A precise measurement of the real part of the elastic scattering amplitude at the SppS

PROCEEDINGS SUPPLEMENTS

Nuclear PhysicsB (Proc. Suppl.) 25B (1992) 266-273 North-Holland

A Precise Measurement of the Real Part of the Elastic Scattering Amplitude at the S]spS UA4-2 Collaboration: G e n o a presented by M. Haguenauer

1

Introduction

The surprisingly high value of the ratio p of the real to the imaginary part of the forward elastic scattering amplitude obtained by the UA4 Collaboration [1] has given rise to various theoretical interpretations. The measured value, p = 0.24 4- 0.04, is substantially higher than the value of about 0.13 predicted by "standard" dispersion relation calculations. It is worth reminding that the UA4 result was obtained in a single SPS run of~h_,,ut two days and systematic effects could not be thoroughly studied. With the remarkable improvements in luminosity and emittance of the SPS Collider since 1986, a new measurement with a substantial reduction of the error and of the sources of possible systcmatic effects could be performed.

Palaiseau - Praha-

2.1

Physics Motivations Dispersion

Reb~]on

Analysis

Dispersion relations, which relate the real and imaginary parts of the forwar~ elastic scattering amplitude, are based on general assumptions only: analyticity and crossing property of the elastic scattering amplitude [2]. They provide a powerful tool to predict the high energy behaviour of the total cross section. Using a simple parametrization of the total cross section as a function of energy, extrapolation from the ISR data [3] predicted a value between 56 and 66 mb for the Collider. The value measured by UA4 [4] confirmed the remarkable predictive power of this type of anal~s~s (figure i.~) Using the same type of parametrization and

Valencia

the total cross section measurement, a value of 0.13 for p was predicted for the Coilider energy. Dispersion relation analysis have been performed by using particular forms of the scattering amplitude as given by theoretical models. Also most of these [5] predict a value o f p around 0.13. The UA4 Collaboration measurement of p performed in a single short SppS run gave , p = 0.24 4- 0.04, nearly three standard deviations away from the predictions. We must consider first the possi~qity that this result might not be correct due to hidden systematic errors. If on the other hand, the result is taken as being correct, the following explanations or interpretations have been proposed to explain its large unexpected value.

2.2

2

Roma-

Possible

Explanations

for

a

High Value of p The large theoretical work b ~ e d on. this new situation can be divided into two main classes: i) "The total cross section rises faster than (ins) 2 above x/~ ~- 0..5 TeV, while the Froissart-Martin limit is recovered at much higher energies". A parametrization of the energy dependence of the total cross section by adding a new threshhold term has been proposed by Martin [6]. A similar approach is proposed in ref. [7]. Illustration of such behaviour is given in figure 1.b. Also in the QCD framework [8], attempts have been made to correlate the rise of the total cross-section to the large and rapidly rising minijets cross section measured by UA1 [9]. ii) "An odd-term is added in the scattering amplitude". The "odderon" hypothesis had

0920-5632/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved.

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Figure 1: Dispersion relation analysis of the imaginary part (total cross section) and real part of the scattering amplitude a." Classical" extrapolations b. Extrapolations with a threshold behaviour. c. Extrapolations with an "odderon term". Solid line corresponds to pp scattering and dashed line to pp scattering.

been introduced several years ago [10], [11], to explain the behaviour of elastic scattering at large t. A fit to the data with a maximal odderon [12] is shown in figure 1.c. A similar analysis is done in ref. [13]. A consequence of this hypothesis is that the pp and ~p cross sections cross over between the ISR and Collider energi~, their difference increases like In s, while their ratio would still tend to 1, thus satisfying the Pomeranchuk theorem [14]. In this case also non-pertubative QCD calculations to estimate the real part of the amplitude [15] have been performed. Any combination of these two hypotheses can explain a high value of p [161. While the data can be accomodated, the physics behind has still to be understood. If the UA4 measurement is confirmed, new lines of research will be opened for the LHC and SSC colliders.

3 3.1

Experimental n a t i o n of p Fitting run

p in t h e

determi-

1985

UA4

The observed t distribution has been fitted usi,ag the following stahdard express[c~ (fig. 2):

"268

M. ltaguenauer/ Elastic scattering amplitude at the S~pS

bimaglnar~ >_ 1. At the upper limit, the value of p from the fit would be reduced by only 0.02. Although these effects might not be fully understood with a new measurement, their influence should be strongly reduced by extending the measurement to lower train. The quoted error of 0.04 resulted equally from statistics (0.025) and systematics (0.025). In addition to the contribution from the uncertainties on the slopes and on ~tot, the dominant contribution to systematic effects resuited from the uncertainty on the relative position of the detectors. In the next chapter, we will see how one can improve the measurement.

61

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Figure 3: Experimental correlation between p and the total cross section

d~

4x(hc)2a2G4(t)

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4.1

.¢r~otC~(p- a~( t ) )G2( t )e-~lql ~

iti (1 + p2)o'~ot e-bltl 16x(hc)2

+ (1)

where the shape of the diffraction peak is described by a single exponential form exp (bt), assumiag the same slope b for the real and imaginary parts of the s-attering amplitude. The value for the quantity (1 +P~)~tot = 63.3 4- 1.Stub was taken from the simultaneous measurements of the low-t elastic scattering and of the inelastic rate of interactions (Luminosity independent method) [4]. The result of the fit to the 1985 UA4 data (fig. 2) was p = 0.24 4- 0.04. The correlation in the fit between p and the total cross section is shown in fig. 3. 3.2

4

Sources

of uncertainties

If the slope of the imagiaary part of the scattering amplitude were not constant at small t, an increase ofbi,n~gina,u by one unit in GeV -2 would lower p by 0.02. Since phenomenological arguments [17] restrict the domain of tile ratio b, eal/bimagiaa,~ to the range 2 _> br¢~z/

Improvements Measurement

to

the

p

Statistics

In the 1985 measurement, the number of events in the final distribution was 7104 events. With the substantial increase of the Collider luminosity (factor 20), mainly due to the new antiproton accumulator, a similar amount of running time would already yield one million events, thus reducing the statistical error. A Monte Carlo study has been performed to evaluate the expected precision on p, O'tot and the :lope b assuming one million events in the final t distribution. The result shown in figt:re A indicates that the error on p can be reduced to a value of 0.01. In addition, ifa value o f train lower than the one in the 1985 run could be reached, an independent determination of the total cross section and the diffractive slope b could be obtained with a further reduction of the sources of systematic errors.

4.2

New

Beam

Optics

The minimum scattering angie O,~,, which can be measured by a detector placed at a distance d,~i, from the beam, is given by:

M. ltaguenauer/ Elastic scattering amplitude at the SppS

269

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(4) 2 where ~ is the beam emittance, and k is a machine dependent constant, which in the previous UA4 measurement was found approximately equal to 20. We obtain the following expression for train = --02minP 2 [18]: k2c 1 1)~ [train[= ~ - fl, (sin

Figure 4: Monte Carlo study on the expected errors with a sample of 10~ events o : p, c~tot and b all free in the fit O: p and O'tot free, b fixed A: p and b free, crtot fixed o : p free only, c~ot and b fixed (as in the 1985 run)

0rai, =

drain Le/!

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(2) (3)

where pd and ~* are respectively the betatron functions at the detector position and interaction point, and A~ is the betatron phase advance between these two points. The minimum distance of approach to the beam can be expressed in terms of the beam size at the detector position by:

p2

(5)

The detectors will be positioned as close a.s possible to the points where AN, - f / 2 . The smallest train is reached with the highest ~ , but as the luminosity goes like l / v f ~ ", a compromise has to be found between trai,, and luminosity. Additional gain in tra~,~ could be obtained by reducing the k factor, i.e. by optimising the beam scraping. 4.2.1

High Beta

For the previous measurement the retained compromise between luminosity and low t was j3* - 1080 m with an asymmetric optics [19] (fig. 5.a). A new beam optics has been designed by P. Faugeras/CERN, with a 8" of 2500 rn (fig. 5.b) and with the essential feature of being perfectly symmetric. This will be of first importance to understand background and systematic effects. This insertion is obtained by doubling the quadrupoles 16 and 20 which are placed on both ends of the LongStraightSeetion, and by increasing their respective strength. For the 1985 measurement, the p~ crossing

M. H~guenauer/ E|astic scattering amplitude at the S#pS

270

4.2.3

Measuring elastic scattering at high values of It ! is also important to study the behaviour of the slope b. In our previous measurement the tmaz Was limited to 0.035 G e V 2 by tne aperture of the bending magnets near quadrupoie 4.20. In the new proposed setup, since ,~.he measuring points stay inside the Long S t r a i g h t Section, the maximum transfer [tma=l will be limited by the 20 cm diameter beam pipe at a maximum value of ]tma~[ = 0.12 G e V 2.

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Figure 5: a. Experimental layout during the 1985 UA4 run

b. Proposed layout for the new measurement

point was placed in the middle of quadrupole 4.18. With the new optics the interaction point will be in the free space between a pair of quadrupoles 18. This avoids a possible source of systematic error, when scattered particles with equM t don't follow the same magnetic path. 4.2.2

M a x i m u m t r a n s f e r tma=

Beam scraping and monitoring

The ~.bsence of beam tails is crucial for th~ experiment and beam scraping will be program]ned at regular time intervals to reduce the b~ckground. The experiment will benefit from the new scraping method proposed for the 1990 pp run [20] and from the already mentioned gain in beam cmittance. The transverse beam position will be obtained with the machine BPCS's during the data taking period. The longitudinal position of the pp crossings will be measured as usual by timing the signals of scintillation counters placed on both sides of the interaction point. They will also serve as relative lumiposity monitors.

5

Total cross surement

section

mea-

M i n i m u m t r a n s f e r tmi.

At V~--546 GeV, the Coulomb scattering f c and the strong interaction amplitudes f,t,o,g are equal in magnitude at It01 "" 1.1 IO-3GeV 2 . The minimum value oft in the final distribution was It~.! - 2 . 5 ! O - 3 G e V ~ • The above expression for h , , , and a value of the beam emittance of 5" 10-Smrad, indicates that a It,~i,~ [ as low as 0.3 10-3GeV 2 could be obtained (fig. 6). Even if a conservative value of0.8-10-3Geg 2 is taken, we will measure below It01 and this will provide a much better control of the systematic errors.

A measurement of the total cross section, (1 + ps)~'tot - 63.3 4- 1.5mb[4], had been used as an input to the 1985 fit. With the proposed set-up a new measurement of ~rtot can also b e obtained. Two methods can be used: i) If as shown in fig. 4, the minimum reachable t will be ~. 0.510-3GeV 2, the total cross section will then be determined with a precision of about 2 mb by using Coulomb scattering as absolute normalization. ii) The total cross section can also be determined by a measurement of the luminosity and the optical theorem. In this case the error on the cross section corresponds

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to half of the error on the luminosity (L). L can be expressed in terms of the revolution frequency(f), the number of collid-

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Scattering

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At the SPS f = 43.375 kHz, and the quantities Np, Ng, and ¢rh, a~ could be determined with a precision of about 2% with the wire scanners already installed near quadrupole 18. Between two "wire scan" measurements the relative beam profiles will be monitored using w u u | ~,g J the synchrotron light detectors, TLA~O t_:...... result in an error of 2% on the total cross section. This method doesn't require that Itmi, I be below lO-sGeV 2.

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Figure 6: a. Detailed view of the betatron functions near the detector positions b. Effective distances in the horizontal plane Leffx and in the vertical plane Leffv c. Minimum distance of approach to the beam d. Valnes of train (assuming an approach to the beam of 20 ~be~,-) and t,~o~

The

"Roman

Pots"

The sensitive part of the detector must reach a position as close as possible to the circulating beam. The "Roman Pots" from the previous measurement ~vhich are still perfectly adequate will be used. A pair of horizontal pots containing two detectors each, should be installed on each side of the crossing point. In the 1985 run, UA4 was using 2 pairs of pots on the ~ outgoing side and only one pair of pots on the p outgoing side. The new experiment will use 4 horizontal pots symmetrically placed on both sides. An easy way to reinforce the bottmi, of the pots reducing the dead space near the beam has been devised (see fig. 7). This will allow a gain in t,ni, of nearly 50%. 6.2 6.2.1

Detectors Horizontal coordinate

The UA4 drift chambers [22] will be used again to measure the main scattering angle. The chambers are made of four drift planes of three classical drift cells each. By staggering

M, ttagueuauer/ Elastic scattering amplitude at the S~pS

272

the drift celk. the chambers will be self calibrated, giving a resolution of 70/~m. 6.2,2

Vertical c o o r d i n a t e

The precision of --. i mm obtained in the past by charge division on a proportional wire plane for the vertical coordinate will no longer be adequate to measure momentum transfers l~sc. than ~ rt-3f,,.I12 To me~ure the vertical coordinate, hodoscopes with staggered 1 mm diameter scintillating fibers arranged on 12 planes have been built. The acceptance tests performed in a SPS fixed target beam have shown that the efficiency is neatly 100% and a resolution around !00 t~m. 6.2.3

Trigger

The general principle of the trigger will be the same as in the previous UA4 experiment [21]. The trigger is based on scintillation countern 50x100 mm 2 placed just behind the drift chamber and the scintillating fibers in each "Roman pot". An overall sketch of the detectors in a "Roman pot" is shown ia fig. 7. Additional counters placed sywmetrically with respect to the interaction point before tile quadrupohs 17 and 19, will be used to determine "on line': the position of the interaction point along the beam axis. They will serve also as relative luminosity monitors.

7

a small modification to the pots, essential to the gain in train,

Acknowledgments

We would like to express our gratitude to the CERN managemeni for their help in making this experiment feasible. Special thanks to Prof. A. Martin for his constant support. The machine optics is an essential part of this experiment. This experiment ~ould,'t have been proposed without ~he contribution of P. Faugeras in designing the new optics. The participation of J.B. Jeanneret in understanding beam scrapi:,g was very helpful. R. Maleyran, who d~signed the "Roman pots" mechanism for the previous UA4 run, has suggested

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Figure 7: Artist's view of the detectors in the "Roman Pot" The presentation of this experiment was the first part of Prof. G. Matthiae's talk. All my gratitude to him to let me (M.H.) discuss it.

References [I] UA4 Collaboration, D. Bernard et aI., Phys. Lett. 198B (1987) 583 [2] A. Martin, Zeitschr. fiir Phys. C15 (1982) 185 and references therein. [3] U. Amaldi et al., Phys.Lett. 66B (1977) 390 U. Amaldi and K. Schubert, Nucl. Phys. B166 (1980) 301 J. Dorenbosch, PhD Thesis, University of Amsterdam 1977.

[4] UA4 Collaboration, M. Bozzo e'. ~I., Phys. Lett. 147B (1984) 385,392. [5] A.Martin, Proc. of the Workshop o~ ,~p Physics, Bern(1984), C E R N 84-09, p.308

M. Haguenauer/ EMstic scattering amplitude at the S~pS

A. Donnachie and P.V. Landshoff, Nucl. Phys. 244B(1984) 322 and references therein A. Donnachie, Summary talk in Prec. Int. Conf. on Elastic and Diffractive Scattering, Blois 1985, ed. by B. Nicolescu and J. Tran Thanh Van R.J. Glauber and J. Velasco, Phys. Lett. 147B (1984) 380 IL Henzi and P. Valin, Phys. Lett. 149B (198') 239 P. Gauron, E. Leader, B. Nicolescu, Phys. P~ev. Lett 54 (1985) 2656 and 55 (1985) 639 M. Block and R.. Cahn, Phys. Lett. 188B (1987) 143 C. Bourre!y, J. Softer, T.T. Wu, Phys. Lett. 196B (1987) 237 B. Nicolescu, in these proceedings K. Kang, ibid.

273

Int. Conf. on Elastic and Diffractive Scattering, New ¥ork,1987 [14] Y. Pomeranchuk, JETP 7 (1958) 499. [15] L.N. Lipatov, in "Perturbative Quantum Chromodynamics", A.H. Miiller ed. (World Scientific,Singapore,1989) [16] P. Kluit and J. Timmermans, Phys. Lett. 202B (1988) 459. [17] J. Dias de Deus and P. Kroli, Acta. Phys. Polon. 9B (1978) 157 J. Dias de Deus, CERN/TH-4759 For a critical discussion, see also: V. Kundrat, M. Lokajicek and D~ Krupa, Phys. Rev. 935 (1987) 1719 V. Kundrat and M. Lokajicek, Phys. Lett. 232B (1987) 263. [18] M. Haguenauer and G. Matthiae in Prec. of the Lausanne LHC Workshop

[6] A. Mar~,in, Prec. Second Int. Conf. on Elastic and Diffractive Scattering, New York 1987, 145 A. Martin, these proceedings

[19] P.E. Fangeras, CERN SPS/84-7 (ARF) 1984

[7] S. Hadjitheodoridis and K. Kang, Phys. Lett. 208B (1988) 135

[20] J.B. Jeanneret, CERN/SPS Internal report

[8] L. Gribov, E. Lenin and M. Ryskin, Phys. Rep. 100C (1983) 1 B. Kope!iovich, N. Nikolaev and I. Potashnikova, Phys. Lett. 209B (1988) 355 L. Durand and H. Pi, Phys. Rev. Lett. 58 (1987) 303.

[21] M. Bozzo et al., Nucl. Instr. Meth. A238 (1985) 35.

[9] UA1 Collaboration, C. Albajar et al., Nucl. Phys. 309B (1988) 405. [10] L. Lukaszuk and B. Nicolescu, Nuov. Cim. Left. 8 (1972) 405. [11] K. Kang and B. Nicolescu, Phys Rev liD (1975) 2461. [12] D. Bernard, P. Gauron and B. Nicolescu, Phys. Lett. 199B (1987) !25 and reference-~,therein. [13] E. Leader, Phys. Rev. Lctt., 59 (1987) 1525 E. Lead.~r, Summary talk, Prec. Second

[22] J. Buskens et al., Nucl. Instr. Meth., A207 (1983) 365.