Fire-string formation at high energies: pp versus pp

Nuclear Physics B216 (1983) 83-99 O North-Holland Publishing Company

FIRE-STRING

FORMATION

A T H I G H E N E R G I E S : pp V E R S U S Op

L. A N G E L I N I , L. NITTI, M. P E L L I C O R O and G. P R E P A R A T A

Istituto di Fisica, Universitd di Bari, Istituto Nazionale di Fisica Nucleare, Sezione di Bari, Italy G. V A L E N T I

Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, Italy Received 7 June 1982 (Revised 23 December 1982) A comparison of hadron production in pp and 15p interactions at x/s = 53 GeV has been carried out using the theoretical approach of fire-string formation. We find basically no differences between the two processes as clearly indicated by recent experimental information.

1. Introduction

The development of quark geometro-dynamics (QGD), a phenomenological approach to the dynamics of confined quarks based on simple geometrical ideas, has made it possible to give a systematic and comparatively simple description of the structure of hadronic final states emerging in high energy collisions [1-4]. The central role in the Q G D programme to describe and understand the structure of high energy hadroric final states is played by an important physical object, the fire-string (FS)*, comprising a coherent superposition of qcl physical (definite mass and angular momentum) excited states, which in high energy collisions mimics as close as possible (within the restrictions posed by quark confinement) quark-parton states. In a sense we can say that the FS has rendered the quark-parton model consistent with the confinement requirement. The basic simplicity of the FS states and of their decay mechanisms, which, in our opinion, constitutes the main appeal of the QGD approach, has allowed us to develop a fairly sophisticated programme to generate and analyse multihadronic events in a variety of high energy scattering processes, ranging from e-e + annihilation [1, 3, 4] to hadron-hadron scattering [2]. On the basis of our theoretical analysis and comparison with experimental information we have ample evidence that Q G D does afford a simple and accurate description of very involved and subtle aspects of high energy hadron physics. But in order to be sure that our theoretical tools are indeed capable of understanding high energy phenomena, it is necessary to submit them to the increasingly demanding test and, * Originally [5] the "fire-string" had been given the name of "fire-sausage", but in view of the reluctance of the physics community (and especially the journals' editors) to homologate this name, we have decided to rechristen it. 83

L. Angelini et al. / Fire-string formation

84

should Q G D continue to pass them in a comfortable way, this would provide precious indications towards building a more fundamental theory of hadrons. Be that Q C D or some alternative [6]. Let us recall that, besides the mere theoretical interest of exposing simple structures and behaviours in high energy scattering, our programme can also be of considerable practical interest to simulate hadronic multiparticle production in a realistic way and help the design and the understanding of the experimental apparatuses at L E P and future high energy machines. In this paper we wish to address ourselves to the very interesting and actual subject of comparing pp and ~p collisions at ISR energies (x/s = 53 GeV). Previous work on p~ collisions at ISR and at the collider energies [2] has shown that Q G D does provide a successful description of the structure of h a d r o n i c final states in terms of simple scattering mechanisms, we shall see that this picture is basically confirmed by the recent experimental findings on pp scattering [7, 8]. The paper is organised as follows: in sect. 2 we recall and discuss the mechanism for the inelastic h a d r o n - h a d r o n cross section; sect. 3 is devoted to a brief presentation of a model for diffractive production. Sect. 4 contains a description of the Monte Carlo generation of fire-strings. A comparison of our results with available experimental information is contained in sect. 5, while sect. 6 comprises the conclusions. 2. The fully inelastic cross section

In Q G D the first question we must ask is how FS's are produced in a given scattering process. Once this answer is available we can proceed and generate (stable) hadrons in the final states according to the mechanisms which we have described and analysed in a number of recent papers [1, 3, 4]. Thus in this section we recall the structure of the fully inelastic cross section (to be distinguished from the diffractive cross section, see sect. 3), which is engendered LEADING

CLUSTER

0 o

0 PAI R CREATION INCOMING PROTON

•

COLOUR BREAKING

I O VIRTUAL STATE

MESONIC

Fig. 1. The breaking of the colour flux of the proton.

85

L. Angelini et al. / Fire-string formation

56(~-e)

/Z"

\., /

FS(M' /

FS(M,~

Np

)

56

Fig. 2. The dominant mechanismfor the fullyinelasticp(~)p cross section.

by the Q G D approach* [2]. According to QGD, in order for the proton (antiproton) to interact, it must first break the colour flux among its three quarks (antiquarks) by producing one qcl pair and a leading baryon (antibaryon) (mostly a member of the 56 (56) representation) and a virtual mesonic state (qq) (see fig. 1). When the proton (antiproton) collides with another particle it is the virtual meson that becomes excited giving rise to one or more FS's. More complicated mechanisms involving more than one q~ pairs are substantially suppressed due to the Q G D perturbative structure (in the number of qcl pairs). Thus the dominant mechanism for the inelastic p(~)p cross section is p(~) + p -->B*(13*) + B* + FS(M2) + FS(M1)

(2.1)

and is drawn in fig. 2. The theoretical description of (2.1) is obtained through the following steps: (i) calculate the process: p(~) -->B*(B*)(p) + q(ql) + ISt(q2),

(2.2)

i.e. the virtual disintegration of the proton (antiproton) into a quark pair with momenta ql and q2 and a leading baryon (antibaryon) of momentum p. According to Q G D this probability amplitude can be calculated by the geometrical overlap of the proton (antiproton) wave function with the baryon (antibaryon) wave function, whose structure has been derived in ref. [10]. In order to appreciate the physics of the problem, we have reported in fig. 3 the calculated distributions of the longitudinal momenta of the quarks generated in the process (2.2); * For a recent review see ref. [9].

L. Angelini et al. / Fire-string formation

86 I

i

1

aN

N

fix

i

i

6 -~

i

_ _

QUARK

. . . .

ANTIGUARK

I

5 I

4

I

0

,2

.4

x

.6

.8

1.

Fig. 3. The normalised x distribution of quark (full line) and antiquark (dashed line) from an incident proton in process (2.2). For antiproton quark and antiquark are interchanged.

(ii) combine the quark from one vertex with the antiquark of the other to produce two FS's with total four-momentum and polarization direction (ql+q~)~ and (ql -q~)/]qx - q ~ [, and (q2 +q~ )~, and (q2-q~)/]q2 -q~] respectively; (iii) let each FS decay into stable hadrons according to the two mechanisms: chain-decay: tree-decay:

FS-~ FS'+/~,

(2.3)

FS-~FS1 +FS2,

(2.4)

where ~ is a vector meson. The important dynamical consequences of the FS decay mechanisms (2.3) and (2.4) have been discussed at length in refs. [1, 9] and shall be not repeated here. However we would like to recall that Q G D gives a complete

L. Angelini et al. / Fire-string formation

87

description of the structure of the hadronic final states emerging from FS decay in terms of two parameters: one controlling the relative weight between (2.3) and (2.4) and the other determining the amount of baryon-antibaryon pair production in FS decay [3]*. All other physical properties like particle multiplicities, transverse momentum distributions, etc., result from a well-defined calculational procedure. In closing this section we would like to stress that, at the present stage, QGD is not able to produce predictions for the absolute values of the fully inelastic cross section. On the other hand QGD predicts the pp and the ~p cross sections to be asymptotically equal and their difference to vanish like s -1/2 [11].

3. A model for single diffractive production High energy Regge behaviour has been shown to hold in QGD [11]. Actually the process (2.1) is the lowest order approximation to the Pomeranchuk singularity. The question we must now address ourselves to is to produce a model of single diffractive multihadron production compatible with the QGD picture. According to usual Regge phenomenology the diagram we are interested in is reported in fig. 4 and its behaviour is given by the parametrization** d2°" -Jg~°(t)12 dtdM z 2M 2

(] ~

_ 2[Ctp(t)

1]

o-vP(M2, t)

(3. 1)

\M]

valid also in QGD. Notice, however, that the parameters appearing in (3.1) have not been calculated, but have been extracted from phenomenological fits to the existing data [12]. In order to analyse the inelastic state X(,X) (see fig. 4) we proceed as follows:

p{O) ~

p(P)

P Fig. 4. Regge diagrams for single diffractive cross section in p(~)p scattering. * These two parameters have been calculated by making a systematic comparison between the e e + experimental data and our theoretical predictions. In the appendix an outline of the calculation of BI3 production in FS decay is given. ** For a good review of this subject see ref. [12].

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L. Angelini et al. / Fire-string formation

P(P/

sect)

FS(M-t-')

FS(MO FS(M,)

~

~S(M:/ p /

p 56

P

Fig. 5. The QGD mechanism for single diffractiveproduction.

(i) we couple the p o m e r o n P to a qcl pair; (ii) we break the p(~) colour flux as in sect. 2; (iii) we match each quark of the P with the antiquark of the proton vertex and vice versa to form two FS's. Thus the Regge diagrams in fig. 4 become Q G D diagrams of fig. 5. At ISR energies the energy available for diffractive FS production is most of the time quite limited. We have carried a detailed study of this question and found out that a good description of this process at this energy is obtained by allowing one FS to be " e m p t y " , i.e. of zero four-momentum, thus leaving only one FS to produce hadrons in the final state. Now that all the relevant theoretical aspects have been sufficiently clarified, we can proceed to describe our calculational strategy and to compare our theoretical results with available experimental information. This shall be done in the next two sections.

4. The calculational strategy 4.1. THE FULLY INELASTIC CROSS SECTION Our results, to be reported in sect. 5, have been obtained by the following Monte Carlo procedure. We have first generated 6000 events for the vertex process at pp (p~) = 26.5 G e V / c : p(O) -* B* (1)*)(p) + q(ql) + q(q2),

(4.1)

where B*(B*) is any member of the SU(6) 56(5-6) representation, weighted by the Q G D probability amplitude.

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L. Angelini et al. / Fire-string formation

We have checked that for incident proton (antiproton) momenta above 10 GeV/c the QGD amplitude scales h la Feynman, so that we can utilize these events (whose generation is quite expensive in terms of computer time) for energies above x/s = 20 GeV by simply scaling the particle momenta by the appropriate factor. Next we pair the quark from one vertex with the antiquark from the other and form a fire-string FS1 and we do the same with the remaining quark and antiquark, i.e. FS2. These two FS's, whose momenta and axes are completely specified, are now allowed to decay according to the QGD decay kernels: K c h a i n and Kt . . . . The details of the FS decay processes have been worked out and discussed in ref. [1, 9] and will not be repeated here. The computer program, EPOS, which implements the QGD description of FS decay is now available in the CERN computer library [13]. The final product of this procedure is a set of stable hadrons statistically distributed according to the QGD probability amplitudes. 4.2. THE SINGLE DIFFRACTIVE CROSS SECTION In the single diffractive events the two vertices are treated in a different way. At the vertex, which is called diffractive, the outgoing proton (antiproton) fourm o m e n t u m is generated according to (3.1) whereas at the other vertex we take the same process (4.1). In order to allow the " e m p t y " FS formation, we assign to the quark (antiquark) coupled to the p o m e r o n the opposite f o u r - m o m e n t u m carried by the antiquark (quark) coming from the inelastic vertex, as shown in fig. 6. The " e m p t y " FS is then formed by the quark (antiquark) from the inelastic vertex that has lower longitudinal m o m e n t u m and by the corresponding antiquark (quark) from the diffractive vertex.

P(P)N. +

FS[M) FS(M) /

s6(~-6)

p(o)

I

s;(~-61

Fig. 6. The QGD mechanism for single diffractiveproduction with "empty" FS.

90

L. Angelini et al. / Fire-string formation

.o

J

+ +

+

k

8

t-

+

÷ II

[

a~ v,~,'

-~..= v

....

"U

+ +

c

tra

+

+

+

© rZ

I

I

91

L. Angelini et al. / Fire-string formation t.3

i (On)~ p

1.2

(o.)

Pp

~ UA 5 • OUR RESULT

1.1 1.0' .9

.8

I

10

ncH

!

~0

30

Fig. 7--(continued).

Finally we build up the total inelastic cross section by taking 80% of fully inelastic events and 20% of diffractive events as indicated by the experimental measurements at the ISR [14]. The results reported in this paper have been obtained from a sample of 20 000 generated events for each production mechanism.

5. Results and comparison with the experiments Our results for the charged particles' multiplicities for pp and ~p at ~/s = 53 G e V are reported in fig. 7. We obtain for the average values (nch)pp = 11.30,

(exp. 1 1 . 5 5 + 0 . 1 7 [8]),

(nch)~p = 11.46,

(exp. 1 1 . 4 7 + 0 . 1 6 [8]).

(5.1)

As we can see from fig. 7 we find basically no difference between the charged particles' multiplicities in the two processes; this is in good agreement with the observations [8]. The pseudorapidity distributions for charged particles obtained by our calculation for pp and 15p and their ratio are reported and compared with the experimental information [8] in fig. 8. While our result for the ratio is in excellent agreement with experiments, some slight discrepancy can be seen for Jr/I > 2. Its origin can be understood observing that our model of 56 (56) dominance of the leading baryonic cluster produces a leading baryon which is much too hard and a few less mesons in the fragmentation regions. This situation could be completely corrected if we

oo

z q

L q •

~

1

•

o

m

i..~m#

"Oi "0

'

i

i

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i

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~l-

-.o

i

0

ro

•

•

•

I

0

|

~

"ol

i

uo1.l~)ruaoJ 8ul.als-~a~.d / .i ~) ~ !U!ld~U V "1

E6

93

L. Angelini et al. / Fire-string formation i

d"~ ~ p k~in

!

pp OUR RESULT

1.2

1.1

.

I

1.C

0.9

0.8

I 1.

|~|

If

I 2,

I 3.

Fig. 8--(continued). t o o k into a c c o u n t , as w e s h o u l d , h i g h e r m a s s b a r y o n i c r e s o n a n c e s . W e shall g e t b a c k to this p o i n t l a t e r . T h e t r a n s v e r s e m o m e n t u m d i s t r i b u t i o n for c h a r g e d p a r t i c l e s in t h e r a p i d i t y i n t e r v a l [yI< 0.8 a r e r e p o r t e d a n d c o m p a r e d with d a t a [7] in fig. 9 for p p a n d Op a n d t h e i r r a t i o ( ~ p ) / ( p p ) . T h e a g r e e m e n t is a g a i n v e r y g o o d but, p e r h a p s , for s o m e slight d e p l e t i o n for P'r > 1.0 G e V / c . A s w e shall see, this can a g a i n b e a t t r i b u t e d to t h e i n c o m p l e t e a d e q u a c y of t h e 56 (56) d o m i n a n c e . In t a b l e 1 w e list t h e m u l t i p l i c i t y r a t i o s f o r d i f f e r e n t t y p e s of p a r t i c l e s in t h e r a p i d i t y i n t e r v a l lyl<0.8 a n d c o m p a r e t h e m with d a t a [7]. W e o b s e r v e s o m e d i s c r e p a n c y o n l y for t h e p r o d u c e d p a n d ~. TABLE 1 Multiplicity ratios for different types of particles in the rapidity interval Jyl < 0.8. Experimental data are from ref. [7] Particle type

Our result

Experiment

all (+) (+) (-)

1.04 + 0.01 1.03 ± 0.01 1.06 ± 0.01

1.00 ± 0.01 0.96 ± 0.01 1.03 ± 0.01

K÷+K K÷ K-

1.04+0.03 1.00 ± 0.04 1.07 + 0.04

0.98±0.04 0.90 + 0.05 1.08 ± 0.06

p+O p

1.11+0.06 1.21 + 0.06 1.02 + 0.06

1.05±0.04 0.93 ± 0.04 1.25 + 0.07

Sd;

100

10

o,~

,

I

~

Pv GeV/c

I

.s

(~.~,o}-,

i

•

~o

SUL

R E F [7]

Iv1
1.5

ld

10

Gin dydpv

o.s

I

I

0,

(~,~)

- -

1.o

I

I

DI

OUR RESULI"

• ,~E,

Fig. 9. The (1/o'i.)(dtrln/dy dpT) for (a) pp and (b) ~p and (c) the (~p)/(pp) ratio for [yl< 0.8. Data are from [7].

,,,,,

do

i

1.5

T~

.r-

95

L. Angelini et al. / Fire-string formation oi. av alp,)- 7 {

ai.

aVdpr /

Ivl
• REV [7]

1.~

OORRImLI.1

1.1

1.C

f 0.9

0.8

s

1

15

Fig. 9 - - ( c o n t i n u e d ) .

6.

Conclusions

The results reported in figs. 7-9 and table 1, clearly indicate that our approach provides a fairly good description of the physics of both pp and Op collisions at ISR energies and in particular of the striking similarities between these processes. This should teach us at least two lessons: (i) the high energy physics of pp and ~p scattering is dominated by very similar mechanisms; (ii) such mechanisms are indeed quite simple and very close to what had been predicted by QGD. In order to fully appreciate the preceding point (ii), we recall that the inputs needed in our calculations have been taken from other processes and not fitted in the present paper. The full list is given in appendix B. We must now comment upon the origin of the slight discrepancies we have observed in figs. 8 and 9 and in table 1. As we have stated above the production of a leading baryon has been approximated by a baryon octet or decuplet (spin - 3+). Even though QGD shows that individually the 56 members of the SU(6) representation dominate, we must take also into account the large proliferation of baryon resonances for Mres > 1.5 GeV. At this stage this cannot be easily done quantitatively. However we expect the following qualitative features from these contributions: (a) the stable baryons from the decay of such resonances would populate the intermediate region between the fragmentation and the central regions (XF~--0.1); (b) mesons from resonances decay would also appear in this region; (c) the pT spectrum of such resonances would also be harder than for the 56-baryons.

96

L. Angelini et al. / Fire-string formation

(mb)

do

~-~

.,,

REF

- -

Os]

OUR R E S U L T

100

lo

'

.i

!

t

.4

I

,,

.~

'

.~

I

1.

Fig. 10. Our calculation for the proton (antiproton) x distribution. Data are taken from [15].

W e can have an idea of how important this contribution should be by looking at fig. 10, when our leading p(~) spectrum do'/dXF is c o m p a r e d with a recent compilation [15]. It is clear that 56 dominance describes about 50% of baryon fragmentation and that it is precisely in the region around xr = 0.1 that we have a definite depletion in the leading P(15) spectrum. On the basis of the above points a, b and c a 50% additional contribution from higher mass resonances would completely r e m o v e the discrepancy. In addition the a m o u n t of p(O) that would spill over into the central region would also r e m o v e the discrepancy appearing in table 1 and give a nice physical explanation of the interesting p h e n o m e n o n discovered at the C E R N ISR*. We hope we shall be able to get back to this very interesting p r o b l e m in the near future. * For extensive reviews see ref. [14].

L. Angelini et al. / Fire-stringformation

97

kl,A Pl --"kl +k2+k3 Pi= ki+k2"k 3

k2,B k3,C

k~.A'

(

~

Pi ,H'

Fig. 11, The relevant graph for the process q~l~ BB. A, A', B, C are the SU(6) indices, i.e.; A = (i, a), i an SU(2) index and a an SU(3) index.

Appendix A FS DECAY INTO A BARYON-ANTIBARYON PAIR T h e amplitude for the process shown in fig. 11, FS--*B+B,

(A.1)

can be calculated by the baryon w.f. overlap, as shown in ref. [10]:

M A ' ( H , H') = ~ d 4k2OAnc(kl, ÷(H) ~'"(~')A'BC'k' k2, k 3jtg k 1, k 2, k3) 2

2

2

x 8R2(k2-- m2)SR2(k3 -- m~),

(A.2)

using the same notations of ref. [10] and denoting with A, A ' , B, C the SU(6) indices, i.e. A = (i, a), i an SU(2) index and a an SU(3) index. Then, the decay of a FS c o m p o s e d by the q u a r k - a n t i q u a r k pair with flavours (a, a ' ) is given by K a' = E , i,i'

E [MAA' (H, H ' ) [ 2 .

(A.3)

I-I, Fl'

This kernel has been calculated numerically and has been implemented in the c o m p u t e r p r o g r a m E P O S [13]. We r e m a r k finally that as the baryon wave function normalization is a difficult task in Q G D [10], we have to fix the normalization of the kernel (2) by a phenomenological parameter.

Appendix B LIST OF PARAMETERS The relevant parameters, which we m a k e use of, are the following. (a) The p a r a m e t e r s defining the hadron wave functions, which we utilize for calculating the probability kernels of the processes (2.2), (2.3), (2.4) and (A.1):

98

L. A n g e l i n i et al. / Fire-string formation

the light quark masses m u,d 2 = 0.01

GeV

2 ,

2

ms = 0.22 G e V 2 •

the bag space-time boundaries of the meson wave functions 2

2

2

2

R s,nt = R oBnt, R t,nt = R o[3nt - C ;

the bag space-time boundaries of the baryon wave functions 2

2

2

R s,.t = R t,nl = R oflnl ,

where Ro = 4 G e V -2 ,

C = - 3 G e V -2 ,

B,l is the nth zero of the spherical Bessel function jr(z). These parameters have been determined by fitting the meson [5] and the baryon [10] spectra. (b) The relative normalization between the processes (2.3) and (2.4) and the amount of the baryon-antibaryon production (A.1) in the FS decays, are described by two parameters a and/3, which have been determined by a systematic comparison between the experimental data of e - e + and our predictions [1, 3, 4]. The numerical values are a = 1.0,

/3 = 0 . 0 9 .

(c) The relative normalization between the inelastic and the diffractive cross sections, which we take to be Ordiff/grinel =

0.25,

as indicated in the analysis of ISR data [14]. (d) The Regge parametrization (3.1) has been assumed from the experimental fitting described in ref. [12]. The numerical values are gpPp(t) = exp (R2t) , !

Otp(t) = 1 +~tot,

R 2 = 4.0 G e V -2 , !

a o = 0.25 G e V -2 ,

orpP(M 2, t ) = const,

in the Monte Carlo generation the numerical value of trpP is irrelevant.

References [1] G. Preparata and G. Valenti, Nucl. Phys. B183 (1981) 53; Phys. Rev. Lett. 47 (1981) 891 [2] L. Angelini, L. Nitti, M. Pellicoro, G. Preparata and G. Valenti, Phys. Lett. 107B (1981) 446; preprint BA-GT/82-09, Fire-string formation at high energies: hadronic production at the CERN p!5-collider

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[3] L. Angelini, L. Nitti, M. Pellicoro, G. Preparata and G. Valenti, preprint BARI-GT/81-21, Baryon-antibaryon production in high energy electron-positron annihilation [4] L. Angelini, L. Nitti, M. Pellicoro, G. Preparata and G. Vatenti, preprint BARI-GT/82-03, Is the gluon hiding under the third jet? [5] G. Preparata, in The whys of subnuclear physics, ed. A. Zichichi, Plenum, 1979 [6] G. Preparata, Phys. Lett. B102 (1981) 327; B108 (1982) 187 [7] T. Akesson et al. (Axial Field Spectrometer Coll.), preprint CERN-EP/81-123, A comparison of ~p and pp interactions in the central region at x/s = 53 GeV [8] K. Alpg~rd et al (UA5 Coil.), preprint CERN-EP/82-5, Comparison of ~p and pp interactions at x/s = 53 GeV [9] G. Preparata, preprint BARI-GT/81-13, Toward breaking the code of hadron final states, inv. talk at Physics in Collisions, Blacksburg (May 1981) [10] G. Preparata and K. SzegS, Nuovo Cim. 47A (1978) 446 [11] G. Preparata, Nucl. Phys. B122 (1977) 29 [12] A. B. Kaidalov, Phys. Rep. 50C [13] L. Angelini, L. Nitti, M. Pellicoro and G. Valenti, A program for generating hadronic final states arising from electron-positron annihilations (EPOS), CERN Program Library (W1034), CERN Comp. Newslett. no. 162 (1982) [14] G. Giacomelli and M. Jacob, Phys. Reports 55 (1979) 1; G. Alberi and G. Goggi, Phys. Reports 74C [15] M. Basile et al., preprint CERN-EP/81-147, A.prediction for the total charge multiplicity in hadronic interactions at extreme high energies and references therein