c

Nuclear

Physics

@ North-Holland

B244 (1984) 23-56 Publishing

Company

A MEASUREMENT OF m+p BACKWARD ELASTIC DIFFERENTIAL CROSS SECTIONS FROM 1.282 TO 2.472 GeV/c D.J. CANDLIN,

D.C.

LOWE,

K.J.

PEACH

and

L.R. SCOTLAND

Department of Physics, University of Edinburgh, Edinburgh,

UK

D.R.S. BOYD, C.J. BRANKIN, I.F. CORBETT, SM. FISHER, G.S. IOANNIDIS, P.J. LITCHFIELD and L.P. MAPELLI’ Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, UK E. ARIK’, M.G. GREEN, G.D. HALLEWELL’, B. POLLOCK4 and A. SHIRANI Department of Physics, Westjield College, London, UK Received

27 February

1984

New high-statistics measurements of rr+p elastic scattering differential cross sections are presented at 30 momentum points between 1.282 and 2.472 GeV/ c, covering most of the angular distribution outside the forward diffractive peak. These data show significant disagreements at some momenta with previous high-statistics experiments and with current partial wave analyses.

1. Introduction

There have been a number of experiments to study 7r’+pelastic scattering in the high-mass resonance region. However, there are only two high-statistics experiments [l, 21 which measured absolute differential cross sections over the whole angular range, and there are significant disagreements between them especially in the backward hemisphere. There are other experiments [3-51 which measured absolute differential cross sections over a restricted angular range, and one [6] which measured essentially only the shape of the angular distribution. There are also some older low-statistics experiments [7-141. In general, there is reasonable agreement regarding the shape and magnitude of the forward diffractive peak. The data reported here represent an improvement in statistical precision for the backward hemisphere, with more closely-spaced momentum points and an extended momentum range. They were obtained at the same time as data on the reaction ‘TI.+P + K+Z+. Some details of the apparatus and method are given in sect. 2; a full Present address: ’ CERN, Geneva, Switzerland. ’ Bogazici University, Bebek, Istanbul, Turkey. ’ Rutherford Appleton Laboratory. 4 Hansen Laboratories, Stanford University, Stanford, 23

CA 94305, USA.

D.J. Candlin et al. / n+p backward elastic differential cross seerions

24

description of the experimental apparatus and the main data-reduction system is given in ref. [15] (referred to hereafter as the KE paper). The data selection criteria are discussed in sect. 3, the acceptance calculation and Monte Carlo simulation in sect. 4, and the normalization in sect. 5. The results are presented in sect. 6, and compared with the partial wave analyses and with other experiments. 7 CYLS (only inner and outer shown)

UPPER COIL i

LOWER COIL J SECTION B-B (side view)

HIGH PRESSURE CHERENKOV COUNTER

B f

SECTION A- A

( top view 1

Fig. 1. Layout of chambers and trigger counters in the RMS magnet.

D.J. Candlin et al, / ~+p backward elastic differential cross sections

2. Experimental 2.1. THE

RUTHERFORD

25

apparatus and track reconstruction

MULTIPARTICLE

SPECTROMETER

(RMS)

The data were obtained in 1977/1978 using the Rutherford multiparticle spectrometer (RMS) at the NIMROD accelerator. The configuration of the principal detector elements within the large magnetic volume of RMS (-4 m ~2 m x 1.3 m) is shown in fig. 1. The beam entered the magnet along the major axis, and the main component of the magnetic field was along the smallest (vertical) axis. The beam position and direction were measured by eight MWPCs arranged along the beam, and the momentum was determined by two further MWPCs at the second horizontally dispersed focus. The beam trajectory was defined by two circular counters CO (diameter 20 mm) and C2 (diameter 80 mm) - see fig. 2. Particles outside this trajectory were vetoed by annular counters A0 and A2 surrounding CO and C2. Protons in the beam were rejected by time of flight supplemented by a pressurised threshold Cherenkov counter above 1.9 GeV/c. Below 1.9 GeV/c the Cherenkov was used at atmospheric pressure to veto electrons. The remaining lepton contamination varied from about 17% at 1.3 GeV/c to 6% at 2.5 GeV/c. The outgoing particles were detected by wire spark chambers, equipped with capacitative readout on both HV and LV planes. There were three groups of chambers: (i) Seven concentric cylindrical chambers, centred on the hydrogen target, with their axes vertical along the main component of the magnetic field; the wire pitch was 1 mm, with the HV wires vertical, and the LV wires at *14” to the vertical. (ii) Two double gap planar chambers to the side of the cylindrical chambers, and of similar construction, but with 1.5 mm pitch.

c2

Fig. 2. Detail

of the trigger

counters,

with A3 and A4 shown

“exploded”.

26

D.J. Candlin et al. / m+p backward elastic differential cross sections

(iii) Four double gap planar chambers spaced uniformly between the cylindrical chambers and the exit aperture of the magnet, with 1 mm pitch and wires angled at *15” to the vertical. The liquid hydrogen target was 150 mm long and 25 mm in diameter. 2.2. THE TRIGGER

The components of the trigger are shown in fig. 2. The principle of the trigger, used for both elastic scattering and K’E+ events, was extremely simple - an incoming beam pion producing a two-prong event with approximate coplanarity, but with no forward-going charged pion in the final state with a momentum of greater than - 1.25 GeV/ c. Approximate coplanarity and the two-prong requirement were imposed by the counters C6 and C7 in coincidence. For elastic scattering, the acceptance was essentially determined by the size of C6, except in the very backward direction. Most multi-prong events were vetoed by the counters A3 and A4, which covered the rest of the solid angle around the target, except for the beam entry aperture. At least one of the particles was required to enter the large planar downstream hodoscope Jl. Pions above - 1.25 GeV/c were vetoed over most of the active area of Jl by a large high-pressure Cherenkov counter which filled the exit aperture of RMS behind the hodoscope. Pions which passed through the hodoscope and into the iron return yoke were not vetoed, extending somewhat the angular range covered. A 100 mm square counter was placed behind the downstream hodoscope to veto non-interacting beam tracks which otherwise could trigger through Cherenkov inefficiency, if for example a delta-ray gave a count in C7. In order to keep the acceptance and resolution approximately constant, the magnetic field was scaled with momentum, reaching a maximum of 1.1 T at 2.5 GeV/ c. 2.3. THE DATA

Some 15.7 million triggers were obtained at 26 momentum settings between 1.282 and 2.472 GeV/ c. At least 250 000 useful triggers were obtained at each momentum, together with beam calibration runs and, at some momenta, target empty runs. For about half the momenta, a second batch of at least 250000 triggers was obtained. For most of the second batches, the momentum was sufficiently different from the first batch, due to different running and targetting conditions of NIMROD, that combination would lead to loss of information, since the statistics were adequate for each batch taken singly. At four of the momenta the two batches were, however, sufficiently close (momentum difference less than -10 MeV/c) that combination was possible. For five of the early batches, the MWPC measuring the beam momen-

D.J. Candlin et al. / rr+p backward elastic differential cross sections

27

turn were not working correctly, and these have not been used in this analysis. Data are thus presented at 30 separate momentum points, with an average spacing of about 35 MeV/c and a typical momentum spread of 10 MeV/c. The proportion of backward elastics in the trigger varied from about 14% at the lower momenta to about 2% at the higher momenta. Details of the data analysed in this paper are given in table 1.

TABLE

Summary Incident

of the data samples

momentum

1

at 30 momentum

Centre-of-mass energy

points

Triggers analyzed

Elastic events

mean

r.m.s.

(GeVlc)

(GeVlc)

1.282 1.322 1.338 1.371 1.392

0.006 0.006 0.010 0.010 0.008

1.822 1.841 1.850 1.866 1.878

420 000 37 1000 273 000 394 000 209 000

56 60 42 56 33

169 020 003 808 670

1.419 * 1.490 1.518 ‘1.588 1.615

0.006 0.010 0.006 0.010 0.007

1.891 1.926 1.939 1.970 1.985

367 677 363 767 348

000 000 000 000 000

62 92 56 88 37

091 909 004 593 345

* 1.682 1.713 1.771 1.808 1.863

0.012 0.007 0.008 0.008 0.008

2.019 2.03 1 2.058 2.074 2.099

804 359 399 466 403

000 000 000 000 000

74 777 32 203 32 195 32 394 21561

1.906 1.965 1.997 2.065 2.098

0.010 0.008 0.010 0.008 0.009

2.118 2.144 2.158 2.187 2.202

394 345 359 333 383

000 000 000 000 000

19 437 16 275 14713 13 318 14944

2.152 2.196 *2.241 2.29 1 2.335

0.010 0.010 0.010 0.010 0.010

2.224 2.243 2.261 2.282 2.300

346 000 327 000 690 000 284 000 318000

11 889 10466 19784 7 646 7 839

2.354 2.379 2.429 2.445 2.472

0.010 0.011 0.010 0.010 0.011

2.307 2.318 2.338 2.344 2.355

326 375 394 380 397

The momenta

(GW

where two batches

are combined

000 000 000 000 000

7 908 8 085 7 565 6 709 7 828

are indicated

with an asterisk.

D.J. Candlin et al. / ?r+p backward elastic differential cross sections

28

TABLET

Summary of the spectrometer precision for beam, downstream and sideways tracks Typical errors for

dplp (Oh1 angles (mrad) horizontal position (mm) vertical position (mm)

Beam tracks

Downstream tracks

Sideways tracks

0.3 1 0.5 0.5

1 2 0.4 1.1

4 5 0.4 1.5

2.4. TRACK RECONSTRUCTION

Tracks were found and reconstructed in the beam MWPC and in the downstream spark chambers using the techniques described in the ILZ paper. A summary of the performance of the spectrometer is given in table 2. The distributions for the track residuals were consistent with those expected from the chamber construction and from multiple coulomb scattering, and the data distributions are well reproduced by a full Monte Carlo simulation of the detector. 3. Data selection 3.1. PRELIMINARY

REMARKS

After track reconstruction a vertex was formed (if possible) between each outgoing track and the beam track. For tracks where this simple vertex fit was successful, the missing mass squared was calculated for pion and proton mass assignments to the outgoing particle. These quantities and their errors, together with the vertex and the point of intersection with the downstream hodoscope, were used in the selection. The basic requirement for the selection procedure was a single track entering the downstream hodoscope with an appropriate missing mass. A kinematically constrained fit was carried out on a sample of the data but was not used for the main analysis. The sample study showed that full kinematic fitting made no improvement in the data selection, but would have led to the unnecessary loss of a substantial fraction of the data. It would also have doubled the already large amount of computer time used. The selection and analysis of the elastic events was based only on the information available after track reconstruction and vertex fitting. The kinematical reconstruction was, however, very useful on a sample of the data, to check the effects of various cut strategies on a selection of good elastic events, and to provide support for Monte Carlo studies of such effects [ 161. The kinematic ambiguity, where both the pion and proton have the same laboratory momentum and angle, was close to the observed angular region for momenta above about 1.9 GeV/ c. The method for dealing with events near this ambiguity is discussed in subsect. 3.4.

29

D.J. Candlin et al. / ~+p backward elastic differential cross sections 3.2. GEOMETRICAL

CUTS

Events were retained for analysis which had one and only one “downstream” (D) track scattering on the opposite side of the beam direction from the side chambers and entering the downstream hodoscope. This track was required to traverse an area of C6 smaller than the physical size of the counter. Cuts were applied to select only well-measured tracks which formed a good vertex with the beam track in the hydrogen target. A cut on the downstream hodoscope rejected tracks which were consistent with pions from forward elastic scatters, but which entered the Cherenkov and failed to veto (perhaps because the pion interacted in the Cherenkov wall).

3.3. KINEMATICAL

CUTS

The missing mass squared distributions to all tracks satisfying the above selection criteria at 1.906 GeV/ c are shown in fig. 3 for both proton and pion mass assignments. The peaks corresponding to both backward and forward scattering are clearly distinguishable, above a background which is respectively -20% and -60%. Also shown on these histograms are the same data after all selection criteria have been applied. The background is considerably reduced, and arises mainly from the tail of the distribution from elastic scattering with the proton and pion tracks interchanged. It was observed that there were small distortions in the central value of the missing mass squared distributions which were approximately linear in cos 8, probably arising from residual misalignments and from small systematic uncertainties in the *lO

3 I

”

Q

< 700 s

(b)

T! 600 9 0 ‘;; 500 E b

400

1.2 0.6 0.4

100

0 0.4 (Missing m0s.s)~ to the proton (G&/cl>

‘IId I

0.5

I

I

0.6 0.7 (Missing moss)l

I

,

-‘ld

0.6 0.9 1. to the pion (GeV/cl).

Fig. 3. The missing mass squared to downstream tracks after geometrical cuts for data at 1.906 GeV/c, assuming (a) the proton mass, and (b) the pion mass. The dashed historgrams are for the same data, after all cuts have been applied.

30

D.J. Candlin et al. / m’p backward elastic differential cross sections

field map. Thus, for each downstream track, a quantity x(D, i) was defined for each mass assignment (proton for backward scattering - x(D, p) - and pion for forward scattering - ,Y(D, 7~)) such that (x(D, i)) = 0,

(~0% 9’) = 1 ,

with

where M is the missing mass to particle i; m is the corresponding recoil mass; c is the estimate of the error on M*; 0 is the centre-of-mass scattering angle for the track, assumed to be the proton; R, a, b are parameters which were determined in a preliminary pass through the data. The average values of Ia\ and (bl were 0.4 with r.m.s. deviation 0.5, and the average value of R was 0.2 with r.m.s. deviation 0.2. The distributions of x(D, i) are shown in fig. 4 for a, b and R at their initial values of 0, compared with the same distributions after fitting for a, b and R, for data at 1.906 GeV/c. The scaling ensured that the effect of the cuts was essentially independent of cos 0, and by separately calculating R, a and b for the Monte Carlo, that the effect of the cuts was similar for Monte Carlo and data. Events were rejected if both Ix(D, p)I and Ix(D, T)I were greater than 5. Although the main selection was based on the measurement of the downstream track, and cos 8 was computed from this track and the beam track, the second track was reasonably well measured for the majority of events. (There was an effective cut of 0.15 GeV/ c for the momentum of the second track, below which the program could not attempt a satisfactory reconstruction.) For events where such a “sideways” *lo 7

P J 1.75

3

r

5

F lLJ1.5

$800

-

I d 700

-

(b)

1.25

1.

0.75

0.5

0.25

X(D.n)

XKbP)

Fig. 4. The distribution

of x(D,

i) for (a) proton, and (b) pion hypotheses, scaling (solid) for data at 1.906 GeV/ c.

before (dashed)

and after

D.J. Candlin et al. / r+p backward elastic differential cross sections

31

20

15

10

5

0

-5

-10

-20

1

I -0.12

I -0.08

I -0.04

‘\I/. 0.

,

I

I

I

0.04

0.08

0.12

Angle difference (Radians)

Fig. 5. The coplanarity versus the difference between the predicted and measured angles of the sideways track for two-prong events, assuming conservation of momentum. The straight lines show the cuts applied to reject events which do not satisfy momentum balance.

(S) track could be identified, and was well enough measured, cuts were applied on the coplanarity and the angle difference between the observed direction of the sideways track and that predicted from the beam and downstream tracks; fig. 5 shows the scatter plot of these two quantities for data at 1.906 GeV/c. The elastic events are seen, against little background. The cuts applied are shown on the figure, and were constant at all momenta. For the events which survived, the appropriate ,y(S, p) and x(S, T) were formed, as for x(D, i), and an event was rejected if x(B)’ = x(D,

P)’ +xK

r12>

9,

x(F)‘= x(D, r)‘+x(S,

~)~>9.

Fig. 6 shows x(D, i) versus x(S, i) at 1.906 GeV/c for the backward and forward elastic scattering hypotheses, and shows very little background outside the cuts indicated by the dashed line. However, events which are nearly kinematically ambiguous are clearly to be seen in the upper right of fig. 6a, and the lower left of fig. 6b. Studies of data and Monte Carlo distributions indicated that the few remaining events outside the x cuts which cannot be attributed to the kinematic ambiguity were probably genuine elastic events, where some scattering on the incoming beam or outgoing tracks caused the event not to fit well to the elastic hypothesis.

D.J. Candlin et al. / rn+p backward elastic diferential cross sections

32,

3

vi

z

‘...’

‘,

4

.,.

. .

.’

,:

a s

.

. . .,

x

.,

4-

.'.. ,
'. ---,_

:

2-

o-

-2

-

-4

I -4

I -2

I 0

I 2

I 4

I

.;,

‘.‘.’ -4

I

I

I

I

-2

0

2

4

I

X(OJ)

Fig. 6. The distribution of (a) x(D, p) versus x(S, r), and (b) x(D, n) versus x(S, p) for data at 1.906 GeV/c which satisfy momentum balance. The main accumulation of data for the appropriate hypothesis is clearly seen. The events in the upper right of (a) and lower left of (b) arise from elastic scattering with the pion and proton interchanged, but otherwise similar configurations.

3.4. EVENT

ASSIGNMENT

The final data consisted of both two-prongs and one-prongs. The two-prongs were classified as backward elastics if Ix(B)1 <3 and ]x(F)I> 3, and as forward elastics if Ix(F)1 <3 and IX(B)) > 3. If both Ix(~)1 and [x(F)1 were less than 3 the events were assigned to both values of cos 8 with a weight given by the relative probabilities of the two hypotheses based on the corresponding x( D, i). The two-prong events have little or no non-elastic background. The one-prongs were classified as backward or forward if the appropriate Ix(D, i)l < 2.5. The one-prongs had a significant background, which arose mostly from the reaction rTT+rop, from genuine elastics where there was considerable scattering on the incoming beam or outgoing downstream track, and from interactions off bound protons in the walls of the target vessel. The background under the one-prongs was taken to be linear in the appropriate x(D, i) distribution. As noted above, the one-prongs were mainly in the region cos 0 < -0.8. Since there is no physical process which can give a missing mass to the forward proton of less than the pion mass, it was assumed that events with x(D, p) < -2.5 arose from genuine elastic events which were, for some reason, poorly measured. It was further assumed that a similar number of events would also have x(D, p) > 2.5, and the balance of the events with 2.5 < x(D, P) < 5 were assumed to be a measure of the one-prong background, and was subtracted from the data. Monte Carlo studies of the ~+.rr’p channel, and fits to the shape of the Monte Carlo and data x(D, i) distributions

D.J. Candlin et al. / ~+p backward elastic digerential

cross sections

33

with a linear background term, indicate that this procedure is justified. The background subtracted in the region of cos 8 < -0.8 varied from about 5% at 1.3 GeV/c to about 20% at -2.0 GeV/c, where the backward cross section is very small. 4. Acceptance calculation

and Monte Carlo simulation

The acceptance was determined by a full Monte Carlo simulation of the apparatus (see the K5 paper for details) producing a record identical to that for the real data, which was then passed through the same processing chain as the data. The events were generated with an angular distribution given by the Helsinki-Karlsruhe partial wave analysis [ 17]* in order to achieve statistically optimal weighting, and also to take into account any effects which might depend on the shape of the angular distribution. In order to take account of a loss of events arising through gating cuts on Jl, the time of arrival and the pulse height from each phototube on the hodoscope elements were calculated from a sample of events at each momentum which were unaffected by the cuts. The observed times were corrected for transit time and attenuation in the scintillator, and for time-slewing in the discriminator, using measured coefficients. Weak pulses were rejected, as well as those outside the timing gate. The average correction for the whole hodoscope as a function of angle and momentum is indicated in fig. 7. The cos 8 range was excluded if the loss was >30% for any one of the three hodoscope elements. With these cuts, the kinematic ambiguity point was outside the range of cos 8 covered by the data at all momenta. Some events at the edge of the accepted range were nevertheless ambiguous because of the finite resolution, and were assigned weights as described in subsect. 3.4. Pions corresponding to the region of cos 6 forward of the ambiguity point hit the forward hodoscope to the side of the Cherenkov where the pions are absorbed in the iron yoke of the magnet. For these events therefore the Cherenkov does not resolve the kinematic ambiguity. Only few events are affected by the ambiguity and so any systematic error introduced by the weighting is small. The angular distributions after all cuts for both data and Monte Carlo at 1.906 GeV/c are compared in fig. 8. The good agreement in shape of the raw data and the accepted Monte Carlo distributions gives confidence that the effects of the apparatus are well understood, and that the Monte Carlo calculation of the acceptance is a reflection of the acceptance of the apparatus. The mean acceptance was between 3% and 4% at all momenta. The cos 8 limits were determined at each momentum by demanding that the acceptance be everywhere greater than 20% of the maximum.

l

We are indebted to G. Hoehler for providing their results in an appropriate form.

34

D.J. Candlin et al. / m+p backward elastic difirential 6 0.5 .5 ?

1282

MeV/c

1419

MeV/c

_

1687

MeV/c

1906

MeV/c

.

2241

MeV/c

----_----_---

i fk e P 0.4 Q

.

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

cross sections

0.3

0.2

0.1

\

0.

-1.

1

-0.8

-0.6

-0.4

-0.2

0.

0.2

0.4

0.6 cos Q

Fig. 7. The average correction for the gating losses as a function of cos fI for a few momenta through the range.

Sufficient Monte Carlo events were generated at each momentum to give a statistical contribution to the final error on the differential cross section smaller than that from the data. 5. Normalization and systematic errors The factors affecting the absolute normalization (essentially, the incident beam flux and the number of target protons) and acceptance are discussed here in some detail. This is particularly important in this experiment because, especially at the lower momenta, the high statistical precision of the data means that the systematic uncertainties may be comparable to, or even greater than, the purely statistical errors on the differential cross section. In the discussion of the contributions to the systematic uncertainty in the normalization and acceptance, the upper limits quoted correspond to an estimate of the 68% confidence limit.

35

D.J. Candlin et al. / ~+p backward elastic differential cross sections

2.

700 .

$ z 9 W 600

a

Data

Mantecarla

500

-1.

-0.8

-0.6

-0.4

-0.2

0.

0.2

0.4

c 6 cas d

Fig. 8. The uncorrected

angular

distribution

at 1.906 GeV/c

far data and Monte Carla,

after all cuts.

The number of beam pions (identified by time of flight or using the beam Cherenkov counter) was corrected for lepton contamination, pion interactions and decays up to the target centre, and for electronic inefficiencies. The systematic uncertainty in the number of beam pions is estimated to be less than 4%. A sample of the data was scanned for two-prong events, and the results of the scan, when compared with the output from the reconstruction program, indicated an event-finding efficiency of the program of 97%. However, a similar study of Monte Carlo events showed comparable losses and, moreover, the regions of the chambers in which the losses occurred were similarly distributed for Monte Carlo and data. No explicit correction was therefore made. The uncertainty in the normalization from this effect is less than 3%. A study of “target empty” runs indicated that less than 1% of the events came from interactions in the target walls. A further correction of about 4% is required for those events lost when the downstream track interacted in the material surrounding the target, or in the material of the chambers, or decayed. The uncertainty in this correction is less than 2%. Data taken with the downstream Cherenkov excluded from the trigger indicated that the Cherenkov vetoed about 1% of the backward elastic events, with an uncertainty of less than 1%.

36

D.J. Candlin et al. / ~‘p backward elastic differential cross sections

The target density was determined to be 0.0706 g cm3 from the pressure and temperature of the liquid hydrogen, and the systematic uncertainty is negligible. The effective length of the target, determined by following beam tracks through the target, was 148 mm, with an uncertainty of less than 1%. Although the appropriate x distributions were scaled for both data and Monte Carlo events, there are nevertheless still small systematic differences between the data and Monte Carlo. These arise from backgrounds and non-gaussian tails in the data which are not reproduced by the Monte Carlo. A detailed study showed that the cuts rejected about 4% more data than Monte Carlo events, and a correction has been made. The uncertainty in this correction is less than 2%. The cuts on the Monte Carlo events to take account of the gating losses on the downstream hodoscope was subject to a systematic uncertainty estimated at about 20% of the correction; the absolute magnitude of this uncertainty varied from less than 5% at 1.282 GeV/c and cos 0 about 0.2 to less than 3% at all angles for momenta above 1.49 GeV/ c. In order to estimate the systematic uncertainty in the acceptance calculation, consistency checks have been applied, using statistically independent data samples. These are: (i) The downstream hodoscope Jl was constructed from three elements, allowing independent measurements of the differential cross section for cos 0 > -0.8. The ratio between the upper and lower elements is sensitive to the vertical position of C6 relative to the beam, and to the precise shape of the vertical profile of the beam. The observed ratio indicates that the effective vertical position is different in the data and Monte Carlo by less than 0.2 mm. Since the hodoscope as a whole is effectively shadowed by C6, the effect on the sum of all three elements is estimated to be less than 0.1% . Of more significance is the ratio of the middle element to the average of the upper and lower elements, which is sensitive to the lateral and longitudinal positions of C6 relative to the beam, and thus to systematic differences between the Monte Carlo and data acceptances. Departures of this ratio from unity were observed which were somewhat dependent on momentum and angle but corresponding to a systematic uncertainty in the acceptance of less than 5%. (ii) The data which were taken in two batches, widely separated in time but with nearly the same central value and distribution of beam momentum, are in good agreement in the shape of the angular distribution, and are systematically different in normalization by less than 3%. In addition to the above considerations, there is also the possibility that the differential cross sections might depend on the cuts imposed on the data. The final values for the differential cross sections are insensitive to the precise value of any particular cut, but may depend weakly but significantly on the strategy adopted. A measure of such dependence can be obtained by comparing the final results with those from a preliminary analysis [ 161.The main differences were that the two-prong

D.J. Candlin et al. / ?r’p backward elastic differential cross sections

37

cuts were much less stringent in the preliminary analysis, and the missing mass cuts were applied in a different way. Comparison of these analyses show differences in the differential cross sections of less than 5%, and do not show any marked momentum or angular dependence. It should also be noted that the K’Z+ total cross sections obtained by earlier low-statistics bubble chamber experiments show excellent agreement with those presented in the KX paper using the same Monte Carlo simulation and correction factors. There does not therefore seem to be any large remaining systematic factor affecting the acceptance. The sources of systematic error described above fall into two classes; those which are constant or which vary slowly with momentum and angle, such as counterinefficiencies, reconstruction inefficiencies and inadequacies in the acceptance calculation; and those which are discontinuous in momentum due to discrete changes in data-taking conditions between momentum points, such as beam profile and intensity. Because most of the contributions are known only as upper limits from the non-observation of certain effects, and because there may also be correlations between the various sources of systematic error, no single number can adequately describe the total uncertainty in the normalization. The systematic fractional error in the differential cross section and the correlation between neighbouring angles and momenta can be represented by E( p, cos 19)= A + B(p) + G( p, cos 0) where A is the mean systematic shift in the normalization for the whole experiment, B(p) is a discontinuous function of momentum which averages to zero, and where G(p, cos 0) is a slowly varying function of angle and momentum which again averages to zero. The best estimates for A, B and G are, of course, also zero: the upper limits on the magnitudes of these quantities, with 68% confidence level, are 0.06 for A, 0.02 for B(p) at any given momentum, and 0.04 for G at any given momentum and angle. It should be noted that the smooth variation of G with angle at any given momentum ensures that the relative normalization between neighbouring bins of cos 8 should be smaller than 0.01. These estimates of the systematic errors on the differential cross section should be compared with the purely statistical errors, which vary from about 3% at 1.490 GeV/ c to about 10% at 2.472 GeV/ c. The uncertainty in the absolute momentum scale is determined by the uncertainty in the magnetic field integrals of
38

D.J. Candlin et al. / ~+p backward elastic differential cross sections

Fig. 9. Differential Helsinki-Karlsruhe

cross sections for ~+p elastic scattering at 30 momentum points, compared with the [17] (solid curve) and CMU-LBL [18] (dashed curve) partial wave analyses. Also shown are representative data from refs. [l-S, 13 and 141.

D.J. Candlin et al. / ~+p backward elastic differential cross sections

Fig. 9-continued.

.D

--_

--

D.J. Candlin et al. / ?r’p backward elastic differential cross sections

41

42

D.J. Candlin et al. / ~+p backward elastic differential cross sections

/ I .! /

Fig. 9-continued.

,

D.J. Candlin et al / ~+p backward elastic differential cross sections

43

6. Results and discussion The differential cross sections at each of the 30 momenta are shown in figs. 9a-e, and are compared there with the Helsinki-Karlsruhe [17] and CMU-LBL [18]* partial wave analyses. The data are also compared with representative data from other experiments [l-5,13,14] which have a momentum within 0.015 GeV/c of the RMS momentum; the data from these experiments have been interpolated linearly to the RMS momentum values. The differential cross sections have been entered into the Durham-Rutherford Appleton Laboratory high energy physics database and are also given in tables 3a-e. The errors shown on the figure and in the [191**, table are purely statistical. The gap in the differential cross sections arises from the geometrical and timing cuts on the downstream hodoscope. The RMS data exhibit differences in both magnitude and, to a lesser extent, shape over much of the momentum range when compared with the partial wave analyses. These are most clearly pronounced around 1.6 GeV/ c, where the differential cross sections reported here are 20-30% lower. The differences are also evident in the direct comparison with other experiments (especially the data of Abe et al.) shown in fig. 9. This disagreement was noted earlier [20] when a preliminary analysis of six-momenta through the range was presented, and indeed it was this observation which prompted the more detailed study presented here. In order to investigate further these differences, the RMS data have been compared in turn with the data of Abe et al. [l], Bardsley et al. [2], Sidwell et al. [3], Ott et al. [4], Jenkins et al. [5], Busza et al. [13] and Kalmus et al. [14]. The RMS data were interpolated linearly to the corresponding momenta of the other experiments. The relative normalization and beam momentum were allowed to vary in order to achieve the best x2 fit for the two data samples to describe the same distribution. The momentum was allowed to move freely within 10 MeV/c of the reported value, and constrained weakly for excursions outside this range. The results of this process are shown in figs. lOa-c for the scale factor, momentum shift and x2 per degree of freedom. Also indicated on fig. 10a is the estimated normalization uncertainty for the RMS data; the errors on fig. lob are taken as 0.5% for each experiment. Table 4 shows the average and r.m.s. spread for the scale factor, momentum shift and x2 per degree of freedom for each of the experiments. The following comments can be made: (i) There is no obvious or consistent trend in the momentum shifts. The results for the relative normalization change little if the momenta are fixed at their quoted values. In addition, the x2 obtained, allowing only a relative momentum shift, are significantly worse.

l

l We are indebtedto R.E. Cutkoskyand R. Kelly for providing their results in an appropriate * Those interested in access to the database should contact M. J. Whalley, Particle Data Group University of Durham, Durham DHI 3LE, UK.

form. (UK),

TABLE 3 Differential (a)

cross sections in p,b/sr for rr+p elastic scattering at 30 momenta in bins of 0.02 in cos 0 (the errors are statistical: systematic errors are discussed in sect. 5) Momentum

(GeV/ c)

cos 6

-0.97 -0.95 -0.93 -0.91 -0.89 -0.87 -0.85 -0.83 -0.81 -0.79 -0.77 -0.75 -0.73 -0.7 I -0.69 -0.67 -0.65 -0.63 -0.61 -0.59 -0.57 -0.55 -0.53 -0.51 -0.49 -0.47 -0.45 -0.43 -0.41 -0.39 -0.37 -0.35 -0.33 -0.3 1 -0.29 -0.27 -0.25 -0.23 0.45 0.47 0.49 0.51 0.53 0.55 0.57 0.59

1.282

1.322

I .338

1.371

1.392

1967+79 1285+41 1215*38 1041*34 868 * 28 755 * 27 655*25 582 * 23 548*23 518*22 526 f 24 485*21 514*23 580*25 616*27 557k.24 583 f 26 594~26 614*28 576+25 658 f 29 655*28 652 + 28 670 f 29 748 f 32 675 f 29 703 f 30 669*28 712+30 700*31 771*53 835 f 59 692 f 49 732+51 585 * 39 667 f 48 567~41 661*52

1774*69 1255*38 1126*34 1034*33 885 * 30 772128 699 * 27 588 f 24 614*25 560*24 557 f 23 593 f 26 526 * 23 569 * 24 572 f 23 689*28 698 f 28 660 f 26 683 f 26 802*32 813*32 802*31 868 * 34 832*31 919*35 905 f 34 937*35 852*33 859*34 961*38 816*32 917*38 885 * 37 766* 32 770*51 733 * 48 737 * 50 838*62

1927*85 1248+44 1265*45 1086+39 904*34 805 f 32 716k31 593 * 27 582*28 571+28 507 f 25 573 f 29 621+31 659+32 609 * 29 786*38 737 * 35 727 + 34 742 * 35 727 * 34 784+36 927 rt 42 937 +42 832~1~36 882*39 850*38 826*36 832*36 906 f 42 885*40 854*41 834 f 39 972 f 73 796 f 58 776* 59 692* 50 786*61 707 f 58

1479*62 1193*39 1061*34 981*33 811+28 756*28 592 f 23 590*24 561*24 500 f 22 584*26 567 f 25 574+24 566*23 680 f 28 705 f 28 749* 30 709+28 753 * 29 779 * 30 843 + 32 796 * 30 858 * 32 969 + 36 935 * 34 968 * 36 932 * 34 927 + 34 920+35 862 f 33 890*34 897*35 911*56 894* 52 860* 53 887*55 820+51 824+ 52

1659*82 1265 f 54 1132*46 1034*43 854*38 829*41 654*33 582*30 593*32 556+31 533*30 598*33 653+36 611+33 613*32 696 f 38 746+ 38 711*38 706 * 36 715*36 837*43 879 * 43 879*44 860 * 43 943 * 46 915*45 904*44 959 *47 902 f 45 976 + 48 923 f 47 960*51 997 f 84 863 f 70 803 f 63 907 f 73 760 f 60 790 f 64

614*32 642 * 32 661*31 692*31 778 + 34 813*38

NO*33 506*32 550*32 559*32 659*35 689 f 35 767~1~41

321*21 313*20 405 f 25 425 f 24 450*25 441~~25 528 f 34

259+25 270*25 298 f 26 393*31 346+27 433*31 438*31 466*38

665+32 672 f 30 791*34 811*33 940 f 38 965 f 36

(b) Momentum

(GeV/c)

CDS e

-0.97 -0.95 -0.93 -0.91 -0.89 -0.87 -0.85 -0.83 -0.81 -0.79 -0.77 -0.75 -0.73 -0.71 -0.69 -0.67 -0.65 -0.63 -0.61 -0.59 -0.57 -0.55 -0.53 -0.51 -0.49 -0.47 -0.45 -0.43 -0.41 -0.39 -0.37 -0.35 -0.33 -0.31 -0.29 -0.27 -0.25 -0.23 0.41 0.43 0.45 0.47 0.49 0.5 1 0.53 0.55 0.57 0.59

1.419

1.490

1.518

1.588

1.615

1691*67 1241*40 1022*32 919*30 782*28 700 * 26 619+24 595 * 25 547 f 23 554+23 533+23 567+23 603 * 24 637+26 710*28 759*29 814+31 786 f 29 864*31 846*30 831+29 916+32 983 f 34 931*32 1053*36 1054*36 1070*37 1024+36 1052*36 1042*37 971*35 1007+36 935 f 34 961*36 923 f 36 834*33 801*48 794*48

1376*45 1024+27 830+ 22 744*21 643 f 20 544* 17 492* 17 447* 16 450* 16 411*14 433* 15 458* 16 532* 17 549* 17 609* 19 648* 19 694+21 717*21 771*22 796 f 23 785+22 826 f 23 871*24 842 * 23 944i25 918*25 892 f 24 929 f 25 888*24 897 f 25 885 f 25 881*25 872+25 908*41 912*42 886+41 828+38 794*36

1011*45 824*31 663 * 24 566 f 23 462* 19 485 f 22 386;t 18 362+ 17 365+ 17 387+18 378* 17 407*18 461+20 479 f 20 594 f 24 602 f 24 641*25 690 f 26 717+27 754528 815*31 841*31 819*30 858+30 953 * 34 855*31 927 * 33 927 + 33 951*34 843 + 30 800*28 870*32 812+30 849 f 32 795*31 794*31 783 f 32 728 f 46

755*29 547* 18 449* 15 383*14 339* 13 294*11 261 f 10 266+11 254~‘~10 275*11 2705 10 311*11 356* 12 393*13 446* 14 468* 14 497* 15 546* 16 534+ 16 589* 17 602zt 17 639* 18 645+ 18 677+ 19 739 f 20 699* 19 738*20 756*21 688 * 19 727 * 20 716*20 697 + 20 679 f 20 646* 19 658 zt 20 702 * 33 676*31 634*30

508*31 414*21 367+ 19 341*19 268~~ 15 237;t 15 204* 13 207~1~14 190* 12 257+ 16 248* 15 270* 15 305zt 16 314* 16 400 f 20 405 f 20 446*21 503*23 484*22 520+23 568 f 25 524*23 608+27 587+25 647 f 27 615*26 675*28 577 * 24 660 * 28 661~~28 589*25 632*28 601*26 607 * 27 551*25 616*44 628 f 44 598 f 44

211+18 208rt 18 253 f 19 218* 16 268 rt 19 300*20 340 + 23 334 * 30

117*10 129*11 119*10 110*9 130* 10 125*9 148+ 10 157* 13 175*21

86*10 94*11 98+12 86;t 10 93*10 119*13 107* 15

125* 10 107*9 109*9 94*8 85*8 85~8 75*6 90*9 124* 17

118k.13 134* 17 91*11 106* 12 82*9 115*16 113*20

46

D.J. Candlin et al. / m+p backward elastic differential cross sections

(c) Momentum

(GeV/ c)

cos 0

-0.97 -0.95 -0.93 -0.91 -0.89 -0.87 -0.85 -0.83 -0.81 -0.79 -0.77 -0.75 -0.73 -0.71 -0.69 -0.67 -0.65 -0.63 -0.61 -0.59 -0.57 -0.55 -0.53 -0.51 -0.49 -0.47 -0.45 -0.43 -0.41 -0.39 -0.37 -0.35 -0.33 -0.3 1 -0.29 -0.27 -0.25 -0.23 -0.21 -0.19 0.35 0.37 0.39 0.41 0.43 0.45

1.682

1.713

1.771

1.808

1.863

383* 19 252+ 10 218*9 195*9 165*8 158*8 135*7 144*7 152+7 162+7 188*8 198*8 232+9 290*11 317*11 331*12 357* 12 360* 12 392* 13 411*13 441* 14 433 * 14 485* 15 496* 16 499* 15 498* 15 507* 15 522+ 16 511*15 508 f 16 520* 16 507* 16 527+ 17 487+ 16 478* 16 462+ 16 521*28 510*28

234* 18 222 * 14 169+11 163+11 131*10 112*8 100*8 112~1~8 142* 10 124+8 159* 10 185*11 175* 10 226* 12 242i 13 285* 15 302* 15 326* 16 329* 16 355+ 16 364* 17 408* 19 400* 18 407* 18 435* 19 469 + 20 453 * 20 440*20 474+21 439 f 20 446*20 465+21 427 * 20 422 f 20 416*20 414*20 396* 19 401*29

204 f 20 137* 10 142*11 99*8 102*8 99i8 91 l 7 99+8 103*8 112*8 117+8 145* 10 174*11 172* 10 228* 13 251+14 266* 13 279* 14 274* 14 293* 14 323* 15 362* 17 355* 17 366* 17 365 + 17 410* 19 375* 17 335* 15 359* 16 3695 17 351*16 386* 18 363 f 17 341+ 16 367* 18 343i 17 241+17 340* 17

108+ 10 107k-8 90*7 91*8 66*6 75*6 79*7 66*5 67*5 83+6 95*7 119*8 125*8 142*9 177* 10 176* 10 185* 10 203*11 225 f 12 239* 12 262* 13 293%15 276+ 13 280* 14 318* 15 342* 16 334* 15 315* 15 34O;t 16 295* 14 328+15 332+ 16 327+ 16 291 f 14 357* 18 333* 17 324* 16 273* 14 290+ 15 285 zt 15

75*9 65*6 75*8 74*8 79*8 62*7 49*5 42+5 48~1~5 57*6 74*7 85*7 92*7 129+9 128*8 151*9 176*11 195* 12 183zt 11 199*11 207zt 12 230+ 13 241* 13 260* 15 249* 13 248+ 13 244* 13 282+ 15 266* 14 284+ 15 296* 16 292* 16 249* 14 258* 14 255* 15 268* 15 249+ 14 242* 14 245*16

206* 212* 152* 155* 156*

216* 212* 202 f 197* 178*

271 f 261 f 230* 232~ 214+

164rt 11 157* 10 150* 10

17 18 13 13 13

15 15 14 14 12

18 17 15 15 15

299* 19 253 * 16 279* 18 259+ 17 202+ 14 216*15

47

D.J. Candlin et al. / m+p backward elastic differential cross sections (c)-continued Momentum

(GeV/c)

cos 9

0.47 0.49 0.51 0.53 0.55

1.682

1.713

1.771

1.808

1.863

128*9 130*9 134* 10 137* 12 149*21

149* 13 152* 15 155*17 136*20

166* 12 148;t 12 179* 19 174+28

182* 13 174* 14 223 zt 29

218* 17 184+ 19

2.065

2.098

(4 Momentum

(GeV/ c)

cos e

-0.97 -0.95 -0.93 -0.91 -0.89 -0.87 -0.85 -0.83 -0.81 -0.79 -0.77 -0.75 -0.73 -0.7 1 -0.69 -0.67 -0.65 -0.63 -0.61 -0.59 -0.57 -0.55 -0.53 -0.5 1 -0.49 -0.47 -0.45 -0.43 -0.41 -0.39 -0.37 -0.35 -0.33 -0.31

1.906

1.965

1.997

53*8 55*6 45*5 50*6 45*6 39*5 45*6 38+5 40*5 50*5 64*7 59+6 79*7 82*7 113*9 125+ 10 131*10 152+11 144*9 171*11 181*12 184*11 198* 12 188+ 12 219+ 13 229* 14 19911~12 256+ 16 245* 14 246* 15 221 f 13 235* 15 236+ 15 238* 15

32*6 43*6 29*4 32*5 33*5 33*6 31*4 41*6 37*5 41*5 46~~6 52+6 54*5 72+7 89*8 94*8 114*9 121*10 125*10 138*11 139* 10 166* 12 169* 12 187% 14 188* 13 207* 15 210+ 15 202+ 14 207+ 14 199* 14 210* 15 213* 15 194* 13 238* 17

25+5 31*5 39*7 31*5 32*5 18*3 25zt4 32*4 30*4 26*4 36*4 39*4 39*4 49*5 64*7 64+6 81*7 77*7 98*9 112*10 112i9 121*10 123* 10 124+ 10 137*11 148+11 154*11 155* 11 155* 12 129+9 171*13 146rtll 154* 11 163* 12

18*3 19*3 24*4 37*6 21*3 29*4 31*4 25*3 28+4 39*5 30*4 36+4 47*5 51*6 48*5 64*7 74*7 68*7 76*7 98*9 94*9 125*11 108~‘~10 130* 12 122* 10 118*10 126* 10 138* 11 142k 12 141*11 140* 12 154* 13 144*11

2656 20*3 23*4 26*4 24*3 17*2 24*3 23*3 24*3 34*5 27*3 24~~3 24*3 30*3 39*5 37*4 46*5 59*6 64+7 71*7 77*7 72*7 67*6 96*9 81h8 102*9 112* 10 110*9 108*9 105*9 129+ 11 114*9 122* 10 118*10

48

D.J. Candlin et al. / m’p backward elastic differential cross sections

(d)-continued

Momentum

(GeV/c)

cos e

-0.29 -0.27 -0.25 -0.23 -0.21 -0.19 -0.17 -0.15 -0.13 -0.11 -0.09 0.27 0.29 0.31 0.33 0.35 0.37 0.39 0.41 0.43 0.45 0.47 0.49

1.906

1.965

1.997

2.065

2.098

224* 14 213* 13 224+ 14 211+14 235+ 15

207;t 15 227~~ 16 182* 13 187*13 209* 15 179* 13 213*15

137* 10 164~1~12 160+11 162* 12 160* 12 173* 13 179* 14 182* 14

168* 14 156*13 132+ 10 158* 12 141*11 142*11 149* 11 151*12

112*9 103*8 103*8 103*8 120* 10 141*11 121*10 117* 10 119*9 126* 10 155*11

284*20 278 * 19 243* 16 270* 18 229* 15 245*17 247* 17 214+ 16 202+ 18 155*23

322*21 294* 19 247+ 17 266* 18 254;t 17 228 f 16 213 f 18 219*27

285 f 285 f 216* 239zk 240* 256+ 217* 192* 202 f

19 20 14 16 16 17 16 17 29

292+ 249* 248* 236* 256+ 236* 194* 245 f

19 15 16 15 17 16 15 25

253 f 17 245+ 15 266* 16 257* 16 245* 15 241+15 206* 13 211*14 246*21 211*28

(e) Momentum

(GeV/ c)

cos 9

-0.97 -0.95 -0.93 -0.91 -0.89 -0.87 -0.85 -0.83 -0.81 -0.79 -0.77

2.152

2.196

2.241

2.291

2.335

38*6 33*4 23*3 26*4 32+4 27+4 25*3 17*3 32*5 24*4 27~~4

60*8 47*6 31*4 20*3 31*5 23*3 28*4 28*4 23*3 24+3 31*4

80*8 46*4 38*3 30*3 25*3 29*3 23*2 29*3 27+3 30*3 33*3

94*11 58*6 38*4 33*4 29*4 33*4 29*4 29*4 29+4 33*4 37*5

83+10 62*6 37*4 35*4 30*3 44*5 42*5 38*4 36*4 34*4 47*5

D.J. Candlin

et at. / ~+p backward elastic diflerential

cross sections

49

(c)-continued Momentum

(GeV/ c)

cos 8 2.152 -0.75 -0.73 -0.7 1 -0.69 -0.67 -0.65 -0.63 -0.61 -0.59 -0.57 -0.55 -0.53 -0.51 -0.49 -0.47 -0.45 -0.43 -0.41 -0.39 -0.37 -0.35 -0.33 -0.31 -0.29 -0.27 -0.25 -0.23 -0.21 -0.19 -0.17 -0.15 -0.13 -0.11 -0.09 -0.07 -0.05 0.25 0.27 0.29 0.3 1 0.33 0.35 0.37 0.39 0.41 0.43

2.196

2.241

29+4 31*4 26+3 37*5 40*5 41*5 46&S 39*5 52*5 62*6 63*6 58*6 75+7 8OLt8 81*8 62*6 93*8 87*8 92*8 91*8 96*8 94*8 105* 10 97*9 94+8 95*8 117*10 97*9 87+8 108* 10 105*9 99*9 100*9

32*4 27*4 29*3 32*4 33*4 44*5 44*5 35*4 47*5 54+6 54*6 59+6 63*7 67*7 82*8 61*6 80*8 92*9 76~~7 74*7 90*8 56+5 73*7 81*8 86*8 79*7 79*8 109*10 74*7 99*9 86*8 96*8 87*8

35*3 31*3 27*2 32*3 29+3 33*3 42*4 46*4 44*4 40*3 47*4 47*4 58zt.4 52+4 61*5 54*4 62i5 63*5 64*5 59*4 65*5 64+5 68*5 67*5 63*5 71*5 66+5 68*5 70*5 74*5 82*6 80*6 86*6 86*6

229* 17 238~ 16 250* 16 225 + 14 232* 15 219+ 14 231+15 23Ort 15 202* 15 229 f 25

252* 17 235* 15 213* 14 228* 14 233 f 14 240* 16 209*13 202 * 14 226* 18 199*26

217k.11 216~~ 10 214* 10 208*9 228* 10 207+9 230*11 219* 12 210+ 16

2.291 24*3 30*4 26*4 32*4 34*4 24*3 31*4 31*4 42+5 35*5 34*4 46*5 52+6 35*4 56*6 49+6 42+5 54*6 46*6 48*6 51*6 44*5 44*6 46*5 45*5 54+6 47+6 48*5 57*6 62+7 59*7 75*8 67~~7 83+8 93*9 89*9 175* 12 195 f 14 186* 13 184* 12 208+ 13 215* 14 2Oli 15 187*17 275 +39

2.335 33*4 38*4 33*4 34*4 37*5 30*4 31*4 30*4 36*5 37*5 30*5 33*4 36*5 37*5 33*4 35*5 39*5 41*5 52*6 51*6 41*5 45*5 37*5 53*6 36*5 42*5 43*5 51*6 53*6 52+6 48*6 52*6 64*1 65*7 61*6 65+7 190* 13 197*14 237* 16 225+ 16 217* 14 232* 19 231*19 196+24

50

D.J. Candlin et al. / r+p backward elastic differential cross sections

(0 Momentum

(GeV/ c)

cos 9

-0.97 -0.95 -0.93 -0.91 -0.89 -0.87 -0.85 -0.83 -0.81 -0.79 -0.11 -0.75 -0.73 -0.71 -0.69 -0.67 -0.65 -0.63 -0.61 -0.59 -0.51 -0.55 -0.53 -0.51 -0.49 -0.47 -0.45 -0.43 -0.41 -0.39 -0.37 -0.35 -0.33 -0.3 1 -0.29 -0.27 -0.25 -0.23 -0.21 -0.19 -0.17 -0.15 -0.13 -0.11 -0.09 -0.07 -0.05

2.354

2.319

2.429

2.445

134* 17 64*-l 31*4 31*4 36*4 42*5 25*3 36*4 34*4 36*4 40*4 34*4 37*4 48*6 3s*5 31*4 39*5 34*5 34*5 31*5 38*5 34*5 40*5 40*5 42*6 33*4 46*6 31*4 42*6 38zt5 44*5 40*5 47+6 39*5 51*6 38*5 47*6 46*5 49*6 48+6 51*6 51*6 62*7 50*6 75*8 64*7

107*11 57*5 57*6 35*4 36*4 38+4 42*4 41*4 47i5 41*5 47*4 52*5 41*4 43*5 43*5 37*4 39*5 37*5 38*5 26+3 43*6 22*3 34*5 34*4 37*5 36*4 31*5 37*5 32*4 37*4 34*4 37*5 43*6 32*4 38*5 35*5 34*5 26*3 40*5 41*5 32*4 47*5 44*5 50*5 41*5 56*6 73*7

130* 14 82*7 45*4 37*4 33*4 39i4 38*4 31*4 44*4 50*5 51*5 42*4 49i5 38*4 40*4 42*5 40*5 35*5 36*5 50*7 24*3 32*4 30*4 26*4 32*5 26*3 34*4 41*5 30*4 25*4 40*5 27*4 28*4 44+6 31*5 34*5 28*4 32*5 27*4 32*4 24*4 33*4 32+4 36*4 41*5 49*5 56*6

109*11 74*7 48*5 38*4 37*4 34*3 40*4 35*4 43*4 44*4 41*4 41*4 43*4 45*5 38*4 30*4 35*4 29*4 33*5 41*5 29*4 36*5 34*5 37*5 31*5 38*5 29*4 26*4 30*4 30*4 28*4 32*4 33*5 28*4 25*4 24+4 25*4 27*4 24*4 25*4 21*4 31*5 30*4 38*5 43*5 41*5 54*6

2.412 164* 17 71*6 48*4 41*4 30*3 31*3 41*4 39*3 48*4 48*4 52+4 53*5 51*5 56*5 46*5 44*5 34*4 39*4 33*4 33*4 41*5 29*4 36*5 31*4 36*5 27*4 25*4 32*4 26*4 29zt.4 28*4 23*3 24*3 25*3 24*4 24*4 25*4 27*4 16*3 22+4 20*3 21*4 23*3 34*5 37*4 40*5 39*4

D.J. Candlin et al. / w’p backward elastic differential cross sections

51

(f)-continued Momentum

(GeV/ c)

cos 9 2.319

2.429

2.445

2.472

64*6 SO+7

60*6 67*7

55*6

56*6

2.354 -0.03 -0.01 0.25 0.27 0.29 0.3 1 0.33 0.35 0.37 0.39

237 f 16 233*15 233’* 16 203 f 14 202i 14 204+ 15 184+ 16 193+23

191*13 202* 14 189* 14 208* 18 261*31

200* 13 196+ 13 207+15 217+ 16 185+18

164* 11 183*12 201*14 176* 15 151*18

163*11 213+15 161*12 195* 18 164*22

Ml.

-7

025

-

0.

1

u

E

I

I

I

I

I

1.4

1.6

1.8

2.

2.2

24

1.4

16

1.8

2

2.2

2.4

’

1

-60L

' 14

I

I

I

I

I

16

18

2

2.2

2 4

MomentvmWI/c

Fig. 10. The results of the comparison of the RMS data with the data of refs. [l-5, 13, 141 showing (a) the relative normalization, (b) the momentum shift, and (c) the ,$ per degree of freedom of the fit. The dashed lines on fig. 10a are the estimated absolute normalization uncertainty of the RMS data: the errors on fig. lob are taken as 0.5%.

52

D.J. Candlin et al. / r+p backward elastic differential cross sections

1

Fig. 11. Comparison

with all experiments

at six-momenta.

D.J. Candlin et al. / ~r+p backward elastic diflerential

co5

cross sections

19

Fig. 12. Comparison with all experiments at the same momenta as fig. 11, after applying The measure of agreement is evident from the observation that the individual points indistinguishable

at the lower momenta.

53

cos ff

the scale factors. in this figure are

54

D.J. Candlin et al. / v+p backward elastic differential cross sections TABLET

A summary

of the average

Experiment

scale factors, momentum shifts and X2 per degree of freedom of other data with the RMS data Momentum shift

Relative normalization

X2 per degree of freedom

WV/c)

mean

r.m.s.

Abe Bardsley Sidwell

1.32 1.11 1.01

Ott Jenkins Busza Kalmus

1.13 0.83 0.98 1.13

for the comparison

mean

r.m.s.

mean

r.m.s.

0.13 0.08 0.06

-8 0 -14

0.32 0.06 0.11 0.11

0 -4 -10 -10

15 12 23 14 11 10 12

1.61 1.14 1.68 I .63 1.52 1.11 1.08

0.75 0.31 0.38 1.51 0.28 0.46 0.27

(ii) The scale factors required for the data of Bardsley et al., Sidwell et al., Busza et al. and Kalmus et al. (apart from the point at 1.43 GeV/c), are essentially independent of momentum. The values of the scale factors required are reasonably consistent with the estimated normalization uncertainties of these experiments. However, at momenta below about 1.8 GeV/ c, the RMS data seem to be consistently lower than these experiments by about lo%, although there is in general good agreement (as expressed by the x2 per degree of freedom) on the shape of the angular distribution. (iii) The comparison with Jenkins et al. is difficult to summarize briefly, in part because their data is mostly in the gap of the RMS data. If all of their data points at each momentum are included in the comparison, it would appear that the normalization of the RMS data is some 15-20% higher than that of Jenkins et al. However, if the data of Jenkins et al. forward of cos 0 = 0.1 is excluded from the comparison, the average and r.m.s. values for the relative normalization, momentum shift and x2 per degree of freedom are 1.04 f 0.14, -7 f 11 and 0.8 f 0.12 respectively. The data of RMS, Sidwell et al. and Jenkins et al. are reasonably consistent for cos t9< 0.1, and thus the problem lies in the data forward of this point. The principal feature of this region which could cause some difficulty is the kinematic ambiguity at about cos 8 = 0.15. In several of the angular distributions presented by Jenkins et al. there appear to be discontinuities in the region of the ambiguity point which could be a result either of misidentification of pions and protons, or of some relative inefficiency in detecting one of the particles. (iv) The data of Ott et al. and Abe et al. are inconsistent in this angular region with the results of other experiments, including RMS, over a wide momentum range; both experiments appear to have systematic differences in normalization which are a strong function of momentum, and which are significantly greater than the quoted errors on the absolute normalization. These variations cannot be ascribed to simple

D.J. Candlin et al. / ~r+p backward elastic differential cross sections

55

shifts in the beam momentum (see fig. lob and table 4). Abe et al. claim a normalization with a systematic error of less than OS%, although they increased it to 2-3% since differences of this order were observed between independent samples of their data. Because of the small quoted uncertainty in the absolute normalization of the data of Abe et al., these data have a dominant influence on the results of the partial wave analyses. It should also be noted that the x2 per degree of freedom is rather poor for the data of Abe et al. above 1.9 GeV/c, indicating that there are problems with the shape of the angular distribution whereas, apart from the lowest two momentum points, the final x2 per degree of freedom for the data of Ott et al. is quite good. As an illustration, fig. 11 shows the full comparison of the various data at six-momenta through the range, and fig. 12 shows the same data after applying the normalization scale factors from fig. 10. The agreement after scaling the normalization is good, except (as noted above) for the data of Abe et al. at the highest momentum. The RMS data have not yet been incorporated into the partial wave analyses. However, a preliminary investigation at the higher momenta [ 161 indicated that the RMS data might be accommodated by making changes to the individual partial waves within the errors quoted by the CMU-LBL analysis [18], if the normalization uncertainty was taken into account. 7. Summary and acknowledgments New data have been presented for 7r+p backward elastic scattering at 30 momentum points. The statistical precision and momentum coverage of the data is better than previous experiments in this momentum range. The data show significant differences with some previous high-statistics experiments [ 1,4,5], but are consistent with several other experiments [2,3, 13, 141. The disagreements cannot be ascribed simply to differences in momentum scale.

Our thanks are due to many people whose efforts have made this experiment possible, in particular, to R. Freeman, M. Gibson, M. Morrissey, R. Nickson, P. Pitts and I. Webb, without whom we could not have built and run the experiment, and to Mrs. J. Gale who scanned many thousands of events. We were also dependent on the dedicated work of all those who maintained and operated the NIMROD accelerator and the Rutherford Appleton Laboratory facilities. One of us (D.C.L.) would like to acknowledge the support of the Carnegie Trust for the Universities of Scotland. References [l]

K. Abe, B.A. Barnett, J.H. Goldman, A.T. Laasanen, and E.F. Parker, Phys. Rev. IOD (1974) 3556

P.H. Steinberg,

G.J. Marmer,

D.R. Moffett

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