Z. Phys. C - Particles and Fields 26, 359-372 (1984) Ze~schn~t P a r t i d e s ~r Physik C

and �9 Springer-Verlag 1984

Study of Strange Particle Inclusive Reactions in n-p Interactions at 3.95 Gev/c

B. Adeva 1, M. Aguilar-Benitez, J.A. Rubio

Junta de Energia Nuclear, Madrid, Spain

J.A. Garz6n, C. Pajares

Facultad de Fisicas, Universidad de Santiago, Spain

Received 6 January 1984

Abstract. Results are presented for the inclusive reactions

n - p - - , A + X n - p ~ K ~ n-p --> S(1385) + X

n- p ~ K(890) + X

at 3.95 GeV/c incident momentum, using data from a high statistics bubble chamber experiment. The total and differential inclusive cross sections are presented and compared with previous measure- ments. The forward backward asymmetries in A and S(1385) production are studied in the context of triple Regge theory. A phenomenological analysis of inclusive A production including the A polarization is presented.

productions of A,K~ and K-+(890) in n-p reactions at an incident momentum of 3.95 GeV/c, which corresponds to a center of mass energy of _ 2.9 GeV. The data come from a large statistics bubble chamber experiment having a sensitivity of

90 events//~ barn. A brief description of the experimental data is

given in Sect. 2. The total and differential inclusive cross sections (in the x and p~ variables) are presented in Sect. 3. The analysis of the forward-backward asymmetry in A and S(1385) production is given in Sect. 4. A determination of the effective trajectories exchanged in the inclusive production process is presented in Sect. 5. A phenomenological analysis of the observed A polarization appears in Sect. 6. Finally, Sect. 7 is left for a brief summary and con- clusions.

1. Introduction

A large amount of data have been collected on in- clusive production of various hadrons in hadron- nucleon collisions [1-10]. However, such data for the production of strange hadrons from an initial state with no strange quark content are still rather meagre [11-18]. It is of interest to examine the hypercharge exchange process since it differs dinami- cally from other hadron-nucleon reactions and gives the possibility to study new effects.

In this paper we present a study on the inclusive

1 Present address: DESY, Hamburg, FRG

2. Experimental Details

The data come from an analysis of approximately 1.7.106 exposures of the CERN 2m hydrogen bubble chamber to n- beams of 3.95 GeV/c average momen- tum. The total sensitivity of the experiment is around 90 events/# barn. The general details of the experi- ment are given in [19].

We recall here that in order to ensure good scanning and measurability conditions, a limited fiducial region was imposed. To take into account scanning biases only V~ with a projected decay length of more than 3 mm were kept for further analysis. This loss and that due to decays outside the fiducial volume were compensated for with the standard weighting procedure. The average weights were 1.13 for K~ and 1.13 for A's.

360 B. A d e v a et ak : S t range Par t ic le Inc lus ive Reac t ions

120~

1000

8 0 0

>.

o eoo

w r, ~u 4 0 0

200

2.~001

2000

1600

o ~200

z t u 8 ~

400

; i i i i i I i i

I 1.:* 1,3 1,4 1,S 1.fi 1.7 1.8 1.g M( A~+)GeV

I 1.2

~ ~ {bl

0

o

i I I l i I I I I I I I I 1.3 1.4 I.S 1.6 1.7 1.8

MIA~')GcV

' 2]0

~ o O o

I i I 1,9 2~

1200

I000

8 0 0

600

-'-00

2OO

. 6

80e

60C o u~ um

20O

. 6

t i ~ i i i i

& ~ (a|

0

.7 .e .g 1.0 1.1 1.2 1.3 1.,-

Mr K.~ n ' l e ,v

' I , t i I , i , i , i b l ) 1 i i

I I I I I I I I I i I i I I .? .e .9 t.o t.~ 1.2 1.3 1.4

MIK~*n-IGcV

Fig. 2a and b. t c~ + K~ - effective mass d i s t r ibu t ions for the inclusive reac t ions n - p - - , K ~ n• X. The curves are the results of the mass fits discussed in the text

Fig. l a and 5. A n +, A n - effective mass d i s t r ibu t ions for the inclusive reac t ions n - p - - , A n • X. The curves are the results of the mass fits discussed in the text

We have extracted samples of the inclusive reactions

r c - p ~ A + X (1) rc-p ~ K ~ + X (2)

rc- p ~ Z+- (1385) + X (3)

rc- p ~ K -+ (890) + X (4)

from events with a visible A or K ~ decay. After the kinematical analysis and the use of bubble density information the A - K ~ ambiguity was of the order of ___ 1.4~ and did not affect our conclusions on reactions (1) and (2). For reactions (3) and (4) we considered all the hypothesis containing a Arc -+ or K~ -+ combination. The non negligible level of ambiguities does not affect our results which are based on fits to the Arc +- and K~ +- effective mass distributions.

Figures 1 and 2 show the Arc-+ and K~ -+ effective mass distributions. Clear signals of the E+-(1385) and K-+(890) resonances are observed. To extract the number of events of reactions (3) and (4) the Arc -+ and K~ +- effective mass distributions were

T a b l e 1. Expe r imen ta l deta i ls of inclus ive final s ta tes

Reac t ion No. of ent r ies in reac t ion

z c - p ~ A + X 45141

z r -p ~ A n + + X 12762 ~ n - p ~ A n - + X 31754 b

n - p ~ E + (1385) + X 2213 __+ 123

n - p ~ ,~- (1385) + X 3886 _ 160

~z- p --, K ~ + X 40774

n - p ~ K ~ + + X 12490 ~

n - p ~ K ~ - + X 15128 a

n - p ~ K§ + X 2313 +__ 70

n - p ~ K- (890 ) + X 1048 + 90

a There are 1.016 entr ies per event b There are 1.08 entr ies per event c There are 1.028 entr ies per event d There are 1.034 entr ies per event

fitted with parametrizations which included an incoherent superposition of a Brei t -Wigner resonance term and a polynomial in the mass for the background.

In Table 1 we present a summary of the number of events (or combinations) used in this analysis.

B. Adeva et al. : Strange Particle Inclusive Reactions 361

<~ I

b

4.

3.

2.

This e x p e r i m e n t

<~

I I 10 100

PLABIGeV)

Fig. 3. The inclusive cross section for A production in n - p re- actions at different values of the beam momentum

3. Cross Sections

3.1 The Reaction n- p ~ A + X

After correcting for ambiguous events and unseen A decay modes the inclusive cross section was calculated to be

o-(n- p ~ A + X) = 952 _+ 35 p barn

In Fig. 3 we present a compilation of the measured values of this cross section for various beam momenta. A fairly smooth increase of the cross section with energy is observed.

The effective mass of the recoiling system is shown in Fig. 4. The K ~ and K~ peaks are clearly visible and dominate the low mass region.

The invariant differential cross section

2E* da

n ~ d x

where x is the Feynman scaling variable defined with respect t o incoming n - beam direction (x =

P rr/Pmax)' E* is the center of mass energy of the particle

and x/~ is the total energy in the center of mass is presented in Fig. 5. For comparison we show similar measurements at other energies. A large fraction of the cross section takes place at negative values of x, with a clear peak at x _~ - 1 corresponding to the exclusive reaction n - p ~ A K ~ indicating the dominance of production in the target fragmentation region.

The behaviour of the inclusive cross section in this fragmentation region ( - 1 < x < - 0.2) can be discussed in terms of Regge-Mueller phenomenology. At large values of M 2 the asymptotic behaviour of the invariant cross section for the inclusive process p 22+ A is given by the expression

\Ms )

+ ~ f l , ( ~ 2 , t ) s ' " ' ~ co, A2

where the first term refers to the Pomeron exchange contribution, which has intercept ap ~ 1 and domi- nates at very high energies, and the other terms corresponding to additional exchanged trajectories, co - f o r p - A2, which are exchange degenerated and have intercept eR(0)_~ 0.5. The prediction of the energy variation of the cross section is then

a(p &A) =/~ +/~Rs -1/2

The available data at different values of the incident beam momentum are shown in Fig. 5. Within the uncertainties due to large statistical and systematic errors the data, in the region - 0 . 8 < x < - 0.2, is consistent with a decrease of the cross section although we cannot extract the precise energy dependence.

I t is interesting to compare our data on the target

fragmentation cross section o-(p Ys with data

1300

1200

I 0 0 0

800

600

,oo Jl 2D0

0 0d*

J], K~

I

0.7 10 13 16 M(X)GeV

I 1.9

Fig. 4. Effective mass distribution of the recoiling system in the inclusive reaction n - p -~ A + X

362 B. Adeva et al. : Strange Particle Inclusive Reactions

rep ~ A X

3.95 GeV 6 GeV

z~ 15 GeV

O le.5 ~=v 20S aeV

+1 _i+- .05

.O2

.OI -1.0

[ -+--

_0.', .0'.~ .0'., .0'.~ ~. 0'.~ 0'., 0'.~ 0'.~ X

Fig. 5. Differential invariant cross section for the inclusive re- action ~- p --, A + X at several values of the incident beam mo- mentum

..~LL �9 r f i

C~

20

15

10

I I i I i

o P a K" / ~ K e ~ T T "

t cnt

I [ I i I ~ -~-pm [ I 0.1 0 .2 0 .3 0 .4

S -~1~ ( GeV "~ )

Fig. 6. Ratio of the inclusive cross section for A production in the reactions a + p ~ A + X , in the r e g i o n - 0 . 8 < x < - 0 . 4 , over the total a + p cross section. For details see [21]

5 ~ ~ 11" p ~ A X

2 \

.1

\

Ja E

.2

.05

.02

o. o'. ' 0'. ' 0'. ' ' ~' ' ' .01 1 2 0.3 /, 0,5 6 D.7 0,~ .9 l. n 12

p2 (GcV 2)

Fig. 7. &r/dp~ r distribution for the inclusive reaction ~- p ~ A + X

relat ive to the processes a(p & A) being a ( = p , K - , p, n - , n +, K § the var ious h a d r o n project i les inducing the inclusive process ap ~ A + X. Fo l low- ing I n a m i and Mie t t inen [20 ,21] we d iv ided the

cross sect ion o - ( p ~ A ) by the a sympto t i c value of the to ta l cross sect ion ar(aP ) which we take at 175 GeV/c [221. I n Fig. 6 we show the results of this compar i son . U n d e r the hypo thes i s of fac tor iza t ion the target f r agmen ta t ion cross sect ions should be project i le i ndependen t in the l imit s ~ 0% a feature which appea r s to be cons is ten t wi th the data . Not ice the s imi lar i ty of the n - p and/~p d a t a and the different behav iou r of the s t rangeness ann ih i l a t ing process K - p -~ A + X which will be re levant when discussing the A pola r iza t ion .

In Fig. 7 the differential cross sect ion da/dp 2 is presented�9 The d i s t r ibu t ion fol lows an exponent ia l behav iou r of the form exp ( - bp2r) with b = 4.56 _+ 0.03 G e V - 2.

3.2 The Reactions rc-p ~ S--(1385) + X

To calcula te the n u m b e r of S-+(1385) events in the ~ - p ---, A ~ -+ + X inclusive reac t ions we have fitted the inclusive A ~ -+ effective mass d i s t r ibu t ions with an incoherent superpos i t ion of a B r e i t - W i g n e r t e rm for the resonance and a p o l y n o m i a l in the mass as represen ta t ion of the backg round . The results of the fits are given in Table 1.

B. Adeva et al. : Stri~nge Particle Inclusive Reactions 363

t I I i t I , I I I

"3 E

0.2

I ~ )"'113851X 4' ;E - (13BS) X

=-P~ ~ K*tBgo)x K" leg0) X

r

' ' 2 ;

PLAB ( G t V I

Fig. 8. Inclusive cross sections for 27-+(1385) and K-+(890) pro- duction at several values of the beam m o m e n t u m

E

f

.001 I ~1. - . 8

~-p~Z~(138s}x

t + §

o ~[* (138S)

�9 • - (1385)

+

- ; -k ' . . . . '8 . . . . 2 ; '2 i ~, X

Fig. 9. Differential cross sections da/dx for the inclusive reactions rc-p --, X--(1385)X

The cross sections corrected for unseen A and S (1385) decays are the following

a(n - p ~ S + (1385) + X) = 53.3 _+ 3.6 # barn

a ( n - p ~ S - (1385) + X) = 93.5 _+ 5.0 # barn

--~,'- ~:" ( 1385 )

~t~ .05

.02

.01

.005

�9 002

[ I I I I I I I I I 0 . I .2 .3 .4 .S .6 .7 -8 .9

P ~ I G c V 2 ]

Fig. 1O. Differential cross sections da/dp~ for the inclusive re- actions n - p ~ 27• (1385)X

In Fig. 8 we present the inclusive S-+(1385) cross sections at different energies. It is interesting to note that the Z-(1385) production is more important at low energies and becomes negligible in the high energy domain.

2 The differential cross sections in the x and Pr variables have been obtained by fitting the A n +- effective mass distributions in the selected x or p~, intervals with a similar form to the one used in the calculation of the total cross sections. In Fig. 9 we present the d a / d x cross sections which are larger around the central region. The da/dp~, distributions are given in Fig. 10 and exhibit an exponential be- haviour (exp(-bpZr)) , the slopes of both charge modes being the same

S + (1385) :b = 4.2 _+ 0.1 GeV -2

~ - (1385):b = 4.1 __ 0.1 GeV -2

3.3 The Reactions n - p ~ K ~ + X

After correcting for ambiguous events and the unseen K ~ n~ ~ decay mode the inclusive cross s

section was calculated to be

a ( n - p - - , K ~ + X) = 809 + 29#b

In Fig. 11 we show a compilation of the measured values of this cross section at several beam momenta.

364

i i

0. ~,

~2. t* + ": + to- E

.9

. 8 ~'

GI .5 This experiment

I, l 10 100

PLAB (GeV)

Fig. 11. The inclusive cross section for K ~ production in ~ - p reactions at different values of the beam momentum

The K ~ inclusive cross section grows faster with s energy than the A cross section implying that double strange meson production (K/~, K/s domi- nates at higher energies over associated production (AK, SK,...).

Figure 12 shows the invariant mass distribution of the recoiling system in K ~ production. Clear peaks s corresponding to the A, Z (1385) and A (1520) hyperons are observed.

The invariant differential cross section for K ~ s inclusive production is given in Fig. 13 together with data at other energies. The peak at x ~ 1 corresponds to A K ~ and S~ ~ associated production. The cross $ s section is concentrated in the beam fragmentation region and tends to become more central at higher energies.

The differential cross section d~r/dp~ is shown in Fig. 14 and follows, in a logarithmic scale, two straight lines with different slopes and a break around p2 ~ 0.3 GeV 2. A fit including two exponentials with a free crossing point gives the results

B, Adeva et al. : Strange Particle Inclusive Reactions

I" T 1 ~ T r 1 T

+ §

+3gso.v ++ - - ~ 16.5 GeV

+ 20s G,v

.09

.08 ~

.07 @

.06 +

..03 I

•

L

T -+-

0.2 0.6 0.6 0.9

Fig. 13. Differential invariant cross section for the inclusive reaction ~ - p ~ K ~ + X at several values of the incident beam momenta

b 1 = 6.38 _+ 0.05 GeV -z

b 2 = 5.00 • 0.04 G e V - 2

the breaking occurring at

p2 _- 0.31 + 0.04 GeV 2

The larger slope at low p~ values is due to K+(890) production and decay through the mode K ~ z +-

2100

1800

1500

1200

g00

600

300

0

A A [1520 ) r 1

I ~ ~ L ~ . ~ I I r'- I I i i i I i i i i 1.0 I,I 1.2 1.3 1./, 1.S 1.0 I.'/ 1,8 1.9 2.0 2.1 2.2 2.3

M (X) GeV

Fig. 12. Effective mass distribution of the recoil- ing system in the inclusive reaction 2.t. rc-p~ K~ + X.

B. Adeva et al. : Strange Particle Inclusive Reactions 365

.05

.02

0.0 011 01.2 013 ol.& OIS 0i.6 01.7 01.0 ol.g :,0

p 21-(0r )

Fig. 14. da/dp~ distribution for the inclusive reaction rt-p~K~ X

3.4 The Reactions re- p --. K+(890) + X

The determination of the number of K • (890) events in the inclusive reactions r c - p ~ K + ( 8 9 0 ) + X was done in a similar way to the one used for S+(1385). The inclusive K ~ rc + distributions were fitted with a superposition of a Breit-Wigner form for the reso- nance and a polynomial background.

The cross sections corrected for unseen decay modes are

.05

.o E

.005

�9 i~'p ~ K• X

�9 K- [8901

_+__

++t t ++

I I I I I l ! "00~t. -0,8 -0.6 -0.4 -0.2 0 0,2 0 ~

X 0.6 0.8

Fig. 15. Differential cross sections da/dx for the inclusive reactions 7r-p --, K• (890)X

>. o .o

",,19

'11" p ~ K Z (0901+ X

o K * 1 8 9 2 )

�9 K - 1 8 9 2 )

cr(rc- p --* K + (890) + X) = 136.7 ___ 6.4 #b

a0r - p --, K - (890) + X) = 61.9 ___ 5.7 #b

A compilation of inclusive K-+(890) production at different values of the incident beam momentum is presented in Fig. 8. The higher cross section for K + (890) production is due to the contribution of the associated production process (strange meson and hyperon) which is asymmetric in the K(890) charges.

The differential cross sections da/dx and da/dpr are shown in Figs. 15 and 16 respectively. The K-(890) cross section is concentrated in a narrower x region than the K+(890). The distributions in p~, show exponential behaviour and a fit to the form exp( - bp 2)

.005

.002

I I I I I I f I I I .1 .2 .3 ./, .5 .6 .7 .8 .0

P~(GeV z )

Fig. 16. Differential cross sections da/dp~ for the inclusive reactions n - p --* K•

~.0

366

gives the following slopes:

K + (890):b = 4.14 + 0.22 GeV -2

K - (890) : b = 6.28 ___ 0.24 GeV- 2

The slope measured for the positively charged mode is similar to the values obtained for A, K ~ and 27-+(1385). However, the K-(890) has a larger value, of the same order as the K ~ coming from K(890), indicating a different production mechanism.

4. Triple Regge Analysis of the Angular Asymmetries

4.1 A Production

As can be seen in Fig. 5, the inclusive data for A production show significant hyperon production in both forward and backward hemispheres*. This is due to the fact that at an incident momentum of 3.95 GeV/c baryon exchange is still important in the beam fragmentation region.

The rt-p ~ A X amplitude in the triple Regge model [23] (when m 2 and s/m~ are both large)

x

is represented by the diagrams shown in Fig. 17. In the first one the A is a fragment of the proton, whereas in the second one the A comes from beam fragmentation. According to duality [24-28] the behaviour at high M~ must average the low M~ region, so that:

A) = A

d~(7 z d a - ~ P A) = B'(M~) %~(~

where A and B are independent of M 2 0~M(0 ) is the intercept of the effective trajectory exchanged in the reggeon-particle collision, which we shall comment later on.

The ratio between the above expressions when u = t gives:

de 27( - A)

- - C" ( 212[=K,(t) - =~,(t)l R - M . da LL~A) 270'

With the standard values for the K(890) and I;(1385) trajectories

ocx,(t ) = 0.34 + 0.88 t 0~x,(t ) = - 0.20 + 0.90 t

we expect:

R = C ' ( M ~ ) I ~

* (We define forward and backward production with respect to the incoming ~ - beam)

B. Adeva et al. : Strange Particle Inclusive Reactions

( a }

(b)

~ " A A

"R"

g,g"

p f ~ . . p

Fig. 17a and b. Triple Regge diagrams for the inclusive reaction - p ~ A X in both fragmentation regions

0.5

.% R--~B

0.05

"rr 'p ~ AX -]- /

I I I I I I I I I I I I I I I I I I I ~ i i i 0"010.1 0 5 1.0 %5 2

MxtGeV}

Fig. 18. The forward ([ u'[ < 0.5 GeV 2)-backward ([ t' I < 0.5 GeV 2) cross section ratio for A production, as a function o f M

We have experimentally defined the fragmentation regions by the cuts I t ' l <0 .5GeV 2 and lu ' l<0 .5 GeV 2, being t ' = t - t . and u ' = u - u : . The

m i l l m i l l

measured values of log R are shown in Fig. 18 as a function of log M~. They rise linearly with log M , in agreement with the previous formula. Moreover, a fit to a straight line yields the value 1.16 ___ 0.04 for the exponent of M~, which agrees numerically

B. Adeva et al. : Strange Particle Inclusive Reactions

with the prediction. The bin which corresponds to the highest value of M is probably outside the region where the triple Regge model is expected to be valid. The value obtained for the exponent is stable within the error for different choices of the cut-off in the momentum transfer in the region [t'l < 1 GeV 2.

4.2 Z +- (1385) Produc t ion

Our data also show evidence for forward and back- ward production of the Z(1385) resonance in both charged modes. An earlier analysis established a significant cross-section for the exclusive process rt- p ~ K + 2:- (1385) in the forward direction [29], which implies exotic meson exchange. In view of the validity of the triple Regge approach for A production, we have assumed the 2:2-+(1385) production to be described by the diagrams of Figs. 19a-d, in which 2 trajectories are exotic in terms of Regge exchanges. We have called these trajectories E and Z, and they have the quantum numbers of the systems p I7- and r~- I2 + respectively.

The ratios between the backward and forward cross-sections depend upon the exchanged trajectories in the following way:

do" e ~( rc - ~ 2:+ (1385))

= = ( M x) R1 dcr ~- A" 2 2[~tK.(t)--~tz(t)l

~-(p ~ 2:+ (1385))

d~ P,22-(1385)) dt - - B . ( M 2 ) 2[ctE(t) -ct~(z) l

R2 da ~- " ~" ~)-(p ----,22- (1385))

[ a l (bl

t IPM

r l i + Tin+

r t - rL-

(c) {d)

r ~ % r * -

IPM

I2 t _ s

E E

IP 0 M

Fig. 19a-d. Triple Regge diagrams for the inclusive reactions - p ---, 22 • (1385) X in both fragmentation regions

T a b l e 2 . trr/a n ratios x 10 - 2

a S - (1385)

367

M.2~t ' [ 0.0 - 0.25 0.25 - 0.60 0.60 - 1.0 0.0 - 1.0

0.0 - 0.65 8.9 _+ 5 41.2 + 21 - - 17 _+ 5 0 .65-1 .15 10.1_+3 47 __16 59.3___14 3 1 + 5 1.15 - 1.65 19.5 + 6 57.9 -+ 17 96.0 + 42 44 -+ 7

b Z'+ (1385)

M ~ [ 0 .0 -0 .25 0.25 -0 .60 0.60 1.0 0 . 0 - 1.0

0.0 -0 .65 - - 30 _+113 - - 11_+56 0 .65-1.15 11.6-1-12 17.3___10 43 _ + 2 3 20___7 1.15 - 1.65 21.0 _+ 5 56 _+ 15 83.5 _+ 15 49 + 6

We have determined these ratios from the number of events observed in corresponding cells of a 3 x 3 grid in the ( M E t') and the (M~, u') planes in the regions [t'[ < 1 6 e v 2 and [u'[ < 1 GeV 2 respectively. The number of resonant events has been calculated by fitting to the Arc -+ mass spectra a function which is the incoherent sum of a Breit-Wigner amplitude and a polynomial background. In Table 2 we present the values of the above ratios for 2:-+ (1385) in several bins of t ' = t - t m i n. In Fig. 20a-b we have plotted

0

-0.5

-1.0

la)

"q-p~E-[13851+ X

(b)

o, -0.5

-1.0 51,,X

-1.0 -0.5 0.5 Log Mx z

Fig. 20 a and b. Logarithm of the ratio between the forward (lu'] < 1 GeV 2) and backward (It'] < 1 GeV 2) cross sections for inclusive I:-(1385) and S+(1385) production, as a function of log M~ 2

I I -"-% -0~ 0 o.5

Log M2x

368

log R i in 3 intervals of log M z, integrated in the region Icl< 1 GeV 2. The data follow a straight line, which is consistent with the triple Regge formalism including an exotic trajectory. We may interpret these trajec- tories as due to Regge-Regge cuts [30]. Under this assumption we expect for ~E(t), which has the quantum numbers of the system p Z- , the following expression:

! t

aP~z- "~ - 1.8 + 0.4 t c~ e (t) = c~p (0) + ~z (0) - 1 + t ~' + , _ p ~

which implies for the exponent in the forward- backward ratio"

f i (S- (1385)) = 2(~E(t ) - ~( t)) ~ - 3.0 - 0.8 t

In the region It[ < 1 GeV 2 the prediction would be fl (S- (1385)) _ - 2.8. Instead, we observe a positive slope fi(S-(1385)) = 0.9 +_ 0.3. (Changing a2(0) by + 0.5 does not modify the discrepancy).

Therefore we conclude that the exotic production of S-(1385) cannot be understood in terms of an absorptive correction in the frame of the Regge formalism.

On the other hand, a similar prediction for the ez(t) trajectory as a Regge cut with the quantum numbers n - Z +, leads to the prediction for the slope in the forward-backward ratio:

fl(Z + (1385)) = 2(e~:(t) - %(0) --- 2.9

which is compatible within the errors with the observed fl(S + (1385)) = 1 ~+ Lo ~ ' ~ - 0.5 "

5. Triple Regge Analysis of the Inclusive Cross-Section

There are arguments [23, 31] in favour of the validity of the triple Regge expressions even at relatively low energies, and we have seen in the previous section good agreement of our data with a specific prediction of the model. In this context, we have performed a more detailed analysis of the A differential cross-

section in the p - ~ A and ~z- p A processes.

5.1 p A Vertex

In the small t region the triple Regge amplitude may be expressed:

d 2 O" t / 2 M 2 h~M(o)- 2~,(t)

where e~,(t) = ex,(0) + e'x, t is the effective trajectory exchanged in the p A vertex. We make use of the crossing symmetric variable ( s - u)/2 instead of s, which is more adequate at low energies in the Regge approximation, e M (0) is the intercept of the exchanged trajectory in the "K* +" n - collision, which we have assumed to be 0.5, corresponding to m - f and

B. A d e v a et al. : S t r a n g e Par t i c le Inc lus ive R e a c t i o n s

p - A 2. We estimate the Pomeron contribution to be small at our energy in view of the small cross- section for the exoticprocesses in Fig. 5 (a = n +, K +, p). F(t) is a factor which does not depend on M 2 .

X

In order to determine the effective trajectory we have performed a Z2-fit to the data in the region 2 M ~ / ( s - u)> 0.2 using the previous formula in 8 bins of t in the region 0.2 < Itl < 1 GeV 2. F(t) and ~M(0)- 2~r,(t) were left as free parameters in each t bin. Figure 21 (a-h) displays the results of the fits over the mass spectra. It is clearly seen how the slope increases when the momentum transfer in- creases. Figure 22 shows the fitted values of the effective trajectory ~K,(t) when we assume aM(0 ) = 0.5. They lie between the extrapolation of the K* and K recurrences from the Chew-Frautschi plot, closer to the first ones, which correspond to positive naturality exchanged. We have also performed an overall zZ-fit in the region 0.2 < I tl < 1 GeV 2 in which F(t) was parametrized as A exp(Bt), and A, B, eM(0)- 2eK,(0 ) and e'K* were determined from the fit. The following values were obtained:

%t(0) - 2%,(0) = 0.09 _+_ 0.08 ~'~, = 0.75 _+ 0.06 GeV-2

B = 0.22 _+ 0.17 GeV- 2

A = 126 _+ 23 #b GeV -2

If the fit is performed using the high energy ap- proximation s ~ ( s - u)/2, the intercept eK,(0) goes down by 0.2 units, closer to the K trajectory, and the interpretation of the mass spectra is also good. The intercept c~K,(0 ) also shows some correlation with respect to the cut-off in 2 M Z / ( s - u), which is needed in order to avoid the region dominated by the resonances, and it changes by 0.1 units in the range 0.09 < 2m~/ ( s - u) < 0.12.

A similar analysis has been done in n - p ~ A X at 15 GeV/c [5] with the result e M ( 0 ) - 2 % , ( 0 ) = 0.17 _+ 0.15. Our data are in agreement with it when we use the variable ( s - u)/2, thus indicating that K* exchange dominates also at our energy. However, if the variable M~/s is used, the effective trajectory lowers down closer to the K-trajectory.

5.2 nA Vertex

We have assumed that the observed A production in the direction of the n - proceeds through hyperon exchange. In Fig. 23 we show the energy dependence of the invariant differential cross-section integrated in the region 0.2 < x <0.8, using published data from several experiments [5, 13, 14, 16, 17]. Our result clearly favours a linear dependence on s-t/2, which indicates normal meson exchanges (p - A 2 a n d f - co) in ~ annihilations. Some authors have proposed exotic exchanges in this process, which appeared to be in agreement with the data [26]. We have performed a triple Regge analysis in the n - A vertex

B. Adeva et al. : Strange Particle Inclusive Reactions 369

100

S 0

ca 6o

,z 4o ,,>,

100

80

60

60

~ ,~

(o) - 0 . 3 < t < - 0.2

t

~ ' ] 1 ,

i i i i i i

.10 .lS 20 .30 .40 2M___L s-u

( c ) ~ -0 ,5< t<-0 .4 ,

y

(b ) -0,4 <t <-0.3

301 ~,

S O l ~

6o

2o

I I i i I i i

.10 .15 .20 .30 .t,0 zm~ s-u

100 ( d )

S0 - 0 . 6 < t < - 0.5

6O

I I I I

.,o .~s .~o ' . ;o ' .~o'.;o .lo .,s .~o ' . ;o ' .~o'.+o 2M~,. 2 ~

s - u s -u

60

6

2O

=> 8

-0.7 < t <+0.6

I / I r I I I I I

.10 .15 .20 .30 ./,0 .50

5-u

( g )

t+' tTt

-0.9 < t <-0.8

I I f I I I I J I .10 +15 .20 .30 .40 .50

2M s-u

{ f )

.10

(h

/ i

.10

-0.8 <t <'- 0.7

' ' ' ; 0 ' ~ 0 ' ~ .15 20

s-u

-1.0 <t <-0.9 i I I i i i i [ I

.15 .20 .30 .40 .50 2M~ s-u

Fig. 21a-h. Recoiling mass distributions for A production in the direction of the proton, compared with the triple Regge model in different

intervals of the momentum transfer t

c=t t )

t t G e V Z ) . -0:9 . -0 .7 . - o : 5 ~ -0 :3 . -0:1

-0.+

, - 0 . 5

, - ' 0 . 9

Fig. 22. Effective trajectory obtained for A production in the proton vertex. The extrapolated trajectories for the K and K* recurrences are also shown as a reference

i 0.8 5 0 F ( x l d x 0,2

40

2 5 0 18.5 15 I I

6 4 PLAB(GeV)

3O

20

10

I I 0 0.1 0.2 0.3 0.4

S'~IZ( GeV -1 J

Fig. 23. Energy dependence of the integrated cross-section p

o-(~- ~ A) in the region 0.2 < x < 0.8

370 B. Adeva et al. : Strange Particle Inclusive Reactions

,,oV [r ] /,o |b| (c) (dJ f + -0.2<u<O.O [ "O't" <u <" 0'2 -0.6 <u <-O,t, -0.8 <u <-0.6

o

~ ,

i

6"r 0 , , o !

~~ q ~ . . . . . . . . z ~ ' . . . . . . . . . . . . . .

S-I S-I S-I S-t

I { e }

t~o -1.o <u <-0.8

2o

l I

.6 il 30 .~5 .20 .30 .t,O 50.60 2M~

s - t

Fig. 24 a-e . Recoiling mass distributions for A production in the direction of the incoming beam, compared with the triple Regge model in different intervals of the m o m e n t u m transfer u

in order to verify the hypothesis of hyperon exchange, using the expression:

d 2 a _ / 2 M 2 '~ ~R(~ - 2~gu)

dud \ s - t }

The da ta have been divided into 5 bins of equal width in the region ]u I < 1 GeV 2, and the cor respond- ing recoiling mass spectra have been fitted separately with G(u) and a(u) = eR(0) - 2e(u) as free parameters . The results of the fit were:

~ R ( 0 ) - 2 e $ ( 0 ) = 1.1 __+ 0.2

e'~ = 0.86 + 0.14 G e V - z

~(u)

u(GevZj

-i.o -o.6 -0.6 -o.4 -0.2 to~ o . ~ I I I I I ~ "

.o.t. / / / ~

+ ;;

Fig. 25. Effective trajectory obtained for A production in the beam fragmentation region. Also the extrapolated trajectories from the I; and 1;* recurrences are shown as a reference

B = 0.79 + 0.37 G e V - 2

A = 30 __+ 10#b GeV - z

The quali ty of the fit is good, as shown in Fig. 24. Under the a s sumpt ion ~R (0) = 0.5, which is suppor ted by the previous da ta on a ( r c - Z A), the effective t ra jectory ~(u) lies very close to the I7(1385) trajectory, with a measured intercept 0 t ~ ( 0 ) = - 0.3 _+ 0.1 (see Fig. 25). If we turn the a rgumen t a round and assume 2;(1385) exchange, this result provides further evidence

B. Adeva et al. : Strange Particle Inclusive Reactions

for eR(0)= 0.5, in contradiction with the hypothesis of exotic exchanges in the "I~" p scattering.

6. Polarization

We have determined the A polarization using the information of the angular distribution of its weak decay through the expression"

3 PA = N ~ cos 0p,

0~ i = l

where N is the number of events, 0~ is A decay asym- metryparameter whichhas the value e = 0.642 + 0.013 and cos 0p = (u a x u _).up where the unit vectors u _, u a hav~ been calculated in the over-all center-of- mass system and up in the A rest frame.

In the context of the triple Regge model, it has been argued that the A polarization in the inclusive process K - p ~ A X has to decrease with increasing energies [32]. The same arguments apply for the r c - p ~ A X process in the proton fragmentation region, because there is no contribution from the scaling term K* K** P to the polarized cross-section PA.a. Although data on Pa are available at different energies in re-p, the errors are still large. In Fig. 26a, b we compare our data at 3.95 GeV/c with another experiment at 18.5 GeV/c [ 13] in the variable x and t'. They show just the opposite trend to the

o

-.5

( a } ~ rl 'p 18.5 GeV

�9 t t-p 3.95 GeV

-1 i I I i

0 2 4 6 5 10

t '[ GcV 2 )

1 ( b } "]- ~'p 18.5 Gr

�9 11"p 3.95 OeV

.5

- .5 l ~ T ~ T

-I I I I I I i i i i

-1. - .6 -.2 0 .2 ,6

X

Fig. 26 a and b. Comparison between the data on A polarization in the reaction n - p ~ A X at 3.95 GeV/c and at 18.5 GeV/c [13], as a function of the variables t' and x

371

0.5

0.3

o.I IL~,* * "

e A , . , I 1

-0.~

-0, t. 05. PT (o=v I

x ~ - p ~ A X at 3.95 GeV

IJl K ' p ~ A X a t 4 .2 GeV

0 K ' p ~ A * K K ' § at 4.2 GeV

Fig. 27. Data on A polarization in the reaction 7r- p ~ A X at 3.95 GeV/c, as a function of Pr, compared with those of the reactions K - p ~ A X and K - p ~ A + K I ~ + X at a similar energy [33]

.4

.2

0

-.2

4?- 0 . 4 < X < 1.0

-~ - 1 < X <-0.2

, t -.4

-.~

-.6

i -1.0 .2

§

I I I , 5 .5 112

PT (GcV)

Fig. 28. PT dependence of A polarization in the proton fragmenta- tion region - 1 . 0 < x < - 0.2 and in the beam fragmentation region 0.4 < x < 1.0

expectation, in the target fragmentation region. However, it is worth to note that the validity of the triple Regge formulae extrapolated to lower values of M 2 which is based upon duality arguments, x ~

does not hold for polarization. A more interesting observation is the behaviour

of Pa as a function of the Pr of the A with respect to the beam. Figure 27 shows our data compared with another experiment on K - p interactions at 4.2 GeV/c [33], in which the contributions from strangeness annihilation and non strangeness annihil- ation have been separated. We see that our data follow the same trend as those of the process K- p A + K/~ + X. A similar behaviour has been observed in a wide number of experiments [34-40], in- dependently of the projectile and of the energy. Several models have been proposed to explain this systematic and intriguing behaviour [41-46] and recently the A polarization has been measured in the beam fragmentation region [47]. In Fig. 28 we split our inclusive polarization data into the target and the beam fragmentation regions separately.

372

W h e r e a s in the first o n e the p o l a r i z a t i o n increases as a f u n c t i o n of P r wi th respect to the to ta l sample , in the second one there is n o s igni f icant po la r i za t ion .

7. Summary

W e have p re sen t ed d a t a o n the inc lus ive p r o d u c t i o n of the s t r ange par t ic les A,K~ in r c - p i n t e r a c t i o n s a t 3.95 G e V / c i nc iden t zc- m o m e n t u m . Th e s ta t is t ical sensi t iv i ty of the ex- p e r i m e n t is _~ 90 even t s /#b .

The d a t a are d i scussed in t e rms of the to ta l a n d different ial (in the F e y n m a n x a n d PT var iables) cross sec t ions a n d c o m p a r e d wi th ava i l ab le m e a s u r e - m e n t s at o the r energies.

The a n g u l a r a s y m m e t r i e s obse rved in A a n d E-+(1385) p r o d u c t i o n are s tud ied in the con tex t of t r ip le Regge p h e n o m e n o l o g y . F o r the A reac t ions the ra t io b e t w e e n the b a c k w a r d a n d fo rward cross sec t ions is u n d e r s t o o d in t e rms of w e l l - k n o w n Regge t ra jector ies . F o r the S-+(1385) r eac t ions a s imi la r s t udy of the b a c k w a r d to fo rward ra t io r equ i r e s two a d d i t i o n a l t ra jec tor ies wi th exot ic q u a n t u m n u m b e r s . The re levan t features of these t ra jec tor ies are c o m - pa red wi th expec t a t i ons f rom Regge cuts. Th e exot ic t r a jec to ry assoc ia ted to the S - ( 1 3 8 5 ) p r o d u c e d in the p r o t o n ver tex is n o t c o m p a t i b l e wi th a R e g g e - Regge cut.

The inc lus ive A cross sec t ion is s tud ied in the b e a m a n d ta rge t f r a g m e n t a t i o n r eg ions wi th t r ip le Regge a m p l i t u d e s a n d the effective t ra jec tor ies exchanged in b o t h types of processes are extracted.

The A p o l a r i z a t i o n in the inc lus ive r e a c t i o n has b e e n m e a s u r e d a n d c o m p a r e d wi th va lues o b t a i n e d at o the r energies a n d in re la ted processes, wi th special e m p h a s i s o n its d e p e n d e n c e o n PT.

Acknowledgements. We thank our colleagues from the CERN- College de France-Madrid-Stockholm Collaboration for per- mission to use their data.

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