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PROTON-ANTIPROTON ELASTIC SCATTERING AND TOTAL CROSS SECTION AT THE CERN
COLLIDERUA4
Collaboration-Amsterdam1-CERN2-Genova3- Napoli4-Pisa5
M. Haguenauer
To cite this version:
M. Haguenauer. PROTON-ANTIPROTON ELASTIC SCATTERING AND TOTAL CROSS SEC- TION AT THE CERN COLLIDERUA4 Collaboration-Amsterdam1-CERN2-Genova3- Napoli4-Pisa5.
Journal de Physique Colloques, 1982, 43 (C3), pp.C3-579-C3-592. �10.1051/jphyscol:1982377�. �jpa-
00221932�
JOURNAL DE PHYSIQUE
Colloque C3, supplément au n° 12, Tome 43, décembre 1982 page C3-579
PROTON-ANTIPROTON ELASTIC SCATTERING AND TOTAL CROSS SECTION AT THE CERN COLLIDER
1 o "\ A R *
UA4 Collaboration-Amsterdam -CERN -Genova -Napoli -Pisa Presented by M. Haguenauer
Division EP, CERN, CH-1211, Geneva 23, Switzerland RESUME
Nous avons mesuré la diffusion élastique proton-antiproton à l'énergie de 540 GeV dans le centre de masse pour des transferts t compris entre -0.19 et -0.05 GeV2. La distribution en t peut être ajustée par une loi exponentielle e ave b = 17.2 ± 1 GeV"2. La mesure simultanée du taux d'interactions inélastiques permet de déterminer par l'intermédiaire du théorème optique la valeur de la section eff icace totale qui est de 66 + 7 rnb*
ABSTRACT
Proton-antiproton elastic scattering at a centre—of-mass energy of 540 GeV was measured in the four-momentum transfer range 0.05 < -t < 0.19 GeV2. The t-distribution can be fitted by the exponential exp(bt) with b = 17.2 ± 1.0 GeV"2. Combination with the simultaneously measured rate of inelastic interactions gives a value of the total cross section of 66 mb ± 7 mb.
Measurements of elastic scattering at low momentum transfer and of the total cross section were performed during the first physics run of the CERN proton- antiproton Collider at /s = 540 GeV. Data were taken during about 15 h of running time with an antiproton bunch of ^ 4 x 10' particles colliding against a proton bunch of -v 5 x 101 • particles. The machine optics in the intersection region was the same as for normal SPS operation. The nominal luminosity was of the order of 102 6 cm"2 s"'.
1. ELASTIC SCATTERING
At the Collider energy the typical value of the scattering angle in the region of the forward diffraction peak is of the order of one milliradian. The detection of elastic events at such small angles requires the use of a technique [1] similar to that employed at the ISR.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982377
JOURNAL DE PHYSIQUE
A side view of the experimental layout is shown schematically in fig. 1.
Elastically scattered particles are detected by a system of four telescopes placed symmetrically above and below the SF'S vacuum chamber at a distance of about 40 m from the pp crossing point. A telescope is composed of two detectors that are 6 m apart. Each detector, consisting of a wire chamber and a scintillation counter hodoscope, is placed in a movable section of the vacuum chamber ("pot") which is connected to the main body of the accelerator pipe by a bellow. Once stable beam conditions are reached, the "pots" are displaced vertically towards the beam.
Particles leaving the ciossing region after interaction traverse the quadrupoles of the machine lattice QL and QR, which in the vertical plane act as a
defocussing and focussing lens respectively. The p and
p
trajectories for 1 mrad scattering angle in the vertical plane are also shown in fig. 1.The wire chamber [21 in each "pot" contains four independent drift planes measuring the vertical ooordinate of particle trajectories. The single-plane resolution, expressed as the r.m.s. deviation of the measured coordinate in the drift plane from the reconstructed track, was about 0.13 mm during actual data taking. The drift planes are followed by a proportional plane with high- resistivity anode wires. Charge division readout of these wires provides the horizontal coordinate of particle trajectories with an r.m.s. accuracy of 0.4 mm.
The mechanical frame of the chambers is U-shaped, the side facing the beam being closed by a glass-epoxy plate of 0.8 mm thickness. A pattern of field-restoring strips on this plate ensured good detection efficiency down to a few tenths of a millimeter from the plate [ 2 ] . For each chamber, the distance to the nominal machine plane is known from the measured displacement of the "pot" and from the overall survey of the experiment with an accuracy of about 0.1 mm. Inside each the wire chamber is followed by a stack of eight vertical scintillators which is in turn backed by a trigger counter, 45 mm wide and 115 mrn high, as shown
in fig. 1. The calibration of the charge division electronics was monitored using the vertical scintillators. The "pots" are provided with 0.1 mm thick steel windows slightly larger than the active area of the detectors. Because of the asymmetric beam optics (fig. I), the minimum detectable scattering angle was determined by the distance from the beam axis of the detectors on the proton side. On this side the active volume of the detectors started at about 18 mm from the beam axis, corresponding to a minimum value of the scattering angle of about 0.8 mrad. The maximum accepted angle as determined by the aperture of the vacuum chamber is about 1.6 mrad. The trigger consisted of the logical OR of the two four-fold coincidences of the trigger counters in the two arms (up-left x down-right) + (down-left x up-right).
ELASTIC SCATTERING LAYOUT Quadrupoles Vacuum chamber Crossing point I I \A I -P i I 16m
i-
37 m I I 2-
Pb Sketch of the elastic scattering set up. A detail of the detector inside the "pot" is shown together with a perspective view.
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For track reconstruction within each telescope it was demanded that at least six out of the eight drift planes contribute a track point. An event has been considered an elastic candidate if the track multiplicity per telescope was one or two, thus allowing for the possibility of an accompanying track due to a 6-ray.
The probability of such an event was, however, less than 1%. It was further checked that the candidate tracks in each of the two telescopes extrapolated backwards to the pp crossing region and that no tracks were simultaneously seen by
-
the other pair of teldscopes.
The measured vertical and horizontal displacements d and d of particle
v
Htrajectories are proportional to the components 8 and OH of the scattering angle,
v
if the primary beam particles travel along the nominal machine axis and interact at the centre of the crossing region. One can write d
-
V(H)
-
'v(H) 'v(H)'
whereL and L are the effective distances from the crossing point of the detector under
v
Hconsideration. L and L are accurately known from the machine optics. The scatter
v
!!plot of 8 (p) versus
e
(p) in fig. 2(a) clearly shows the ridge of elasticv v
events, well identified by the collinearity requirement. The distribution of the quantity 8
v (p)-e v
(p) has a standard deviation of about 0.05 mrad corresponding to a transverse momentum unbalance less than 15 MeV/c. The intrinsic vertical angular spread of both beams contributes c 0.03 mrad. A transverse displacement of the crossing region away from the machine axis can be derived from the observed coordinates of the scattered proton and antiproton. While the vertical offset turned out to be negligibly small, the horizontal shift of the interaction region was found to be about 4.5 nrm. The horizontal componentseH
for 5 and p were corrected for this beam displacement. The asymmetry in the horizontal acceptance, as seen in the scatter plot of fig. 2(b), is a consequence of this offset. The distribution of 8 (p)-8 (p) has a standard deviation of about 0.06 mrad to whichH H
the angular spread of the beams contributes e 0.035 mrad.
Elastic events were selected by applying a three-standard-deviation cut to both collinearity distributions. The t-dependence of the data was described by the exponential form exp(bt). Since the incoming beams were known to form an angle with the machine axis, the value of the slope parameter b was determined from a fit of the two-dimensional (8 8 ) distribution, simultaneously for both
v' H
arms, in which the beam angle was left as a free parameter.
The result of the fit is b = 17.2 f 1.0 GeV-'. The systematic uncertainty on the slope parameter b due to local chamber inefficiencies, alignment errors and acceptance calculations was estimated to be
2
0.5 GeV-'. The vertical and horizontal components of the beam angle as determined from the fit were0.11 f 0.01 mrad and 0.15 f 0.05 mrad, respectively, consistent with those derived from direct measurements by beam position monitors. The acceptance-corrected
M. Haguenauer
Scatter plot and collinearity histograms for the elastic candidates in the vertical plane (a) and in the horizontal plane (b).
The smooth line in the collinearity plots is a gaussian fit to the data.
. . :;.& ' -
. . . . . .
8p'
. ., ... , *,= .,.. . . _ 8 , .
. . .:. . . . .!.": . . . . . . . .:.? ..,;.. A::
'-:.:
. :.. . . '..* ' . . . . . . .
* .'.%. I ,. .
... ...,. a. . ; . . .
' . ,
:.y:..::
. .. . .
. .
-
I , , , , , .
2
-
aI
T O -
8
-2 -1
'0 I
(
mrad? -0.4 0 0 4
! mrad
)e V ( P ) OH (PI
400
300
P
5200
2;
100
0 -0.4 0 0.4
[mrad
)(mrad
)Qv(P)-
e v(p) S"(P)
-8,(p)
Fig. 2
- . . . _ . . . .
-
0.4-
,
- .
-
a r0 -
a3
-0.4
...
- 2 -
. . . ..'_
.. .
C3-584 JOURNAL DE PHYSIQUE
t-distribution for the 1480 events in the range 0.05 < -t < 0.19 GeV2 is shown in fig. 3. The line represents the result of the fit described above. The acceptance of each arm varies from 13% at -t = 0.05 GeV2 to 7% at -t = 0.19 GeV2.
In fig. 4 our result on the slope parameter b is plotted together with othe- measurements for proton-proton and proton-antiproton scattering. Data [31 were selected for which the t-range is at least partially overlapping with that of the present experiment. When data [4] were presented in a parametrization of the form exp(~t + Ct2), the points plotted in fig. 4 correspond to the local slope
calculated at the middle of the t-range of this experiment. Although the selected set of data is not completely homogeneous because of the variation of the local slope with t, the compilation of fig. 4 should nevertheless be representative of the trend with energy at -t
*
0.1 GeV2.Ir
The present measufement shows that the shrinkage of the forward diffraction peak persists into the new energy domain of the CERN pp Collider. Our result is
-
compatible with a rise of the slope with at least the first power of log s between the lowest ISR energy and the Collider energy. However, in spite of the sizeable error due to limited statistics, our result can hardly be accomodated by a recent fit with asymptotic log s behaviour [5] of slope values up to ISR energies, which predicted a slower increase of b with log s. On the other hand, model approaches exist that indicate ranges of values encompassing our experimental result, like for instance, the prediction of b = 17-18 GeV-Z in our t-range which is
obtained [61 when the scaling expression for the elastic amplitude in Reggeon Field Theory is fixed by a fit to ISR data.
THE TOTAL CROSS SECTION
The total cross section o was obtained by means of a method pioneered tot
at the ISR 171. It is based on the simultaneous measurement of low-t elastic scattering and of the total inelastic rate. By using the optical theorem one can write the differential elastic rate at low t as
dNel = u 2 (1 + p2)
-
totdt 16n(6 cI2 exp(bt)
where p is the ratio of the real to the imaginary part of the forward elastic scattering amplitude and L is the machine luminosity. Moreover,
-
Nel + Nin
-
atotwhere N and N. are the elastic and inelastic rates, respectively. Combining e 1 ~n
the two previous expressions gives
M. Haguenauer
Fig. 3
t-distribution of elastic scattering events in the t-range from -0.05 to -0.19 GeVZ.
o Amaldi (71.77) FNAL
j
Ayres (771~Fajordo (81 )
6 - -
U A 4
4- ' " 1 ' ' ' " ' " 4 1 ' '
10' loe 10' 10' 10'
s G ~ V ~
Fig. 4
Compilation of measured values of the slope parameter b for pp and pp
-
elastic scattering in approximately the same t-range as this experiment.
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The total cross section can thus be obtained without the need of an independent determination of the machine luminosity. At present this method provides the only possibility of measuring the total cross section reliably
because an accurate measurement of the luminosity is not available at the Collider.
Inelastic interactions are observed in a vertex detector (fig. 5) consisting of two identical systems of three telescopes (D,, D, and D,) placed symmetrically on the left and right sides of the crossing region and covering angles from% 0.5O to % lo0. The range in the pseudo-rapidity variable q covered by these detectors is from 2.5 up to 5.6, while the beam rapidity is 6.3. Each telescope is composed of six drift chamber planes backed by a plane of trigger counters (TI, TI and T, respectively) of full azimuthal coverage. The coordinate along the drift wire is measured by means of a delay line close to the drift wire itself [8], thus
yielding the coordinates of a space point directly. This arrangement leads to considerable simplification of the procedure of pattern recognition. The readout of the delay line at both ends provides a constraint that facilitates handling of multiple hits. During data taking the r.m.s. values of the spatial accuracy for
the drift and delay line measurements were found to be about 0.4 mm and 4 mm respectively, including the uncertainties in calibrations and in the geometrical survey.
For both elastic and inelastic events, the trigger logic was timed with respect to a gate signal synchronous with the bunch crossing in the intersection region. It was ensured that the elastic and inelastic rates were obtained at the same luminosity by alternatingly enabling the two triggers. The number of bunch crossings between the enabling and the occurrence of a trigger was recorded. The average rates of elastic and inelastic events were obtained from the total live times of the elastic and inelastic triggers respectively.
Data were mainly taken with two inelastic triggers using the trigger planes T, and T, :
(a) A double-arm trigger (left-right coincidence), covering 2.6 units of rapidity on each side (3.0 < < 5.61, which is expected to detect most of the non- diffractive inelastic events.
M. Haguenauer C3-587
(b) A single-arm trigger, coxering the range 3 . 0 < 11 < 5 . 6 on the outgoing side, which allows detection of events that escape the double-arm trigger, in particular single diffractive interactions. The
5
side was chosen because it was less affected by background; the observed rate was then multiplied by two. As a check of this trigger, a low statistics run was taken with a special diffractive trigger defined as the coincidence between an elastic arm and the opposite inelastic arm. The rate and topology of the eventscollected in this run were in satisfactory agreement with the results of the single-arm trigger.
The following procedure was used to identify inelastic interactions. Events were rejected if the time-of-flight analysis showed that a trigger plane was hit by a halo particle accompanying the incoming beams. This selection caused a 0 . 2 % loss of true beam-beam interactions. A vertex search was then performed on the remaining events. Tracks were reconstructed in the D,, D, and D, telescopes with the requirement that at least four out of six planes contributed a track point.
The longitudinal and transverse distributions of reconstructed vertices are shown in fig. 6. The accuracy in the determination of the vertex position (a 1 cm in the transverse plane and a 10 cm in the longitudinal direction) was adequate to identify beam-beam interactions unambiguously.
In a short test run, T, was also used in order to extend the rapidity
coverage of the double arm trigger to the interval 2 . 5 <
In!
< 5 . 6 . The additional contribution of this more inclusive trigger was found to be negligible within the limitation of present statistical uncertainties.The different contributions to the total inelastic rate are listed in
table 1, where the quoted errors are statistical. The majority of the events have tracks in both arms and trigger the left-right coincidence. About 20% of the events have tracks on one side only and are recorded by the single-arm trigger.
The fraction of events escaping detection, due to the limited coverage in polar angle of the detectors, was estimated by extrapolation. For each event of the single-arm trigger, the tracks having the smallest and the largest production angle,
emin
and 8,
were considered. Extrapolation of the observed 8max max
distribution of event rate to the experimentally unaccessible region
0' < B < O.SO allows to estimate the number of events with all secondaries max a
travelling inside the vacuum pipe. Similarly, the losses at large angles were estimated by extrapolation of the 8 distribution. As shown in table 1, the
min
losses are estimated to amount to no more than a 2% of the total inelastic rate.
This can be understood by noting that, while the angular range covered in this experiment is relatively small, the corresponding 11-range is large. It is in
JOURNAL DE PHYSIQUE
~nelastic detector
,
A 2 Central defechx
7) acceptance
T3 4.4
-
5.6Fig. 5
Layout of one arm of the inelastic detector; the assembly is symmetric with respect to the crossing region. The central detector of experiment UA2 placed in the same intersection region is also sketched. The n acceptance of the trigger
planes Tt
,
T2 and T, is indicated.XY DISTRIBUTDN OFMRTEX Z-X DlSTRlBUTlON OF VERTEX (cm)
Z w
2
80X-COORD. OF VERTEX Z-COORD. OF VERTEX(cm1
Fig. 6
Transverse (x, y) and longitudinal (2) distributions of reconstructed vertices.
M. Haguenauer
fact the same as for a 4n angular coverage at an energy & = 20 GeV. Moreover, the density of secondaries per unit rapidity range increases with energy.
TABLE 1
From the corrected number of events given in table 1, the average rate of inelastic interactions per bunch crossing was found to be Nin = (9.90 f 0.21) x
x eventsjcrossing. In addition to the .-u 2% statistical error, the inelastic rate is affected by a systematic error of .-u 2% mainly due to uncertainties in the extrapolation procedure and inefficiency of the trigger and of vertex finding for very low multiplicity events.
Left-right trigger Single arm trigger Extrapolation to small angles Extrapolation to large angles Correct ion for random incoming beam Total
The total number of elastic events was calculated from the observed number of events in the interval 0.05 < -t < 0.19 GeVZ under the assumption of an
exponential t distribution with a constant slope parameter b = 17.2 G e V Z , equal to the value measured in the accessed t-range. In that case (dN /dt)t,O = bNel.
el
The average rate of elastic events, after correction for acceptance, for chamber and track finding inefficiencies and for particle loss due to nuclear absorption was N = (2.43 f 0.12) x lo-' events/crossing.
e 1
By substitution of the observed rates into eq. (I), one obtains atot = 66 f 7 mb for p = 0. The quoted error is purely statistical and is mainly due to the uncertainty in the extrapolation to the optical point. The systematic error due to setting the factor (1 + p2) equal to unity is expected to be small compared to the statistical error; the dispersion relation fit of ref. 191 predicts a value of p of about 0.1 at Collider energies. An estimate of the systematic uncertainty arising from the possibility that for -t < 0.05 GeV2 the slope parameter b differs
Fraction of the total
78.2%
20.0%
0.7%
0.9%
0.2%
100%
11-range 3.0< In1 < 5.6
3.0 < n < 5.6 1111 > 5.6 In1 < 3.0
Number of events 4996 f 71 (2 x 639) f 110
45 f I0 55 f 25 15 f 10 6389 It 134
JOURNAL DE PHYSIQUE
this experiment
J2
E
Total cross section data for proton-proton (open points) and proton-antiproton (full points) intera~tions. To the compilation of ref, [ P I
the more recent results for pp at the ISR 1111 and for pp and pp at FNAL 1141 were added. The lines represent the dispersion relation fit of ref. [61.
Baumel et al., ref. [9], Amaldi et al.,
and M. Block and R. Cahn, CERN TH-3307 and CERN TH-3342.
M. Haguenauer C3-59 1 from the value in the covered t-range can be given by mentioning that a change of 1 G e V 2 in the value of the slope parameter at -t = 0.05 GeV2 would lead to a change in the total cross section of about 3 mb. The same change would result from a 5% error in the inelastic rate.
The simple "geometrical scaling" model predicts that the ratios oel/otot and b/otot do not vary with energy. Our results are o
elfotot = 020 and b/otot = 0.26 GeV2/mb with an overall error of about 10%. It should be noted that because of the assumption of a constant slope parameter, the two ratios are not
independent. For proton-proton interactions, over the ISR energy range, oel'otot and bfatot are almost constant and take the values 0.18 and 0.30 GeW2/mb, respectively [lo]. The proton-antiproton results [ll] at f i = 53 GeV are consistent with the pp data.
The value of the proton-antiproton total cross section at = 540 GeV is plotted in fig. 7 together with pp and pp results at lower energies. The full
-
line in fig. 7 is the result of a dispersion relation fit [9] of data on otot and p up to I S R energies (but not including the recent I S R p t measurement of
ref. [Ill); the dashed lines indicate the uncertainty of the fit itself. Cosmic ray data were reported [12] in this energy region. They are affected by serious systematic uncertainties. However, under a certain choice [13] of the primary radiation spectrum, the data of ref. [I21 interpolate fairly well between the I S R and Collider data points.
Our result indicates that the pp total cross section continues to rise strongly from the I S R to the Collider energy range. The experimental value of 66 f 7 mb agrees well with the fit of ref. [91, which follows a (log s ) ~ dependence, but due to the sizeable uncertainty limits our result is also compatible with a slower increase with energy.
REFERENCES
*
R. Battistons, M. Bozzo3, P.L. Braccinis, F. Carbonarar, R. Carraras,
R. CastaldiS,F. Cervellis, G. Chiefari*, E. Drago*, M- Haguenauer2, B. ~oene',
G . Matthiaes, L. Merolas, M. Napolitanos
,
V. palladino2, G. sanguinettis 9G. Sciacca*
,
G. Settea, R. van swell,
J. ~immermans',
C . vannini2,J. Velasco2 and F. ViscoS
[I] U. Amaldi et al., Phys. Lett.
9
(1973) 231.[2] J. Buskens et al., (submitted to Nucl. Instr. and Methods).
JOURNAL DE PHYSIQUE
[3] K. Biickmann et al., Nuovo Cimento A42 (1966) 954;
-
D. Birnbaum et al., Phys. Rev. Lett.23 (1969) 663;
V. Bartenev et al., Phys. Rev. L e t t . 2 (1973) 1088;
U. Amaldi et al., Phys. Lett. Z B (1971) 504 and 66B (1977) 390;
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M. Holder et al., Phys. Lett.
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36B (1971) 400;G. Barbiellini et al., Phys. Lett.
39B
(1972) 663;L. Baksay et al., Nucl. Phys. E l (1978) 1.
[4] Yu. Antipov et al., Nucl. Phys. B57 (1973) 333;
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D.S. Ayres et al., Phys. Rev. Dl5 (1977) 3105;
v
L.A. Fajardo et al., Phys. Rev.
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(1981) 46.[5] J.P. Burq et al., Phys. Lett. 109B
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(1982) 124.[6] J. Baumel et al., Nucl. Phys. B 2 (1982) 13.
[7] CERN-Pisa-Roma-Stony Brook Collaboration, Phys. Lett. 62B (1976) 460 and Nucl.
Phys. B145 (1978) 367.
[8] For details on the contruction of these chambers sze:
A. Bechini et al., Nucl. Instr. and Meth.
156
(1978) 181;F. Carbonara et al., Nucl. Instr. and Meth.
171
(1980) 479.191 U. Amaldi et al., Phys. Lett. 66B (1977) 390.
[lo] L. Baksay et al., Nucl. Phys. %1 (1978) 1;
U. Amaldi and K.R. Schubert, Nucl. Phys. g 6 (1980) 301.
[Ill G. Carboni et al., Phys. Lett. 113B (1982) 87;
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M. Ambrosio et al., CERN/EP 82-65 (to be published in Phys. Lett. B.)
1121 R.A. Nam et al., Proc. 15th Int. Conf. on Cosmic Rays, Plovdiv, 1977, vol. 7, p. 104
[13] S.C. Tonwar, J. Phys. G: Nucl. Phys.1 (1979) L193;
T.K. Gaisser and G.B. Yodh, Ann. Rev. Nucl. and Part. Sci. (1980) 475.
1141 A.S. Carroll et al., Phys. Lett. J3OJ (1979) 423.
DISCUSSION'
A. M&?TT~~(CERN).- I wish t o make a remark which I should have done during the paraliiet session. We have seen t h a t the sZopes given by UA4, around 17.2 G~T', and
UA1, around 13.3 ~ e l r ~ , at larger
]
t1
are hardly compatible. I t i s perhaps relevant t o indicate t h a t the theorem says t h a t Iff the t o t a l cross section behaves l i k e(tog s ) 2, b f s , o ) also behaves l i k e (log s j 2 , and b ( s , t ) / b ( s , o l + 0 for t < 0 .
So as t h e energy increases the variation of the slope with t i s more and more marked.
M. HAGUENAUER.- Concerning t h e c o m p a t i b i l i t y o f t h e UA4 and UA1 r e s u l t s , and t h e v a r i a t i o n o f t h e slope w i t h t, I want t o p o i n t o u t that2UA4 w i l l measure i n t h e near f u t u r e t h e
It1
d i s t r i b u t i o n from about .006 t o 1.4 GeV-,
c o v e r i n g l a r g e l y t h e UA1 range.Nevertheless, even i f t h e slope would be 13.3 GeV-2 i n t h e UAl range, t h i s would o n l y a f f e c t t h e t o t a l cross s e c t i o n by 2 p e r m i l .
