isospin.pdf - cern indico

Nuclear Physics AS28 (1991) 754-770

North-Holland

HADRON PRODUCTION IN NUCLEON-NUCLEON COLLISIONS

AT 200 GeV/c - A COMPILATION

M. GAZDZTCKI

Institute of Experimental Physics, University of Warsaw, Warsaw, Poland

Ole HANSEN

KVI der Rijksuniversiteit, Groningen, The Netherlands and

University of Frankfurt, Fachbereich Physik, Frankfurt, Germany and

Brookhaven National Laboratory, Upton, NY 11973, USA

Received 20 August 1990

(Revised 15 October 1990)

Abstract: Data on stable hadron production in p + p and p + n interactions at 200 GeV/ c are reviewed.

Methods to construct missing data in the p + p, p + n, and n + n interactions are derived from charge

symmetry and charge, baryon and strangeness conservation, and used to yield nucleon-nucleon

interaction results. These may be useful for evaluating nucleus-nucleus collision measurements in terms of enhancements and suppressions. Parameterizations of p: and rapidity distributions are

presented to provide yields in acceptance cuts for comparisons to nucleus-nucleus data. As an

example the derived nucleon-nucleon multiplicities are reduced to the acceptances of the NA-35

CERN S+S experiment.

1. Introduction

One of the hopes in the study of high-energy nucleus-nucleus (A,, + A,) collisions

is to observe systems that deviate in a nontrivial way from a mere superposition of

independent nucleon-nucleon (N+ N) interactions. It is customary to compare

results for A,, + A, collisions to corresponding p + p data. This is, however, not really

a relevant comparison, as A,+A, collisions contain a mixture of p+ p, nfn and

p+ n interactions, and are always dominated by p+n rather than p+p.

It thus seems worthwhile to establish N + N data in a direct way. To this end we

have compiled p+p and n-kp results from the literature and used bombarding

energy systematics and various symmetries, in particular charge symmetry, to com-

plement the measured results and to construct the missing data in a model indepen-

dent way. We thus end with a set of standard p+p, pt n and n+n results from

which one can construct properly weighted averages to form the basis of comparison

to A,, + A, measurements.

In A,+ At as well as in p+A, collisions, a nucleon may interact more than once,

the second and subsequent interactions happening at lower and lower center of

0375-9474/91/$03.50 0 1991 - Elsevier Science Publishers B.V. (North-Holland)

M. Gazdzieki, 0. Hansen / H~dr~n ~rod~~i~on 755

mass energy. Such reinteraction effects will show up as “enhancement” when

nucleus-nucleus or p-nucleus data are compared to the N+N results presented

below. It is beyond the scope of the present paper to treat such dynamical effects

in any further detail.

While the methods used in this report are general, we have concentrated on data

at 200 GeV/c (for v’% = 19.4 GeV) and on strange-particle yields important for the

CERN heavy-ion experiments.

Relations obtained from isobaric symmet~ and from various conse~ation laws

are presented in sect. 2. Sect. 3 deals with multiplicities while sect. 4 presents

parameterizations for transverse momentum (p,) and rapidity (y) distributions. In

the last section, as an example of the use of this compilation, we construct N+N

results relevant for interpretation of the NA-35 streamer chamber data ‘) from S + S

interactions.

2. Inclusive cross section relations

2.1. CHARGE SYMMETRY INVARIANCE

Strong interactions conserve isospin. We shall exploit mainly invariance under

rotation in isospin of 180” around the y-axis,

RI = exp (-iTI,,), (1)

also denoted as “charge symmetry” (see e.g., ref. ‘)). Ignoring relative phases, the

operation (1) [see e.g., ref. “) or ref. ‘)I changes

pen, K+eK*, K-ZIP,

n=n, LF%?, lr++71-, 0, 0 r 7n=. (2)

The general rules for inclusive cross sections under charge symmetry invariance are

~(p+p+a+X)=a(n+n+a*+X*), (3)

a(p-t-n+a+X)=cr(p+n+a*+X*). (4)

Here X stands for “anything but a”, and a* is the charge symmetric partner of a

(see e.g., eq. (2)). As X does not include particle a, X” has no a* and the right-hand

sides of (3) and (4) thus represent inclusive cross sections. Table 1 gives the explicit

relations for the inclusive cross sections for or, K, A, and N, relations that are used

in sect. 3. The charge symmetry relations do not connect nf p interactions to p+ p

or n-l-n.

2.2. A SPECIAL RELATION FOR THE ISOTROPIC CASE

The p-l-n channel is composed of two isospins,

/p+n)=~~I=l,lZ=O)-~~l=O,IZ=O). (5)

156 M. Gazdzicki, 0. Hansen / Hadron production

TABLET

Charge symmetry relations for inclusive cross sections “)

Reaction 1

inc. ch. + exit ch.

equals

Reaction 2

inc. ch. + exit. ch.

P+P

P+P

P+P

P+P

P+P

P+P

P+P

P+P

P+P

n+P

n+P

n+P

n+p

2 Tr+/?-- K+/K’

K-/l?

P/n

Wfi

flril z”

rr+/ 6

K+/ K” K-1 i?’

P/n

n+n

n+n n+n

n+n

n+n

n+n

n+n

n+n

n+n

n+p

n+p

n+P

n+P

?r” P-/P’ K”/ K+

l?/ K-

n/P ii/b

n9A 9

a-/ 7r+

KO/ K+ lF/K_

n/P

“) Entries with a / stand for two relations; e.g. for p + p + rrf/6 = n + II+

Y/rrTT+ read cr(p+p+r+)=a(n+n+Y) and u(p+p+rr-)=a(n+n+

P’).

As the strong interaction depends on the isospin of the channel the I = 0 part of

the p+n interaction cannot be related to the I = 1 part by isobaric symmetry. In

the particular case, where the elementary interactions happen with a two-time

weighting of n+p, i.e. as

(p+p)+(n+p)+(p+n)+(n+n), (6)

the 1, substates for the combined I = 1 and 1= 0 system occur with equal probability.

The system is, in other words, spherically symmetric in iso-space and consequently,

in the final state, all members of an isospin multiplet have the same cross section.

For this case one then has (see also ref. 4)):

a(p+p+ 7r+)+cr(n+n-+ r+)+2a(n+p+ rr+)

=cr(p+p+~“)+a(n+n+rro)+2u(n+p+71-0)

= v(p+p+ C)+a(n+n+ &)+2a(n+p+ rr ) . (7)

As the last equality can be derived from the first using the charge symmetry relations

in table 1, only one new relation is obtained. (Note the “+X” has been dropped in

the inclusive cross section notation.) From table 1 and the first equality in (7) it

follows that

~(p+pWi-+)+a(p+p+~-)-2a(p+p+7r”)

=2u(n+p+ 5-O)-2a(n+p+ 3-+) , (8)

M. ~~zdzi~k~ 0. Hansen f Ha&on ~rodMc~io~ 757

where the cross sections are all inclusive. For isoscalar or isospinar particles there

are no new relations in addition to those in table 1. It may be noted that the case

of eq. (6) is relevant for A, + A, physics namely for the collision of two nuclei where

each has 2 = N

2.3. CORRECTIONS FOR ELECTROMAGNETIC PRODUCTION

In addition to production by strong interactions, where isospin is conserved, the

yields of some particles receive non-negligible contributions from the isosymmetry

breaking electromagnetic interactions, e.g. pions from the electromagnetic decay of

the n, and A from the 2’ decay.

The charge symmetry relations of table 1 are not changed by the r] and 2’ decays,

because both have I, = 0.

As the v” branch of the n-decay is different from the charged pion branch, eq.

(8) is affected. Each inclusive cross section should be reduced by the amount that

is due to ~-production and n-decay. Denoting the average multiplicities per q-decay

(T*)~, (TV),, = (+V3 a correction should be added to the right-hand side of eq. f8),

Corr=-(2a(p+n+ n)+20-(p+p-+ n))((rO), -{T+>,), @a>

where the second factor equals 0.90 [ref. ‘)I.

2.4. RULES FROM CHARGE, BARYON AND STRANGENESS CONSERVATION

The mean multiplicities for negatively charged particles (n-) and charged particles

(n”) are connected through conservation of charge,

+2 for p+p

(n*)=(n+)+(n-)==2(n-)fQinc, where Qinc = 4-l for p+n (9) 0 for n+n.

Written in terms of multiplicities, the law of baryon conservation for p-l-p, pi-n,

or n + n interactions is

(10)

where n stands for neutron and Y for hyperon. Strangeness conservation gives

(I?)-+-(K’)+(T}=(K-)+(K’)+(Y) (11)

for all three entrance channels.


TABLE 2

Charged particle multiplicity data “)

Reaction Energy (GeV) (n’) Refs.

P+P 200 2.86 * 0.05 7.7110.10 P+P 205 2.8410.04 7.68 i 0.07 n+p 195 3.28 * 0.03 7.56kO.06 n+p 200 3.13io.04 7.26+0.10

“) All numbers are from data in the literature as referenced.

Y

‘)

a)

‘)

3. Average multiplicities at 200 GeV/c

3.1. CHARGED PARTICLES AND PIONS

In the following the average multiplicity of particle x from the interaction a+ b

is denoted (x, a+b). Table 2 shows the negative charged particle (n-) and charged

particle (n’) multiplicities measured at 195-205 GeV/c. As the different data sets

agree rather well we have adopted in table 3 the averages weighted inversely with

the square of the uncertainties and we have used a final uncertainty

unc = l/ W, W=Z:,l/a2,, (12)

where Us is the uncertainty of the nth measurement. The adopted (6) values of

table 3 may be tested for consistency against the empirical rule

(n-,n+p)-(n-,p+p)=0.28*0.07, (13)

which has been established by Dado et al. lo) and is independent of A. The value

of (n-, n+ p) - (n-, p + p) from table 3 is 0.38 f 0.05, consistent with eq. (13).

The experimental values for pion multiplicities are given in table 4. rTT+ and 6

multiplicities have not been measured at 200 GeV/ c, and the results in the table are

from the systematic interpolation expressions in & of refs. ‘l,l*). A more precise

value for (Y) may be derived from the relation

(14)

TABLE 3

Final charged multiplicities at 200 GeV/c “)

Reaction (n-) (n*) (r-) (p’) (PO)

P+P 2.85 + 0.03 7.69 * 0.06 2.62 * 0.06 3.22ztO.12 3.34ztO.24 n+p 3.23 * 0.02 7.48 f 0.05 3.01+ 0.04 3.01* 0.04 3.06ztO.25 n+n 3.42*0.13 6.84 * 0.26 3.22zt0.12 2.62 f 0.06 3.34zkO.24

“) The table is explained in the text.

M. Gazdzick( 0. Hansen / Hadron production

TABLET

Pion multiplicity data “)

759

Reaction Energy (GeV) (7+7 (w-j (-‘) Refs.

P+P 20.5 3.34io.24 P+P PO01 2.8 * 0.4 3.4*0.4

13 j’ 11

P+P WOI 2.7 * 0.4 3.3 Zto.4 I2 )

“) Brackets [ ] on the energy entry mean results obtained from interpola~on paramete~zations in &.

and the adopted values of (n-> (table 3), (K-), and (p) (tables 7 and 8, respectively).

Eq. (14) should also include _I-, but the correction is inconsequential. The result

is the one quoted in table 3. The (z+) value used in table 3 follows from another

empirical relation (ref. “)).

(P+, p+p)-(7~-, p+p)=O.60*00.10, (15)

where the uncertainties of the right-hand side of eq. (15) and of (7r -> have been

treated as independent. The values of (P-, p+p> and (w+, p+p) derived in this

manner are close to, but slightly below the interpolation values of table 4. The value

for (TO, p+ p) is somewhat high as judged by the rule (see, e.g., ref. 14)),

(TO, P+P) =f((r’, P+P)+(m-, p+p)) , (16)

which would give (G-O) = 2.92 * 0.07, a 2a deviation.

The remainder of table 3, pion multiplicities for n+p and all the n-kn multi-

plicities, is filled by construction. The (7~, n + n) values follow from the p + p results

using table 1. (n-, n f n) is obtained from the definition (14)

(n-,n+n)=(p-,n~n)f(K-,n+n)+(B,n+n). (17)

Values for (F, n + n) = (7r+, p+p) from table 3 and for (K-) and (p) from tables 7

and 8 were used to yield the result quoted in table 3. The ( ni, n + n) value is derived

from the (n-, n+n) result and eq. (9). Eq. (9) is fulfilled for both p+p and n+p

demonstrating the internal consistency of the corresponding (n-) and (n+> values.

The (C, n+p) result is derived from the measured (n-> result and eq. (14), with

IC and p input from tables 7 and 8 below and (r+, nf p) then follows from table 1.

(Z-O, n+p) was estimated from eq. (S), with the assumption that a( p+n+ r)) =

a(p+p+ 7) and using the empirical result (ref. ‘“)) that a(p+p-, r])/a(p+p+

C) = 0.1. If the assumption on the q cross section is wrong by a factor of two the

value for (TO, n+p) is only affected by =O.l, well within the error estimate. It may

be noted that the n-t-p pion values satisfy eq. (16), probably signalling that the W’

estimate is valid also for situations of non-isotropy of the isospin substate population.

760

V' multiplicity data

Reaction

P+P

P+P

Energy (GeV)

200

205

(K:)

0.161tO.02

0.18*0.014

(A+1;o) (~-+X0) Refs.

0.08 f 0.02 0.02 f 0.01 “)

0.10*0.01 0.012+0.004 13 )

3.2. STRANGE PARTICLES

Table 5 gives the available data on A +X0, ,!% + 2’; and Kz production; there are no p + n data near 200 GeV/ c, and the standard kinematic V” analysis includes X0 and 2’ as part of the A and A yields, respectively. The iI measurements suffer from poor statistics. There are no K+, K- results at 200 GeV/c, so we are forced to use the & systematics of ref. ‘I> for an estimate (table 6).

The p+p entries in the final results (table 7) represent weighted averages as defined in sect. 3.1, as the two data sets in table 5 are consistent. Using the standard relation between Kz, KF, and K” and K” multj~licities

(K:) = (KY) = $((K’+ K’)) (18)

(see, e.g., ref. 14)), we may deduce that

(K~,n+n)=~((K”,n+n)f(‘Ko,n+n))

=%K+, P+P)+K-, P+P)), (19)

where the last step relies on table 1. Eq. (19) was used to derive the n+n value in

table 7, for (K3. TABLE 6

Charged kaon multiplicity data “)

Reaction Energy (GeV) (K+) (K-) Ref.

P+P r2001 0.28 f 0.06 0.18~0.05 11 )

“) The results are from interpolations in &.

TABLET

Final strange particle mu~tipli~ties at 200 GeV/c “)

Reaction

P+P

p+n n+-n

(K:) (K”) (K-) (A f ZO} (d + 20)

0.17*0.01 0.28 f 0.06 0.18+0.05 0.096 * 0.01 0.013 f 0.004

[0.20] CO.241 [0.17] [0.096] [0.013]

0.23 f 0.03 0.19*0.04 0.15*0.04 0.096 + 0.01 0.013 It 0.004

“) The p f n numbers are the average of the corresponding p+ p and n+ n results (see the text). When

using these p+n numbers, we have applied uncertainties that follow from the rule of construction, i.e.

10.02 (KE), 0.04 (K”), 0.03 (LX-), 0.01 (A +X0), and 0.04 (x+x’)

M. Gazdzicki, 0. Hansen / Hadron production 761

(I(‘) and (IC) values for the n+n channel may be estimated by using charge

symmetry, strangeness conservation, relation (18), the empirical rule r4), valid at the presently considered energies,

(U,p+p)=(1.6*o.l)((n+~“,p+p) (20)

and the assumption that eq. (20) is also valid in the p t p channel for the corresponding antiparticles. Table 1 and eq. (18) yield,

(K~,n+n}+{K-,n~n)=2{K~,p+p}. (21)

The difference (K”) - (K-) is given by table 1 and eq. (1 l),

(K~C,n+n)-(K-,n-i-n)=(Ko,p+p)-(Ko,p+p)

=KP+P)-@,P+P)+(~(-,p+pHK+,p+pb (22)

The right-hand sides of (20) and (22) are available from table 7 and yield the nf n

entries for (K+) and (K-). The n+ n values for the neutral hyperons follow from table 1.

As remarked earlier, the nfp numbers cannot be derived from p+p, and consequently the n+p entries in table 7 should be left open. As the data in table 3 always give n + p values that are in between the p + p and n + n, we have made the arbitrary assumption that the strange multiplicities satisfy

(strange, n + p) = $((strange, p + p) + (strange, n + n)) (23)

and quoted the relevant numbers in the table in square brackets. The internal consistency of the n-l-p results can be checked to some extent. We have, via (1X) and table 1, that

=0.5((K’,n+p)+(K~~,n+p)). (24)

a relation which is fulfilled by the values in table 7. At lower energies (lo-29 GeV) n + p data show that (I(:, n + p) = (Kz, p + p> to within 20% and, to the same accuracy, that (A +.Z’, n+p) = (A -i-Z’, p+p>. Both relations are obeyed by the results in table 5.

3.3. NUCLEONS AND ANY-NUCLEONS

There is no measurement of the proton multiplicity at 200 GeV, but the numbers may be derived from tables 3 and 7. Noting that

(n”>=(n”>+(n-), (25)

and that, in analogy to eq. (14),

(~‘)=(P>+(~+)+XK+), (26)

162 M, Gazdzicki, 0. Hansen / Hadron production

TABLET

Final nucleon and anti-nucleon multiplicities “)

Reaction (P) (n) (P) (a)

P+P 1.34zto.15 0.61 f 0.30 0.05 bO.02 [0.05]

p+n 1.00*0.08 1.00 * 0.08 [0.05] [0.05]

n+n 0.61 f 0.30 1.34xto.15 co.051 0.05 f 0.02

“) The (p, p+p) number is from the interpolation rules of ref. I’). The numbers in

square brackets are assumed and in any use of these guesses a *50% uncertainty was

employed.

(where the Z+contribution is again negligible), we have

(p)=(n*)-(n-)-(rr+)-(K+) (27)

valid in all three channels. The ( p) entries in table 8 are from eq. (27). The ( p, p + p)

value of table 8 agrees well with the experimental result (ref. ‘“)) at 69 GeV/c

((p) = 1.22 f 0.04) but is somewhat lower than the ISR data 11) at higher bombarding

energies ((p) = 1.63 f 0.2). The values for neutrons follow from the proton values

via table 1.

For antiprotons there are no data near 200 GeV. We have used the 6 interpolated

results of ref. 11) as the main anti-nucleon entry in table 8. In order to construct the

remaining numbers for p and ii we have made two arbitrary assumptions, namely that

(P,p+p)=(fi,p+p)=(P,n+p). (28)

Eq. (28) has no support in the various rules of sect. 2, nor in any measurements.

The baryon results of tables 7 and 8 may be checked for consistency in the p+p

channel via the baryon-conservation equation (10) and the empirical rule (20). The

baryon number B is, B( p+p) = 2.0*0.3, in good agreement with the expectation

of two. If the rule eq. (20) also holds in the p + n channel, we get from tables 7 and

8 that B(n + p) = 2.0 f 0.15 and for the n + n channel (where eq. (20) is valid because

of charge symmetry) B(n+ n) = B( p+p). The procedures as a whole are consistent

but the uncertainties combined with the small magnitudes of (fi), (ii), (A + A’“) and

(A +s”) do not allow any conclusions on the validity of the arbitrary relations,

eqs. (23) and (28), to be drawn.

4. Rapidity and transverse momentum distributions

Ideally one would like to extract from the p+p data a function

d’aldp, dy =f(~t, Y) . (29)

where y stands for rapidity and pt for transverse momentum. For the cases of Kf,

A +X0 and & which is our main concern here, this is not possible as only cross


sections integrated over a broad interval of the other variable have been measured.

Thus, we may extract parameterizations,

Pm,, Y.n,X da/dY = g(Y) =

I f(~,, Y) dpt, daldp,= Q,) =

I f(p,, Y) dy. (30)

Pml" Ymin

The purpose of such parameterizations is to “cut” p + p or N + N data into some

given acceptance for comparison to heavy ion data. Use of eq. (30), in the form of

functions g or h obtained from fitting to data, is in general not equivalent to the

“correct” procedure of using eq. (29). Only if f satisfies

f(P,, Y) ‘fi(PtMY) (31)

are the two approaches consistent. Eq. (31) is normally not satisfied, e.g. pt spectrum

slopes vary with y. Use of (30) thus introduces errors, that are hard to estimate but

it is the best we can do. We have assumed that spectrum shapes do not depend on

incident channel p +p or p + n. The meager evidence, mostly on mean pt values,

see, e.g., refs. ‘,16), support this assumption. We have further assumed that the pt

and scaled (see below) y distributions for p+p interactions do not change shapes

between 200 and 300 GeV/c, an assumption well supported by the measurements

refs. 13,17-22 1.

We have not attempted systematic fits to (n-) or pion data as the S + S results ‘)

on n- are so close to 4~ coverage (-95%) that the relevant results of the previous

section could be used directly.

4.1. NEUTRAL STRANGE PARTICLES

The p: distributions at 205 and 300 GeV/c are shown in figs. l-3 for Ki, A + Z”,

and il+L?‘, respectively (refs. 13717Z18)). Th e ex p erimental distributions are partially

integrated over y and were fitted to the appropriate thermal form, eq. B.ll, ref. 23)

1 da --= C&exp (-m,/B), c d(d)

(32)

where m, = dpf i- m2. The fits are shown in figs. l-3 and the parameters C and B

are given in table 9. Note that the data at higher energies (360 GeV/c and up ‘“,“))

systematically show two distinct slopes in the p: spectra, assumed in the Kt case

to stem from the increasing population of K” resonances.

The il result in table 9 is from a fit to the four point distribution of ref. ‘), the

only available.

The rapidity distributions have been fitted to the form

1 du ;z=D+Ez2+Fz4, z = y*/y*(beam) (33)


” ’ I ” ” I ” ” / I’:

i p+p->K,‘+X

Fig. 1. Invariant cross section versus p: for p + p + Kz+ X interactions. Open squares indicate data from

Jaeger et al. at 200 GeV/c [ref. r3)], open diamonds correspond to 300 GeV/c results of Sheng er al. 17), and the black squares are the data points from LoPinto et al. “) also at 300 GeV/c. The curve is the

least squares fit of the form of eq. (32) with the parameters of table 9. The cr in the factor multiplying

the cross section is the inclusive Ki cross section; the area under the curve is unity.

where y* is the rapidity in the p+p center-of-mass system. The choice of scaling

variable z follows the suggestion of ref. ‘“). The functional form of (33) is even in

z to reflect the symmetry about y* = 0 but has otherwise no physical significance.

It was chosen to be able to fit both the single “hump” Kz distribution and the

double “hump” A distribution by the same form. The data are from refs. 13,17*18),

and the resulting parameters are given in table 10 while the corresponding distribu-

tions are shown in figs. 4-6 together with the data. Data points that were more than

3 standard deviations from the fit curve were omitted from the fitting procedure.

5. NA-35 S+S acceptances, an example

For S + S interactions we take

(N+N)=0.25(p+p)+0.50(n+p)+0.25(n+n) (34)

as the number of neutrons equals the number of protons for both projectile and

target; the rules of isospin isotropy (eqs. (7) and (8)) are fulfilled for this case.


101

100

10-l

10-z 0 0.5 1 1.5

pt” (GeV/“@

Fig. 2. Invariant cross section versus p: for p-i-p+ A fX interactions. Symbols are as explained in the caption to fig. 1.

The acceptances used in NA-35 are different for different particles. For A-f-E0

and x+2’ the acceptance is

p > 1.15 , 0.41< pt < 2.0 ) 5.4<8<60.0, y<3.0, (35)

while Kr was observed in the acceptance

p > 1.52, 0.54 <pt < 2.0 ) 5.4<8<60.0, yC3.0. (36)

Here p is the magnitude of the momentum, 8 the polar angle with respect to the

beam direction in degrees and y the lab rapidity. All momenta are in GeV/c and

for 200 GeV/c protons y*(beam) = 3.04.

The ratio of particles satisfying the acceptance conditions to the total number

particles can be calculated by numerical integration or by Monte Carlo generation

of particles according to the function g{y)~~p~), The ratio gives the needed reduction

factor in the corresponding N + N multiplicity.

The acceptance for n-’ in the S + S run is defined as

p>O.l, 0 < 60.0 (37)

and is close to full y-pt coverage. The cut of eq. (37) reduces (n-) by 0.14+0.06

and leads to the numbers quoted in table 11 for (n-, N-t N) via use of eq. (34). It

is sometimes useful to derive a non-strange negative charged multiplicity, 27) which


101

100

10-l

10-z

Fig. 3. Invariant cross

DfD- >n+x

section versus p: for p+p --) x+X interactions. The data are from ref. I*).

also caption to fig. 1.

TABLE 9

Fit parameters for ps spectra at 200 GeV “)

Particle (G:V) (GeV’/2 c’)

Range

(GeV/ c)’ X2

[per DOF]

KZ 0.157 + 0.006 (14.2+3)x 10’ 0.0-1.5 1.2 /Ii-z0 0.110*0.005 (6.6 * 3) x lo4 0.0-1.3 1.4

A+$0 0.089 * 0.01 (8.8 11) * x lo5 0.0-0.9 0.3

“) Fit parameters relating to eq. (32). The range is the pt range of the data used in the fit.

DOF stands for degrees of freedom.

TABLE 10

Fit parameters for scaled rapidity distributions “)

See

Particle D E F Range ,$/DOF

KZ 0.96 f 0.04 -1.9iO.2 0.9 * 0.2 -1.0-0.0 0.8

A+Y 0.30*0.05 2.7 * 0.3 -3.5 * 0.4 -0.9-0.0 1.2

A+SO 1.13*0.15 -3.3 * 0.1 2.6ztO.5 -0.8-0.0 1.7

“) Fit parameters relating to eq. (33). The range is in the scaling variable z as defined in eq. (33) and the text.

-1 -0.75 -0.5 -0.25 0 Z

0.25

0.00

Fig. 4. The multiplicity distribution in the variable z =y*/y*(beam) for pi-p-, Ky+X interactions. The

variables and the functional form of the least squares fit curve are explained in the text (eq. (33)). The

data symbols are as defined in the caption to fig. 1.

1.50

0.00

pi-p->h+X

-1 -0.75 -0.5 -0.25 0 Z

Fig. 5. Multiplicity distribution for p+p+A +X interactions. See captions to figs. 4 and 1 for further

definitions.

768

Fig. 6. Multiplicity distribution for p + p + x+X interactions. See captions to figs. 4 and 1 for further

p+p->Kf-x

Z

definitions.

we define as

(n-, nonstrange, N C N) = (n-, N + N) - (K-, N + N) ,

which is also quoted in table 10. The acceptance reduction from eq. to be the same as the one derived for (n-).

(38)

(37) is taken

Results for FL:, A +_.E’, and x-t 2” are also given in the table 11. The errors assigned do not reflect the troublesome product assumption for the probability distributions.

TABLE 11

N+ N multiplicities “)

Particle Full phase space NA-35 act. Ace. definition Reduction factor

(n-, N+N) 3.22 f 0.06 3.06 f 0.06 (37) 0.95

(n-(ns.), Nl-N) 3.06 * 0.08 2.91 rt 0.08 (37) 0.95

CR:, N+N) 0.20 i 0.03 0.026 It 0.004 (36) 0.13

(A fZO, N+N) 0.096*0.015 0.019~0.003 (35) 0.20

(ii+s*, N+N) 0.013 * 0.005 0.0014+0.0006 (35) 0.11

“) The column marked full phase space is the result of constructing multiplicities from tables 3, 5 and 6 in accordance with the weights of eq. (34). The next column gives the multiplicities for the acceptances of the SC S experiment of NA-35 (ref. r)) defined by eqs. (35), (36), and (37), derived as described in

the text. The reduction factors are the ratio between the multiplicity of column 3 and that of column 2.

(ns.) stands for non-strange, see eq. (38).

769

It has been shown that it is possible from the data in the p +p and n+p literature at ~200 GeV/c to construct an almost complete set of stable hadron multiplicities for p f p, n + p, and n + n interactions by applying charge symmetry, conservation of charge, baryon number and strangeness, and isospin “isotropy”. The lack of experimental data on strangeness production in p + n interactions made it necessary to introduce one arbitrary rule, eq. (23). The internal consistency of the resulting multiplicities as checked against ~onse~ation laws and empirical rules is good.

The data on pt and y distributions are much poorer and a consistent approach could not be devised, mainly because only quantities integrated over large intervals of either y or pt have been measured.

The situation at the second CERN heavy ion energy, 60 GeV/c per nucleon, is quite similar to the 200 GeV one discussed here. At the Brookhaven AGS heavy ion energy of 14.6 GeV/c per nucleon more n +p data and some K+ and K- results are available, but at this low energy the yields depend strongly on & and the relative differences between p +p, p+n and n+ n interactions are larger. The methods of sect. 2 are general and should prove a valuable tool in addition to the commonly used event generators.

The authors gratefully acknowledge helpful discussions with Drs. E. Skrzypczak and H. Bialkowska. The authors want to thank Dr. R. Stock for numerous critical comments; without his needling this work would, never have been done. One of us (OH.) is indebted to the A. von Humboldt Foundation of Germany for travel support and to the Institute for Experimental Physics of the University of Warsaw for support and hospitality. Iie is also indebted to Prof. R. Siemssen and the KVI in Groningen, The Netherlands, for hospitality and to F.O.M. of Utrecht, The Netherlands for financial support during his stay in Groningen. Part of the work was done under contract number DE-AC02-76CH00016 between the United States Department of Energy and Brookhaven National Laboratory.

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