-PUB-1930 SLAC April 1977 (T/E) HADRON PRODUCTION IN NUCLEAR COLLISIONS 4 A NEW PARTON MODEL APPROACH* Stanley J, Brodsky Stanford Linear Accelerator Center Stanford University, Stanford, California 94305 John F. Gunion Department of Physics of California, Davis, California
University
95616
J, H. Kchn Max Planck Ins$itut fcr Physik und Astrophysik Munchen 40, Germany ABSTRACT We consider a simple quark-parton nucleus interactions lated in rapidity model for inelastic hadron-uncorreinde-
where the wee partons of the projectile
- interact with the wee partons of essentially The ratio of multiplicities
pendent nucleons in the target. region is given by --HA RA=<n>=-+z-HN
in the central
; 2
3 v+l of
inel inel where v = AcHN / aHA is the average number of inelastic collisions the projectile ticle regions, Predictions collisions H in the nucleus. this prediction
Including the effects of the leading paris in excellent agreement with experiment. distributions in hadron+mcleus collisions.
are also given for multiplicity and for multiplicities
produced in nucleus-nucleus
The model, which is consistent with Glauber theory,
predicts the ab-
sence of shadowing at large q2 (independent of w) in electroproduction or whenever the momentum transfer of a subprocess is large.
(Submitted to Phys. Rev, Lett,)
*Work supported in part by the Energy Research and Development Administration,
-2Although the quark-parton model has been very successful in predicting the underlying mechanisms the in.-
short distance behavior of hadronic interactions, volved in the production of hadrons in ordinary been specified 0 In the case of particle mental uncertainty to an extraordinary perimental
high energy collisions
have never this funda-
production on nuclear targets,
of the parton approach becomes amplified, range of divergent predictions
and this has led
for even the most basic ex-
parameters.
In this letter we present a new approach to this probapplication of parton model concepts, The re-
lem based on a straightforward
sulting picture for nuclear collisions experiment.
is very simple and in good agreement with excited and
It is based upon (1) the assumption that each inelastically
nucleon in the nuclear target produces hadrons independently of the others, (2) a specific hadronic collision gous to the Drell-Yan3 model based on wee parton interactions2 process, of hadron-hadron
analo-
pair production
We begin with a simple parton model description actions, Each hadron has a Fock-space decomposition
inter-
in terms of multiparton
states 0 An interaction parton in the target (A).
occurs via a collision
of a parton in the beam (B) with a form 354
The cross section takes the typical Drell-Yan
(1)
where
, s = C$+k;)/(p;+pz,)
and
Xa
= ck; - kz,b(p; - P;) (pi > 0, pi < 0) of the beam and target, respec-
are the light-cone tively, and
fractions
-3A
S
2 2 amb ab =XaxbS+~ (For simplicity Expression we do not
is the collision
energy squared of the subprocess. momentum dependence.)
display the transverse invariant
(i)
is Lorentz-
for boosts along the beam (z) direction.
We presume that Gab falls exchange 2y5 or
rapidly with increasing
sab, as would be typical of quark-parton
q-4 annihilat ion processes, 6 and that each distribution wee parton distribution and the location formly
G(x) has the Feynman2
xG(x) - C # 0 at x - 0. In this model oBA(s) cx log s, of the parton-parton collision ; is distributed uni-
in rapidity
throughout the central region,
where neither xa nor xb is forced into the collisions, the partons
finite x, power-law
damped regions of G(x) 0 In inelastic
in the beam materialize terialize
as hadrons for $2 y c;YB, and those in the target maYA < y <, q0 Note that real hadron production
throughout the interval
from the beam partons cannot extend much below G since this forces propagators off-shell where interactions are suppressed. we shall assume that, aside from small bindeach nucleon in the nucleus indepenThus the partons of different nu-
Turning to nuclear collisions, ing corrections
and Fermi motion effects,
dently develops its own parton distribution. cleans interact with each other only minimally with one another, projectile 7 In a high energy collision
and do not shadow or coalesce the various wee partons of the nucleons. -The rapidity disin of the separa-
can interact with the wee partons of different collisions
locations of the parton-parton tributed in the central region.
ii are uncorrelated
and uniformly
Each nucleon in the nucleus A participates inelastic collisions
only one interaction,
whereas the mean number of
inel me1 beam hadron H is V = AuHN / aHA D On the average, then, the rapidity tion between parton collisions is Ay 2 Yc/(Y+l)
where Yc is the total length of
-4the central rapidity sions isillustrated each inelastically region,, A typical multiparticle distribution rapidities for v = 3 colli-
in Fig, 1. Since the collision
are uncorrelated, on the average increases, the
excited nucleon produces hadronic multiplicity .As the number of collisions extends further
halfway across the- central region. range of the projectile
hadron distribution
and further
into the
central region to the minimum ;Ay = (;/(;+l))Yc. the central region
ii -on the average over a rapidity
length in
Thus we immediately
obtain for the ratio of multiplicities
nHA-i+-i <wHN 2
v+l
H is through the definition of 3.
(2)
where the only dependence on the projectile The distribution of particles
averaged over events produced from the exThe ratio of distributions collisions in
citation of the nuclear partons is wedge-shaped. the central region for hadron-nucleon
to hadron-nucleus
is simply (yA=O)
Although Eqs, (2) and (3) are derived assuming a uniform central region, corrections
plateau height in the
to this shape tend to cancel in the ratio. regions. Eq. (1)
Thus far we have ignored the effects of the fragmentation predicts that the fast (e.g.,
valence) partons interact only weakly8 and thus fragmentation region, and RA(y) = ? in the target
RA(y) = 1 in the projectile fragmentation particles within Ay obtain region.
and <n > be the average number of Let <n f ragH frag N and nucleon fragmentation regions (i.e.,
produced in the projectile frw
N 2 units of the incident rapidity).
Then, instead of Eq, (2), we
;I
-5
-
<ntotH%
> + v<nfra xN + <nfr <ncentral <ntotHN
-1
: I
/
(4)
where <ntot>HN = <ncentral> + <nfragN plicity for the H-N collision. are small, In practice + <nfragH is the total produced multicorrection terms
the fragmentation
of order (Ay)frag/Ytotal
- O(l/log
s) compared to c/2. in Fig. 2 It is in In addi-
This result is compared with the data summary of Busza et al. for Plab = 200 GeV, taking <n > /<n > /<ntot> - .2. tot> N <nfrag N frag H
good agreement with the data for charged pion and proton collisions, tion, the shapes of the observed multiplicity distributions
are consistent with the
predicted forms of Eq. (3) and Fig. 1. The slight energy dependence predicted in Eq. (4) is also consistent with the trend of the data. 10 We have analyzed the total nuclear cross section in this model and have found it to be consistent with the usual Glauber theory. 11 In this picture the incident hadron, which is represented interact elastically (diffractively) by its Fock-space parton distribution, can
via elastic parton interactions
in the central
region and can continue to propagate and interact as a coherent hadron through the nuclear medium. series. projectile Nonetheless, 12 Thus one obtains the usual multiple-scattering Glauber
the multiplicity
density dN/dy produced from the incident Be-
parton distribution
is not increased by the repeated collisions., the cross section of course does not factorize: limit.
cause of the Glauber series,
me1 inel approach the geometric %A - OpA
The model proposed here is consistent with energy and momentum conservation. In the equal velocity frame, the central particles produced in the pro(rni =m2+~k;2>),
jectile direction
have a typical total energy of order &nT,
-6which can be compensated by a small loss of energy of the leading the particles prejectile region, a correction of relative order ?rnT//-sO distributions in in
-.
One may also use this picture to predict the multiplicity nucleus-nucleus collisions. 12
For the central region one obtains
(5) where i;
A1/A2
A lNA2 = uA A 12 excited nucleons in A, in collision
I
is the average number of inelastically projectile A2
with a
AZ/N
Each such excited A1 nucleon interacts
inelastically
with 3
nucleons in A 2 so that the average rapidity length of excited partons in A1 is / 1 Iyfi2/~I A2/N + l,J yc statements apply to V The above result preA2/A1 and Al/N0 N 3.8 for A2 > 100, which is in agreement diets, for example, <n>QA /<mNA 2 2 13 with cosmic ray data for alpha-particle collisions, Corresponding Finally, we wish to point out the connection between our hypothesis of indeand materializing on nuclei, nuclear parton chains and deep inelastic The latter directly probe the parton disone should obtain
pendently interacting scattering tributions
measurements
within nuclei, and, according to our hypothesis,
(6)
for all (including arbitrarily scaling region. 14 small) xBj = - q2/2MNv 5 1 once q2 is in the Bjorken
> 1, Fermi motion corrections can be included and For xBj 15 computed using quark counting, but otherwise nuclear binding corrections to
i
-7-
(6) are considered negligible 0 Thus there is neither shadowing nor antishadowing16 of the partons of one nucleon by the partons of other nucleons, we predict the absence of shadowing - independent of beam energy -for action where the effective collision the Drell-Yan energy of the.subprocess In general, any refor
is large, e.g.,
Process pA - 1+1-X at largeA
hadronic reactions - ignoring multiple
as well as for large pT m+a- scattering effects. 17 The absence of RA(x) = (dn/dx)HA/
shadowing is also apparent in the ratio of distributions
tdnldx) HN where x is the Feynman variable k,,mO/kFg 0 0D At infinite energy RA(x) reduces in our model to a step function RA(x) = vQ(-x) + 6(x) since the central region is confined to x - 0. If we identify the nuclear parton distribution shape with the multiparticle to the absence of shadowing: In summary, distribution for x < 0, this again corresponds
(dg/dx)HA = A(dg/dx)HNO l8
we have found that the parton model can be consistent with low mul-
both the strong absorption of nuclear cross sections and the relatively tiplicity of hadron-nucleus collisions.
Another problem which could be anaof virtual 19,20 quark states and unstable reso-
lyzed in this model is the propagation nances through the nuclear medium. Acknowledgements We wish to thank X. Artru, Krzywicki, tions 0 H. Miettinen,
J. Bjorken,
A. Capella,
T. Jaroszewicz,
A.
W. Ochs, and V. I, Zakharov for helpful conversa-
-8
-
References 1. Fo3; a review of the data and various theoretical Proc. VII Int. Colloquium on Multiparticle models, see W. Busza, in Germany,
Reactions,
Tutzing,
21-25 June 1976. 2. R. P. Feynman, Photon-Hadron Reading, Mass., 30 Interactions (W. A. Benjamin, Inc.,
1972) and references
therein,
S. Drell and T. M, Yan, Phys. Rev. Lett. 25, 316 (1970) and Ann. Phys. (N-Y.) 66, 578 (1971).
4.
A model of this form was considered by P. V. Landshoff and J. Polkinghorne, Nucl, Phys. B 32, 541 (1971).
5. R, Blankenbecler,
S, J. Brodsky,
and J. F. Gunion, Phys, Rev. D g, 287 therein.
(1973), Phys. Rev. D 2, 6. 7.
3469 (1975), and references
P. V. Landshoff and J. Polkinghome,
Phys. Rev. D 10, 891 (1974). corrections are not of
We emphasize that nuclear binding and Fermi-motion
related to the A 2/3 I surface or nuclear size effects characteristic shadowing. 8. 9. This was first discussed by 0. Kancheli, W. Busza, P. Luckey,
JETP Lett. 18, 274 (1973). and J. Elias, Tbilisi, USSR, ,
L. Votta, C. Young, C. Halliwell,
paper submitted to XVIII Int, Conf. on High Energy Physics, 15-21 July 1976. 10. Recently, A. Capella and A. Krzywicki, Orsay preprint
LPTHE 7712
(1977), proposed an extended multiscattering Glauber terms correspond to the interaction
model in which higher order of n = 1,2, 0DD independent con-
stituent systems within the projectile, ergy roughly equally, well with experiment, ^sN s/n, However,
each of which shares the incident en-
At present energies their model also agrees the energy dependence of this model
-9differs from the model discussed here; e.g., fragmentation the nuclear chains all extend
t&the projectile ergy.
region and <n>HA/<n>HN - i; at infinite enon the parton distribution of the pro-
The effect of the multichains
jectile (vW2H) must also be understood. 110 R. Glauber, in Lectures in Theoretical Physics, Vol, I, ed. W. E. Brit-
ten and G. Dunham (Interscience,
New York,
1959). The generalized states
Glauber theory resulting from this model includes inelastic diffractive which can be treated in the fashion of photon-hadron Brodsky and J. Pumplin, JETP 30, 709 (1970). scattering interactions,
...