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II. EXPÉRIENCES PASSÉES ET FUTURES / II.
PAST AND FUTURE
EXPERIMENTSELECTRON-POSITRON INTERACTIONS AT 5 GeV IN THE
CENTER-OF-MASS : BHABHA SCATTERING AND MULTIHADRON PRODUCTION
H. Newman
To cite this version:
H. Newman. II. EXPÉRIENCES PASSÉES ET FUTURES / II. PAST AND FUTURE
EXPERIMENTSELECTRON-POSITRON INTERACTIONS AT 5 GeV IN THE CENTER-OF-
MASS : BHABHA SCATTERING AND MULTIHADRON PRODUCTION. Journal de Physique Col-
loques, 1974, 35 (C2), pp.C2-21-C2-28. �10.1051/jphyscol:1974204�. �jpa-00215513�
11. E X P ~ E N C E S PASS^ ET FUTURES.
/I. PAST A N D FUTURE EXPERIMENTS.
ELECTRON-POSITRON INTERACTIONS AT 5 GeV IN THE CENTER-OF-MASS : BHABHA SCATTERING AND MULTIHADRON PRODUCTION (*)
H. B. N E W M A N
Laboratory for Nuclear Science, Massachusetts Institute of Technology and
Cambridge Electron Accelerator, Cambridge, Massachusetts, USA
Rbsumb. - Nous avons termine une mesure des sections efficaces pour la diffusion Clastique electron-positron, ainsi que pour I'annihilation electron-positron en trois hadrons ou davantage, a une energie de 5 GeV dans le systeme du centre de masse. 228 i 15 evenements e + e- + e+ e- ont ete observes a des angles de diffusion conipris entre 50:' et 130°, cependant que la luminosite intkgree sur le temps etait, d'apres nos mesures, de (1,22 i 0,06) 1034 cm-1. Un calcul de la section efficace theorique (basee sur I'electrodynamique quantique) donne, pour le rapport entre les sections efficaces experimentale et theorique pour la diffusion Bhabha, la valeur : 1,03 & 0,08.
Nous avons Cgalement observe, au cours de la m&me experience, 108 evenements du type e+ e- -t
multihadrons, correspondant a une luminosite, integree sur le temps, de (1,14 i 0,06) x 1034cm-2.
Nous avons ainsi obtenu une liniite inferieure, independante de tout modele, de 9,5
*
1,l nb pour la section eficace de production de hacrons. Des calculs d'efficacite de detection, bases sur I'espace de phase invariant pour la production de pions, ont conduit pour la section efficace totale a une valeur estimee de 22<,
5 nb, ce qui represente 6,3+
1.4 fois la section efficace theorique pour Abstract. - We have completed a measurement of the cross sections for electron-positron elastic scattering, and electron-positron annihilation into three or more hadrons, at 5 GeV center- of-mass energy. (228 ::15) ei e--
e + e events were observed with scattering angles between 50" and 130°, while the time-integrated luminosity was measured as 1.22 t 0.06 x 1034 cm-2.A calculation of the theoretical (QED) cross section yields a ratio of the experimental to the calcu- lated cross section for Bhabha scattering of 1.03 ,t 0.08. We also observed 108 events of the type e+ e- -t multihadrons, between scattering angles of 45" and 135'), during a period of the same experimental run corresponding to a time-integrated luminosity of 1.14 : 0.06 x 1034 cm-2.
We therefore obtain a model-independent lower limit 011 the liadron production cross section of 9.5
*
1.1 nb. Detection efficiency calculations based on invariant phase space production of pions lead to an estimatcd total cross section of 22 i 5 nb, which is 6.3 i: 1.4 times the e+ e- -t jr+ p-theoretical cross section.
1. Introduction. - W e have used the electron- positron colliding-beam facility a t the Cambridge Electron Accelerator (CEA) t o measure tlie cross sections f o r e ' e - + e + e - and e + e - + multihadrons a t 2 E = 5 GeV center-of-mass energy (E is the beam energy). T h e events were detected by the non-magnetic Bypass On-Line Detector (BOLD) [I], [2], [3] : the charge of the final-state particles was not determined.
2. The CEA bypass. - 2.5 GeV electron a n d positron beams collided head-on in a straight section of the (( bypass )) [4] t o the main synchrotron. The beams were strongly focused by a (( low-beta )) section
(*) Work s~~pported in part by thc U S Atomic Energy Commission under Contracts No. AT ( 1 1-1)-3063, No. AT (11-1)-3064, No. AT ( 1 1-1)-3060, a n d Nat~onal Science Foun- dation Grant No. G P 33/22?.
t o increase the probability of collision. The high rf frequency leads t o a short bunch length. T h e ave- rage current in each beam was typically 4 mA, and the peak luminosity (defined as the counting rate divided by the cross section) was 4 x cm-'. S - l .
3. Luminosity measurement. - The measurement of luminosity is based on the event rate from the
+ -
double-bremsstrahlung reaction e' e - -+ e e yy.
This process is dominated by low momentum transfers, where quantum electrodynamics is expected t o be valid.
The brenisstrahlung ;l rays in a sma!l angular region around tlie incident electron and positron beams (11 = O0 and 180'') are r~leasured by ten-radiation- length lead-scintillator sandwich counters placed outside the charged particle trajectories. These coun- ters were extensively tested, and ccilibrated, before, during. a n d i f t e r the experiment.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1974204
H. B. NEWMAN
CEA SMU
Technion Harvard
BOLD-I BOLD-I1
( I 972) (1973)
-
-R. Averill ... 7
J. EsheIman ...
-+
G Hanson ...
+
A. HofmannJ. Koch
A. Litke ... +
R. Little ... +
R. Madaras
H. Mieras ... +
H. Newman ... +,
J. M. Paterson R. Pordes J. Sisterson
K. Strauch ... + G. Tarnopolsky ...
-+
G.-A. Voss
Richard Wilson ... +
H. Winick ... +
Random coincidences, chiefly from single brems- strahlung, are subtracted continuously from true coincidences using the difference in arrival time for pulses from each counter. Charged particles are
(Q) $-view of BOLD
I r o n
,
Area \\ //
WSC
vetoed by an additional scintillator placed in front of each sandwich counter.
The calculation of the luminosity and the associated errors must take into account the effects on the double- bremsstrahlung counting rate o f : (1) the counter resolution, (2) the geometrical aperture, (3) the charged particle veto, (4) the dead time, and (5) the uncertainty in the energy threshold for y detection.
These effects have been considered in great' detail [l], [5] particularly the effect of the finite counter resolu- tion. The counter resolution effect has been analyzed by extensive Monte Carlo and numerical integration techniques. The (luminosity) dt for the 1973 expe- riment at 2.5 GeV per beam is l .22
+
0.06 x cm-'.An improved value of the J'(luminosity) dt for the 1972 experiment at 2 GeV per beam has also been determined as 1.02 f 0.09 x lo3" cmP2, a decrease of 4
%
from the previously quoted value [I].
4. The Bypass On-Line Detector (BOLD). -Charged particles and gamma rays in the angular range 450
<
0 < 1350 and in a range of cp covering appro- ximately 70%
of 2 n (Fig. 1) were detected in BOLD.The main portion of the detector is a non-magnetic array of 20 scintillation counters and 48 magneto- strictive wire spark chambers comprising four qua- drants. The remaining 30 "/, in cp is covered by addi- tional (( Acp
),
scintillation counters. Cosmic rays were rejected by measuring the time-of-flight between the outer scintillators.Behind each horizontal quadrant is a large assembly of two double-gap wire spark chambers and iron plates, the (( hadron converter D, to aid in the separa-
( b)
@ - v i e w o f BOLD( Upper and Lower Quadrants Removed)
Flight
I 1
Counter
Floor + 4 8 " ( 1 . 2 5 m ) +
- 7 7 7
FIG. 1. - Layout of the Bypass On-Line Detector (BOLD) : a ) the cp view, 6 ) the 0 view.
ELECTRON-POSITRON INTERACTIONS AT 5 GeV IN THE CENTER-OF-MASS C2-23
EACH WSC = 2 G A P S
FIG. 2. - Detailed view of one BOLD quadrant.
tion of hadrons from muons. Hadrons are absorbed in the 1.8 collision lengths of iron, while muons from the two-body reaction (e+ e- -+ 11' p - ) pass straight through. Hadron absorbers were not installed above and below the top and bottom quadrants because of space limitations.
As a charged particle emerges from the interaction region into a BOLD quadrant (Fig. 2), it first passes through three double-gap, low-mass, wire spark chambers. These serve to define the particle trajectory.
The particle then passes through a scintillation counter in which dE1d.u is measured. The next three double- gap chambers are interleaved with iron-clad lead radiators and scintillation counters totaling 7 radiation lengths, in which electromagnetic showers are ini- tiated and observed through the number and dis- tribution of sparks. Scintillation counters in the shower region are used to triggel- the apparatus as well as t o sample the enel-gy of a shower.
Photons are also observed as showers in each quadrant, with no visible trajectory in the first three spark chambers. Hadrons have a reasonable proba- bility of scattering in the radiators, and sometimes end in nuclear stars, as observed through the spark confi- gurations in the quadrants.
BOLD was designed to detect the reactions :
e+
+
e- -+ hadrons . (4)This paper presents results for reactions (1) and (4) from our experiment with electron and positron beams of 2.5 GeV each.
5. Results for Bhabha scattering (ef e- -t e + e-). -
Thee+ e- -+ e + e- (Bhabha scattering) reaction occurs both by the scattering amplitude with space-like four- momentum transfer ( q Z = - 4 E~ sin2 0/2), whose average value was
<
q2>
= - 8.3 ( G ~ V / C ) ~ , and by the annihilation amplitude with time-like four- momentum transfer [q2 = 4 E 2 = 25 (GeV/c)'].Bhabha scattering events were identified, basically, by the observation of charged collinear showering particles in BOLD. A restricted angular region of 50° < 0 < 130. and cp within 300 of the normal to a quadrant was chosen to ensure > 99
%
detection efficiency for electrons and positrons. Each of the detected charged particles was required to produce a large pulse in the BOLD shower counter system.I n addition, the particle trajectories were required to intersect in the interaction region
( I I cm long x 2 cm x 2 cm) and to be within 15" of back-to-back [6].
An analysis based on thc 228 e f e- -+ e + e - events satisfying these criteria, and on the time-integrated luminosity of 1.22 0.06 x cm-', agrees with the theoretical Q E D prediction for the cross section (with radiative corrections) [7]. The ratlo of the measured to the predicted cross section is 1.03 f 0.08. Usjnga form factor F($)= I i c l Z / ( q Z - A : ) to parametrize deviations from Q E D in terms of a
C2-24 H. B. N E W M A N
heavy photon mass, we find A + > 10.0 GeV, and A - > 10.6 GeV (95 "/, confidence).
Figure 3 summarizes the comparison of theory to experiment for center-of-mass energies of 1.4 to 5.0 GeV for wide-angle Bhabha scattering. Recent Frascati data [8]-[lo] as well as CEA data are shown.
The 4.0 GeV CEA point has been revised from 0.88 f 0.10 [ l ] to 0.92 f 0.10 by an improved eva- luation of the luminosity [5].
I'
B H A B H A SCATTERINGFIG. 3. - Ratio of experimental Bhabha scattering cross sections to the predictions of QED for recent available data.
We have also obtained an angular distribution for the scattered particles. For each event the angle 0 was obtained by averaging the two values measured for the individual electron and positron tracks. The experimental distribution is shown in figure 4 where it is compared with the QED predictions taking into account the geometric acceptance and radiative corrections. The theoretical curve is normalized to give a predicted total number of events equal to the number observed. We find a
x 2
= 3.9 with nine degrees of freedom, corresponding to a probability > 90%.
I
FIT. x2=39 FOR 9 D E G R E E S OF6. Hadron production by e + e- annihilation.
-
6 . 1 THE DATA SAMPLE. - The BOLD Group has measured the cross section for electron-positron anni- hilation into three o r more hadrons, with at least two detected charged particles in the final state, and found it to be considerably larger than the point- like annihilation cross section e f e- + ,uf ,LL-.The apparatus was triggered by charged particles or electromagnetic showers in at least two of the four quadrants. Charged pions with a kinetic energy greater than 95 MeV or showers depositing at least 800 MeV in a quadrant could trigger the detector.
The multihadron data sample was defined as follows (before background and contamination sub- tractions) :
3 Z
(1) BOLD detected two or more prongs which came from a volume centered around the interaction region, and which penetrated material equivalent to at least 10.7 g/cm2 of iron.
I I I I I I I I I
(2) If an event had only two prongs, the prongs had to be at least 200 away fi-on1 collinearity as well as 200 away from coplanarity.
50 60 70 80 90 100 110 120 130 SCATTERING ANGLE €3 (DEGREES)
FIG. 4. - Observed angular distribution of the scattered par-
ticles in e+ e- + e+ e- at 5 GeV center-of-mass energy, and
comparison to the prediction of QED.
(3) The vertex point of all the tracks had to lie in a volume about the interaction paint as determined by the e + e- elastic scattering events.
6 . 2 BACKGROUND SUBTRACTIONS. - 175 events were found satisfying the above criteria. From this number we subtracted tr background )) events, not originating from e + e- reactions, and (( contamina- tion )) events, arising from e + e- reactions other than one-photon annihilation into hadrons.
Statistical background subtractions were made for beam-gas scattering and for cosmic-ray showers.
We subtracted 10 two-track and 1 three-track events due to gas scattering backgrounds, and 1 two-track event due to cosn~ic-ray background. Beam-gas events were observed along the beam line (our z coordinate) in volumes adjacent to the interaction region. Single beam runs at lo2 to 103 the normal operating gas pressure were used to determine both the multiplicity distribution and the vertex distribution along the beam direction of the beam-gas events. Knowledge of the vertex distribution allowed us to extrapolate along z from the adjacent vol~lmes into the interaction region itself. Cosn~ic-ray showers are expected to show a uniform distribution of vertex points, even away from the beam line. Sampling regions of empty space adjacent to the interaction region along the transverse coordinates .u and J. lead us to subtract the one additional event mentioned above.
6 . 3 CONTAMINATION SUIXTRACTIONS (OTI-IER T I - I A N
TWO-PHOTON PROCESSES). - Five events arising from radiative modifications to Bhabha scattering (eC e- + e i e- y ) and satisfying the requiretnents for the hadron sample were identified by the non- collinear high-energy electrons present ( 2 1.5 GeV deposited in the BOLD quadrant (( shower )) region).
ELEC TRON-POSITRON I N T E R A C T I O N S A T 5 GeV IN T H E CENTER-OF-MASS C2-25 This compares with a peaking approximation calcu-
lation predicting that 6 events should be detected.
N o 'i/ / L - y events were identified in the sample, and none were expected according to our calculations.
6 . 4 CONTAMINATION FROM TWO-PHOTON PROCESSES.
- Given a detector with 4 n s r geometric acceptance and n o energy threshold, the observed rates for the two-photon reactions [I I], [I21 :
would increase as [In (E/nr,)I2 in the approximation 171,/E + 0. The rising behavior of the cross sections with E would cause them to eventually rise over the corresponding processes :
which show a leading 1/E2 behavior.
At o u r energies, one might at first suspect that the two-photon diagrams are a significant if not major contribution to o u r data. Experimental evidence, however, a n d detailed computations [13] which take into account the BOLD experimental conditions, show a low level of (( contamination D. This is princi- pally due t o (1) the range requirement, and (2) the non-coplanarity requirement (in the case of two-track events).
It has been demonstrated that
falls rapidly with M, the invariant mass of the final state X [I I]. This leads to the fact that the rates for detecting two-photon-process final states are sensitive to Ad,,;,,, the value of the invariant mass where the produced particles have the minimum kinetic energy needed to :
( a ) Trigger the apparatus, and
(6) Satisfy the identification criteria for the data sample.
The BOLD trigger conditions [2] require at least two of the detected charged particles to have 95 MeV or more if pions o r muons, o r
-
500 MeV or more if electrons. Moreover, in the case where two charged tracks are detected, the non-coplanarity requirement sets a minimum total transverse momentum of approximately 60 MeV for the two equivalent photons.This criterion requires that the equivalent photons either be emitted at angles with respect to the incident beam greater than the characteristic angle 0 , =
J ~ E ,
or if emitted a t small angles, that they have a high longitudinal momentum. Thus, the effective threshold center-of-mass energy for produced particles detected in BOLD is relatively high.
Along with the energy constraints. we must consider the geometrical acceptance of the apparatus. Since BOLD co\.el-s only wide production a n l e s , nlost of
the produced particles from two-photon reactions are not detected. This is due to the fact that the center-of-mass of the produced particles is not sta- tionary. Computations [ I 31 of the detection efficiency as a function of /I, the velocity of the center-of-mass of the two equivalent photons as seen in the LAB, show that for states such as e + e - -+ e f e - n + n - no the efficiency is suppressed by a factor
-
10 withrespect to e + e - -+ y* -+ n + n - no.
Recent experimental evidence confirms the above discussion. Tagging counters to detect recoil elec- trons o r positrons from two-photon processes were available ; these had an efficiency
-
40%
for thedetection of electrons (or positrons) that had lost from 2.3 %, to 22 %, of their initial energy of 2.5 GeV.
Of 20 two-prong events we observed which satisfy our selection criteria except that 1600 <
I
AcpI
< 1800, thirteen ( o r 65PC;)
trigger at least one of the tagging counters. On the other hand, only one of 48 two- prong events [I41 in our sample triggers a tagging counter, a number which is entirely consistent with the 5 %, accidental rate expected on the basis of observations with the Bhabha scattering events.Of 72 events with three o r more prongs, two trig- gered one of the tagging counters, which is also consistent with the expected accidental rate. However, because our tagging system was not sensitive to electrons (and positrons) scattered with large loss of energy, the tagging efficiency for two-photon final states with high-mass multihadron systems was low.
We therefore must rely on theoretical estimates of the contamination, which are model dependent for e + e- + e + e -
+
hadrons.Recent estimates [13] of contamination from the two-photon mechanism computed in the equivalent- photon approximation [I I], [I21 are summarized in table 11. The estimate of e + e - -+ e + e - 11' (958 MeV) is conservatively based on f,,,,,, = 40 keV, the latest experimental upper bound in the particle tables. In order to compute e +
+
e - + e ++
e-+
hadrons,we adopted the estimate given by Brodsky et a/. [I21 :
o p g - h a d r o n s
-
0.3 pb.Swnmary of BOLD-11 two-plloton contamination Process Calculated events in sample
- -
eAe- +e-e-p+{f- % 1
e - e - -'e e - z b z -
e e-
-
e -1 e- -? hadrons < 1(a,, -z hadrons Z 0.3 pb)
Results of the computations far the earlier experi- ment at 2 GeV per beam, along with a more extensive discussion of the two-photon contamination question, have been presented in a previous paper [15].
C2-26 H. B. NEWMAN At the present stage of the analysis, no subtraction
has been made from the data to correct for the two- photon contamination.
6 . 5 LOWER LIMIT FOR a(e+ e- -+ MULTIHADRONS). -
After subtractions we are left with a total of 108 events.
'The prong counts are as follows : 37 two-prong, 31 three-prong, 26 four-prong, 10 five-prong, 2 six- prong, 1 seven-prong and 1 eight-prong. The event with eight charged tracks detected (Fig. 5) illustrates the hadronic nature of the final-state particles. Over-all, the data sample contains 348 charged tracks. Of these, 42 scattered through angles of more than go in the BOLD radiators, 8 scattered backward, and 5 ended in nuclear stars. Simple calculations using the Mott cross section set a conservative upper bound of three prongs scattered by more than 80 if the data sample were composed wholly of muons.
,
5 0 c m,
ABSORBER MAINLY LEAD IRON
6 . 6 EFFICIENCY CALCULATIONS FOR e + e- + MUL- TIHADRONS. - In order to deduce the total cross section a,,, the model-independent lower limit must be divided by the event detection efficiency E,. The calculation of [13], [16] is of course model-dependent.
We have assumed that all particles are pions produced according to a Lorentz-invariant phase space distri- bution, an assumption which agrees with the distri- bution of the angle in space between pairs of prongs taken from the data.
The first step in the calculation of E, is the deter- mination of the efficiencies ~ ( p , q) for detecting p-charg- ed tracks in BOLD, given that q-charged pions are produced through the reaction e +
+
e- -+ qn*+
n7n0.Parent states where q = 2, 4, 6, ..., 14, m 6 2, and q
+
111<
16 are assumed to contribute to the detected events. The values of ~ ( p , q) are computed by a Monte Carlo program based on NVERTEX. The program accounts for the geometric acceptance and trigger conditions of BOLD, considers the effects of nuclear absorption including secondary pion regeneration, and accounts for ionization losses in the lead radia- tors. Of the events generated by the program, only those which pass the same criteria used for scanning the real data are considered (( detected )) as multi- hadronic events. The efficiency corresponding to each of the assumed final states is listed in table 111.Each entry in the table is averaged over m, the number of no's, because ~ ( p , q) generally varies by < 20
%
of its listed value for different n7.
Given the observed number of events with prong count y , N,, the unknown partial cross sections a,, (ei e- + qn*
+
neutrals) must satisfy the rela- FIG. 5. - A view along the beam line of the eight-prong event tionships :in BOLD at 5 GeV center-of-mass energy. Particles are seen
to stop in the iron absorber and scatter through large angles. N , = L q = 2 , 4 ,
x
..., 14 ~ ( p , q ) a , , p = 2 , 3 , 4 , . . . , 8 where .L is the time-integrated luminosity. These Based on the count of 108 events, and on a time- equations have been solved [13], [16] with the physical integrated luminosity of 1.14t
0.06 xern-',
restriction a, 3 0. This requirement precludes exact we calculate a model-independent lower limit on the solution of the equations, so (( optimal )) solutions cross section for e f e- -+ multihadrons of 9.5+ 1 . I nb. are found by varying the partial cross sections a,Number
Number of
of observed prongs events
A -
P NP
Average detection efJiciet7cy
ELECTRON-POSITRON INTERACTIONS AT 5 GeV I N T H E CENTER-OF-MASS C2-27
over positive values, and finding a set of numbers N,: errors in the luminosity measurement are also taken
that minimizes the quantity into account.
While the partial cross sections a, are not well
1
(Nb - N , ) ~ / N ,.
determined, the value of a,,, L, where a,,, =C
a,,P 4
Further discussion of these techniques is given in reference [13].
The errors quoted were calculated by computing an ensemble of solutions where the N , are allowed to fluctuate independently according to Poisson statistics (a simulation of redoing the experiment), and looking at the distributions of a,,, L, E,, and n generated. The
R a ~ ( e + e - - - + HADRONS) u(e+e--+ pCp7
6 0 ACO
A NOVOSIBIRSK FRASCATI GROUPS
:IA
o BOSONx P T
COLORED
- - f - - - -
QUARK MODELS - ORDINARY
I
- - -is found to be 248 f 49 events, corresponding to a total efficiency E, of 46 -1 9 "/,. The average charged multiplicity n is 4.3 0.6.
6 . 7 CROSS SECTIONS A N D MEAN MULTIPLICITIES FOR
e + e- + MULTIHADRONS. - From the measured value of L and the computed number of events a,,, L we calculate a value for the multihadron production cross section by electron-positron annihilation at s = 25 GeV2. The raiio R of this cross section to the theoretical cross section for e + e- + p f p - at 5 GeV center-of-mass energy is 6.3
+
1.4. This is compared with recent data in figure 6 [8], [17]-[22]. Parton models suggest that R approaches a constant value in the asymptotic limit of large s. Identifying the partons with a single triplet of spin f quarks gives R = f , while assuming the existence of three triplets (quarks with (( color ))) gives R = 2.We also present a plot of the average charged multiplicity n vs. s for recent data [23] in figure 7.
if
l
AVERAGE CHARGED MULTlPLlClN VS. In S0 FRASCATI (CERADINI ET AL) FRASCATI ( Y Y GROUP) CEA
FIG. 6. - R = o(e+ e- + multibody hadrons)/o(e+ e
-
p+ p-) 1 2 1 3 I 4 I 5 1 6 I 7 8 9 1 0 I 1 1 1 I I - I ,versus the square of the center-of-mass energy s in GeVl. 20 S ( G ~ V ~ )
The dotted lines give the asymptotic predictions of parton FIG. 7. - Average charged multiplicity versus s in GeV2 for models assuming ordinary and colored quarks. recent available data.
References [I] MADARAS, R. et a/., Pliys. Rev. Lett. 30 (1973) 507.
[2] MADARAS, R., Ph. D. Thesis, Harvard University, Cam- bridge, Massachusetts (~~npublished).
[3] MADARAS, R . et crl., Nlicl. I t ~ s r r . & Metll., to be published.
[4] AVERILL, R. PI nl., Cambridge Electron Accelerator Report No. CEAL-3063-03 (~lnpublished).
I51 NEWMAN, H. et rrl., Eleclrotr-Positm S c n t t ~ r i t i g ot 5 GeV Cetiter-of-Mass Etiergy, International Symposium on Electron and Photon Interactions at High Energies, Bonn, 1973.
[b] The observed transverse dimensions of the interaction region al-e chiefly determined by multiple scattering in the beam pipe and by the track reconstruction accuracy of the spark chambers.
[7] TAVERNIER. S.. Laboratoire dc I'AccPICratcur 1-ineairc.
Orsay. Report No. R I 6817, 1968 (~~npuhlihhcd).
[8] BERNARDINI, C., Reslrlfs otz e+ e- Reactions at Adotle, International Symposium o n Electron and Photon Interactions at High Energies, Cornell, 1971.
[9] BARTOLI, B. et ul., Phys. Rev. D 6 (1972) 2374.
a ) Errors on Frascati points at or below 2 E = 2.4 GeV are statistical only. The systematic errors in the nor- malization due to the e+ e- + e+ e- small angle scat- tering monitor are
+
5 % for p n Group data andi - 6.5 % for Boson Group data.
--
[lo] CONVEKSI, M. et 01.. Litnits to Possible Scolrrr-Boson A4~ss ntl(/ C o ~ l p l i t ~ g fiotti e 1 e Colli.riot~.s, Bonn Confe- rence, 1973.
[ I l l AI(T~:<;A-ROM~:KO, N., JA(Y.AI<INI, A.. K E S S L ~ R , P. and PAICISI, J., Pllj1.s. Rc.13. D 3 ( 1971) 1569.
[I21 BI<OIISKY, S., KINOSCII-IA, T., TEIIAZAWA, H., P/I.I's. Rev.
D 4 (1971) 1532.
[ I ? ] T A I ~ N O P O L S K Y , C;., I). Sc. Thesis, Technion, tlaifa ( u n p ~ ~ h - lishcd).
C2-28 H. B. NEWMAN [I41 Clearly identified e+ e- + e+ e- y events are excluded
from this discussion.
[15] NEWMAN, H., Resiclts orr ef e- Reactiotrs at tlre CEA (2.0 and 2.5 GeV per Beam), Topical Conference on Deep Inelastic Scattering, SLAC, 1973.
[16] TARNOPOLSKY, G., internal CEA memos, 1972-73.
[I71 LITKE, A. et al., Phys. Rev. Lett. 30 (1973) 1189.
[I81 COSME, G. ef al., Phys. Lett. 40B (1972) 685.
[I91 KURDADZE, L. M. et a[., Phys. Left. 42B (1972) 515.
[20] GRILLI, M. el al., Nuovo Cir~tmto 13A (1 973) 593 ;
CERADINI, F. el al., paper
+
9 submitted to 1973 Bonn Conference.[21] BACCI, C . et at., Phys. Left. 38B (1972) 551 ; B ~ c c r , C. et a / . , Pl~ys. Lett. 44B (1973) 533 ;
BACCI, C. et a/., paper iti 271 submitted to 1973 Bonn Conference.
[22] The CEA point at s = 16 GeVr has been corrected for the improved luminosity evaluation discussed in section 3 of this paper.
1231 CERADINI, F. et at., Plrys. Lett. 42B (1972) 501.
DISCUSSION E. CALVA-TELLEZ. - It seems that the ratio
o(hadrons)/a(pf p-) is compatible with a behaviour
-
116. This behaviour can be obtained by using a generalized vector dominance model.H. B. NEWMAN. - Yes, within the error bars this behaviour is not ruled out, but there is no conclusive indication.
A. ZICHICHI. - There are several generalized vector dominance models, for instance that of Greco et al.
E. CALVA-TELLEZ.
-
Exactly, one may start from that model and choose the parameters in such a way that the behaviour is indeed- 114s.
On the other hand, I have a question : What is the role of the radiative corrections in the ratio a(hadrons)/a(pf ~ i - ) ?H. B. NEWMAN. - It is less than 5
%.
S . ORITO. - HOW is your multihadron cross section stable with the assumptions you made. For instance, if you put 10
%
kaons in the final state, what is the resulting cross section ?coming from another conference where our results were presented, and therefore I have with me a trans- parency where you can see how our results compare with those reported by Dr. Newman.
K. STRAUCH. - Your QED results are unfortunately presented in such a way (i. e. without details for each individual energy) that they cannot be put on summary graphs.
H. TERAZAWA.
-
1 want to make the following comment : You have presented your data in such a way that you subtract the two-photon contribu- tion from the total, leaving the one-photon annihi- lation events. The subtraction, however, strongly depends on our estimate of the cross section for yy -+ hadrons. As you know, the estimate is made by factorization, i. e. a,,,, - (a ,,,,
)2/a ,,,,,
which
should be approximately good at very large .I.
(- 10 GeV2), but may not be correct at such a small s as is relevant at the CEA energy. By s, I mean the invariant mass squared of two virtual photons, but not the total energy squared of the colliding beams.
For small s, lower mass resonances may enhance H. B. NEWMAN. - The change is not significant
our estimate by, say, several times.
compared to our errors.
An extreme attitude would be the following : S. 0 ~ 1 ~ 0 .
-
NOW, I have another question : You could present your data in the following way : Can You say something about Your tagging system '? Assuming the three-triplet model or the Han-NambuH. B. NEWMAN. - Tagging counters are placed between the bending magnets in the bypass, close to the beam line. I show you an additional transparency containing further details.
B. STELLA. - Did YOU try, actually, to separate pions from kaons ?
H. B. NEWMAN. - NO, we had no way of reliably separating pions from kaons in our data sample with our apparatus.
A. ZICHICHI. - The report by Dr. Newman has covered an unexpected area : QED and a(ef e - -+
hadrons). For completeness, I would like to say that, in both fields, the results obtained by the Bologna- CERN-Frascati (BCF) group have not been included.
As far as QED checks are concerned, we have measured the .+dependence of the reaction e f e- -+ e f e - from 1.44 to 9.0 GeV2 with f 2 '%, accuracy, including first order radiative corrections. Regarding the (e+ e- -+ hadrons) problem, it just happens that 1 am
model for one-photon annihilation, you can subtract the one-photon events and say what is left is the two-photon process.
H. B. NEWMAN. - I don't agree with your extreme approach at all. We took conservative estimates of o(yy + hadrons) based on c~rr.r.ent11. u~:ailahle, definite theoretical models in the literature. I also calcula- ted a(yy -+ hadrons) based on parton models given by Berman et al., and the most conservative esti- mates gave a(yy -+ hadrons) < 0.6 pb.
S. J. BRODSKY. - 1 will give a discussion of the assumptions which go into estimates of o(yy 4 hadrons).
T. F. WALSH. - I think that one can say the follow- ing : from the CEA results, one can conclude that either one-photon annihilation at high energy is much bigger than anybody expected or yy -+ hadrons at low energy is much bigger than anybody expected.
1 can't see how one can clearly choose at that stage.
