c

Nuclear Physics B169 (1980) 365-372 © North-Holland Publishing Company

DIFFRACTION

D I S S O C I A T I O N IN T H E F I N A L S T A T E 0p'rr+'n - A T 12 G e V / e

G.W. VAN A P E L D O O R N , D. HARTING, D.J. H O L T H U I Z E N , B.J. PIJLGROMS, M.M.H.M. RIJSSENBEEK and J.M. W A R M E R D A M - D E L E E U W

NIKHEF-H/ Zeemanlaboratorium, Universiteit van Amsterdam, Amsterdam, The Netherlands" V. KARIM.AKI, R. KINNUNEN and M. K O R K E A - A H O University of Helsinki, Helsinki, Finland P. JOHNSON, P. MASON, P. MICHAELIDES, Ch. M I C H A E L I D O U , H. M U I R H E A D and G.D. PATEL

University of Liverpool, Liverpool, UK** T. M O A and Ch. W A L C K

University of Stockholm, Stockholm, Sweden Received 12 February 1980 In a study of 4.7k events of the reaction 0p~lSprr+~r - at 1 2 G e V / c a cross section of 0.57+0.04 mb and a slope of the t distribution of 14.8+ 1.5 G e V / c -2 for - t < 0.1 GeV 2 are obtained for the diffraction dissociation [~lS~r+~r -. This slope agrees with the slope of the t distribution for elastic Op scattering. Also the energy behaviour of diffraction dissociation is similar to the energy behaviour of elastic 15p scattering. A comparison is made with the analogous reactions in pp interactions.

1. Introduction It is w e l l - k n o w n that a certain fraction of the reaction lbp ~ ~p~+rr -

(1)

can be described by the diffraction dissociation mechanism as visualized by the diagrams of fig. 1, in which either p~plr+~r -

(2)

p-~ plr÷~r - .

(3)

or

This fraction is low at low values of the b e a m m o m e n t u m , but increases to almost " Part of the research program of FOM and ZWO. ** Supported by the SRC. 365

366

G. W. van Apeldoorn et al. / Diffraction dissociation

P

P

[

P

P

Fig. 1. Diagrams for diffraction dissociation.

100% in the hundred G e V / c region. The energy dependence of the cross section trD of this process, can be parametrized by the function trD = Cs-"

,

(4)

where s is the total c.m. energy squared. The s dependence given by relation (4) with , = 0 . 3 4 + 0 . 0 9 is found to be valid down to an antiproton b e a m m o m e n t u m of 7.2 G e V / c . This was shown in a study of antiproton interactions in the C E R N 2m H B C [1]. The proportionality constant C for diffraction dissociation in one vertex was found to be 1.56+0.05 where trD is in mb and s in G e V 2. To check the conclusions drawn at 7.2 G e V / c , also with respect to the t distributions, the analysis has been repeated at 12 G e V / c , again using the C E R N 2m HBC. A total sample of 4718 events of reaction (1) is available at 12 G e V / c . A subsample of 1057 p (~) diffraction dissociation events was isolated by the simple selection procedure on angular parameters described in [1]. This subsample represents 50% of the diffraction dissociation events of reaction (1).

2. Analysis of the diffraction dissociation sample The determination of the cross section for diffraction dissociation was based on a value of 2.35 + 0.11 mb for the cross section of reaction (1) at 12 G e V / c , which was obtained by comparison with the topological cross section for four-prong events. A cross section of 0.57 ± 0.04 nab was obtained for diffraction dissociation in each vertex. This value included corrections for scan and m e a s u r e m e n t losses. The result is in agreement with eq. (4) which for the given values of n and C predicts a cross section of 0 . 5 2 ± 0 . 0 2 rob. In fig. 2a the energy behaviour of the cross section for diffraction dissociation in one vertex is shown [1-4]. The results of the counter experiment at 25 G e V / c are not presented because a different mass range was used in that analysis [2]. The mass distribution of p~r+~r - for selected diffraction dissociation events is presented in fig. 3a and shows the characteristic peaks at 1.5 G e V and at 1.7 GeV.

G. W. van Apeldoorn et al. / Diffraction dissociation .

"~.g

.

.

.

.

.

.

.

i

.

.

367

.

.

.

.

i

a

.8

b

.'7

.5

.4 t.J .3

.2

o

~'o

~o

4"o 5"o " " :;o'o

200 ~o

s

( OeV

20

30

40 .o

~ ]

too

s

200 ( OeV

~ )

Fig. 2. T h e cross section of diffraction dissociation (in one vertex) as a function of s. (a) pp interaction, (b) pp interaction. T h e straight lines correspond to the p a r a m e t r i z a t i o n (4).

100

i

r

a

8 g -g

50

Z 3

2

H{

200

~

pn''rr"

4

[ GeV

]-CC

]

i

IOQ

o ~Q

Z. 0 0

.~

1.0 - L

I 15 [ GeV

2.0:t

Fig. 3. T h e p~r*~r- mass distribution (+cc) in (a) and the t distribution in (b) for the diffraction dissociation events. The curves correspond to the fit to the parametrization mentioned in the text.

368

G. W. van Apeldoorn et al. / Diffraction dissociation

The distribution of the squared four-momentum transfer t between incoming proton (antiproton) and outgoing prr+rr - (~rr+lr -) system is shown in fig. 3b. At 7.2 G e V / c both distributions were simultaneously parametrized in a phenomenological way. The same kind of fit was performed at 12 GeV/c. The mass distribution is described by a gaussian distribution for" the first peak (a Breit-Wigner did not fit here) and a Breit-Wigner for the second one together with another Breit-Wigner function with large width to describe the tail of the mass distribution. This parametrization of the mass distribution serves only to admit a fit to the t distribution and is used to take care of the mass dependence of tmin- The fitted parameters are given in table 1. The t dependence is approximated by exponential functions of t with slopes that have different values bl, b2 and b3 in three regions of t separated by the break points tl and t2. The fitted curves are shown in figs. 3a, b. The fitted values of bl, b2, b3, tt and t2 are given in table 2. TABLE 1 The results of the resonance parameters of the simultaneous fit to the mass and t distributions of diffraction dissociation events Mass (GeV) N(1500) N(1700) Tail

1.409±0.007 1.688 ± 0.001 2.0 ±0.07

Width (GeV)

Fraction

0.087±0.061 ")

0.27±0.01 0.61 ± 0.01 0.12

0.221 ± 0.001 0.394±0.002

°) A gaussian distribution has been used.

TABLE 2 The fitted parameters of the t distribution Region i

Interval (GeV 2) lower limit

1 2 3

--train a) 0.169±0.007 0.61 + 0.01

upper limit 0.169±0.007 0.61 ±0.01 -tin,, ")

Slope b (GeV -2)

9.8 +0.3 6.2 +0.3 1.63 ± 0.08

a) train and tm,x are the extreme values of t.

TABLE 3 The fitted parameters of the first t interval for reactions (2) and (3) separately Reaction

(2) (3)

Interval (GeV 2) lower limit -tml, --train

upper limit 0.23 +0.05 0.095 ± 0.006

Slope b (GeV -2)

9.0±0.5 14.8 ± 1.3

G. W. van Apeldoorn et al. / Diffraction dissociation

369

The aim of the parametrization is to compare the slope values at small - t with the slope for elastic scattering. In general the results for reactions (2) and (3) agree very well so that the distributions for these reactions can be added. However, for very small - t values (table 3) the slope value found for process (2) is unreliable because of large measuring errors in the fast antiproton tracks, due to distortion in the bubble chamber [5]. The measurement of this slope in process (3) does not suffer from systematic errors because it involves only the measurement of the energy of a relatively slow proton. The slope at small values of - t found in process (3) is therefore taken to be the right one. It equals 14.8+ 1.3 GeV.

3. C o m p a r i s o n with other data

The parameters C and n o f relation (4) between cross section and s have been fitted for reactions (2) and (3) using the available ~p data but excluding the 25 G e V / c counter data. The values in table 4, n = 0.36 ± 0.06 and C = 1.7 + 0.4, agree with the old values obtained in refs. [4, 1]. The corresponding cross sections for pp interaction are shown in fig. 2b. These cross sections were calculated by Denegri [6] using published data. The fit gives n = 0.26 :t: 0.08 which is (insignificantly) lower than the value obtained for ~p interactions. For comparison the cross sections for elastic ~p and pp scattering have also been parametrized by relation (4). The total cross sections have been analyzed in the same way. Only the energy region between 7 and 100 G e V has been used [7-13]. The results are shown in figs. 4 and 5 and in table 4. This parametrization gives quite reasonable agreement with experiment for elastic scattering. The total cross section of ~p interactions does not follow relation (4) at low values of s, but above s = 25 G e V 2 these cross sections are reproduced by the fitted curve. The total cross section for pp interactions is reproduced over the whole s region considered. TABLE

4

The fitted parameters C and n in the relation tr= Cs-" for diffraction dissociation, elastic (-)

(-)

(-)

scattering, total p p cross section and for the reactions p p--, p p~r+~rParameters

n

Interacting particles

C

pp

15p

pp

OP

p-~ p w ~r

0.26 ±0.08

0.36 ±0.06

1.2 ±0.4

1.7+0.4

Elastic scattering Total cross s e c t i o n

0.24 +0.02 0.019±0.002

0.32 ±0.04 0.082±0.004

22.1 ±0.8 42.10±0.09

32 ±2 64.4±0.6

0.56 ±0.09

0.55 ±0.04

12.6 ±2.0

13.3±1.4

I-)

(-)

(-)

÷

_

~-)

pp~ppcr+~r -

370

G. W. van Apeldoorn et al. / Diffraction dissociation .

.

.

.

.

.

.

I

E 2o

a

b

u

~o g 8

7

.

~to

2'0

,

30

,

4o

. . . .

i

50

i

too

~0o

s

t

O e V

to

2'0

3o

.

40

:r )

i

,

,

,

50

I

tOO

s

200 [ O e V

;e ]

Fig. 4. The cross section for (a) elastic lbp and (b) pp scattering as a function of s. The straight lines correspond to the parametrieation (4).

1oo

.

.

.

.

.

.

.

i

b

a

BO

70 --;

SO

~

SO

m o

40

3O

~I o

2'0

.

30

.

4o

,

~0 s

,

,

,

,

t

100 [ GeV

~00 I 2 I

2'0

3'0

,

4o

, so

s

,

,

,,

L too

2o0

[ GeV

~ ]

Fig. 5. The total cross section of ~p (a) and pp (b) interactions as a function of s. The straight lines correspond to the parametrization (4).

The value of n for lbp elastic scattering is significantly larger than the value for pp elastic scattering. The diffraction dissociation for pp has the same energy dependence as the elastic scattering of pp (n equals 0.26 + 0.08 and 0.24 + 0.02 respectively). In the same way the diffraction dissociation for ~p equals the elastic scattering of ~p (n equals 0.36 + 0.06 and 0.32 + 0.04, respectively). The s dependence of the total cross section is much weaker than the s dependence of the cross section of elastic scattering but it is again different for pp and ~p. The ratios of the corresponding cross sections of ~p and pp reactions are in all cases in agreement with an s dependence of s - ° o6~o oo4 found for this ratio in the case of the total cross sections. On the other hand, the cross section of reaction (1) equals the corresponding cross section in pp interactions in the energy range from 7 to 100 GeV. The energy behaviour is shown in fig. 6 [1-4, 11, 15-18]. The values of n and C are equal for the two processes (table 4). The slopes of the t distributions for elastic scattering of proton and antiproton have

G. IV. van Apeldoorn et al. / Diffraction dissociation

371

been compared to those for the diffraction dissociation reactions. The comparison has been made for small values of - t because it is expected that in this region the slope of the t distribution for diffraction dissociation is the same as that for elastic scattering. The slope values for elastic lbp scattering group around 12.2 + 0.2 G e V -2 (fig. 7a) and the slope values for elastic pp scattering have a value of 10.0 + 0.1 G e V -2 (fig. 7b). (See also Lasinski et al. [19].) The diffraction dissociation events in ~p interactions have a mean value of 12.7 ± 1.0 (fig. 8). For pp diffraction dissociation only one value for the slope is available, about 10 G e V -2 at 69 G e V / c [6]. 4. Conclusions The reaction ~p ~ 15pzr+rr- can partly be described by the diffraction dissociation mechanism. The relative importance of this production mechanism increases with energy. Between 7 and 100 G e V / c the energy dependence is given by the relation

!

t

b

2 Ln ul bn o LJ I

9 8 "7 10

2'0

30

40

50 s

100 ( GeM

20010 ~ )

20

30

50 s

40

100 ( GeV

200 ~ )

Fig. 6. The cross section for 13plr+w - (a) and for ppcr+cr - (b) production as a function of s. The straight lines c o r r e s p o n d to the parametrization (4). 25 e~

a

15

o t,,q

+

10

•

.

,

t

*

t

~

i

5

, 010

2'0

30

,

,

40

50 s

,

,

,

,

I

,

100

200

( GeM

~' ]

10

2'0

30

,

•

40

50 s

,

,

,

, I tO0 ( GeV

200 ;r ]

Fig. 7. T h e values of the slope parameters of the t distributions for elastic 13p (a) and pp (b) scattering as a function of s. T h e m e a n value is indicated by the straight line.

372

G. W. van Apeldoorn et al. / Diffraction dissociation 25

.

?-

o -L4

.

.

.

.

.

.

•

,

i

to

5

o

I0

2'0

i

10

,

40

i

50 g

i

,

I

tO0

( OeV

~00 2 )

Fig. 8. The values of the slope parameter of the t distribution for reaction (3) as a function of s. The mean value is indicated by the straight line.

with n = 0.36 + 0.06. This energy behaviour agrees with the behaviour of elastic 15p scattering. Also, the slope of the t distribution of diffraction dissociation agrees for small values of - t with the slope of the t distribution of elastic scattering. These results are in agreement with those for the analogous reactions in pp interactions. However, the energy dependence goes with a lower value of n, n = 0.24 + 0.02. The total cross sections of ~p and pp interactions have a value of n much closer to zero, but again larger for ~p than for pp. tr = Cs-"

We acknowledge the excellent work of the C E R N PS and the 2m H B C staff and the indispensable efforts of many colleagues involved in the scanning and measuring.

References [1] [2] [3] [4] [5] [6] [7] [83 [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]

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