Measurement of the parameters D0n0n and K0nn0 in pp elastic scattering between 0.84 and 2.7 GeV

Nuclear Physics B315 (1989) 284-294 North-Holland, Amsterdam

MEASUREMENT OF THE PARAMETERS Do.o. AND Ko..o IN pp ELASTIC SCATTERING BETWEEN 0.84 AND 2.7 GeV C.D. LAC and J. BALL

Laboratoire National Saturne, CEN-Saclay, France J. BYSTRICKY, F. LEHAR, A. de LESQUEN and L. van ROSSUM

DPhPE-SEPh, CEN-Saclay, France F. PERROT 1 and J.M. FONTAINE

DPhN / ME, CEN-Saclay, France P. CHAUMETTE, J. DERI~GEL and J. FABRE

DPhPE-STIPE, CEN-Saclay, France V. GHAZIKHANIAN

UCLA, Los Angeles, California, USA A. MICHALOWICZ

LAPP, Annecy, France Y. ONEL2

DPNC, Universit~ de Gen~ve, Geneva, Switzerland A. PENZO

INFN, Trieste, Italy Received 29 August 1988

The spin-dependent observables D0.0. and K0.n0 in pp elastic scattering were measured at 11 energies between 0.84 and 2.7 GeV using the SATURNE II polarized proton beam and the Saclay frozen-spin polarized target. The beam and target polarizations were oriented along the normal to the scattering plane. Below 1 GeV the present data agree with previously existing measurements. Below 1.3 GeV they are compared with the predictions of the Saclay-Geneva phase-shift analysis. The results will improve the phase-shift analysis solutions and will contribute to their extension towards higher energies. 1 Present address: EP Division, CERN, 1211 Geneva 23, Switzerland. 2 Present address: Iowa University, Iowa City, IO, USA. 0550-3213/89/$03.50©Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

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1. Introduction The present measurements are part of complete sets of experiments designed to determine explicitly the scattering amplitudes in the energy range up to 2.8 GeV. We use the same beam, target (PPT), detectors, acquisition and analysis as described in ref. [1] (preceding paper). The beam and target polarization were oriented in the vertical direction, i.e., perpendicularly to the beam momentum k. The principal aim of the experiment was to measure the beam and target analyzing powers A00,0 = Aooo. [2, 3] and the spin-correlation parameter A0o~n [3,4] given by the left-right asymmetry of the beam scattered on the PPT. Simultaneously, we measured the left-right asymmetries in the second scattering of recoil particles on a carbon analyzer. Averaging over the beam or target polarizations yields the two Wolfenstein parameters D0n0n and K0n,0, respectively. Both parameters are linearly independent [5] in the CM angular region 0 < OcM < 90 °. For pp scattering they are simply related by equality Do,o,(OcM) =Kon,o(180 ° - 0CM). The only three-spin index observable accessible in this measurement, N o. . . . gives no independent information since it is equal to the analyzing power Ao0,0. In addition, the recoil-particle polarization P0,oo can be measured from the left-right asymmetry on the carbon analyzer when averaging over both beam and target polarizations. Its value must be equal to Aoo,o = A00on. Our results are compared with all existing data for the same parameter [6-11]. Most of these measurements were done at Gatchina, below 1 GeV. Up to 1.3 GeV they are also compared with the Saclay-Geneva phase-shift analysis (PSA) predictions [12] where the present data were not introduced. Throughout this article we use the four-index notation of the observables and the nucleon-nucleon formalism developed in ref. [5] (see also ref. [1]). The first and second subscript refer to final-state polarization of the scattered and recoil particle, respectively. The third and fourth subscript specify the initial polarization of the beam and target, respectively. If an initial particle is unpolarized or the polarization of a final particle is not analyzed, the corresponding label is set equal to zero. The orthonormal laboratory system for beam and target particles is defined by three unit vectors

k,

.=[kxk']/l[kxk']l

and

s=[-xk]/l[.xk]l,

(1.1)

where k is oriented in the beam-momentum direction and k' is in the direction of the scattered particle. In our experiment n is close to the vertical direction n v and s is practically in the horizontal plane in the direction s h = n v x k. The horizontal plane (s h, k) is the mean scattering plane. The laboratory orthonormal system for the recoil particle is defined by vectors

k",

n,

and

s" = [n x k " ] / l [ n x k " ] l ,

(1.2)

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C.D. Lac et a L / pp elastic scattering (I1)

where k " is oriented along the momentum of the recoil particle.

2. Beam, target and experimental set-up The polarized beam and its extraction are described in refs. [13,14]. The polarization PB of the extracted beam is vertical and the spin direction is reversed from burst to burst by selecting the RF transition in the ion source. The polarization is monitored continuously by the beam polarimeter [15] in the first focus of the extracted beam, measuring the left-right asymmetry o n C H 2 and C targets. The beam polarization was PB > 0.90 at the lowest energies and PB > 0.70 at the highest energy. The beam flux in front of the target was monitored by two counters SP which worked at reduced voltage with thresholds sensitive to large signals from pile-up and interactions. Up and down forward arms of another polarimeter [15], positioned after the last beam-transport element, were used as an independent beam-flux monitor. The frozen-spin polarized proton target [16], 2 cm in diameter and 4.2 cm long, is made of doped pentanol in a 3He-4He dilution refrigerator. It is polarized to IPa-I - 0 . 8 at 0.2 K in the homogeneous field of a 2.5 T superconducting solenoid. After the target has been polarized, this solenoid is removed and the polarization is held at 40-50 m K in a field of 0.3 T produced by the holding coil which produces a field in the vertical direction. The vertical holding coil field has no effect on the vertical beam polarization. The target polarization is also oriented in n v direction. Consequently, no admixture of other parameters occurs in this configuration. The target polarization was reversed by repolarizing in opposite direction. The direction of the holding field, and thus the magnetic deflections of the scattered and recoil particles, were always the same for a given incident particle energy. For relative normalization of successive runs with opposite signs of target polarization, a small CH 2 target 3 or 10 mm thick and 2 cm in diameter was placed 45 mm downstream from the center of the polarized target, i.e. at a distance sufficient to distinguish between events from the two targets. Normalization by the number of events from the CH 2 target takes into account, not only the integrated beam intensities but also possible time-dependent changes in event detection and reconstruction efficiencies [2,17]. The experimental set-up [17] is the same as in ref. [1]. Scattered and recoil protons are detected in a two-arm spectrometer. Each arm has an acceptance of _+11 ° lab in the horizontal plane and of _+5 ° in the vertical plane. Two angular positions are necessary to cover the region from 0cra(min ) to 0cM > 90 °. Recoil particles could be rescattered on a carbon analyzer, typically 5 cm thick. The laboratory angles (~2, 02) describe pC ~ p'X scattering in the analyzer. Scatterings in the analyzer are accepted only if the "mirror event" at (]02q- ~ would have been detected. This condition is satisfied for 02 < 20 ° at the center of the analyser, and for 02 < 12 ° at

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the edge of the fiducial region. The lower limit of angular acceptance for the first scattering is given by the energy of the recoil proton, which must be larger than - 100 MeV for sufficient pC analyzing power. The tracks of scattered and recoil particles are reconstructed from the information of multiwire proportional chambers (MWPC) CO, C1, C2, C3, C l l , C12, C13 ad C14 (ref. [1]). Particle hits in the MWPC's are read and clustered by CAMAC modules. The information is then transmitted to a concentrator module and read by a CAC (Controleur Auxiliaire de Chassis). The CAC-module is based on the M O T O R O L A 68000 microprocessor. It reads and treats on-line the information coming from all the modules of a single CAMAC crate. Since the microprocessor is faster than the on-line computer (MITRA 115) it is used for event-by-event acquisition, as well as for on-line treatment such as histogramming and fast event selection. The electronics of the apparatus is described in detail in ref. [17]. Depending on the energy, only a few percent of events scattered on the polarized target give a useful rescattering of the recoil particle on the carbon analyzer. The thickness of the analyzer was 5 cm in most of the measurements. For larger thicknesses more particles are rescattered but the uncertainty in the second vertex position increases owing to multiple scattering in carbon. Since the thickness of 5 cm is close to the one used in other laboratories, it allowed us to introduce in our analysis their measurements of pC ~ p'X analyzing power [18-24]. The existing pC analyzing power data were compared with the ~results deduced from our measurements and completed where it was necessary. Since the present experiment was designed primarily for measurement of the spin correlation parameter A00n~, the selection of events, performed on-line from the MWPC's information in the CAC program, concerns only the scattering of incident particles on the PPT and does not take into account the rescattering of recoil particles. The selection criterion verifies that at least one hit is found in two of the three planes X (vertical wires), Y (horizontal wires) and U (15 ° inclined wires) of each relevant chamber. Moreover, it checks if in either arm a straight line passing approximately through the PPT can be reconstructed in both horizontal and vertical projections. The events with useful rescattering in the carbon analyzer were selected in the off-line analysis only. Statistics of these events, in contrast to ref. [1], are of considerably lower accuracy.

3. Off-line analysis and determination of observables For each reconstructed event one determines the laboratory angles 0 and cp of the scattered particle by a fit requiring the particle momentum measured in the spectrometer magnet to be consistent with elastic pp scattering. From the measured laboratory angles of the scattered particle one then calculates the expected CM angles Ocalc and q0c~c for the recoil particle, assuming elastic pp scattering. From the measured laboratory angles of the recoil track one calculates the recoil CM angle

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C.D. Lac et al. / pp elastic scattering (II)

0mea~ and ¢Pmca~ under the same assumption. The histograms of the differences Zl0 = 0c~ac- 0mcas and A~ = ¢Pc~¢- ¢Pmeas show narrow "hydrogen peaks". The final kinematic cuts reject 63% to 90% of the registered events, depending on the energy. About 95% of the selected events represent elastic scattering on free polarized protons on the PPT. The background is mostly due to quasi-elastic scattering on unpolarized protons in the target nuclei. It increases with increasing beam energy. The wings of the distribution in A~ are used to subtract the carbon and inelastic background. For the second scattering (carbon analyzer), the rescattered particle track is reconstructed from the information from two MWPC's after the carbon analyser. Only one-track events are selected. An event is accepted if the second vertex is found in the carbon and if the "mirror" particle track would have been detected. The rescattered events represent less than 3% of all events, selected by the kinematic cuts. Angles 82 and q02 of the second scattering of each particle are used to determine the pp observables involving the recoil-particle spin index. The energy of proton incident on the carbon analyzer and the scattering angle 02 determine, for each event, the corresponding value of the pC analyzing power. The numbers of events for different signs of beam and target polarizations are normalized to the same integrated beam flux using the monitors described in sect. 2. The observables are calculated from the normalized numbers of selected scattering events recorded for opposite signs of PB and PT- The general expression for the elastic scattering differential cross section with polarized beam, polarized target and rescattering of scattered and recoil particles is given in ref. [5], eq. (4.3). For arbitrary orientation of the beam and target polarizations, and when only the polarization of recoil particles is analyzed, the general formula reduces to an expression given in ref. [1]. In the present experiment the beam and target polarizations were oriented vertically and only the normal component of the recoil-particle polarization was measured in the second scattering. Under these conditions, and assuming that the first scattering plane is the horizontal plane, the general formula reduces to E (PB, PT) = / C ° { [1 + PBAoo.o + PsPTAoo.. ] + P c [(Po.oo + PBKo..o + PTDo.o. + PBPTNo...) cos q~2] } (3.1) where I c and Pc are the differential cross section and analyzing power for the second scattering on the carbon analyzer, respectively. They depend on the angle of the second scattering O2 and on the energy T2 of the recoil-proton incident on the analyzer. The symbol a denotes the pp differential cross section for unpolarized beam and target, and ¢P2 is the angle between the normals of the first and the second scattering. The difference between the scattering plane and the horizontal plane, given by the azimuthal angle ~, was taken into account. The angular

C.D. Lac et al. / pp elastic scattering (II)

289

TABLE i Observable Do.o. in pp elastic scattering. T k i n is the beam kinetic energy. Errors are statistical and random-like instrumental uncertainties. Systematic errors (not shown) are 5:7 percent (relative) for each set.

Oonon Zki n =

OCM

0.834 GeV Exp. value

49.0 53.8 58.8 65.8 73.8 82.0

0.500 0.477 0.599 0.781 0.863 0.576

5:0.149 5:0.136 + 0.107 5:0.107 _ 0.129 +_ 0.183

Tkin = 0.874 GeV OcM 46.4 50.3 53.9 58.9 66.1 73.8 82.3

Tkin = 0.995 GeV 49.2 54.0 59.0 65.9 73.9 81.4

0.846 0.748 0.773 0.650 0.543 0.641

5:0.156 5:0.147 5:0.134 5:0.151 _ 0.189 5:0.261

Exp. value 0.602 0.814 0.581 0.691 0.501 0.402 0.493

5:0.115 ± 0.158 + 0.133 5:0.125 ± 0.137 + 0.162 5:0.230

Tki n =

OCM 48.4 53.9 58.9 66.0 77.4

Tkin = 1.095 GeV 41.0 45.2 52.2 58.9 65.9 73.6 83.3

0.389 0.556 0.838 0.625 0.678 0.734 0.263

5:0.086 5:0.075 + 0.133 _+0.137 5:0.150 5:0.194 5:0.254

0.934 GeV Exp. value 0.675 0.506 0.530 0.522 0.635

+ 0.123 5:0.136 5:0.126 +_ 0.140 5:0.143

Tun = 1.295 GeV 40.6 45.4 52.6 58.8 65.8 74.1

0.580 0.705 0.746 0.838 0.430 0.380

5:0.080 ± 0.076 5:0.145 ± 0.188 5:0.187 5:0.227

Donon Tki n =

33.4 35.9 37.9 40.8 46.0 52.6 59.2 66.2 74.4

1.596 GeV 0.558 0.801 0.754 0.671 0.607 0.842 0.537 0.767 0.768

+ 0.130 5:0.140 + 0.163 5:0.126 5:0.136 5:0.185 5:0.219 5:0.234 5:0.279

Tkm = 1.796 GeV 32.1 36.6 43.5 56.8 66.0 78.1 89.8

Tkin = 2.396 GeV 32.6 62.8 82.0

0.741 + 0.196 0.792 5:0.205 0.585 5:0.219

0.486 0.759 0.696 0.784 0.596 0.577 0.580

5:0.155 + 0.183 _+ 0.152 5:0.126 5:0.177 5:0.148 5:0.256

Tmn = 2.696 GeV 39.0 85.0

0.763 + 0.097 0.624 5:0.223

Tti,, = 2.096 GeV 30.6 35.9 38.0 40.9 45.8 55.4 66.1 73.9 86.8

0.568 0.624 0.957 0.852 0.606 0.436 0.325 0.534 0.324

5:0.074 _+ 0.156 _+ 0.167 _+ 0.133 _+ 0.149 _+ 0.187 ± 0.268 ± 0.305 + 0.241

290

C.D. Lac et al. / pp elastic scattering (II) TABLE 2 Observable Ko..o in pp elastic scattering. Tun is the beam kinetic energy. Errors are statistical and random-like instrumental uncertainties. Systematic errors (not shown) are + 7 percent (relative) for each set.

Konno Tkin = 0.834 GeV 0CM 49.0 53.8 58.8 65.8 73.8 82.0

Exp. value 0.267 0.544 0.415 0.659 0.774 0.787

± ± ± ± ± ±

0.140 0.128 0.102 0.102 0.119 0.176

Tkin = 0.874 GeV 0CM 46.4 50.3 53.9 58.9 66.1 73.8 82.3

Tkin = 0.995 GeV 49.2 54.0 59.0 65.9 73.9 81.4

0.458 0.718 0.517 0.939 0.701 0.626

± ± ± ± ± ±

0.152 0.143 0.131 0.149 0.185 0.257

0.269 0.152 0.470 0.506 0.452 0.224 0.363 0.716 0.705

+ 0.109 ± 0.120 ± 0.085 ± 0.119 ± 0.141 ± 0.157 ± 0.169 _+ 0.201 ± 0.181

41.0 45.2 52.2 58.9 65.9 73.6 83.3

0.168 _+ 0.226 0.322 + 0.180

± ± ± ± ± ± ±

0.089 0.123 0.103 0.095 0.106 0.125 0.180

48.4 53.9 59.0 66.0 77.4

0.296 0.500 0.894 0.656 0.714 0.738 0.623

± ± ± ± + ± ±

0.068 0.060 0.117 0.120 0.131 0.172 0.226

34.3 43.5 56.8 66.0 74.1 82.1

0.272 0.238 0.291 0.380 0.421 0.248

+ 0.113 _+ 0.143 + 0.117 + 0.163 + 0.185 + 0.207

Tki n = 2.696 GeV

39.0 85.0

0.294 + 0.099 0.312 + 0.235

E x p . value

0.555 0.634 0.679 0.728 0.741

± ± ± ± ±

0.102 0.113 0.104 0.115 0.118

Tkin = 1.295 GeV 37.4 40.6 45.4 52.6 58.8 65.8 74.1 83.5

Tkin = 1.796 GeV

Tkin = 2.396 GeV 26.5 50.7

0.393 0.367 0.697 0.649 0.709 0.767 0.865

0CM

Tvan = 1.095 GeV

Tkin = 1.596 GeV 33.4 35.9 39.3 46.0 52.6 59.2 66.2 74.4 84.3

Exp. value

Tkin = 0.934 GeV

0.389 0.409 0.498 0.665 0.543 0.325 0.671 0.444

± + ± ± ± ± ± ±

0.078 0.069 0.065 0.112 0.142 0.142 0.173 0.189

Tki n = 2.096 GeV

30.6 35.9 38.0 40.9 45.8 66.1 73.9 86.8

0.080 0.273 0.176 0.356 0.304 0.219 0.385 0.421

+ 0.072 +_ 0.152 + 0.162 ± 0.129 + 0.143 ± 0.243 + 0.277 +_ 0.219

C.D. Lac et aL / pp elastic scattering (If)

291

dependence of the observables Aoo.o, Aooo. and Aoo.. has been reported previously [2-4]. As was mentioned above Po.0o = No... = Aoo.o due to the Pauli principle and by time-reversal invariance (TRI) [25]. The result for Po.0o, representing an average over beam and target polarization, is obtained with relatively large statistical errors and may be affected by a possible instrumental asymmetry in the recoil polarimeter which is not cancelled out by beam or target-spin reversal. For this reason we assume Poo.o = No... =Aoo.o=Aooo. and we introduce in the analysis the wellknown data for Aoo.0 a n d / o r A0oo.. The determinations of Po.oo and No... were used only as tests of internal consistency of the measurements. The (82,~2) distribution in the second scattering on the carbon analyzer with known Pc =

10 O~

1.0

Q~ 08 O.d

06 Q: 0/4 (

02

~E

0

O~

0.8

Ol

v

Q,

0.6 CL i (3. v

0.4

o =

0.2

o r",,

Q: (:3

(

0 0.8 0.6 0.4 0.2 0

O, 934 GeV

.

.

.

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0

30

60

90

120 OCM (deg)

150

180

0

30

60

90

120 eCM (deg)

150

180

Fig. 1. Observables DOnOn(OCM)and Ko.no(180 ° - 0CM) in pp elastic scattering as a function of a scattering angle OCMat 11 energies. Error bars show statistical and random-like instrumental uncertainties. Full d o t s - Do,,o.(0CM ), this exp; full s q u a r e s - Ko..o(180 ° - 0CM), this exp; open s q u a r e s D.o.o(0cM), ref. [6]; open circles- D.O.O(SCM), ref. [7]; open diamonds - K.oo.(180 ° -0CM), ref. [8]; cross ( × ) - Dnon0(90°CM), ref. [9]; cross ( + ) - D.O.O(90°CM), ref. [10]; open triangles- D.o.o(0cM), ref. [11]; solid lines - PSA [12] predictions for D,,o,o(0cM). The present results are not introduced.

292

C.D. Lac et a L / pp elastic scattering (II)

P¢(02, T2), measured

with different combinations for the signs of PB and PT, forms a redundant set which allows one to remove some instrumental asymmetries. The observables Do,o, and K0,,0 are obtained as " p u r e " observables, i.e. the corresponding asymmetries do not depend on other parameters. Eq. (3.1) may be used to determine these two linearly independent parameters by the maximum-likelihood method. This method has been used in order to obtain first results. As mentioned in ref. [1], in the following analysis we have applied the momentum method, used with success and described by the Geneva University group [26, 27]. This method, adapted to our experiments, is treated in detail in ref. [28]. Several tests show that the maximum-likelihood method and the momentum method give the same results. 5. Results

The measured values for Dono~ and Ko,~0 are given in tables 1 and 2, respectively. The angular dependence of the observables is shown in fig. l a - k for 11 1.0 0.8 0.6 0.4 0.2 0

.................................

1

.

0

~

~

i++++

0.6

"~ 0.2

~d

1.796 GeV

2396Gev

h)

O

t l:

n

g g

1.0

r'~

0.6

:f

0.~

.

0

.

.

.

.

.

30

.

.

.

.

.

.

60

.

.

.

.

.

.

90

.

.

.

.

.

.

.

120

.

.

.

.

.

150

TI

!

.

180

0

eCM (deg)

Fig. 1 (continued).

30

60

90

120 150 ecM(deg)

180

C.D. Lac et al. / pp elastic scattering (lI)

293

energies. Here, the observable K0,,0(180 ° - 0 c M ) is plotted in the same figures as the observable Do,0,(0c~a). Below 1.3 GeV our results are compared with the Saclay-Geneva PSA predictions [12]. The results in the forward hemisphere are lower than the PSA predictions. The results for the same parameters measured with another beam and target-spin configuration confirm the present data and will be published in forthcoming papers. Present results below 1 GeV are compared with the Gatchina measurements of the parameters Dno,o = D0,on [6,7] and with the results of K,0o, = K0n,0 [8]. We plot also one point measured at the Birmingham accelerator [9]. At higher energies we compare our results with one point at 1.9 GeV measured at the BNL Cosmotron [10] and with three points at 2.205 GeV measured at the A N L - Z G S [11] (see, also, ref. [29]). We observe a good agreement of our results with the Gatchina data as well as with the Birmingham point. The BNL and ANL data points are higher than our measurements.

6. Conclusions

The results presented here, together with our results for the analyzing power Aoono = A0oo,, spin-correlation parameters Aoo,n, Aookk, Aoosk, the rescattering observable Nonkk, Dos,Ok,, Kos,,ko and with the data for the total cross-section differences Ao T and AaL, will contribute to an extension of the PSA towards higher energies. The present results are necessary for the direct reconstruction of the pp elastic scattering amplitudes. We are grateful to J. Arvieux, P. Borgeaud, G. Bruge, R. Hess, J.F. Detoeuf, R. Hess, P. Lehmann, A. Miller, P. Prugne, G. Smadja, J. Saudinos and J. Thirion for their support of this work, and to C. Lechanoine-Leluc and P. Winternitz for useful discussions and comments. We greatly acknowledge the assistance of M. Arignon, D. Benoit, S. Brehin, D. Gautherau, P. Genest, H. Martin, F. Petit and P. Veluard. The good performance of the accelerator was due, in particular, to R. Vienet and C. Fougeron and to the efforts of the operating crew. Special thanks are due to A. Nakach for carefully conducting the beam through the depolarizing resonances. Rapid tuning of extraction and external beam line at each change of energy was possible due to the beam-chamber system and corresponding programs developed by the group of G. Milleret.

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C.D. Lac et al. / pp elastic scattering (11)

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