78-3 (May 1978). [14] E. Amaldi, M. Beneventano, B. Borgia, A. Capone, D. De Notaristefani, U. Dore, F. Ferroni, E. Longo, L. Luminari, P. PistiUi, I. Sestili, G.F. Dell, L.C.L. Yuan and J. Dooher, Nuovo Cim. Lett. 19 (1977) 152; 20 (1977) 409. [15] F.W. Bfisser, L. Camilleri, L. Di Lella, B.G. Pope, A.M. Smith, B.J. Blumenfeld, S.N. White, A.F. Rothemberg, S.L. Segler, M.J. Tannebaum, M. Banner, J.B. Ch6ze, H. Kasha, J.P. Ponsart, G.M. Smadia, J. Teiger, H. Zaccone and A. Zylberstein, Nucl. Phys. B106 (1976) 1. [16] K. Eggert, K.L. Giboni, W. Thorn6, B. Betev, P. Darriulat, P. Dittmann, M. Holder, K.T. Mc Donald, H.G. Pugh, G. Vesztergombi, T. Modis, K. Tittel, V. Eckardt, J.H. Gebauer, R. Menike, O.R. Sander and P. Seyboth, Nucl. Phys. B98 (1975) 49.
SINGLE DIRECT PHOTON PRODUCTION IN pp COLLISIONS AT x/s = 53.2 GeV IN THE Pt INTERVAL 2.3 TO 5.7 GeV/c E. AMALDI, M. BENEVENTANO, B. BORGIA, A. CAPONE, F. DE NOTARISTEFANI, U. DORE, F. FERRONI, E. LONGO, L. LUMINARI, P. PISTILLI and I. SESTILLI Istituto di Fisica "G. Marconi" dell 'UniversitY, Roma, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Rorna, Italy G.F. DELL * and L.C.L. YUAN * Brookhaven National Laboratory, Upton, New York, USA G. KANTARDJIAN CERN, Gendva, Switzerland J. DOOHER * Adelphi University, Garden City, New York, USA Received 23 October 1978
We report the results of an experiment made at the CERN ISR to investigate the possible direct production of single photons in pp collisions at ~/s = 53.2 GeV at 90° and in the Pt itaterval 2.3 to 5.7 GeV/c. The value of the ratio R = n3,/nnO is compatible with zero for low Pt <~3 GeV/c but, in spite of the large error, shows a trend to increase for larger Pt.
1. Introduction Direct production of single photons at large Pt was foreseen years ago from a few theoretical models developed for describing high-energy collisions. The thermodynamic approach leads to direct gamma and dilepton production as was shown by Russian authors, in particular by Feinberg [I] ** The production of single photons has been considered also in the frame of par* Research supported by the US National Aeronautics and Space Administration and US Department of Energy. ** An extensive bibliography of precedent publications is given in this paper. 326
E. Amaldi et al. / Photon production
327
ton models of the nucleon [ 2 - 8 ] . If in the model the partons are identified with the quarks and gluons of QCD, the ratio R = nT/nno is expected to increase from negligible values at Pt 2 - 3 GeV/c, to a sizeable amount at Pt around 5 - 6 GeV/c [5-8]. In this paper we report in detail the results of an experiment made at the CERN ISR for x/s = 53.2 GeV, only part of which have been already published [9]. The experiment is based on the detection of photons produced either directly or in the decay of particles, mainly n o and 7?. Our main results are: (a) an upper limit for the ratio R for 2.2 ~< Pt ~ 3.4 GeV/c of about 5%, in disagreement with the conclusions reached by the Aachen-CERNHeidelberg-Dubna collaboration [ 10] which find for the same Pt interval a ratio R of the order of 20%; (b) an indication, in spite of the large statistical error, for R to increase at larger values o f p t . A BNL-Caltech-LBL collaboration [11 ] working at x/s = 19 GeV finds values of R compatible with a few per cent. A similar result is obtained by a FNAL-John Hopkins University collaboration [12] at x/s = 27 GeV and 2.5 ~
2. Experimental set-up and data collection The photon detector consists of a matrix of 9 X 15 lead glass counters 10 X 10 cm 2 in area and 35 cm long [9] placed behind two matrices of scintillation counters (1 cm thick) which allow the rejection of charged particles (fig. 1). The whole detector was mounted on a chariot moving on horizontal rails placed outside the storage rings perpendicular to the bisectrix of the two colliding beams. Such an arrangement allows the change, from the control room, of the distance r between the center of the interaction region and the front face of the lead glass array. The most delicate points in the search for single direct gamma ray emission are of two different types. The first is the danger of interpreting a gamma produced in the decay of a rr° or ~7as a single gamma ray, either because its companion is not observed in the solid angle of the apparatus above the energy threshold of the counters, or because the two gamma rays are not geometrically resolved. The second delicate problem is the background due to antineutrons annihilating in the lead glass with a large fraction of the energy emitted as lr°'s.
328
E. Amaldi et al. / Photon production (b)
50 cm
A
J 5x2
(a)
_!
-
I
~
9x15
Ilrflllllllllll
Fig. 1. Experimental layout. A and B are scintiilator hodoscopes for rejecting charged particles. C is a lead glass counter matrix. The distance r was different for different triggers. (a) Top view. (b) Front view of various sets of counters. In order to deal with the first difficulty we have collected the data under two geometrical configurations characterized by different values of the distance r. At large distance all n°'s of energy not greater than a certain value can be geometrically resolved by the lead glass counters but a large fraction of them give only one gamma ray within the detector. The opposite is true at the shorter distance provided an appropriate trigger is adopted. For the two gamma decay o f the r/meson, at large distance only one o f the two photons enters the detectors, and this is true also at short distance for a large fraction of them. For separating the fraction o f events due to antineutrons from those due to photons, we have measured the absorption in lead o f the neutral radiation incident on the detector. In this material the antineutrons have an interaction mean free path (Lco u ~-- 7 cm) much longer than the radiation length (Lrad "" 0.56 cm). The determination of the ratio R = nv/n~o is also affected by other instrumental effects, the most important o f which is the non-linearity of the energy response of the lead glass, and, to a much less extent, the absolute calibration o f the photon energy (k) scale. These points will be further discussed below. The data were collected under three different conditions: (i) the trigger Dma x is defined by the following recipe: (a) the distance r between O and I (fig. 1) is r = 4.70 m; (b) the lead glass counters are grouped in 15 submatrices of 3 × 3 = 9 counters connected in parallel, and we require that at least one of them shows a deposited energy greater than an electronic threshold eth = 1.25 GeV.
E. Amaldi et al. / Photon production
329
(ii) The trigger D2~ is defined by: (a) the distance between O and I is reduced to r = 1.47 m; (b) the output of any one of the 15 (=5 horizontal × 3 vertical) central lead glass counters shows a deposited energy greater than an electronic threshold eth = 0.5 GeV. The trigger submatrix is identified in fig. l b b y the shaded area. (iii) The trigger D2h is defined as D2~ except for the value of the electronic threshold that was eth = 1.25 GeV. At both distances we collected data also with lead layers of various thicknesses in front of the whole detector in order to separate high-energy photons from antineutrons. Besides the pulse height of the single lead glass counters and the time of flight from the scintillation and lead glass counters, we always recorded the time of flight from a set of downstream counters of the CERN-Holland-Manchester collaboration experiment, placed in the same interaction region *. About 80% o f our events were in coincidence with signals o f at least one of these counters. The coincidences allowed the rejection o f events not coming from the interaction region. The luminosity was monitored by the same CHM counters. The lead glass counters were calibrated in electron beams, part at DESY (Hamburg) part at CERN PS, before and after the data collection for the experiments described in previous letters **. Thus the second calibration was made immediately before the data taking of the measurements described in the present paper. From the measurements taken between 0.5 and 4.0 GeV we found that the calibration curves never deviated from linearity by more than 15% and in any case very little from one counter to the other. Therefore, we used corrections by averaging the calibration curves observed in each counter. This is well-represented by the expression (fig. 2) k = kobs(1 - - y ) ,
(1)
where y =a+b
e-Ckobs ,
with kob s denoting the energy observed in the lead glass counter, k the corresponding corrected value, and a = 0.126,
b = 0.564,
c = 1.51 GeV -1 .
A check of the calibrations was made during the data analysis by reconstructing the 7r° mass spectrum obtained with each individual lead glass counter. From these measurements we found that the calibrations did not change appreciably during the whole data taking of this experiment. This was due, at least in great part, to the pos* We thank the members of this group (J. Armitage, P. Benz, G.J. Bobbink, F.C. Ern6, P. Kooijman, F.K. Loebinger, H.E. Montgomery, P.G. Murphy, J. Poorthuis, J.C. Sens, D. Stork and J. Timmer) in particualr Drs. F.C. Ern6 and J.C. Sens. ** A few more details can be found in ref. [14].
330
E. Amaldi et aL / Photon production
.5/
1,5
2n
I
2.5
I
3.0
t
3.5
I
4.0 k(GeV)
_&,
Fig. 2. Linearity correction of lead glass counters: y is defined by eq. (1). sibility of displacing the chariot carrying the lead glass array far away from the interaction region whenever danger of blackening of the glasses from stray radiation was expected. While no systematic effect from blackening was observed, we had to introduce small corrections (only exceptionally up to 10%) to the equivalent energy of single lead glass counters. After the application of these corrections we obtained a distributoin of the reconstructed mass of the n o for each of the 135 lead glass counters very similar to each other. The distribution of the corresponding 135 mean values shows a fullwidth half maxirrium of less than 4% (-+3 MeV). This result is satisfactory from the point of view of the relative calibration, while for the absolute calibration we checked the histogram of the reconstructed rr° mass spectrum obtained with the Dma x configuration with the result of a Monte Carlo calculation (fig. 3a) based on an energy resolution (FWHM) A k / k = 0.17k-1/2 GeV. We find that the uncertainty of the absolute calibration is less than -+3%. This comparison is made for the Dmax configuration because in this case the resolution is mainly determined by the energy resolution and only very slightly from the angular indetermination due to the transverse dimensions of the glass blocks. 3. Analysis of the data 3.1. Operational definitions and general remarks We have used the following operational definitions of cluster, single photon and reconstructed 7r° as in previous papers [9].
331
E. AmaMi et al. / Photon production
Events/lOMeV
a)
150
100
l
I 200
t
300 M~,IMoV) Fig. 3. Mass distribution of reconstructed neutral pions. Full line resolution computed oy Monte Carlo calculation superimposed to background (dashed line) estimated from pairs of photons due to different decays; (a) for trigger Dmax, (b) for trigger D2~. loo
(a) Any lead glass counter which shows a maximum deposited energy with respect to adjacent counters defines an energy cluster whose energy is the sum o f the energies deposited in the involved counters. Only counters with a deposited energy >50 MeV are considered. The analysis thresholds for the energy o f the leading cluster
332
E. Amaldi et al. / Photon production
are Eth = 2.2 GeV for Dma x ,
Eth = 1.0 GeV for D2Q,
Eth = 2.0 GeV for D2h . For other clusters: Eth = 0.05 GeV. (b) We define as a single photon a neutral cluster (i.e., a cluster without a signal from the corresponding scintillation counters) included in any set of 2 X 2 lead glass counters. This bperational definition is justified by the fact that, in the Dma x configuration, it is fulfilled by 98% of the pairs of separated clusters involved in the reconstructed 7r°'s. In addition no photon pair from unresolved go can give a 2 X 2 pattern in the D 2 configurations for Pt < 3.0 GeV/c and in the Dma x configuration for Pt ~< 6.0 GeV/c. We found that the loss of single photons due to the overlap of another uncorrelated cluster is negligible in the case ofDma x and amounts to 4% for Dz. (c) A neutral cluster not satisfying the previous condition is considered an "unresolved 7r°'', whenever it is kinematically compatible with a ~o decay. (d) We define as "reconstructed 7r°'' all pairs of clusters with an invariant mass in a convenient interval around the n ° mass after subtraction of the background (fig. 3). In the Dma x configuration (fig. 3a) the background is obtained by smooth interpolation between the observed data outside the n ° peak. In the D2~ configuration (fig. 3b) the background is obtained from the observed 3-cluster events, by combining the leading cluster of the n°'s with the third cluster. By this procedure the n°4r ° correlations are taken into account. Two corrections have been applied to the neutral clusters: (i) the conversion of photons into electrons in the material in front of the lead glass; (ii) the accidental pulses in the scintillators due to charged secondary particles crossing the matrices A and B (fig. 1) at the same time as the neutral secondaries triggering the lead glass. These two effects were measurea together by suppressing the anticoincidence requirement for one or both decay photons of the same neutral pion. By this procedure we found a global correction for (i) + (ii) of (+9 -+ 2)% to be applied to all neutral clusters. Two final remarks are in order. The first one is that in the following we consider only events with one or two clusters in the lead glass matrix C (fig. 1), and we look for single emitted photons only in one-cluster events. Therefore, we neglect single emitted photons accompanied by a second photon (due to the decay of a 7r° or 77). Since we throw away also three-cluster events, we also reject n ° accompanied by photons of any origin. It can be easily shown that in the absence of correlations, these two effects cancel each other. We will come back to this point in the discussion of systematic errors (sect. 4). To obtain from the observed number of single photons the direct photon contribution and the ratio R, we have to subtract the following effects:
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E. Amaldi et al. /Photon production
(l) gammas from 7r° (C1) and ~ (C2) whenever the other decay photon is either outside the matrix or below the minimum energy required to detect a cluster. (2) Antineutron annihilations (C3) in lead glass satisfying the requirement (b). The computation of R involves the differential invariant cross section for inclusive production of ~o around 90 °. Its determination from our data is discussed in subsect. 3.2. Subsect. 3.3 contains the determination of the C2 and C3 contributions. In subsect. 3.4 we present the determination of R. 3. 2. D i f f eran tial p t d i s t r i b u t i o n o f 7r° 's
Fig. 4 shows the invariant cross section E d 3 o / d p a obtained (around 90 °) from our data, part in the Dmax, part in the D2~ configurations. The corresponding numerical values are given in table 1.
EdS~ dp3
(cn~
1(?
o [}~x
103~
1~) 3:
2.5
3.0
L
J
3.5
4.0
4.5 pt(Ge~5.O
Fig. 4. Invariant cross section for ~T0 inclusive p r o d u c t i o n at 90 °.
E. Amaldi et al. /Photon production
334
Table 1 Invariant cross section for 7r0 production (cm 2 - c 3 • GeV - 2 at x/s = 53.2 and 0 = 90 °) Pt
D2~
Dmax
(GeV/c) 2.1 2.3 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9 4.1 4.3 4.5 4.7 4.9 5.1
(9.2 (4.7 (2.1 (1.0 (5.8 (2.8 (1.6
-~ 0.7) -+0.5) +- 0.2) -+ 0.1) -+ 1.1) ± 0.4) ± 0.3)
-
30 30 30 30 31 31 31
(5.8 (2.8 (1.7 (8.9 (4.7 (3.3 (2.1 (1.2 (8.7 (4.8 (3.4 (2.0
± 0.6) -+0.3) ± 0.2) ± 0.9) ± 0.5) ± 0.4) ± 0.3) ± 0.2) ± 1.6) ± 1.1) ± 0.9) -+ 0.7)
-31 --31 -31 32 -
-
3 2
32 -32 32 -32 -33 -33 -33 -
-
The open circles represent the results for configuration Dma x. They are obtained from the reconstructed n°'s, corrected for their detection efficiency (fig. 5a). The closed circles represent the results for configuration D2~. They are o b t a i n e d from the "reconstructed + unresolved n ° ' ' with an efficiency correction given in fig. 5b. The absolute values o f the Dma x points have been decreased b y 10% in order to o b t a i n the overlap shown in fig. 5. This correction is an indication of the u n c e r t a i n t y of our normalization. The curve shown in fig. 4 represents the best fit of the data to an expression d3o 1 E ~ p 3 = A p-~ exp{ - b P t }
cm 2" c 3 / ( G e V ) 2 ,
(2)
w i t h A = (8.78 -+ 1.50) × 10 -27, n = 7.8 -+ 1.0 and b = 0.51 -+ 0.34 (GeV/c) - 1 in good agreement with the values given in ref. [15] and in fair agreement with ref. [10]. The absolute value of the cross section agrees within 30% with that o f ref. [15]. If this discrepancy is a t t r i b u t e d completely to differences in the absolute calib r a t i o n of the energy scale, our energies would be overestimated b y 3%.
3.3. Contribution to the observed single photons due to known processes The c o n t r i b u t i o n to the single observed p h o t o n s due to the 7r° decay, Cl(k), is obtained from the relation no k Cl(k ) = (~)MC
(nlrO)obs ,
(3)
E. Amaldi et al. /Photon production
335
100 ~b)
80
6O
I
I
I
I
I
I
/ . - ~a) ----
0
I
2.5 3J] 35 4.0 4.5 5.0 k(6eVk) Fig. 5. Efficiency for ~r0 detection for 45 ° ~<0 < 135°; 0° < ~o< 360°; (a) in configuration Dma x, (b) in configuration D2~.
where (HTrO)obs is the number of observed n ° according to the definition given in frO subsect. 3.2, and (n 7 (k)/n~o)Mc is the ratio computed from a Monte Carlo calculation of the number of single photons of energy k seen in the detector, to the total number of detected nO's. In this computation we have used the expression (2) for the Pt distribution of the produced nO's. The contribution C1 (k) should not depend on the threshold adopted for the secondary cluster, if the Monte Carlo represents the data correctly. This effect has been studied by repeating the analysis with various cuts (between 50 and 500 MeV). We found that Cd (k) is independent of the cut's value. The ratio (n~ (k)/n~o)Mc is small and slowly varying in the D2~ configuration.
336
E. Amaldi et al. / Photon production
Integrated over the whole k interval it amounts to 0.07. It is large (~5) in the Dma x configuration. This different behaviour is due in part to the fact that in D2 the trigg6r is provided only by the central part of the matrix so that the solid angle covered by lead glasses for the other photon of the same decay is much larger than it is in the Dma x case. In the most part however, it originates from the difference in the values of the thresholds for the leading cluster: in the case of D2~ the threshold (1 GeV) allows the detection of neutral pions in all decay configurations, while in the D m a x case the requirement of at least one photon with k > 2.2 GeV gives a detection efficiency different from zero only for asymmetric decay configurations. The situation described above is clearly expressed by the efficiency curves of fig. 5. The contribution C2, i.e., the observed single photons originating from the decay, has been computed by a very similar procedure: its value is given by C2(k)=(n'~(k)l
(n~O)obs ,
(4)
\ nTr0 ]MC
and has been computed under the assumption that the Pt distribution of the ~'s follows the same law (2) as do the 7r°'s [15] but using the value o n XB07 ~ 23')
=
0.19 + 0.03.
(5)
Ozr0
This value is obtained in the D2h configuration in which we collected a statistically significant sample of r/'s, as shown in fig. 6 where we have plotted the twocluster invariant-mass distribution. The value (5) is in satisfactory agreement, with the result 0.22 -+ 0.02 given in ref. [15]. The contribution C 3 due to antineutron annihilation is derived by the following procedure. A semilogarithmic plot of the absorption curves of the neutral secondaries, obtained with the trigger D2~ by placing lead absorbers of various thicknesses a in front of the whole detector are shown in fig. 7: the open circles refer to the "single observed photons", and the closed circles to the photons belonging to reconstructed neutral pions. These are well-represented by a straight line as expected for a pure sample of photons. The different behaviour of the data represented by circles is due to their composite nature, photons and antineutrons. The dashed curve represents a fit obtained by adding a constant background (B~, due to antineutrons), to an exponential distribution with the same slope as that of the full line. Using a constant antineutron background is justified by the large value of the interaction length for antineutrons. A correct estimate of this length involves the knowledge of the antineutron spectrum and of their detection efficiency, but it is not needed because of the smallness of the effect. The value of B~ integrated over k > 2 GeV amounts to 2% of the number of produced lr°. In conclusion we write
c3(k) =Bn(k). L. ~(D),
E. Amaldi et al. /Photon production
337
Evmts/40 MeV
100 500
I
[
I
I
[
200
400
600
800
1000
600 (MeV) 700
MT~ IMeV)
Fig. 6. Invariant-mass distribution of the ~. The insertion shows the same points after subtraction of the background. The curve is the resolution obtained by a Monte Carlo computation. where B~ is referred to one unit of luminosity and solid angle, L is the integrated luminosity of the data under consideration, and co(D) the solid angle covered by the detector with the trigger D. 3.4. Determination o f R = nv/n.o The interval of values of k in which we can measure the ratio R is different in the three configurations. In the configuration Dma x we have 2.2 ~< k ~< 5.7 G e V / c , where the upper limit is determined by the statistics. For D2~ and D2h we have 2.0 ~< k < 3.0 G e V / c , with the upper limit determined by the single gamma definition: see subsect. 3.1. Table 2 shows the results of the analysis.
338
' E. A m a l d i et al. / Photon production
N~nts (a.u.)
10C
~
'-~.~
10-
1
I
10
15
I 20
mm Pb
Fig. 7. Absorption curve of neutral radiation, photon + antineutrons: (a) absorption curve of single observed photons; (b) absorption curve of photons belonging to reconstructed rr0. The total number of 7r°'s produced in the phase space of the apparatus to be compared with direct single photons is given by nrro = @/nO)reconstructed + (nnO)unresolve d + (nnO)undetecte d , where the last term is the number of rr°'s with both photons below threshold computed from the Monte Carlo. In the configuration D2h we can not rely on the reconstructed lr ° for the normalization because the threshold in deposited energy is large (2.0 GeV), and therefore most of the observed pions are unresolved and affected by a small but unknown background. For this reason the normalization in the D2h configuration is based on the reconstructed ~'s, with the result that the errors are dominated by the uncertainty on the value (5) of (~n ×B(r~ ~ 27)/o7ro.
E. AmaMi et aL/ Photon production
339
Table 2 Experimental determination and upper limit on R for 2.3 ~
Dma x
D2~
D2h
Integrated luminosity (cm -2) Pt interval (GeV/c)
82. 1035
1.5. 1035
219. 1035
2.5-3.4
2.3-3.4
2.3-3.4
(1) reconstructed n o (2) unresolved n 0 (3) single observed photon from decay (C1) (4) undetected n 0 (A) total number of n ~ produced in the phase space of apparatus (1+2+3+4)
770 ± 30 0 3590 ± 160
560 ± 25 252 ± 16 73 ± 6
(18.1 ± 2) - 103 (22.5 ± 2) - 103
0 885 ± 30
(99 ± 10) • 103
(1) single photons (2) contributions to single photons C1 C2 C3 C 1 + C2 + C 3 (B) direct photons (1-2)
4957 _+ 70
156 ± 13
17900 ± 135
3590± 160 780±120 364± 55 4734 ± 210 223 ± 220
73-+ 6 49± 7 19± 3 141 ± 10 15 ± 16
7800-+800 6800±700 2800±400 (17.4 ± 1.1) • 103 (500 ± 1100)
(1.0 ± 1.0) • 10 - 2
(1.7 ± 1.8) • 10 - 2
0.5 • 10 - 3
~<2.7%
~<4.7%
<2.3%
direct photons total produced upper limit at 95% C.L.
R =
a) Quoted errors include all uncertainties of statistical nature. Here we consider errors due to statistics plus the u n c e r t a i n t y on the b a c k g r o u n d subtracted f r o m the ~? invariant-mass distribution. The total n u m b e r o f n o shown in table 2 for the D2h configuration, is c o m p u t e d f r o m the values o b t a i n e d with the o t h e r configurations by taking into a c c o u n t the corresponding integrated luminosities. A shown in table 2 we obtain in all three configurations in the Pt region 2 . 3 3.7 G e V / c a value for the total n u m b e r o f direct p h o t o n s consistent with zero, and an upper limit for the ratio R = n~t/nno o f 4% with 95% confidence level taking into account only the statistical errors. These results c o n f i r m our previous conclusion [ 9 ] The configuration Dma x allows the extension o f the Pt interval towards higher values and thus provides the possibility o f studying the behaviour o f R versus Pt. Table 3 and figs. 8, 9 show our results. Fig. 8 represents the energy s p e c t r u m o f observed single p h o t o n s after subtraction o f 7/and ff contributions. The curve is the e x p e c t e d s p e c t r u m ( c o m p u t e d by the Monte Carlo m e t h o d ) o f single p h o t o n s due to 7r° decay n o r m a l i z e d to the observed n u m b e r o f reconstructed 7r°. Fig. 9 shows, as a
3872-+ 62 10 85+ - 33 360_+19 74 + 9 29,+ 6 10 -+ 4
2.50-2.96 2.96-3.42 3.42-4.00 4.00-4.55 4.55 5.13 5.13-5.70
2683 727 240 57.8 16.3 4.7
± 130 -+ 33 ÷ 11 _+ 2.6 ,+ 1.0 ,+ 0.2
605 171 56 12 4 1.3
Co nt ri but ion due to no ~
+- 81 -+26 -+ 8 ,+ 2 -+ 1 -+ 0.2
292 70 19 3.4 0.5 0.1
ff
-+ 44 -+ 10 -+ 3 ,+ 1 _+ 1 -+ 1
110 ± 170 117 -+ 54 45 _+ 24 1 ,+ 9 82 + 6 3.9,+ 4
Direct photons
17100 5400 1360 486 150 57
no _+10%
0.7 -+ 1 2.2÷ 1 3.3_+ 1.8 0.2 ,+ 1.8 5.4 ,+ 4 6.8,+ 7
R
2.4 3.8 6.3 3.2 12.0 18.0
Upper limit 95% C.L.
a) The numbers of single photons given here are the measured numbers after subtraction of accidental background. This was appreciable only in the last two bins.
Single photons a)
Pt interval
Table 3 Determination of R in the D ma x configuration for 2.5 < Pt <~ 5.7 GeV/c
E. AmaMi et al. /Photon production
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lOOd Events/tO0MeV
10Q
I 311
i 411
I 511
kIGeV/cl Fig. 8. Spectrum of observed single photons after subtraction of ~ and fi contributions. The continuous curve is the result of a Monte Carlo computation of the ~0 contribution.
function o f p t , the ratio R ---nT/n~o. The quoted errors are statistical. Our points indicate a very small value, consistent with zero, for Pt less than ~3 GeV/e and in spite of the large statistical error a trend to increase with Pt reaching values of the order o f 10% for Pt around 5 GeV. This behaviour is what is expected from the theoretical prediction given in ref. [8] and represented by the full line in fig. 9.
4. Systematic errors The most important source of systematic errors is the energy dependence of the response of the lead glass blocks. Since we compare the nuhabers of single photons with the number o f 7r° of m o m e n t u m given by the composition of two photons of lower momenta, a deviation from linearity, combined with the steep dependence of
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E. Arnaldi et al. / Photon production
J~E
a0
6.0
0t tat~)
Fig. 9. Ratio R = nT/nTrO versus Pt. The curve represents the results of the QCD prediction given by Field [8]. the 7r° invariant cross section on Pt, can produce an appreciable change in R. The uncertainty in the linearity correction affects mainly the D2Q results bringing the corresponding upper limit from 4% to 6%. The reason is that with this trigger we include all decay configurations of the n ° and therefore the energy of single photons is about one half of that of the n°'s. Furthermore, we fall in an energy region where the linearity corrections vary very fast with energy (fig. 2). On the contrary, in the Dma x configuration the effect of this uncertainty is negligible in the region of low Pt values (~<3 GeV/c), because the majority of the resolved 7r°'s are in asymmetric configurations so that the single photons and the 7r°'s fall in about the same momentum region. In this case the upper limit for R found in sect. 3 remains practically unchanged and equal to 4%. Also for large Pt (~3 GeV/c) the effect of uncertainties in the linearity corrections is negligible because we fall in the energy region where the linearity correction varies very slowly with energy (fig. 2). As a further test of the reliability of the value of the contribution C1 (k), we have repeated its computation by changing by one unit the exponent n in expression (2). Its value did not change appreciably. Some further consideration is in order about the use of only one- and two-cluster
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events in the derivation o f R (subsect. 3.1). This procedure is certainly correct under the assumption of no strong correlations between directly produced photons and other particles. The limited influence of correlations o f this type on our results has been checked by comparing the values o f two ratios, r I and r2, which should be equal under our assumption, rt is the ratio of the numbers of reconstructed ~°'s + one uncorrelated photon (i.e., three-cluster events) to the number of reconstructed ~°'s. r2 is the ratio o f two-cluster events not due to reconstructed zr°'s to one-cluster events. We found for the Dma x and Dz~ configurations: r I -- 10% and 35%, r2 = 10% and 32%. In conclusion, an overall estimate of systematic errors gives +0.02 almost independent from Pt. The contributions of co and other radiative decays have been estimated to be smaller than the systematic error.
5. Conclusions Our main conclusions are summarized in tables 2 and 3 and figs. 8, 9. In the region 2.3 ~
References [1] E.L. Feinberg, Nuovo Cim. 34A (1976) 391. [2] C.O. Escobar, Nucl. Phys. B98 (1975) 173. [3] G.S. Farrar and S.C..Frautschi, Phys. Rev. Lett. 36 (1976) 1017; G.S. Farrar, Phys. Lett. 67B (1977) 337. [4] R.D. Field and R.P. Feynman, Phys. Rev. D15 (1977) 2590; Nucl. Phys. B136 (1978) 1. [5] F. Halzen and D.M. Scott, Phys. Rev. Lett. 40 (1978) 1117. [6] R.P. Feynman, R.D. Field and G.C. Fox, Nucl. Phys. B128 (1977) 1. [7] R. Riickl, S.J. Brodsky and J.F. Gun/on, Slac-Pub-2115 (May,1978). [8] R.D. Field, Rapporteur talk at 19th Int. Conf. on High-energy physics, Tokyo, August 1978.
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[9] E. Amaldi, M. Beneventano, B. Borgia, A. Capone, D. De Notaristefani, U. Dore, F. Ferroni, E. Longo, L. Luminari, P. Pistilli, I. Sestili, G.F. Dell and L.C.L. Yuan, Phys. Lett. 77B (1978) 240. [10] P. Darriulat, P. Dittmann, K. Eggert, M. Holder, K.T. Mc Donald, T. Modis, F.L. Navarria, A. Seiden, J. Strauss, G. Vesztergombi and E.G.H. Williams, Nucl. Phys. B110 (1976) 365. [ 11 ] R. Walker, presented at the Chicago Meeting of the American Physical Society, 1976. [12] J. Cronin, presented at 1977 Int. Symp. on Lepton and photon interactions at high energies (Hamburg) 1977. [13] A.J. Lankford, Measurements of vector meson production in pp at the ISR, CERN, internal report 78-3 (May 1978). [14] E. Amaldi, M. Beneventano, B. Borgia, A. Capone, D. De Notaristefani, U. Dore, F. Ferroni, E. Longo, L. Luminari, P. PistiUi, I. Sestili, G.F. Dell, L.C.L. Yuan and J. Dooher, Nuovo Cim. Lett. 19 (1977) 152; 20 (1977) 409. [15] F.W. Bfisser, L. Camilleri, L. Di Lella, B.G. Pope, A.M. Smith, B.J. Blumenfeld, S.N. White, A.F. Rothemberg, S.L. Segler, M.J. Tannebaum, M. Banner, J.B. Ch6ze, H. Kasha, J.P. Ponsart, G.M. Smadia, J. Teiger, H. Zaccone and A. Zylberstein, Nucl. Phys. B106 (1976) 1. [16] K. Eggert, K.L. Giboni, W. Thorn6, B. Betev, P. Darriulat, P. Dittmann, M. Holder, K.T. Mc Donald, H.G. Pugh, G. Vesztergombi, T. Modis, K. Tittel, V. Eckardt, J.H. Gebauer, R. Menike, O.R. Sander and P. Seyboth, Nucl. Phys. B98 (1975) 49.