Luminosity measurement with the MD-1 detector at VEPP-4

Nuclear Instruments and Methods m Physics Research A273 North-Holland, Amsterdam

(1988) 31-39

31

LUMINOSITY MEASUREMENT WITH THE MD-1 DETECTOR AT VEPP-4 A.E . BLINOV, A.E . BONDAR, A.D . BUKIN, S.G . KLIMENKO, G.M . KOLACHEV, A.P . ONUCHIN, A.G . SHAMOV, V.I . TELNOV, Yu .A . TIKHONOV arid V.N . ZHILICH Institute

Received

of Nuclear Physics, 8

April

Novosibirsk, USSR

1988

For the luminosity measurements with the MD-1 at VEPP-4, elastic Bhabha scattering at small angles and single bremsstrahlung were used . The relative errors of the luminosity measurements were 1.5% for a small angle monitor and about 3% for a single bremsstrahlung monitor. The absolute luminosity calibration was performed using the processes of double bremsstrahlung and large angle Bhabha scattering. The accuracy of the calibration was estimated to be 2.5% 1 . Introduction The processes e+ e - - e +e-, e + e - - j_t + [. - and e + e- --> yy at large angles usually serve for luminosity measurements at storage rings. For fast monitoring, tuning the storage rings and accelerator experiments, the processes with high counting rates are used : small angle Bhabha scattering, single and double bremsstrahlung. The use of these processes for absolute measurements needs special care due to possible systematic errors . The small angle elastic scattering was used for the first time at the e -e--machine VEP-1 in Novosibirsk [1]. Now this process is used at nearly all the e +e--rings . Its disadvantage is its strong counting rate dependence on the beam position . Single bremsstrahlung (SB) was the first process detected at the storage rings [2]. The cross section of the SB (- 1 b) is much larger than that of all other processes at e + e --storage rings. The SB photons are concentrated in a cone with angles of 1/y (y is a relativistic factor). It is difficult to use the SB for luminosity measurements at storage rings with long straight sections because of a high background due to the bremsstrahlung in the residual gas. Nevertheless, the SB was applied for monitoring at ADA, VEP-1, VEPP-2M, and VEPP-4 [1-4]. The detector MD-1 at VEPP-4 with a transverse magnetic field in the interaction region [4] provided a low background level (- 10 -4 ), since only the radiation from a small part of the orbit hits the SB detector . An interest2 ing phenomenon has been observed in the process of SB at MD-1 : the effect of the limitation of the impact parameters [5]. An experiment [5] has shown that the SB cross section is less than that obtained by the standard QED calculation . The cross section is decreased because the beam sizes in storage rings are much smaller than the characteristic impact parameters in the SB. 0168-9002/88/$03 .50 (D Elsevier Science Publishers B.V . (North-Holland Physics Publishing Division)

The process of double bremsstrahlung (DB) was observed for the first time at VEP-1 in Novosibirsk [6] and was used for luminosity measurements at VEP-1, VEPP-2, VEPP-2M, ACO, ADONE and VEPP-4 [3,5-7]. The characteristic features of the DB are the large cross section (independent of the beam energy), and the fact that two photons are concentrated in opposite directions to a cone of angle 5/y. During experimental runs in 1981-1985 with the MD-1 detector at VEPP-4 small angle Bhabha scattering, and single and double bremsstrahlung were used for luminosity measurements. In this article our experience with different monitors at MD-1 is summarized . 2. Main characteristics of the processes for the luminosity measurements In this section we present the convenient formulas for the cross section calculations and discuss the main characteristics of the processes. More details can be found in ref. [8]. 2 1. Small angle elastic e ' e - -.scattering The elastic cross section of the e+ e --scattering at B«1 is da,,,-

ro'

where ro is the classical electron radius . The effect of the polarization of the beam to e+e -scattering at 0 << 1 is negligible [9]. The radiative corrections to eq . (1) depend on the experimental conditions. The most convenient form of the differential

32

A E . Bhnoc et ai / Luminosity measurement

cross section for the Monte Carlo simulation is presented in ref. [10] . The results of ref. [11] can be used to estimate the radiative corrections 22 . Single bremsstrahlung,- Compton scattering of the synchrotron radiation by a colliding beam

The standard QED calculation [12,13] gives the following equation for the SB section: da °

dw

=4ar,21

n1

)(V-3)1In I \\ qmm

-11,

16-3 10_^ 10 - `'

where V=

Eww

r1T~~

E-w E

E

+E-W,

m

w

9mm=4y2(E-w),

a is the fine structure constant, w is the photon energy, E is the beam energy and m is the electron mass . The radiative corrections to eq . (2) constitute less than 1 % at w/E >_ 10 -4 [141 . The angular distribution of the photons has a weak dependence on the photon energy [8] and the emission is concentrated in a cone of angle - 1/y [8]. The SB cross section is much higher than that of other processes. The value of the cross section integrated over the photon energy (the threshold w = 1 MeV) is 5 X 10 -25 cm2 at E = 5 GeV. The process of the SB has the characteristic property that the formation of the main part of the bremsstrahlung takes place at large distances [5,15,16]. Then external effects can significantly reduce the emission probability. The standard QED eq. (2) is not valid in this case. There are three macroscopic effects which impose restrictions on the applicability of eq . (2) in the experiments : the length of the straight section of the storage ring [16], the transverse beam size [5] and the transverse magnetic field in the intersection point [15-18]. Among these effects the most essential is that associated with the finite transverse sizes of the beams. It is dominant for all operating storage rings. This effect was observed with MD-1 at VEPP-4 in 1980 [5] . Eq . (2) can be used if the transverse beam size d 1 is larger than the characteristic impact parameters p [5]: dl

50-

4y 2 (E- w) w

m

For example, at E = 5 GeV and w = 10 MeV, p - 10 cm, whereas the vertical rms beam size at VEPP-4 equals 2 X 10 -3 cm . The equation which takes into account the beam transverse sizes is given in refs. [17-20]. The most convenient expression for the SB

10i.i

Fig 1 A spectrum of SB photons : (1) standard QED calculation (eq. (2)), (2) calculation, taking into account the beam transverse sizes, refs [5,18,191 at E = 5.0 GeV, d, = 2 X 10 - ' cm and ,1,, = 4 5 X 10 -z cm. cross section (for the Gaussian distribution of the beam density) has the form [19] : d ay E -w =4arti214W ( w )(V- ) dw Xlln~

J, ~` á +4 j xc(dr

11

+1n2+ c + V 2 V- T

where c = 0.577 is the Eiler constant : A, 4 y are the vertical and radial rms beam sizes, respectively ; h e is the Compton wavelength of the electron . The equation holds when ilmm

Dy

"

L

«1 .

When

3, 13 z 4mm di ~+4, `1 we have used the results from ref. [18] for numerical calculations . Fig. 1 shows the calculations of the SB spectrum, according to eqs. (2) and (4) * . At the VLEPP energy [21] the correct cross section is two times less than that from the standard QED calculation . This effect also takes place at e - p colliders. At HERA [22], where the SB will be used as the main monitoring process, the cross section is about 15% less [23] . * For w/E >I 0 - 1 we have used ref. [18] .

A . E. Blinou et al / Lummositi, measurement

If the interaction region is situated in the transverse magnetic field, the background due to the Compton scattering of the synchrotron radiation (SR) by a colliding beam arises [5,19,24-26] . The beam magnetic field should also be taken into account. In ref. [19] it was noted that in the bremsstrahlung process to a magnetic field there is no sharp boundary between real intermediate photons and virtual ones . An exact theoretical calculation is very complicated and has not yet been done . We have made the calculation considering all photons as real [5,24-26]. The calculations with this assumption overestimate the background (the error depends on the photon energy [5]) . 2 .3 . Double bremsstrahlung

With DB the case in which the photons move in the direction of their present electrons is of most practical interest . The DB cross section integrated over photon emission angles has the form [8]: 2 dw da°Y= 8a'ro dw t ? R(wi)R(w2)~ 02

where

E2 , 2

R (w)

E,)+

7h(1

5 'Il = 4+8 3,

i13

-

SS3 =

i13 - co

1 .052 .

The accuracy of this equation is about 0.5% and it is valid at all photon energies, except for the narrow region E - qi.2 - m . To calculate the DB angular distribution one can use the results from ref. [27] . The DB photons are concentrated in a cone of angle - 5/y. The radiative correction to the DB cross section has been obtained in ref. [28] :

33

Na7(7e)

Fig. 2. Layout of the detector MD-1 (a : upper view, b - section by vertical plane) (1) central part ; (2) additional bending magnets; (3) system for detection of scattered electrons, (4) counters for luminosity monitoring by small angle elastic scattering ; (5) lenses ; (6, 8) counters for polarization measurement by SR, (7) counters for luminosity monitoring by e +e -> e+e -- y, (9) doubled ionization chambers ; (10) lead plate of 13 mm thickness; (11) lead plate of 5 mm thickness. detect the SB and DB photons and to study the two photon processes [29,301. 3.1 . Small angle Bhabha scattering monitor

To detect the e +e--events we used scintillation counters. Fig. 3 shows the geometrical scheme of these counters. The electrons and positrons were detected in the angular region of 10-20 mrad . The "small" counters P11, P12, P21, P31, P32, P41 and P42 fixed the angles of the scattered e- and e + . The threshold of the "small" counters was 0.4 MeV. The large counters SI, S2, S3 and S4 with a 4 MeV threshold served to suppress the soft background .

da 2Y =da°,,(1 -8), where 8=0.011 In

(

E +ln E ) . wi w2

The DB is formed at a distance of the order of the electron Compton wavelength, Jt c = 3.8 x 10 - " cm . Thus, the macroscopic factors should have no influence on the DB process. 3. Experimental setup The layout of the interaction region with the MD-1 is shown in fig. 2. The magnetic field of the MD-1 is perpendicular to the orbit plane. Such a geometric scheme of the interaction region is very convenient to

Pli PI 1

w Fig 3 . Schematic view of the SA monitor .

34

A E Blinoc et al. / Luminosuy meaurement

The 5X o W convertor was placed in front of these counters . The energy losses the in large counters equal 50 MeV at E = 5.0 GeV. FEU-84 photomultiphers were used in all counters. The PMT gain stability control was carried out with the help of e + e--events and light diodes . The accuracy of the control was 10% . To measure the luminosity the following types of coincidences were used : S1 X P11 x S3, S1 x P12 x S3, S2 x P21 x S4, S2 x P21 X S4, S3 x P31 x Sl, S3 x P32 XS1,S4XP41XS2andS4XP42XS2 .Thesumofthe coincidences depends weakly on the beam displacement [31]. For our geometry of the counters the dependences of the counting rate on the beam displacements are the following. 1) The vertical displacement by Sz S n=»(0)11+15 8z ) 2~, (d 1

where d is the distance from the beam axis to the edge of the "small" counters . 2) The rotation by SB in the vertical plane ISB 2 ii =n(0)~1 +15( d ) ~,

where 1 is the distance from the interaction point to the counters . 3) The radial displacement by Sy

where 2yo is the size of the "small" counters in the radial direction. 4) The rotation by 80 in the radial plane ri=n(0){1-5

15~

1 2 yo 12

The background from the accidental coincidences was measured simultaneously with the effect . For this purpose, the coincidence counting rate was measured with a delay of the positron counter pulses by the revolution time of the particles in the storage ring . The refection of the correlated background was carried out using the time-of-flight . A check of the photomultipliers and electronics was performed with the help of light diodes . The visible cross section of the e + e- scattering can be obtained from eq . (1) : aSA -2

2

rY1 l

l

1 - _1

zi

z2

_1 + 1 arctan Yo zi / Yo z~

zi 1 z2 1 arctan Yo + - -arctan - - arctan z, Yo Yo zi Yó ( (see notations in fig. 3) .

The radiative corrections and the "albedo" are ignored in eq . (7). The radiative correction was estimated to be about 5% . The increase of the visible cross section caused by the "albedo" effect is roughly 40%. ("Albedo" is due to interaction of electrons with the vacuum pipe and chambers of the tagging system for 2y physics [30] .) To obtain the visible cross section with good precision one can use the Monte Carlo simulation using the differential cross section . However, such a calculation takes too much computer time and it will not provide good accuracy due to the very complex geometry near the SA monitor counters . A more practical way in our case was to maintain a high relative accuracy of the SA monitor and to perform the absolute calibration by the DB and large angle Bhabha scattering (see section 5) . The factors which determine the relative accuracy of the SA monitor are: the beam displacement and the instability of the photomultipliers . The beam position was stabilized by synchrotron radiation with the help of the ionization chambers [25] . The instability in the vertical angle did not exceed 2 X 10 -6 and was 10 win in the vertical direction . In this case the counting rate deviation was negligible . Sometimes it was necessary to change the angle of orbit (- 10 -° in the vertical angle) for machine tuning and for the background reduction, which resulted in about 0.5% change of the counting rate . The check of the SA monitor was carried out by comparison of different types of coincidence and by comparison with the SB monitor. 3.2 . SB monitor The photons were detected by four scintillation counters : two counters on each side (see fig. 2) . The size of each counter was 0.5 x 5 x 10 .0 cm3. The coincidence of two counters from each side was used to measure the luminosity . The effective threshold (50 MeV) in the photon energy was determined by a 5 mm Pb plate between the counters . The Pb plate (13 mm) in front of the counters served as photon convertor as well as for the protection of the counters against the synchrotron radiation. The counter thresholds were set at the 3-4 photoelectron level . In this case, the counting rate depends weakly on the instability of the photomultiplier gain . The SB visible cross section was calculated by using eq . (4). At E=4.7 GeV, d Y = 5 X 10 -2 cm and 4 z = 2 x 10 -3 cm ; a, = 1 .20 X 10 --25 cm 2 . The contribution from the Compton scattering of synchrotron radiation by the colliding beam was estimated to be a., = 0.25 X 10 -25 cm2 . The total visible cross section in the SB monitor was asß = aY + a, = (1 .45 + 0.20)

X

10 -25 cm2.

35

A . E . Blmou et al. / Luminosity measurement

The systematic error was determined by two factors: 1) dependence of a s , on the beam size (the accuracy of the beam size measurement was 15%) ; 2) the uncertainty in the theoretical calculation of ac . At large luminosity the SB counting rate is close to the beam revolution frequency. In this case, the probability to have two and more photons in one collision is high . From the Poisson distribution we can derive the following expression for a real counting rate :

where f is the revolution frequency, it . is the measured counting rate, n is the real number of detected photons per second . At L = 4 X 10 cm -2 s -1 and f = 818 kHz: n m /ri = 0.6 . The SB monitor was checked by comparison of the counting rates in the electron and positron directions . But this check does not take into account the following factors : 1) the dependence of the SB cross section on the beam size ; 2) the nonoptimal convergence of the electron and positron beams in the interaction point. These effects determine the relative accuracy of the SB monitor (see sect . 4.2). 3 .3 . DB monitor

The process of the DB has been used for luminosity measurements in the experiments at MD-1 [5,32,33]. The photons were detected by Nal(TI) crystals of 47 x 12 X 12 cm3. The energy scale calibration was performed with the isotopes 137 Cs and 65 Zn, by cosmic rays and by the edge of the SB spectrum. The absolute accuracy of the luminosity measurement was about 3% . The accuracy was mainly determined by the error in the energy calibration of crystals . The DB is very attractive as absolute monitoring process owing to the reliable theoretical calculations, 100% detection efficiency and simplicity of the experimental setup. We have used the DB in the MD-1 to perform the absolute calibration of the SB and SA monitors . (The apparatus and calibration experiment will be described in sect . 5.1) 4. Experimental results The MD-1 detector was installed at VEPP-4 in 1981 . A total integrated luminosity of about 30 pb -1 was collected (about 28 pb -1 in the years 1984-1985) . In the present article the 1984-1985 experimental results concerning the behaviour of luminosity monitors are reported . The VEPP-4 luminosity during this time was (1-4) X 10 3° cm -2 s -1 .

4.1 . Background condition

In our experiment the main background for e + e-scattering was produced by the accidental coincidences due to the SB . The mechanism of this background is as follows: due to the SB, electrons and positrons hit a vacuum pipe wall or the frames of the tagging system chambers causing an electromagnetic shower . The particles from this shower are detected by the SA monitor counters . The experimental dependence of the ratio K` .e (=effect/background) on the luminosity is K~'e_ -- 1/L which is in agreement with this mechanism of the background . The main background for SB is the residual gas bremsstrahlung . The ratio K, = (effect/ background) has the form : K =

L

asa

fNASn( az )'

where Ne is the number of electrons in the bunch, 4 S is the length of the orbit part which radiates the SB detector, n is the density of the residual gas, a, is the cross section of the bremsstrahlung on the residual gas. The vacuum at the MD-1 interaction point was about 2 x 10 -3 Torr so that at E = 4.7 GeV and I + X I - = 5 x 5 (mA) the background level was negligibly low (K Y = 0.5 X 10 4 ). The background for DB is mainly determined by the accidental coincidences of the SB photons . The expression for the ratio K2 ., (=effect/background) is the following : °2Y K2Y = (,SB

f

aSL

.

The experimental dependence of K2 .y on the luminosity is in good agreement with eq . (8). At E = 4.7 GeV, L=10 28 cm -2 s -1 and at Wi,2=0JE (W 1 , 2 are the photon thresholds), K2 Y = 0.5 . 4.2 . The relative accuracy of the luminosity measurements

As the main monitoring process in MD-1 we used the e+ e- small angle scattering . The stability measurement of the SA monitor was performed by measuring the ratio 013/024, where 013 is the sum of the coincidences Sl X PI 1 X S3, Sl x P12 x S3, S3 x P31 x Sl, S3 x P32 X Sl and 024 is the sum of S2 X P21 x S4, S2 X P22 x S4, S4 X P41 X S2, S4 x P42 x S2 . 013 and 024 are independent luminosity measurements . The sum of 013 and 024 weakly depends on the beam position . The ratio of 013/024 strongly depends on the vertical beam position . Fig. 4 shows the ratio 013/024 for all runs in 1984-1985. The two peaks in this distribution correspond to beam positions with two different vertical angles . The difference is equal to AB = 10 -4 . The devia-

36

A . E Bhnov et al / Lummosity measurement 1000

1000

z

z

rr

0 o

0 0

500 -

7-500

096 i04 160 0 092 100 108 112

092 '

4 6N

'96 '

168

i i2

LSA/LsB

0f ")/ 024

Fig. 4. The ratio 013/024 (see fig. 3) : 013 is the sum of the coincidence Sl x Pll x S3, Sl x P12 x S3, S3 x P31 x Sl, S3 X P32 x S1 and 024 is the sum of the coincidences S2 x P21 x S4, S2 x P22 x S4, S4 x P41 x S2, S4 x P42 x S2

Fig. 6. The ratio LSA/L8ß : LSA is the luminosity measured by the SA monitor, L sB is the luminosity measured by the SB monitor

tion of the counting rate m this case is On/n = 0.5% . The rms of each peak in fig. 4 is 0.7% and it is mainly

comparison of the counting rates in the electron and positron directions . The experimental distribution of the

determined by the statistics of the e+ e --events. The gain instability of photomultipliers can also

contribute to the relative accuracy of the SA monitor. The accuracy of the gain measurements was about 10% .

In this case, as the experimental study shows, the contribution to the relative error of the SA monitor due to the

gain instability is equal to about 1% . During the 1984-1985 energy scanning, the energy varied in the region 2 E = 3.60-5.15 GeV. The relative

error of the SA monitor due to the energy change was estimated to be 1% . The total relative error of the SA monitor was equal to 1 .5%.

is

shown to fig. 5 . The rms of this

distribution is 0.8%. The contribution of the statistics of -z the SB events is negligibly low ( <_ 10 %) . The rms of

0.8% is mainly connected with the apparatus instability as well as with the collision effects. The independent check of the SB and SA monitors consists of the com-

parison of these monitors with each other. In fig. 6 the

ratio LSA/Lsc is shown. The rms of this distribution is 3% and is mainly determined by the SB monitor . The SB cross section depends on the beam size. During the experiment the vertical beam size varied from 10 to 40 pin. The correction to the luminosity is equal to 12% in

interaction point also leads to the error in luminosity . This effect was estimated to be 2-3% . The correction

connected with the discounts was as large as 50%. The

tn z

0 0 z

ratio Lsß/LSB

this case. The error of the luminosity due to this correction is estimated to be 2% . The nonoptimal e + e- beams convergence in the

-5000 1

cl,

The check of the SB monitor was carried out by

uncertainty of this correction

results in an error of

about 1 % in the luminosity . Thus the estimated total

2000

relative error of the SB monitor is about 3-4%, i .e . is in good agreement with the direct experimental measurement (3%) . 1000-

5. Absolute calibration of the monitors The processes of e+ e -scattering at large angles and DB have been used to perform the absolute calibration 092

096

100

L'si;

1014

IL -st

408

112

Fig. 5. The ratio L5ß /LSB : LSB is the luminosity measured by the SB monitor in the positron direction, LSB is the luminosity measured by the SB monitor m the electron direction .

of our monitors .

5.1 . The calibration by DB The photons in electron and positron directions were

detected by

Nal(TI) crystals

with sizes 12 x 12 x 47

37

A .E. Bhnoo et al / Luminosity measurement

cm3 . The trigger required the coincidences of the photons with energy CO 1,2 > 0.08E . The accidental coincidence background was continuously measured by the delayed coincidence method . For the energy scale calibration of Nal(T1) crystals the edge of the SB spectrum has been used . The energy resolution of the Nal(TI) crystals was equal to 1.5% at E = 4.7 GeV. To decrease the dependence of the photomultiplier gains on the counting rate the following stabilization system was created. With the help of lightdiodes the current through the photomultipliers was set a factor of ten greater than that at a maximum operating counting rate [5]. These lightdiodes were operating in a mode of synchronization with the beam phase in the storage ring . The stability check was carried out with the help of lightdiodes and at the edge of the SB spectrum . The instability did not exceed 1% . The VEPP-4 luminosity was set at 10 28 cm -2 s - I to have an effect/ background ratio of about 0.5 . Before data taking we checked that the ratio Ls,{/LSB did not depend on the luminosity, with an accuracy of 1% . The integrated luminosity of 0.6 rib -1 was collected. For luminosity measurements the photons within the interval wt .2 = (0 .18-0.82) E m the DB spectrum were selected . The calculated DB cross section at these thresholds is : a 2 y = (5 .25 ± 0.09) X 10 -29 cm 2 . The systematic error in a2Y is determined by the following factors: 1) the uncertainty in the photon thresholds : 1 .5% ; 2) the instability of the apparatus: 0.5%; 0.5%. 3) other possible effects: The main characteristics and results of the experiment are presented in table 1. So the visible cross section of the e + e--scattering (measured by DB) in the SA monitor at E = 4.7 GeV is a °B = (3 .60 ± 0.08) X 10 -29 cm2 . The statistical and systematic errors of the calibration were added by squaring. 5.2 The calibration by e + e - -scattering at large angles

This method has the obvious advantage since it is based on the same parts of the MD-1 detector which were used for the investigated processes.

2E - 946G .V

fLdt=3 .577pr /Vre 2666-52t f3

W

z

w

w

50

40

60

FAQ., CHANNELS

Fig. 7. The energy spectrum for e + e --events: EA, is the sum of amplitudes from shower-range chambers . The trigger required firing of at least one scintillation counter and five Z-layers of shower-range chambers . To reduce the beam background, the ± 10 cm strip in the shower-range chambers near the orbit plane was switched off from the trigger. The cosmic radiation background was suppressed by synchronizating with the phase of particle revolution to the storage ring . For selection of the e + e--events information from the coordinate and shower-range chambers was used . At the first stage the events were selected off-line, according to the following criteria : (1) exactly two tracks in coordinate chambers with momentum P, > 500 MeV/c; (2) polar angle 0, > 30 ° ; (3) a collinearity angle AS2 < 15 ° . The second stage was to eliminate the event near the edges of the shower-range chambers and to have the tracks with 5 layers in coordinate chambers . The solid angle in this case was 0.085 X 4Tr near 0 = iT/2 . The final cuts used the total colorimetric energy from the shower-range chambers. The experimental energy spectrum for e+e--events is shown in fig. 7. To get the calculated visible cross section the Monte Carlo simula-

Table 1 Mam characteristics and results of the experiment Process e + e- - e'e- yy e'e- - e'e-

Number of events Effect

32035 22201

Cross section X 10 29 cm2 Background 59666 15

Calculated

5.25 ± 0.090 3.10±0.60

Experimental

3.6±0 .05 (stat)±0 .06 (syst)

38

A E.

Blinoo et al. / Lummostty measurement

Table 2 Experimental results E [GeV] 473 4.73 3.6-4.0 50-5 .2

N(e -e - ) at small angles

7.14 X 10 7 6.30 X 10 7 7.08 X 10 7 3 81 X 10 7

N(e+e- ) at large angles

aSÁ = (4

1478 1303 1514 825

tion of the Bhabha scattering with radiative correction was used . It includes the QED effects up to O(a 3) as well as the electro-weak effects [34] . Then the Monte Carlo simulation of full histories of particles in the detector has been performed. The total systematic error of the simulation is about 1% . The detection cross section obtained by a Monte Carlo simulation at E _ 4.73 GeV is - ` cm'. aMr = (0 .774 ± 0 .018(stat) ± 0 .008(syst)) X 10 The background was estimated by simulation of the possible background processes. The results are: (1) two photon processes 0.1%, (2) reaction e + e - -> -r + T 0.5+0 .5%, (3) reaction e+ e- - hadrons : the nonresonant region 0.1%, 0.5 +0 .3%, the -y-region e+e(4) decay y 3.5 +0 .5% . Using the Bhabha cross section at large angles from the Monte Carlo simulation and the measured number of events at small and large angles we have obtained the detection cross section (USA) m the SA monitor. The experimental results are presented to table 2 . Four energy regions have been taken : 3.6-4 .0 GeV, two regions near 4.73 (at different times) and 5.0-5 .2 GeV. The cross sections are normalized to the 4.73 GeV energy . The systematic errors consist of two parts . The first one is connected with the instability of the apparatus, mainly with the space resolution of the coordinate chambers . (The track reconstruction efficiency depends on the space resolution .) Another part is due to the difference between the real dependence of the space resolution on the track angle and a simulated one. The results for 4 regions are in agreement: P(X 2 ) - 25%. The sum of the 4 regions is -29 cmZ . aSÁ = (3 .64 ± 0 .12) X 10 The systematic and statistical errors of the experiment and Monte Carlo simulation were added by quadrature. 6. Summary We performed the calibration of the SA monitor by two independent methods and both results are to agree-

73/E)2

X 1029 CM2

3 74+0 .10 (stat)±0 .06 (syst) 3.75±0.10 (stat)±0 .06 (syst) 3.46±0.10 (stat)±0 06 (syst) 3.57±0 12 (stat)±006 (syst)

ment : CiSAB = (3 .60 ± 0 .08)

X

10-29 CM2

X

10 -29 cm2 .

and aSÁ = (3 .64

± 0.12)

The weighted mean result is -29 cm 2 . QSA = (3 .6l ± 0.07) X 10 To estimate the total absolute error of the SA monitor one must take into account the 1.5% relative error in luminosity measurements by an SA monitor. The final result for the visible cross section in the SA monitor isaSA -

(3 61 ± 0.09)

X

10 -29 cm Z .

Thus, the absolute error of the SA monitor at MD-1 is equal to 2.5% and is comparable to that of the accurate method using the processes at large angles (for example. at the detectors MAC, ND-1, CELLO, JADE, ARGUS, C LEO) . 7. Conclusion The single and double bremsstrahlung as well as elastic small angle scattering were used in MD-1 at VEPP-4 for luminosity measurements during 1981-1985. A large experimental program has been performed at MD-1 during this period . A high counting rate of the single bremsstrahlung monitor allowed fast tuning of the VEPP-4 machine. We had the possibility to investigate the processes with a large cross section (e + e - - e + e- y [5], e + e - -> e + e- e+ e - [32]) and ye -> y'e' [36] using the single (double) bremsstrahlung and small angle monitors with the high counting rate . The described methods are reliable and simple in operation. Acknowledgements In conclusion we would like to thank the members of MD-1 and VEPP-4 groups for their contribution to the experiment . Special thanks go to S.E . Baru, O.E .

A.E Blmoo et al / Lummosity measurement Lasarenko, V.M . Aulchenko, A.E . Volkov and V .A . Kutovenko for the design and maintaining of the electronics .

References

[4]

[5] [6] [71 [81 [91 [101 [11] [12] [131 [141 [151

P.I . Golubmchy et al ., Yad Fiz. 7 (1968) 1240 . C. Bernaridim et al ., Nuovo Cimento 34 (1964) 1473. G.M . Tuinaikin; Proc 10th Int. Conf. on High Energy Accelerators, Protvmo (1977) . S.E . Baru et al., preprint INP 83-39, Novosibirsk (1983) ; G. Gldal et al ., Major Detectors in Elementary Particle Physics, LBL-91, Suppl. UC-34D (1985) . A.E Blmov et al ., Phys. Lett. 113B (1982) 423. P.I . Golubmchy et al ., At. Erierg 22 (1966) 168 I. Augustin et al ., preprint LAL-1249 (1971) . V.N . Baier et al ., Phys . Rep. 78 (1981) 295. E.A . Kuraev et al ., Yad. Fiz. 32 (1980) 1059 . A.d. Bukin and E.A . Kuraev, preprint INP 84-109, Novosibirsk (1984) . S.M Sukhanov et al ., Dok. Akad. Nauk SSSR 178 (1968) 822. G. Altareli and F. Buchella, Nuevo Cimento 34 (1964) 1337. V.N . Baier et al ., Zh. Eksp . Teor Fiz. 51 (1966) 1135 E.A . Kuraev et al, Zh. Eksp . Teor . Flz. 65 (1973) 2155 . V.N . Baier and V M. Katkov, Dok. Akad . Nauk SSSR 207 (l972) 68

39

[16] V.M. Katkov and V.M . Strakhovenko, Dok. Akad. Nauk SSSR 231 (1976) 582. [17] V N . Baier et al ., Dok. Akad . Nauk SSSR 260 (1981) 861. [18] V.N . Baler et al ., Yad. Fiz. 36 (1982) 163. [19] A.I Burov and Ya .S . Derbenev, preprint INP 81-64, Novosibirsk (1981) . [20] G.L, Kotkin et al ., Yad. Fiz 42 (1985) 692. [211 V.E. Balaken and A.N . Skrmsky, VLEPP project (Status report), preprint INP 81-129, Novosibirsk (1982) . [22] Preprint DESY HERA 81/10 (1981) . [23] G L Kotkm et al ., Yad. Fiz. 42 (1985) 925 . [24] A.P . Onuchnm and Yu A. Tikhonov, preprint INP 77-77, Novosibirsk (1977) . [251 V.E. Blmov et al ., Nucl. Instr. and Meth . A241 (1985) 80. [26] V A. Tayursky, Candidate thesis, Novosibirsk (1986) . [271 V.N . Baler et al ., Zh . Eksp. Teor, Fiz. 50 (1966) 1611 . [28] V N . Baler and V V. Geidt, Yad. Fiz. 13 (1971) 350. [291 S.E . Baru et a] ., Proc 3rd Int. Conf . on Instr. for Colliding Beam Phys ., Novosibirsk (1984) [30] V.M Aulchenko et al, Nucl . Instr and Meth A252 (1986) 267. [31] S.I . Serednyakov and K. Fuke, preprint INP 18-71, Novosibirsk (1971) . f32] V.E. Blinov et al ., Yad. Fiz. 44 (1986) 626 [33] V.M. Aulchenko et al ., preprint INP 133-82, Novosibirsk (1982). f34] A.D . Bukin, preprint INP 85-124, Novosibirsk (1985) . [35] A.E. Blinov et al ., Yad. Fiz. 45 (1987) 1008 .