- Email: [email protected]
The energy dependence of σ(e+e− → hadrons) in the total centre-of-mass energy range 1.2 to 3.0 GeV
Volume 51B, number 2
PHYSICS LETTERS
THE ENERGY
DEPENDENCE
22 July 1974
O F o ( e + e - -~ H A D R O N S )
CENTRE-OF-MASS
ENERGY
RANGE
IN THE TOTAL
1.2 T O 3 . 0 G e V
M. BERNARDINI, D. BOLLINI, P.L. BRUNINI, E. FIORENTINO, T. MASSAM, L. MONARI, F. PALMONARI, F. RIMONDI and A. ZICHICHI CERN, Geneva, Switzerland Istituto Nazionale di Fisica Nucleate, Bologna, ltaly lstituto di Fisica dell'Universitd Bologna, Italy Laboratori Nazionali del CNEN, Frascati.Roma, Italy
Received 20 June 1974 4"
__
We have observed 1085 events of the type e e ~ hadrons, m the total centre-of-mass energy range x/~ = 1.2 to 3.0 GeV. The energy dependence of the total annihilation cross-section, parametrtzed in the form tr(e e ~ hadrons) = A.s n, is measured to b e n -- - - ( 1 . 5 4 _+o.17 0 . 2 9 ) in the above energy range. .
.
The purpose o f this paper is to report on the resuits obtained in a study o f the reaction e+e - ~ hadrons
.
.
.
÷
--
and for a kaon E K > 223 MeV. The trigger was therefore of a semi-inclusive nature, i.e. (1)
in the total centre-of-mass energy range, 2 E = x/s = 1.2 to 3.0 GeV. The experiment was performed at Frascati using the (e+e - ) colliding beam machine. The experimental set-up has already been described [ 1]; it consisted of two identical sets of telescopes, placed symmetrically about the colliding beam axis, with one inside and one outside the storage ring. The basic elements in each telescope were: i) thin-foil spark chambers for precise geometrical reconstruction; ii) heavy-plate spark chambers for particle identification: electrons make showers, muons show only Coulomb scattering, while hadrons show a typical strong interaction pattern; iii) thin and thick plastic scintillation counters - to allow a fast trigger with good pulse-height analysis and high-resolution timeof-flight measurements. On each side of the ring the telescopes subtended a range o f polar angles 45 ° < 0 < 135 ° and 30% of the total azimuthal angular range, i.e. Aq~ = 60 ° centred on the storage ring plane. The solid angle covered by the apparatus was ~ 20% of 47r. The trigger required that on each side there must be at least one charged particle with an energy cut-off (depending on the type of particle and its inclination in the telescope) which for a pion was E~ 3> 130 MeV, 200
.
e+e - ~ h e + h ~ + anything,
(2)
where h ± stands for either a 7r-+ or a K +-. We have determined the relative abundance o f ¢r's and K's for a two-body annihilation [2]; the admixture of Tr and K is not known for the many-body annihilation case (2). In the following, we will assume that h ± --- rr± . One o f the basic points o f the experiment was to be sure o f the hadronic nature of the events. To this end, the scanning criteria were verified b y performing a special calibration experiment at CERN. There, momentum-selected beams of known particles (Tr, g, e) were sent into a telescope, identical to the four actually used in the (e+e - ) annihilation experiment. These data have been published [3] and we will recall here only the key-point of this problem. The rate of hadronic events, reaction (1), was measured [3] to be of the same order of magnitude as the rate of radiatively produced, non-coplanar e+e - events [4]. These non-coplanar (e+e - ) events are characterized by a large energy imbalance in the final state of the (e+e - ) pair; one or both members of the pair having an energy much lower than the value proper to the two-body final state. Now, our direct calibration runs established [3] that a low-energy electron can simulate a stopping 7r meson unless special care is taken to study the detailed regularity of the track
Volume 51B, number 2
PHYSICS LETTERS
along its whole length, so we must conclude that there could be a serious source of background if events are identified as pions whenever there is a large acoplanarity between the tracks or whenever the tracks do not look like full energy electrons or muons. For these reasons, events were carefully analysed and compared with the calibration data taken at CERN, and we were thus able to demonstrate directly [3] that in the final state produced from (e+e - ) interactions there was a component with a "hadronic" nature. The next step was then to determine the energy dependence of the hadronic annihilation crosssection and here enters the second basic problem: the uncertainty in the details o f the final states produced. To obtain the partial cross-sections for the various final-state channels and also the total cross-section, it is necessary to use the observed rates for the various particle combinations which are actually detected. To carry out such an analysis without bias requires a 41r solid angle, an unbiased trigger, and a high detection efficiency for all particles which are produced. The apparatus used was primarily designed to have a very good particle identification power for pions, muons, and electrons. However, for reasons of cost [5], the solid angle was restricted to about 0.8zr for each charged particle and to about 0.2n for 7-rays. Since the angular distributions, momenta spectra, and correlations of the final-state particles as well as the branching ratios into the various charged-neutral pion states are unknown, there will be biases in the result, and our aim is to present the data in a way which minimizes these biases. To this end, the data have been analysed in three different ways. The first m e t h o d was to investigate the total events rate, normalized to the integrated luminosity at each energy so that the full statistics may be used to the best advantage to look for any structure in the total cross-section [6]. No convincing statistically significant structure is observed in the data. The second m e t h o d was to assume an over-all model for the distribution o f charged states. Within the limitations o f the model, this then gives the most efficient use of the statistics to obtain the total cross-sections. We have considered several models, the most plausible o f which we consider to be the (tip) model with phase-
22 July 1974
space corrections. In this model, we take the finalstate mixture used by Hebert and Mes [7] to fit the charge states measured in (~p) annihilation at rest. To take into account that the centre-of-mass energies available in the present experiment differ from that o f ( g p ) annihilation at rest, we use phase-space corrections. It should be noted that, in the onephoton approximation, the two annihilation processes (e+e - ) and (~p) have certain similarities: (gp) annihilation can produce only I = 0 and I = 1 states* just as in (e+e - ) annihilation. Moreover, 99% of the (ffp) annihilations at rest occur in the L = 0 states (3S 1 and 1S0), the triplet being a state* w i t h J PC = 1 - - . If the triplet dominates (it should be three times stronger than the singlet), then (ffp) annihilation at rest produces states with the same quantum numbers as those o f the time-like photon in the onephoton approximation of reaction (1): (see fig. l). Fig. 2 shows a self-consistency check for the (gp) model; namely, the observed charged multiplicities and those expected on the basis of the model. The agreement is satisfactory and we believe that the choice o f the model is justified. Fig. 3 shows the resuits obtained for o(e+e - ~ hadrons) as a function of the total centre-of-mass energy. In the third method, use is made o f the track detection in the kinematic chambers, the solid angle of which is bigger than that o f the complete telescope and is ~ 2zr. Various models are used [6] just to give the neutral particle multiplicity distribution for each charged state so that phase-space momenta distributions may be used to estimate the efficiency for each * I -- lsospin; J = intrinsic angular m o m e n t u m ; P = parity; C = charge conjugation.
~
~--- h a d r o n s
Fig. 1. Feynman diagram describing reaction (1), in the onephoton approximation. 1 = isospin; J = intrinsic angular momentum; P = parity; C -- charge conjugation.
201
Volume 51B, number 2
PHYSICS LETTERS
22 July 1974
1 0 t l 600 MeV
L
\
300
0,6 08 a4 (12
r
750 MeV
BOO
MeV
B50 MeV
200
2
06 04 (?2
b
o,
925 MeV
950 MeV
970 MeV
1OO
08-
02
41o l
990 MeV
1050 MeV
2'.~
•
+
3'.o
_
Fig. 3: Total annihilation cross-section, o(e e --* hadrons), as a function of the total centre-of-mass energy 2E for the (~p) model. The curve is the best fit to the form o = A.s n.
1300MeV
1400 MeV
~ 1500 MeV
04 0.2 N2 N3 N N5
N~ N3 N. N~
N: N. N~. Ns
Fig. 2. Track multiplicity distributions at various colliding beam energies. Those expected on the basis of the (~p) model (histogram) are compared with the experimental data (points with errors). Each histogram contains four bins, from 2 to 5 observed tracks N2, N3, N4, Ns. The vertical scale shows the fraction of events in each class.
charged multiplicity. In this way, the observed charged particle multiplicity distributions may be used to obtain the cross-section for each charged state. This is the least model-dependent analysis, and we will call it the quasi-model-independent method. The results for o(e+e - -~ hadrons) obtained with this method are consistent with the (~p) model mentioned above, and are shown in fig. 4. Table 1 shows the data and results obtained at the various energies investigated: the beam energies; the number of electron pairs (used as a monitor reaction) observed in the same solid angle; the integrated luminosities; the observed numbers of hadronic events; the beam-gas background events estimated from runs with single beams, and finally the values of o(e+e - ~ hadrons) obtained 202
£o
2E (GeV)
1200 MeV
Oo; 08 |
~'.s
by the two methods. We note that the results of neither of these two methods show any evidence for a statistically significant structure, in agreement with the result of the first method. Moreover, the exponent of the
/
I001 i
1.O
Fig.
i
1.5
i
i
2.O 2 E (GeV) •
2.5 +
i
3.O
_
4. Total annihilation cross-section o(e e ~ hadrons), as a function of the total centre-of-mass energy 2E for the quasimodel-independent method described in the text• The solid curve is the best fit to the form A.s n. The bdst fit from fig. 2 is shown by the broken curve. The standard point-like crosssection o(e+e # *# - ) is shown as a reference.
Volume 51B, number 2
22 July 1974
PHYSICS LETTERS Table 1
E (GeV) 1.2 1.3 1.4 1.5 1.6 1.7 1.85 1.9 1.94 1.98 2.1 2.4 2.6 2.8 3.0 TotMs
Ne±e~
Integrated luminosity (nb -1 )
Number of hadronic events
691 765 843 2080 1470 1754 1178 2118 668 747 4650 741 1680 1296 1797
6.59 9.46 12.54 36.14 33.60 48.50 41.94 64.59 25.94 29.02 204.15 48.11 106.06 88.30 197.28
12 21 16 88 85 95 56 91 30 32 236 66 108 49 100
22478
952.22
1085
Beam-gas background
O(hl) (nb)
< < < < < < <
194 188 90 148 134 93.7 56.8
1 1 7 4 4 5 4
(nb) +ST $8 -,*2 +22 -47 16 _+ 17 -
+41
+ 14 - 15 +
_ 19`6 + 87.6 .6
< 8
58.5
_ +
< 3 < 3 17 ± 9 19 ± 10 36 ± 14 8±4 11 ± 8
46.8 45.0 43.0 31.7 20.3 12.0 12.3
+_136 +_ 7.9 ± 3.3 ± 8.1 ± 4.8 ± 3.8 ± 1.9
67~1
218 305 100 148 135 126 73 71 68 53 54.6 42 33 17.8 28.7
± 108 ± 88 ± 70 -+ 26 ± 25 ± 18 ± 15 ± 14 ± 21 ± 18 ± 3.3 ± 24 ± 14 ± 8.9 ± 6.7
oh =- o(e+e - ~ hadrons); (1) indicates the 2nd method, (2) indicates 3rd method of deriving oh. n b --- 10 -30 cm ~.
energy d e p e n d e n c e o f the total annihilation crosssection is, within one standard deviation, the same for the t w o m e t h o d s . The energy d e p e n d e n c e is o b t a i n e d by fitting all the data w i t h the expression o(e+e - ~ hadrons) =
A's n,
where A and n are free parameters. The results are: n 1 = - ( 1 . 6 3 -+ 0.08) using the ( p p ) m o d e l w i t h phasespace corrections; n 2 = - ( 1 . 4 4 + 0.15) using the quasi-model-independent m e t h o d . Combining the two results and taking as error limits the two e x t r e m e cases, we have for n: n =-
(1.54 + 0.17a _ 0.29 j •
In conclusion our data show that for the two extreme m e t h o d s used, the value o f n is non-zero, i.e. in our energy region o(e+e - ~ hadrons) c a n n o t be constant [9], as seems to be the case for energies between 3.0 and 5.0 GeV [10, 11]. In o t h e r words, in the energy range from 1.2 to 3.0 GeV, the total hadronic annihilation cross-section a(e+e - ~ hadrons) decreases w i t h energy at least as fast as the point-like cross-section. We w o u l d like to acknowledge the collaboration o f our technicians and scanning girls: Messrs. G. Baccherini, A. Borghi, L. Daniello, F. Ferioli, M. Ferrari, V. Lelli, F. Martelli, F. Massera, G. Molinari, R. Pilastrini, O. Polgrossi, V. Russo, G. Sola; Mrs. L. Maselli, Mrs. F. Nicoli and Miss L. Zitelli.
We have checked that w i t h i n -+2% the large-angle (e+e - ~ e+e - ) m o n i t o r has the correct energy dep e n d e n c e [8]. 203
Volume 51B, number 2
PHYSICS LETTERS
References [ 1] For details of the set-up, see V. Alles-Borelli, et al., Phys. Lett. 40B (1972) 433 and refs. [2, 12] quoted therein. [2] M. Bernardini, et al., Phys. Lett. 44B (1973) 393. [3] V. Alles-Borelli, et al., Prec. First EPS Conf. on Meson resonances and related electromagnetic phenomena, Bologna, 1971, eds. R.H. Dalitz and A. Zichichi (Editrice Compositori, Bologna, 1972); V. Alles-Borelli, et al., Prec. 8th Course in the Int. School o f Subnuclear Physics, Eriee, July 1970, in Elementary processes at high energy, ed. A. Zichichi (Academic Press, New York, 1971), p. 790. [4] V. Alles-Borelli, et al., Phys. Lett. 36B (1971) 149; M. Bemardini, et al., Phys. Lett. 45B (1973) 169. [5] For the same reason, we had no magnetic analysis available, as in our first proposal: M. Bernardini, et al., Experimental investigations proposed for ADONE, INFN. A/E-66-10, 7 November 1966.
204
22 July 1974
[6] The details will be reported in a forthcoming paper to be published in I1 Nuovo Cimento. [7] J. Hebert and H. Mes, Nuclear Phys. B4 (1968) 244. [8] M. Bernardini, et al., Phys. Lett. 45B (1973) 510. [9] For previous Frascati and Novosibirsk data see: B. Bartoli, et al., Phys. Rev. 6D (1972) 2374; C. Bacci, et al., Phys. Lett. 38B (1972) 551 ; 44B (1973) 533; M. Grilli, et al., Nuovo Cirnento 13A (1973) 593; F. Ceradini, et al., Phys. Lett. 47B (1973) 80; Data on o(e*e- ~ hadrons) have also been obtained at Novosibirsk by L.M. Kurdadze, et al., Phys. Lett. 42B (1972) 515. [10] A. Litke, et al., Phys. Rev. Lett. 30 (1973) 1189; G. Tarnopolsky, et al., Phys. Rev. Lett. 32 (1974) 432. [ 11 ] Data reported by B. Richter at the Conf. on Leptoninduced reactions, Irvine, December 1973.
PHYSICS LETTERS
THE ENERGY
DEPENDENCE
22 July 1974
O F o ( e + e - -~ H A D R O N S )
CENTRE-OF-MASS
ENERGY
RANGE
IN THE TOTAL
1.2 T O 3 . 0 G e V
M. BERNARDINI, D. BOLLINI, P.L. BRUNINI, E. FIORENTINO, T. MASSAM, L. MONARI, F. PALMONARI, F. RIMONDI and A. ZICHICHI CERN, Geneva, Switzerland Istituto Nazionale di Fisica Nucleate, Bologna, ltaly lstituto di Fisica dell'Universitd Bologna, Italy Laboratori Nazionali del CNEN, Frascati.Roma, Italy
Received 20 June 1974 4"
__
We have observed 1085 events of the type e e ~ hadrons, m the total centre-of-mass energy range x/~ = 1.2 to 3.0 GeV. The energy dependence of the total annihilation cross-section, parametrtzed in the form tr(e e ~ hadrons) = A.s n, is measured to b e n -- - - ( 1 . 5 4 _+o.17 0 . 2 9 ) in the above energy range. .
.
The purpose o f this paper is to report on the resuits obtained in a study o f the reaction e+e - ~ hadrons
.
.
.
÷
--
and for a kaon E K > 223 MeV. The trigger was therefore of a semi-inclusive nature, i.e. (1)
in the total centre-of-mass energy range, 2 E = x/s = 1.2 to 3.0 GeV. The experiment was performed at Frascati using the (e+e - ) colliding beam machine. The experimental set-up has already been described [ 1]; it consisted of two identical sets of telescopes, placed symmetrically about the colliding beam axis, with one inside and one outside the storage ring. The basic elements in each telescope were: i) thin-foil spark chambers for precise geometrical reconstruction; ii) heavy-plate spark chambers for particle identification: electrons make showers, muons show only Coulomb scattering, while hadrons show a typical strong interaction pattern; iii) thin and thick plastic scintillation counters - to allow a fast trigger with good pulse-height analysis and high-resolution timeof-flight measurements. On each side of the ring the telescopes subtended a range o f polar angles 45 ° < 0 < 135 ° and 30% of the total azimuthal angular range, i.e. Aq~ = 60 ° centred on the storage ring plane. The solid angle covered by the apparatus was ~ 20% of 47r. The trigger required that on each side there must be at least one charged particle with an energy cut-off (depending on the type of particle and its inclination in the telescope) which for a pion was E~ 3> 130 MeV, 200
.
e+e - ~ h e + h ~ + anything,
(2)
where h ± stands for either a 7r-+ or a K +-. We have determined the relative abundance o f ¢r's and K's for a two-body annihilation [2]; the admixture of Tr and K is not known for the many-body annihilation case (2). In the following, we will assume that h ± --- rr± . One o f the basic points o f the experiment was to be sure o f the hadronic nature of the events. To this end, the scanning criteria were verified b y performing a special calibration experiment at CERN. There, momentum-selected beams of known particles (Tr, g, e) were sent into a telescope, identical to the four actually used in the (e+e - ) annihilation experiment. These data have been published [3] and we will recall here only the key-point of this problem. The rate of hadronic events, reaction (1), was measured [3] to be of the same order of magnitude as the rate of radiatively produced, non-coplanar e+e - events [4]. These non-coplanar (e+e - ) events are characterized by a large energy imbalance in the final state of the (e+e - ) pair; one or both members of the pair having an energy much lower than the value proper to the two-body final state. Now, our direct calibration runs established [3] that a low-energy electron can simulate a stopping 7r meson unless special care is taken to study the detailed regularity of the track
Volume 51B, number 2
PHYSICS LETTERS
along its whole length, so we must conclude that there could be a serious source of background if events are identified as pions whenever there is a large acoplanarity between the tracks or whenever the tracks do not look like full energy electrons or muons. For these reasons, events were carefully analysed and compared with the calibration data taken at CERN, and we were thus able to demonstrate directly [3] that in the final state produced from (e+e - ) interactions there was a component with a "hadronic" nature. The next step was then to determine the energy dependence of the hadronic annihilation crosssection and here enters the second basic problem: the uncertainty in the details o f the final states produced. To obtain the partial cross-sections for the various final-state channels and also the total cross-section, it is necessary to use the observed rates for the various particle combinations which are actually detected. To carry out such an analysis without bias requires a 41r solid angle, an unbiased trigger, and a high detection efficiency for all particles which are produced. The apparatus used was primarily designed to have a very good particle identification power for pions, muons, and electrons. However, for reasons of cost [5], the solid angle was restricted to about 0.8zr for each charged particle and to about 0.2n for 7-rays. Since the angular distributions, momenta spectra, and correlations of the final-state particles as well as the branching ratios into the various charged-neutral pion states are unknown, there will be biases in the result, and our aim is to present the data in a way which minimizes these biases. To this end, the data have been analysed in three different ways. The first m e t h o d was to investigate the total events rate, normalized to the integrated luminosity at each energy so that the full statistics may be used to the best advantage to look for any structure in the total cross-section [6]. No convincing statistically significant structure is observed in the data. The second m e t h o d was to assume an over-all model for the distribution o f charged states. Within the limitations o f the model, this then gives the most efficient use of the statistics to obtain the total cross-sections. We have considered several models, the most plausible o f which we consider to be the (tip) model with phase-
22 July 1974
space corrections. In this model, we take the finalstate mixture used by Hebert and Mes [7] to fit the charge states measured in (~p) annihilation at rest. To take into account that the centre-of-mass energies available in the present experiment differ from that o f ( g p ) annihilation at rest, we use phase-space corrections. It should be noted that, in the onephoton approximation, the two annihilation processes (e+e - ) and (~p) have certain similarities: (gp) annihilation can produce only I = 0 and I = 1 states* just as in (e+e - ) annihilation. Moreover, 99% of the (ffp) annihilations at rest occur in the L = 0 states (3S 1 and 1S0), the triplet being a state* w i t h J PC = 1 - - . If the triplet dominates (it should be three times stronger than the singlet), then (ffp) annihilation at rest produces states with the same quantum numbers as those o f the time-like photon in the onephoton approximation of reaction (1): (see fig. l). Fig. 2 shows a self-consistency check for the (gp) model; namely, the observed charged multiplicities and those expected on the basis of the model. The agreement is satisfactory and we believe that the choice o f the model is justified. Fig. 3 shows the resuits obtained for o(e+e - ~ hadrons) as a function of the total centre-of-mass energy. In the third method, use is made o f the track detection in the kinematic chambers, the solid angle of which is bigger than that o f the complete telescope and is ~ 2zr. Various models are used [6] just to give the neutral particle multiplicity distribution for each charged state so that phase-space momenta distributions may be used to estimate the efficiency for each * I -- lsospin; J = intrinsic angular m o m e n t u m ; P = parity; C = charge conjugation.
~
~--- h a d r o n s
Fig. 1. Feynman diagram describing reaction (1), in the onephoton approximation. 1 = isospin; J = intrinsic angular momentum; P = parity; C -- charge conjugation.
201
Volume 51B, number 2
PHYSICS LETTERS
22 July 1974
1 0 t l 600 MeV
L
\
300
0,6 08 a4 (12
r
750 MeV
BOO
MeV
B50 MeV
200
2
06 04 (?2
b
o,
925 MeV
950 MeV
970 MeV
1OO
08-
02
41o l
990 MeV
1050 MeV
2'.~
•
+
3'.o
_
Fig. 3: Total annihilation cross-section, o(e e --* hadrons), as a function of the total centre-of-mass energy 2E for the (~p) model. The curve is the best fit to the form o = A.s n.
1300MeV
1400 MeV
~ 1500 MeV
04 0.2 N2 N3 N N5
N~ N3 N. N~
N: N. N~. Ns
Fig. 2. Track multiplicity distributions at various colliding beam energies. Those expected on the basis of the (~p) model (histogram) are compared with the experimental data (points with errors). Each histogram contains four bins, from 2 to 5 observed tracks N2, N3, N4, Ns. The vertical scale shows the fraction of events in each class.
charged multiplicity. In this way, the observed charged particle multiplicity distributions may be used to obtain the cross-section for each charged state. This is the least model-dependent analysis, and we will call it the quasi-model-independent method. The results for o(e+e - -~ hadrons) obtained with this method are consistent with the (~p) model mentioned above, and are shown in fig. 4. Table 1 shows the data and results obtained at the various energies investigated: the beam energies; the number of electron pairs (used as a monitor reaction) observed in the same solid angle; the integrated luminosities; the observed numbers of hadronic events; the beam-gas background events estimated from runs with single beams, and finally the values of o(e+e - ~ hadrons) obtained 202
£o
2E (GeV)
1200 MeV
Oo; 08 |
~'.s
by the two methods. We note that the results of neither of these two methods show any evidence for a statistically significant structure, in agreement with the result of the first method. Moreover, the exponent of the
/
I001 i
1.O
Fig.
i
1.5
i
i
2.O 2 E (GeV) •
2.5 +
i
3.O
_
4. Total annihilation cross-section o(e e ~ hadrons), as a function of the total centre-of-mass energy 2E for the quasimodel-independent method described in the text• The solid curve is the best fit to the form A.s n. The bdst fit from fig. 2 is shown by the broken curve. The standard point-like crosssection o(e+e # *# - ) is shown as a reference.
Volume 51B, number 2
22 July 1974
PHYSICS LETTERS Table 1
E (GeV) 1.2 1.3 1.4 1.5 1.6 1.7 1.85 1.9 1.94 1.98 2.1 2.4 2.6 2.8 3.0 TotMs
Ne±e~
Integrated luminosity (nb -1 )
Number of hadronic events
691 765 843 2080 1470 1754 1178 2118 668 747 4650 741 1680 1296 1797
6.59 9.46 12.54 36.14 33.60 48.50 41.94 64.59 25.94 29.02 204.15 48.11 106.06 88.30 197.28
12 21 16 88 85 95 56 91 30 32 236 66 108 49 100
22478
952.22
1085
Beam-gas background
O(hl) (nb)
< < < < < < <
194 188 90 148 134 93.7 56.8
1 1 7 4 4 5 4
(nb) +ST $8 -,*2 +22 -47 16 _+ 17 -
+41
+ 14 - 15 +
_ 19`6 + 87.6 .6
< 8
58.5
_ +
< 3 < 3 17 ± 9 19 ± 10 36 ± 14 8±4 11 ± 8
46.8 45.0 43.0 31.7 20.3 12.0 12.3
+_136 +_ 7.9 ± 3.3 ± 8.1 ± 4.8 ± 3.8 ± 1.9
67~1
218 305 100 148 135 126 73 71 68 53 54.6 42 33 17.8 28.7
± 108 ± 88 ± 70 -+ 26 ± 25 ± 18 ± 15 ± 14 ± 21 ± 18 ± 3.3 ± 24 ± 14 ± 8.9 ± 6.7
oh =- o(e+e - ~ hadrons); (1) indicates the 2nd method, (2) indicates 3rd method of deriving oh. n b --- 10 -30 cm ~.
energy d e p e n d e n c e o f the total annihilation crosssection is, within one standard deviation, the same for the t w o m e t h o d s . The energy d e p e n d e n c e is o b t a i n e d by fitting all the data w i t h the expression o(e+e - ~ hadrons) =
A's n,
where A and n are free parameters. The results are: n 1 = - ( 1 . 6 3 -+ 0.08) using the ( p p ) m o d e l w i t h phasespace corrections; n 2 = - ( 1 . 4 4 + 0.15) using the quasi-model-independent m e t h o d . Combining the two results and taking as error limits the two e x t r e m e cases, we have for n: n =-
(1.54 + 0.17a _ 0.29 j •
In conclusion our data show that for the two extreme m e t h o d s used, the value o f n is non-zero, i.e. in our energy region o(e+e - ~ hadrons) c a n n o t be constant [9], as seems to be the case for energies between 3.0 and 5.0 GeV [10, 11]. In o t h e r words, in the energy range from 1.2 to 3.0 GeV, the total hadronic annihilation cross-section a(e+e - ~ hadrons) decreases w i t h energy at least as fast as the point-like cross-section. We w o u l d like to acknowledge the collaboration o f our technicians and scanning girls: Messrs. G. Baccherini, A. Borghi, L. Daniello, F. Ferioli, M. Ferrari, V. Lelli, F. Martelli, F. Massera, G. Molinari, R. Pilastrini, O. Polgrossi, V. Russo, G. Sola; Mrs. L. Maselli, Mrs. F. Nicoli and Miss L. Zitelli.
We have checked that w i t h i n -+2% the large-angle (e+e - ~ e+e - ) m o n i t o r has the correct energy dep e n d e n c e [8]. 203
Volume 51B, number 2
PHYSICS LETTERS
References [ 1] For details of the set-up, see V. Alles-Borelli, et al., Phys. Lett. 40B (1972) 433 and refs. [2, 12] quoted therein. [2] M. Bernardini, et al., Phys. Lett. 44B (1973) 393. [3] V. Alles-Borelli, et al., Prec. First EPS Conf. on Meson resonances and related electromagnetic phenomena, Bologna, 1971, eds. R.H. Dalitz and A. Zichichi (Editrice Compositori, Bologna, 1972); V. Alles-Borelli, et al., Prec. 8th Course in the Int. School o f Subnuclear Physics, Eriee, July 1970, in Elementary processes at high energy, ed. A. Zichichi (Academic Press, New York, 1971), p. 790. [4] V. Alles-Borelli, et al., Phys. Lett. 36B (1971) 149; M. Bemardini, et al., Phys. Lett. 45B (1973) 169. [5] For the same reason, we had no magnetic analysis available, as in our first proposal: M. Bernardini, et al., Experimental investigations proposed for ADONE, INFN. A/E-66-10, 7 November 1966.
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[6] The details will be reported in a forthcoming paper to be published in I1 Nuovo Cimento. [7] J. Hebert and H. Mes, Nuclear Phys. B4 (1968) 244. [8] M. Bernardini, et al., Phys. Lett. 45B (1973) 510. [9] For previous Frascati and Novosibirsk data see: B. Bartoli, et al., Phys. Rev. 6D (1972) 2374; C. Bacci, et al., Phys. Lett. 38B (1972) 551 ; 44B (1973) 533; M. Grilli, et al., Nuovo Cirnento 13A (1973) 593; F. Ceradini, et al., Phys. Lett. 47B (1973) 80; Data on o(e*e- ~ hadrons) have also been obtained at Novosibirsk by L.M. Kurdadze, et al., Phys. Lett. 42B (1972) 515. [10] A. Litke, et al., Phys. Rev. Lett. 30 (1973) 1189; G. Tarnopolsky, et al., Phys. Rev. Lett. 32 (1974) 432. [ 11 ] Data reported by B. Richter at the Conf. on Leptoninduced reactions, Irvine, December 1973.