c

Volume 50B, number 3

PHYSICS LETTERS

10 June 1974

MEASUREMENT OF THE REAL PART OF THE FORWARD SCATTERING AMPLITUDE IN K+p E L A S T I C S C A T T E R I N G B E T W E E N 0 . 9 A N D 2.6 G e V / c P.BAILLON, C. BRICMAN .1 , M. FERRO-LUZZI, J.M. PERREAU, R.D. TRIPP .2 and T. YPSILANTIS CERN, Geneva, Switzerland Y. DI~CLAIS.3 and J. SI~GUINOT University of Caen.4, France Received 1 April 1974 The differential cross section for K~p elastic scattering has been measured in the forward meson direction (0.0008 < t < 0.1 GeV2) in an electronics experiment at incident momenta between 0.9 and 2.6 GeV/c. The high statistics and absolute normalisation of the data allow a good determination of the real part of the forward nuclear scattering amplitude by means of the Coulomb-nuclear interference effect. We report on the measurements of the differential cross section for K~p and K - p elastic scattering at very small angles over the incident momentum region from 0.9 to 2.5 GeV/c. The range of angles covered by the measurements extends from ~ 2 0 to ~ 2 0 0 mrad, thus spanning the region from pure Coulomb to pure nuclear scattering. The purpose o f the experiment is to measure with a high degree of accuracy the effects due to the Coulomb-nuclear interference and use them to determine the real part of the forward scattering amplitude. There is no need to stress the importance of the later quantity, whether this be in connection with partial wave analyses where it represents an additional constraint on the amplitudes, or with dispersion relations for the determination of the KNA coupling constant. To our knowledge these are the first direct measurements o f the forward scattering in the momentum region reported here. The experiment has been performed in the M 7 beam of the CERN Proton Synchrotron. This is a onestage partially separated beam yielding K ~: up to 3 GeV/c; the kaon intensity ranges from a few hundred near 1 GeV/c to ~ 30 000 near 3 GeV/c for PS bursts of 1012 protons on the internal target, with IISN, Bruxelles. ,2 LBL, University of California, Berkeley. .3 Now at CERN. ,4 Work supported by IN2P3. ,i

a 400 msec spill time, a momentum bite of +- 1% and a rr/K ratio of ~ 15 at the highest momentum. Fig. 1 shows the experimental lay-out. The incident particles are defined by the C 1 and C 2 scintillators. The pion background is identified by the ethylene gas Cherenkov counter operated at pressures ranging from 3 to 25 atm. At the highest momenta, where the proton (or antiproton) background is noticeable, we have used the time-of-flight between C 2 and a counter 10 meter upstream, at the mass slit, to reject the unwanted particles. The target, a cylinder 25 cm in length and 6 cm i n diameter, is wrapped by 3 mm copper sheath (to stop 300 MeV/c recoil protons) and is surrounded by a box (Cpb) made of scintillator-lead sandwidches representing a total of "~ 3 radiation lengths. A small opening at the entrance wall of the box allows the incoming beam to reach the target; the exit window on the opposite wall subtends ~ 3 0 0 mrad from the center of the target. The purpose of the box is to reject interactions other than small angles scatterings. Both electronic tests and Monte Carlo simulations based on known differential cross sections agree in setting an upper limit of ~ 10 - 3 on the contamination of inelastic events which escape detection by the box and send a charged track through the front window. Turning now to the outgoing branch, C 4 is a round scintillator with a diameter optimized at each run to detect scatterings with a transferred momen377

Volume 50B, number 3

PHYSICS LETTERS

10 June 1974

Fe

C5

W

% W4 W5 CI

beo

~

-,r-,l[J

Wl

" 11

W2

El

If

/

,t----n

.=

target

I0 cm[.~ 20cm

uILl

Fig. 1. Lay-out of the apparatus.

tum q less than 20 MeV/c. The purpose of C4 is to increase the rate of useful data-taking by rejecting most of the unscattered (or multiple scattered) beam particles which might saturate the data acquisition system. The trigger condition is then ~ (or TOF < r). CI' C2"Cpb"(~4, where r is taken at each momentum so as to separate the K from the background of higher mass. Counter C3, subtending "- 100 mrad from the center of the target, is a permanent monitor of the state of the target. Anomalous fluctuations or wrong operations are easily detected and rejected. In addition, C3 provides the data for a measurement of the total cross section which, in turn, gives a check on our absolute normalization. Behind C3 is a block of iron of variables thickness (40 to 80 cm) whose purpose is to stop particles other than muons. The particles which traverse the block are detected by the 120 X 140 cm 2 scintillator C5 . This information is used with the corrections discussed below to discriminate against K~2 decays of the beam. The detection part of the apparatus consists of seven multiwire proportional chambers (W 1 to W7), two in the incident and five in the outgoing branch, with a total of ~ 4000 wires. Each chamber represents a set of two orthogonal coordinates (x, y) at 2 mm intervals. Details on the construction and operation of the chambers are given in refs. [1,2]. The maximum

378

recording rate of the data acquisition system is ~ 260 triggers per PS burst. The event reconstruction, done separately on the x- and y- projections, is different for the incident and outgoing branch. The incident track is defined only by two chambers and is reconstructed when two and only two sets o f x and y coordinates are available. This excludes from our sample 4,10 to 15% of the triggers. A detailed examination of the rejects shows that they are due to: a) accidentals, b) interactions in the Cherenkov counter or other material along the incident branch, c) inefficiency of the chamber. The outgoing track was reconstructed according to a procedure where all or a subset of the five available chambers were used in a least-square fit. The procedure is based on the use of single unambiguous coordinates to select the correct coordinates in other chambers where ambiguities may exist and makes the maximum use of the redundancy of the outgoing branch to ensure a reconstruction efficiency near to 100%. From the observed x2-distributions we have determined the average geometrical uncertainty of a coordinate over a 5-point track to be + 0.6 mm. A X2 cut at the 1% confidence level is then applied to each track so as to reject the possible decays occurring in the region between W3 and W7. The incident and outgoing track having been determined, the distance

Volume 50B, number 3

PHYSICS LETTERS

Table 1 Total data taken (all categories) and number of events after reconstruction and cuts. F is for full- and E for empty-target data. Momentum (GeV/c)

Triggers (106) F E

Eveiatsaccepted (103) F E

(a) K-p

0.935 1.181 1.418 1.620 1.790 2.608

2.5 1.8 4.6 1.4 8.8 7.4

1.1 0.7 1.8 0.7 3.5 3.5

19.0 23.2 83.0 28.8 112.1 102.3

2.6 4.2 18.7 6.6 29.8 34.5

(b) K÷p

1.209 1.798 2.608

3.2 3.5 4.2

1.1 1.4 2.1

40.2 78.7 112.1

9.8 21.9 41.4

of closest approach is then calculated and a cut-off applied on the events which exceed the limits expected from the multiple scattering and the geometrical uncertainty. The interaction vertex is next defined as the point of minimum distance from the two tracks; events with vertices falling outside the geometrical boundaries of the target are discarded. The effects of the last two cuts is to reject: a) decays occuring between the interactions point and the chamber W3, b) interactions taking place outside the target, c) spurious track combinations due to accidentals or secondary interactions. In particular - due to the second cut - the full/empty target ratio is increased considerably. The events are then subdivided respectively in the "/a" or "~" category depending on their association or not to a C 5 signal. The presence of direct Ku2 decay of beam tracks along the target is clearly evident in a detailed comparison of the "/a" and " ~ " events, particularly for the empty-target runs. When calculating the cross section we have systematically used the "~" category, relegating the "/a" events to a role of comparison and control. Another category of events acquired and used specifically as a control set is that for which the trigger condition C4 was dropped. Triggers of this type were accepted at regular intervals during the data acquisition at rates of ~ 10% of the total. This category of "beam" events consists mostly of unscattered particles and has been used mainly as a check on the normalization and the acceptance correction at small values of t. The data-taking procedure consisted of alternating full and empty runs. Typically, one full tape contains

10 June 1974

~ 3 . 5 × 105 triggers and was taken in one hour. Table 1 gives the total number of triggers accumulated at each momentum together with the number of accepted events (q t> 20 MeV/c) used for the cross sections. Most of the rejected triggers are q < 20 MeV/c scatters retained by the C4 anticoincidence because of the beam spread. The cross sections were calculated by a full-empty target subtraction and subjected to the corrections summarized below. The incident flux, counted by the ~" C 1 • C 2 coincidence, was corrected for: a) decays occuring between C 2 and the middle of the target, b) absorption through the first half of the target (only for full target runs), c) 6-rays emitted during traversal of the target which trigger the Cpb box (only for full target runs), d) beam contamination due to decays between C and W 1 . The number of outgoing tracks was corrected at each angle for: a) the geometrical acceptance of the apparatus (chambers W3 to W7, front window of the box, limit on small angles imposed by C4) b) the rejects due to recoil protons sufficiently energetic to traverse the target and trigger Cpb, c) the contamination of backward scatterings, i.e. events where the meson escapes Cpb through the entrance opening and the proton is seen by the outgoing branch, d) the decay of scattered particles between the target and the last chamber, e) the absorption of the scattered particles through the target, f) the ×2 cut of the reconstruction program, g) the contamination of particles other than muons going through the iron and triggering C5 . The above corrections, calculated via Monte Carlo whenever necessary, depend generally on the angle and the incident momentum. Most of them do not exceed a few percent. Notable exceptions are the decay corrections which are as large as 34% at the lowest momentum, the effect due to the transmission through the iron which is as much as ~ 10% at the highest momentum and, finally, the backward scattering which is important only for K - at 0.9 GeV/c and K÷ at 1.2 GeV/c and requires a correction of the order of 10% for angle between 20 and 100 mrad. The results are shown in fig. 2 as a function of the momentum transfer t = q2. Over most of the t-region the geometical acceptance of the apparatus is complete. The full circles represent measurements for which the acceptance correction is smaller than "~ 10%, the empty circles indicate instead that the acceptance correction is important (reaching factors 379

Volume 50B, number 3

PHYSICS LETTERS

10 June 1974

K +p

K-p

104

,•

0.935 GeV/c

+°3 ~

,

",

1,181 GeV/c

i

1,209 GeV/c

j

~

£\

103

I01 \ \ "

+ I02

.

•

J

I0

1

-

v

t

,

o

L. o!',

~

!÷

I

t

I 0.04

0.02

,

1

J

i

I

I0

,

,

,

I. 6

!

0.~

,

,

,

20 GeV/c

0.0406

,,-,,+,+,

t+,

0.04

0.04

0.08

1,798 GeV/c

;

103

I05

I05

io 3 Iot ~

E

i01

''~'

I0= ;-\\ ' \ , ~

!\

\\ io b -0

I

0.02

1.418 GeV/c

o~ > O) ~. ..Q

I

0

10 4

o+.i

'°,

102

_

i ~ . 1 "'-. L

0

I0

i

0.004

I

0

O.OOB

1

l

i

t

I

i

0.004

I

',, +

-: .

!

"-.

,

I

1.7 9 0 GeV/c

,

0t308 _

I

,

I,

2 . 6 0 8 GeV/e

2 . 6 0 8 GeV/c

103 ~

1

102

to' -\ ",,

i0 !

io 2

°ol

o,(~4

+c ~',

0.0<36

,

0

A

",'"-. , 0.004

0,008

IO

~.

--

0

I

i

I

004

I

i

i

1"~- =

o

'$ i

t

\\ ,,,

e

0,004

•

e

i 0ore

q

°

I

008

0

0.04 t (GeV

0.08

0

0.04

0.08

2)

Fig. 2. K+p and K-p differential cross sections as a function of the momentum transfer at the incident momenta given on the graphs. The insets reproduce in detail (0 ~ t ~ 0.01 GeV 2) the region of the interference. The points at t = 0 give the forward cross section expected from the total cross section via the optical theorem for a zero real part. The dashed, dotted and dash-dotted curves show respectively the contribution to da/dt due to the nuclear interaction, the Coulomb interaction and the interference between these two (absolute value). The solid curve is the result of the fit.

380

Volume 50B, number 3

PHYSICS LETTERS

10 June 1974

Table 2 Result of the fits. The number of degrees of freedom ND is indicated beside the x2; the limits of the fitted t-region are tmin and tmax. The real part of the forward scattering amplitude (D) is in the laboratory system and has been derived from c~and ot. Momentum (GeV/c) (a) K-p

0.935 1.181 1.418 1.620 1.790 2.608

(b) K+p

1.209 1.798 2.608

b

ot (rob)

×2 (ND)

tmin tmax ( 10-2 GeV2)

± 0.03 -+0.05 ± 0.03 -+0.03 ± 0.02 ± 0.03

11.7 +- 1.6 4.8 ± 0.7 7.8 ± 2~9 8.6 +-0.4 7.2 ± 0.3 7.8 ± 0.3

45.3 ± 0.5 37.7 ± 0.4 31.3 ± 0.3 34.3 ± 0.3 31.6 ± 0.2 27.7 ± 0.2

34.7(32) 28.3(40) 43.6(48) 52.6(55) 48.6(56) 41.2(54)

0.08 0.12 0.10 0.14 0.10 0.15

4.0 6.0 8.0 10.0 10.0 10.0

-0.43 ± 0.04 -0.45 -+ 0.02 -0.44 +-0.03

0.4 ± 1.5 2.5 +-0.4 3.3 ± 0.3

18.5 ± 0.2 18.0 ± 0.1 17.6 ± 0.2

26.1(34) 52.1(54) 66.9(50)

0.07 0.14 0.33

6.2 9.7 9.8

a 0.52 0.02 0.21 0.20 0.04 0.00

of 2 or more at the largest t-vatuas) and are shown only to illustrate the continuity of the data near the boundary of the fits discussed below. It should be pointed out that the errors shown, although including some systematic effects, are mainly due to statistics alone; we estimate that the total effect of the systematic errors does not exceed a 1% overall scale uncertainty. One can notice the following general features: i) At small t-values the data are dominated by the Coulomb cross section; we have verified by means of the " b e a m " sample that the direct multiple- and plural-scattering effects are well below our lowest t. ii) The Coulomb and nuclear cross sections are of the same order of magnitude in the region from t = 0.002 to 0.004 GeV2; here we expect the maximum interference effects between the two interactions. iii) Beyond t ~ 0.03 GeV 2 all cross sections are purely nuclear and appear to follow an exponential law. We have taken the form given by ref. [3] for the Coulomb amplitude and an exponential expression to represent the nuclear amplitude. The complete differential cross section has the form

do~dr = (do/dt)c + (d~o/dt)N + (do/dt)i where

(1)

D (fm) 0.88 0.04 0.37 0.45 0.09 0.00

± 0.06 ± 0.09 ± 0.05 +- 0.07 ± 0.05 ± 0.08

-0.38 -+0.04 -0.59 +- 0.03 --0.81 ± 0.05

(do/dt)l = _ 2 Q x / ( d o / d t ) c ' ( d o / d t ) N X (tx cos~ +Q sinS)/x/1 + tx2 . The cross sections are in rob, the m o m e n t u m transfers are in GeV2; the constants are A = 260.6 X 10 - 6 , B = 0.0511, Q = -+ 1 for positive and negative particles respectively; the Coulomb phase shift has the form = - [ln(9.5t) + 0.577]/137~. To account for the multiple scattering of the experimental tracks we have folded a Gaussian distribution over the theoretical expression (1); the root mean square of the Gaussian is taken at each m o m e n t u m from the spread observed in the "beam" sample. The folded theoretical values are then compared to the measurements and the free parameters ct and b of eq. (1) determined by 7(2 minimization. The/total cross section o t which also appears in eq. (1) is a known quantity; its value, taken from the best fit of two independent highprecision experiments [4], was introduced in each fit as an additional measurement and allowed to vary within + l % t . Table 2 gives the results of our twoparameters fits. The curves in fig. 2 show the distributions expected from these parameters for the differential cross section and for the separate contributions due to the Coulomb, the nuclear scattering and the interference between the two. The fits agree extremely

(do/dt)c = A((3 t) - 2 (1 +t/0.71) - 8 (do~dON = B o2(1 +or2) e -bt

t We have preferred not to use our own measurements of ot because, although in general agreement with those of ref. [4], they do not have a comparable reliability and accuracy.

381

Volume 50B, number 3

PHYSICS LETTERS

well with the measurements, perhaps even too well according to the X2. If one remembers that the Coulomb part of the cross section contains no adjustable parameters, this agreement supports our claim that the effect of systematic errors on the data is below the 1% level. In the above fits we made the assumption that c~ and b are constant with respect to t and that spinflip term is negligible. As for the latter, we have calculated its contribution from the available partial wave analyses and find it is smaller than 0.2%. As for t-dependent effects on ct and b, we have tried fitting these two parameters to separate linear expansions in t. The confidence levels of the fits are not significantly better than those of the t-independent solutions and the values at t ='0 are well within the errors of the latter. Thus, although the possibility of a t-dependence cannot be excluded, we retain the simpler assumption of constant ct and b as an adequate description of the data. Finally, table 2 lists the real parts D± of the forward scattering amplitude calculated using as imaginary parts the values deduced via the optical theorem from the total cross sections. A comparison with the pre-

382

10 June 1974

dictions of partial Wave analyses and dispersion relations shows that the former generally agree, qualitatively if not qualitatively, whereas the latter are mostly at variance with our results, particularly the K - p . These and the problem o f the determination of the NAK coupling constant are further discussed in the following letter [5]. The support of Professor Ch. Peyrou has been very much appreciated. We thank G. Amato and E. Chesi for their invaluable technical contributions.

References [1] G. Amato, E. Chesi, Y. D~clais and J. Se~uinot, CERN internal report D.Ph.II/17-3-1970, presented at the Dubna Int. Conf. on Instrumentation for High Energy Physics (1970). [2] E. Chesi and Y. Dgclais, A read-out system and fast coding logic for MWPC, CERN internal report D.Ph.lI/K72-1, unpublished. [3] M.P. Locher, Nucl. Phys. B2 (1967) 525. [4] R.L. Cool et al., Phys. Rev. D1 (1970) 1887; D.V. Bugget al., Phys. Rev. 168 (1968) 1466. [5] P. Baillon et al., Phys. Lett. 50B (1974) 383.