SLAC-m-1937. May 1977 ..... charge in rapidity for the process of Fig. 8. III. A Model for Jet Fragmentation3 .... The fragmenting jet is then an octet (A)8 with the.
I
SLAC-m-1937
May1977 (T/E) JETPRODUCTIONANDTHEDYNAMICALROLEOF
COLOR*
Stanley J. Brodsky Stanford Linear Accelerator Center Stanford University, Stanford, California 94305
Abstract: We discuss how multiparticle jets which originate from quarks, multiquarks, hadrons, or gluons can be distinguished by their (a) quantum number retention, (b) leading particle distributions, and (c) hadronic multiplicity. The possible quantitative connection between initial color separation and hadron Evidence for wee quark exchange as a dominant multiplicity is emphasized. We also discuss several new mechanisms hadronic mechanism is presented. Finally, we consider the possibility of utilizing a high for gluon jet production. multiplicity trigger to e,xpose gluon exchange and production contributions in hadron- and lepton-induced reactions.
(Invited talk presented bbch 6-18, 1977)
at the XII Rencontre
de Moriond,
Flaine,
*Work supported by the Energy Research and Development Administration.
France,
-21.
Introduction The production
of multiparticle
jets appears to be a common feature of all high en’ Despite the indications
ergy hadron- and lepton-induced
reactions.
multiplicity2
momentum distributions
underlying
and transverse
current fragmentation and multiquark
region of lepton-induced
corresponding
We also expect di-quark
the jet-like
Sections VI and VII, the primary hadronic interaction
In the case of
and even jets of hadronic parentage
Even more intriguing,
forward
discriminate flavor,
color,
phenomenological
questions in particle origin,
i.e.,
left behind in the target fragmentation interesting
then, is how to
how to distinguish
the
In this
properties
(the power-law
at x-- 1) (Section IV), and the possible
region in deep inelastic because of theoretical
of the hadron’s parton wavefunction. Finally,
if the
including dn/dy (the height of the rapidity
retention of charge and other quantum numbers (Section II).
controls
physics,
number of quarks or gluons of their parent systems.
falloff and quantum numbers of leading particles
color separation
systems are
but as we shall discuss in
plateau in the central region) (Section VII), the fragmentation
tems in Section II.
In the case of ordinary
as being due to gluon or quark exchange.
between jets of different
Yan process is especially
of jets
parents of these systems could well be colored,
paper I will discuss a number of discriminants,
multiplicities
if one takes quantum
and backward multiparticle
hadronic origin,
can be identified
(qq)
massive pair production.
in any of these processes.
usually considered to have a conventional
One of the important
we
sca&ering as well
subprocess.
to gluon fragmentation
forward hadronic reactions,
composition
In particular,
at face value, one must expect at some level, the production
chromodynamics
the
region in deep inelastic
one expects quark, multiquark,
depending on the hard scattering
empirically
reactions.
jets in the target fragmentation
large pT reactions,
similar,
jets of various flavors in e+e- -) hadrons , as well as in the
as in the beam and target region in Drell-Yan
different
are surprisingly
quark and gluon content of these jets can be quite diverse.
expect quark fragmentation
initial
that their average
The multiquark scattering uncertainties
jet which is
and the Drellregarding
the
We discuss special tests for such sys-
in Section VII we speculate on the possibility
the height of the multiplicity
that the initial
plateau, and that events with large
are sensitive to gluon exchange contributions.
-3II.
Charge Retention by Quark and Multiquark Feynman4 originally
Systems3
proposed the elegant ansatz that the total charge of a jet
,= c Qhjl %dx= heJ could reflect,
0
gjmaX~c.Iy d”h/J hcJ y.
c
in the mean, the charge of its parent.
However,
as noted by Farrar
Rosner, 5 this connection can fail in specific model calculations, has been little
subsequent interest
and accordingly
(2.1)
and there
in using this method as a jet discriminant. .
In order to see why exact charge retention fails,
consider the simple model for hadrons shown in Fig. 1. The
e+e- JP-+qi-rapidity
1y I < ymax ,L 2 log s is filled
interval
uniformly
by the production
of neutral gluons,
which subsequently decay to qi pairs.
Fig.
These
then recombine with the leading quarks to produce mesons.
1. Simplified model for the rapidity distribution of virtual gluons and mesons in e+e- -qS - hadrons. See also Section III.
If we could cut through a
meson and sum all the charges to the right of the point y,, then clearly However,
Q,(y > y,) =Q-. q since we must sum over hadron charges an extra quark is always included in
the sum, and the total charge corresponding
to the antiquark
jet
J=Qq+vQ
is 395 (2.2)
-where 77 = sea is the mean charge of quarks in the sea: nQ =L2 (2/3 - l/3) = l/6 for an
Q
.
SU(2)- (or SU(4)-) symmetric sea.
Actually
sea, and77Q =$ (2/3 - l/3 - l/3) = 0 for an SU(3)-symmetric
this result is quite model-independent,
which need a quark for neutralization. B, S, etc.,
and Eq. (2.2) will apply to all jets
More generally,
for any conserved charge A =IZ ,
one predicts 395 QbJ=hJfQ
(2.3)
where A J is the quantum number of the parent quark or multiquark
system and the sign is
Notice that 77 is independA 3 The result (2.3) is unent of the process and of the jet type and is a universal number. 6 of the quark affected by resonance decay or baryon production. From parametrizations
f (-) if the parent needs a quark (antiquark)
to neutralize
it.
-41 --dN+ dy
Q = 2/3
dNdy
txbj
Fig. 2. Parton model diagram for VP-P-X as viewed in the 1Ap c.m. system for the valence region (xbj 2 0.2). distribution determine
functions,
Fig. 3. Idealized distribution as s-00. r
one can already
empirically
responding to partial
,11*.,
40
that nQ’O. 07, corsuppression
the usual quark models,
I
I
l
h++h-
.,
0
30
qIz = 0.
ttt
t
5
t
c 20 s: az l-
t
+ o”
quantum number retention
t Oooo
O
0
t.
d
0
4&j&&
can be a viable method for identifying
initial
’ 5 + > 90” s > 25
I
II
IO
For example,
I
I cp,
(a)
versal numbers which can be established
specific quark and multiquark
I
t
Given the fact that the qn are uni-
empirically,
I
I
o h+- hm protons
of the
strange and heavy quarks in the sea. For
for @p - X (up -p-X)
0
++ 000
I
I
1
ok+!-
0
I
2
3
JO
OS5I-
systems.
Fig. 2 shows the expected
quark flow in the W+p c. m. sys-
tem for VP-p-X,
in the valence quark -4-3-2-l
>O. 2, and Fig. 3 indicates the xbjpredicted hadronic charge distribution region
Yc.m.
Fig. 4. dN+/dy - dN-/dy expected at very large For x . ~0.2, the presence of bl sea quarks which can be hit by the W+
s = (q+p)2.
tends to further
increase the asymmetry
between the two hemispheres.
4 MPAI,
Data from the Fermilab 15 ft bubble chamber for VP-/A% 7 The rapidity distribution and the charge structure dl@/dy - dN’/dy of the final state are shown, as well as the transverse momentum distribution of the emitted hadrons. The curve for cpT(y)> is from pp reactions.
Taking
qQ=O. 07, this implies that the plateau height will be ~2.3 times larger
in the target (uu)
fragmentation
The data7 (Fig. 4a)
region compared to the current(u)
fragmentation
region.
dN+ --dy
dNdy
Fig. 5. The Drell-Yan mechanism and the expected charge distribution for ?fp - @1-+X in the valencevalence region (x~, xp 2 0.2). seem consistent with this prediction. momentum distribution
Fig. 6. The Drell-Yan mechanism for K-p - I?!‘+X in the valencevalence region (xK, xp 2 0.2).
It is also interesting
to note that the transverse
of W+-induced events is the same as that measured in pp colli-
sions, shown by the solid lines in Fig. 4b. One of the most interesting to confirm
the underlying
areas of application
quark structure
example consider r*p -1+1-X
of the charge retention
predicted by the Drell-Yan
technique is
process. ’
For
in the valence quark region (xa, xb 2 0.2; xa-xb = xL,
n
xaxb czAZ/s).
The predicted
quark-flow
diagrams and the charge distribution
of the
final state hadrons are shown in Fig. 5. We estimate that the width of the charged fragmentation regions is -2-3 units in rapidity separation.
so very large s is needed to make a clear
Even at moderate s, though, one can study the ratio of the charge-difference
plateau heights. Because of the high energies available,
and the possibility
s y stematic measurements
of the hadron fragmentation
tum fractions
xa and xl,
the Drell-Yan
process can lead to essential information
function in both the wee and valence quark domain. distribution
in the valence region for K-p -m’n-X
previous examples,
of controlling
at large
xbj’
quarks are nearly equal to the initial
For example,
the expected charge
is shown in Figs. 6 and 7. As in the
and that the rapidities rapidity.
region in
on the complete hadron wave-
we assume that the (uud) Fock space wavefunction
component in the proton
the momen-
is the dominant
of the spectator u and d
If we now consider events with -xb small
-6-
I-dy dsy+ cw
c
or wee, diagrams 8a and 8b become important
K-
(with a dominant
because Qi= 46:).
fragmentation region
In models
where the extra uii pair is crea-
proton fragmentation region
ted from a neutral system, --logs I
-
1
u
1-
e. g.,
from gluon decay as in Ref. 9,
Fig. 7. The expected distribution of charge in rapidity for the process of Fig. 6.
then the wee quark charge is compensated locally in rapidity, and one expects the charge distribution
(0)
is also the prediction
of the
“holell fragmentation
model of
Bjorken
Fig. 8. The Drell-Yan mechanism for K-p -) 1+1-X in the “valence-sea” region (xK z 0.2, “p5 0.2).
shown in Fig. 9. This
10
and Feynman. 4 On
the other hand, the charge distribution
of the proton fragments
may be more homogeneous, since it is possible that the interacting wee quarks are constituents of virtual
charged and neu-
tral mesons, as suggested in Ref. 11. The same result is Fig. 9. The expected distribution rapidity for the process the “hole fragmentation”
of charge in of Fig. 6 in model.
predicted
if we assume that the
bound quarks of the spectator 19
system exchange momentum and tend to equalize their velocities. distribution
would thus resemble Fig.
flow in the hadron fragmentation retical
models.
collisions
LA The resulting
10. Thus detailed measurements
charge
of the charge
regions could well distinguish bet\veen these basic theo-
Comparison between the Drell-Yan
process,
IC,production,
and ordinary
should be illuminating.
Other tests of charge and quantum number retention, are discussed in Ref. 3.
especially in e+e- annihilation,
-7-
dN+ dy
Fig. 10.
III.
dNdy
An alternate possibility for the distribution of charge in rapidity for the process of Fig. 8.
A Model for Jet Fragmentation3 One of the basic uncertainties
in the quark model is the nature of the space-time
evolution of the final state hadrons.
In constructing
a model one must keep in mind that
(aside from resonance decay) the emission of one hadron cannot cause nor directly ence the emission of other hadrons, model for e+e- -chadrons, mechanism,
10
which is a realization
in rapidity.
assumes that each gluon lives,
color singlet mesons.
a
The hadron production t2-x2=d2,
x=t=O
The
Fig. 11.
quark and antiquark are thus free for a
time t cc & which justifies
them as being treated
in the calculation
lation cross section.
gluons are
to form
which meets the quark world line at t N yd.
as free particles
(virtual)
cascade
producing
which recombine
then occurs near the hyperboloid,
frame,
inside-outside
A simple
One
on the average,
proper time T= l/d,
quarks and antiquarks
initial
of Bjorken’s
separation.
is shown in Fig. 11. After the qS begin to separate,
emitted with flat distribution
characteristic
since they are at a space-like
influ-
of the annihi-
In the e+e- center-of-mass
ln.2
Space-time evolution of the hadronic final state in e+eannihilation. The initial qq pair is produced at x=t=O and the hadrons are produced near the hyperboloid, t2-x2=d2. The transverse direction is not shown in the diagram.
i i
the fastest mesons are emitted last. l3
Although this model is grossly many characteristics baryon production
oversimplified,
it is causal and covariant
expected in gauge theories and jet production. can also be included.
and has
Resonance and
The model can serve as a simple testing ground
for the effects of quark mass and valence effects,
etc.
An application
is the quantum
.
f i
:
-anumber retention
rule,
Eq. (2.3).
Further,
is roughly equal to the gluon multiplicity feature further IV.
in this simple model the meson multiplicity
and grows logarithmically.
in the color model of Section VI.
Leading Particle
Behavior
In addition to its retained quantum numbers an important x--l
behavior of its leading particles.
bility that one constituent
(or subset of constituents)
12a. The proba-
state, has nearly all
constituents,
In fact, assuming an underlying
of a jet is the
consider a fast
See Fig.
a, in a virtual
the momentum of A must vanish rapidly as the remaining are forced to low momentum.
discriminant
The basic idea is as follows:
moving composite system A with a large momentum FA//z.
tors,
We discuss this
the n(a)
specta-
scale-invariant
model one finds14 Ga/A(x) =
dN a/A(x)
q1-x)2n(d) (X’ 1)
dx
where x is the light cone momentum fraction, probability G ,/gw(l-x),
distribution
are discussed in Ref. 1.
application
of the counting rule (4.1) is the prediction
dependence of the forward
of a composite system.
For example,
for fast nuclear collisions
$$$(A+B--p+X) -
inclusive
to low momentum.
cross section for the dissociation
(see Fig. 12b) (4.2)
(l-~~)‘(~-l)-l
and N (i-xL) 6 (A-A’)- 1
since there are 3(A-A’)
of the
one predicts
L
+j -$$(A +B~AI+X)
This result for the
VW -G q,pw -wG3, vW2p-x), 2P etc. Comparisons with experiment, correc-
GM,Bw(1-x)5,
tions and other modifications
XL’P, c. m* ~GG.x
x= po+pz / p. + p, (” “) CA A)-
(4.1)
leads to the predictions
Gri,p~(l-x)7,
An immediate
-I
quark spectators
(4.3) forced
These and other predictions
have recently been shown in a beautiful by Schmidt and Blankenbecler
15
-7R-”
analysis
to be in striking
Fig. 12. (a) Fragmentation of A into a subset of constituent a. The number of elementary constituent spectators is n(a). (b) Fragmentation of A+B--a+X.
-9agreement with measurements
of deuteron,
alpha, and carbon dissociation
prediction
GP,d - (1-x)5 is also consistent with the Fermi ments of ed -epn for x= -q2/2pd*q- 1. 16 One of the most intriguing
at LBL.
The
motion observed in measure-
applications 17 of the counting rule (4.1) is to forward
clusive hadron reactions pp --xX,
etc.
For xL -, 1 this is normally
domain of the triple Regge mechanism,
in-
considered the
where dcr/dx (A+ B -) C +X) - (l-x) lm20@).
How-
ever, in the range 0.2 < xL < 0.8 the measured cross sections 18 appear to have pTindependent powers of (l-x)
(especially
when parametrized
and is thus more suggestive of a fragmentation At this point we shall distinguish
in terms of xR=pcSm’/p~~’
mechanism.
three possible fragmentation
models for high energy
hadron collisions 19: (1) The incoming beam is dissociated by the Pomeron. i7 Then as in Eq. (4.1) clo/dx(A+B-C+X)-(l-~C)~~(~~)-~;
i.e.,
(Although xc is defined as the light-cone
the fragmenting
variable,
jet is the excited hadron A.
xc =xR should be sufficiently
accurate. ) (2) Inelastic
collisions
NussinovZ1 model.
See Fig. 15e’.
same quark structure (3) Inelastic
begin with the exchange of a color gluon, as in the Low2’-
as A.
collisions
The fragmenting
Again, one predicts
do/dx(A+BdC+X)
give do/dx-(1-x)5,
mechanisms.
- (,-x~)~~(‘~)-~
of a wee quark, as jet then has one fewer
We thus have 19 .
GeV, 0.4=$
(lOg5-
E”
&~/a~>,
(s >>m2)
1) log2
log s log Lm2 k2 min
(6.2)
(In the model we
to &. )
(for kmm # 0) behaves as log2 s at high energies
The result that the QED multiplicity
and perhaps deserves further
comment.
We first emphasize that
is not dominated by the photons produced at large kT relative
charged lines. 2g Even if we were to impose a cutoff at kT =k sin B,kmax, integral
still yields logarithmic
momentum distribution Gaussian3’ perturbation
form
I do2/(e2+ m2/s)
of the photons is interesting:
theory component takes over.
to the
the angular
- log s. The actual transverse the infinite
sum in Q! falls off as a
for moderate k; whereas at high kT, the scale-invariant
has a hint of the ‘lseagullll effect.
less than
we then have
discussed in Section III this region grows in proportion
this contribution
In QCD
color singlet system and
-1 is the size of the color separation region. min
is somewhat surprising
infinite.
the gluons of very long wavelength emi,
decouple since they only see an overall
can be finite.
where the hadronic k
serves to modify the
Furthermore,
dk$/i$
hard photon
the single photon distribution
If we use light cone variables
with x= (ko+k3)/(p2pi),
-15 y= log x+ C then the leading p+“p
term in Eq. (6.1) gives
Q/T & Thus &I$
= ki+ x2m2 b +gm’/(2xp+.
grows with x2m2 at small i$.
x-0 (m/h)),
the rapidity
Chromodynamics
distribution
(6.3)
p-)2]
Notice that in the central region (e.g. ,
is essentially
flat, with dN/dy-a/7r
is of course much more subtle and complicated
log sg
m.m.
than electrodynam-
ics, and all we shall do here is argue that QED at least provides a covariant and consistent model for multiparticle
production
which may represent
a pattern for gauge theories.
We also note that the work of Ref. 31 suggests the possibility
that the radiation
of gluons in QCD may exponentiate into an effective Poisson form when gluons of the same order in the quark current are properly VII.
grouped together.
A Two Component Color Model An intriguing
all reactions
feature,
evident from the perturbation
can be classified
according to whether the initial
and ?! of color or separates octets of color. production,
This is illustrated
(b) massive muon pair production,
esses, and even (e) ordinary
theory structure
forward
interaction in Fig.
(c) e+e- annihilation,
interactions.
of &CD, is that separates a 3 15 for (a) electro-
(d) high pT proc-
In each case only the initial
tion is shown; there is then subsequent gluon (and hadron) radiation
interac-
which neutralizes
the
colored systems. Using the color model
12
discussed in Section VI, we expect all of the reactions
the left side of Fig. 15 to have the identical
plateau height dn/dy for rapidities
central region between the separated 3 and 3 systems. -2 , quantum number distributions,
on
in the
In fact all of the jet parameters
etc. should be indistinguishable
in this region.
contrast to this we shall argue that whenever color octets are separated, height in the central region connecting their rapidities
In
the plateau
will be 22 times as high:
dn66/dy = 9/4 dn3s/dy; the number 9/4 [=2/(1- nw2) in color SU(n)] is derived from the lowest order perturbation
graphs for gluon emission.
12
Roughly speaking, an octet has
a color charge equal to 3/2 that of the triplet. We can also give an intuitive rapidity
argument which shows why octet separation
height at least twice that of separating triplets.
leads to a
32 Consider the gluon exchange
- 16 -
3-3
P
SEPARATION
OCTET
SEPARATION
(a)
(a’)
(b)
(b’)
:
3 e+
9
Y 8
*
e>---;$ 3 (cl
4 . 3A+
3
P
3
IdI
(d’)
8
P
9 P
+zz- 8( (e)
5-77
Fig.
15.
(e’)
3191113
Contributions to electroproduction, massive pair production, e+e- annihilation, large pT hadron production, and forward hadronic collision, from both 3-3 and octet-octet separation in color. In (e), the qi can annihilate to a color singlet or a wee quark can be exchanged.
- 17 diagram in Fig.
It is clear that there must be two neutral-
15d’ for a large pT reaction.
ization chains connecting the top and bottom 3 and 3’s, and the multiplicity that of electroproduction
at the corresponding
kinematics
for 3-3 separation,
Fig. 15a. At low pT, the same graph reduces to the Low Pomeron,
Fig. 15et, and the two neutralization
not destructive multiplicity
since that would correspond
20
-Nussinov21
loops will interfere.
charged lines
the soft photon radiation
At small pT the interference
along each outgoing lepton.
in the case of the color,
the interference
associated multiplicity.
Thus we speculate
12
large pT reactions
analysis of Section IV.)
of the radiation
two units of charge.
and octet-separation
and by
(See also the
universal,
2 in all of these reactions.
consider events with high multiplicity,
only on events with at least double the usual hadron multiplicity.
Kogut
gives
model)
model),
(wee quark exchange 4p 12).
plateau is observed to be essentially
Bjorken,
com-
because of the extra
(Fig. 15b) (the Drell-Yan
on the right side of Fig. 15 will be favored,
33 gluon-exchange
contribution
scale-invariant
15b’ will be dominant.
contribution
exposing the
Furthermore,
from gluon exchange to pp -p+p-X
(Notice that, unlike the Drell-Yan
bution gives the same production
In this
for high pT jets, and the Low-
Nussinov gluon exchange mechanism for low pT hadron reactions.
Fig.
Notice that
This ansatz, plus the color model, then can account for why the
case the color octet diagrams
essentially
from different
(Fig. 15d) (the constituent interchange
On the other hand suppose we specifically
Berman,
via photon
that quark exchange and annihilation
to typical small pT hadron reactions
trigger
-e+e-e+e-
at least at low energies,
the dominant mechanism for massive pair production
multiplicity
or e+e- -4
effect vanishes if ncolor - ~0.
ponents, but that the latter is suppressed,
e.g.,
Thus the resulting
has the usual plateau height
It is possible that all hadron processes have both triplet-
low multiplicity
is
causes the plateau height to vanish in the case of photon exchange, but
times the height if the photon could transfer
continuity
model for the
plateau height must be at least double that of electroproduction
For a high pT collision
as in
The interference
to color singlet exchange.
The QED analogue of this result would be positronium+positronium exchange.
will be double
shown in
mechanism,
cross section for proton and antiproton
a new
this contri-
beams. )
- 18 Similarly,
the double multiplicity
trigger
in e+e- -, hadrons will enhance the ece- - q&
contribution. A two component color model for ordinary a correlation
forward
between left and right hemisphere
reactions
multiplicities
automatically
leads to
of the type observed at the
ISR34: the gluon exchange component will be dominant for events with a large rapidity plateau height dn/dy are considered,
thus giving a large multiplicity
throughout the cen-
tral region. Finally, plicity
we emphasize that by studying events with at least double the average multi-
in pp collisions,
one may be able to study qq -qq
scattering
as it gradually
evolves from the low pT region (Fig. 15e’) to high pT scale-invariant (Fig. 15d’).
This can provide anearly bias-free
way of determining
jet production the jet-jet
cross
section. 35 Aside from its dependence on the effective coupling constant asbT) emphasize that the gluon exchange term is scale-invariant, change, does not contain a strong pT cutoff of the forward VIII.
we
and thus unlike quark exjets.
Conclusions In this talk we have emphasized how the discrimination
determine ular,
of various jet phenomena can
the basic quark gluon mechanisms which control hadron dynamics.
we have shown how quark, gluon, and multiquark
retained quantum numbers, plateau height.
the leading-particle
A summary of representative
sive pair production
reactions A + B -1+1-+X
In partic-
jets can be distinguished
by their
x dependence, and the multiplicity jet parameters
is given in Table I.
should be particularly
interesting
Masto study
since the nature of the associated jets changes as one probes the wee and valence quark region,
It is also interesting
to study these quark and multiquark
jet systems in a
nuclear environment. We have also emphasized the essential two-component vant role of quark- and gluon-exchange
mechanisms.
wee quark exchange is the dominant hadron interaction that gluon exchange and production multiplicity
trigger
contributions
could be an important
nature of QCD and the rele-
In particular
we have argued that
at present energies.
The ansatz
can be made dominant by using a double
phenomenological
tool.
establish the dynamical role of color separation in multiparticle
Its confirmation production.
would
I
- 19 Table I Jet Type
Multiplicity
q
n3+)
Example
Global Charge
U
2 8-Q
d
--- 1 3’Q
7r+, (l-x) .
current induced, large p I Drell- I?&
7r-, (l-x)
quark exchange reactions, Drell-Yan, baryon spectators I
P, (1-x) %.I
“3$s)
(uu) 3
;+v
Q
7r+, (1-x)3 M, (1,~)~ logs
gluon
“88(S)
g
0 B, (l-~)~ logs
“88 03)
B8
@ud)8
1
P, (I-x) n+, (1-x)5
1
538 w
P, (1-x)5 P, (l-x)
B
M
constant
P
constant
+ 7r
1
gluon exchange in hadronic reactions, I B+B-X
-1
A, (1-x) 7r+,(1-x)5 7r+,(l-x)
e+e--q&, PP--YX, large pT , t current induced
gluon exchange in hadronic reactions, I M+B-cX
?r+, (l-x) M8
Typical Reactions
Leading Particle
diffractive I dissociation
-1 diffractive dissociation
1 K+, (l-x)
Acknowledgments Most of this talk is based on work done in collaborations W. Caswell,
J. Gunion, R. Horgan, and N. Weiss.
with M. Benecke, J. Bjorken,
with R. Blankenbecler,
I am also grateful
T. DeGrand, F. Low, and H. Miettinen.
for discussions
I
- 20 References 1.
For a review and references, national Colloquium
2.
The multiplicity
see S. J. Brodsky and J. F. Gunion, Proc.
on Multiparticle
Reactions,
data are summarized
VII Inter-
Tutzing (1976).
in E. Albini et al.,
Nuovo Cimento 32A, 101
(1976). 3.
This section is based on work done in collaboration
with N. Weiss.
Brodsky and N. Weiss, Stanford Linear Accelerator
See S. J.
Center preprint
SLAC-PUB-
1926 (1977). 4.
R. P. Feynman,
Photon-Hadron
Interactions
(W. A. Benjamin,
New York,
1972);
Phys. Rev. Letters 23, 1415 (1969). 5.
G. Farrar
and J. Rosner,
E. Colglazier,
Phys. Rev. D 2, 2747 (1973).
Phys. Rev. D9-, 2658 (1974); J. L. Newmeyer and D. Sivers,
Phys. Rev. Dz,
2592 (1974); D. Novseller,
Phys. Rev. D 12, 2172 (1975).
6.
R. D. Field and R. P. Feynman,
7.
J. Vander Velde, presented at the IV International Physics,
S. D. Drell and T.-M.
9.
V. A. Novikov,
10.
Caltech preprint
Salando, Spain (1976)) University
8.
ITEP-112
See also R. Calm and
CALT-68-565
(1977).
Winter Meeting on Fundamental
of Michigan preprint.
Yan, Phys. Rev. Letters 25, 319 (1970).
M. A. Shifman, A. I. Vainshtein,
and V. I. Zakharov,
preprint
(1976).
J. D. Bjorken,
Proc.
erator Center reports
Summer Institute
on Particle
Physics,
SLAC-167 and SLAC-PUB-1756
(1976).
Stanford Linear AccelA. Casher,
J. Kogut,
and L. Susskind, Phys. Rev. Letters 31, 792 (1973). 11.
R. Blankenbecler, and references
12.
S. J. Brodsky,
and J. F. Gunion, Phys. Rev. D 12, 3469 (1975)
therein.
S. J. Brodsky and J. F. Gunion, Phys. Rev. Letters 5, thank T. DeGrand for discussions
on color interference
13.
See also F. Low, XII Rencontre de Moriond
14.
R. Blankenbecler
and S. Brodsky,
Phys. Rev. Ds,
242 (1974).
1153 (1973).
402 (1976).
I wish to
phenomena.
(1977).
Phys. Rev. D 10, 2973 (1974).
S. Brodsky and G. Farrar,
J. F. Gunion,
Phys. Rev. Letters 3l-,
- 21 15.
R. Blankenbecler
and I. Schmidt,
SLAC-PUB-1881
(1977),
Stanford Linear Accelerator
See also S. Brodsky and B. Chertok,
37, 269 (1976), and Phys. Rev. Ds,
Center preprint Phys. Rev. Letters
3003 (1976).
16.
R. Arnold et al. , Phys. Rev. Letters 35, 776 (1975).
17.
S. Brodsky and R. Blankenbecler,
Ref. 14. See also H. Goldberg,
Nucl. Phys.
B44, 149 (1972). 18.
quoted in W. O&s,
J. C. Sens --et al.,
Nucl. Phys. , to be published.
--et al. , Phys. Rev. D 14, 1217 (1976).
The p--x/p
with (1-x)8 Or g. 0. Overseth,
communication
private
-A
F . E. Taylor
ratio on nuclei is consistent and W. Ochs, XII Rencontre
de Moriond (1977). 19.
S. Brodsky and J. Gunion, Ref. 1 (and to be published). Rencontre de Moriond
See also W. Ochs, XII
(1977).
20.
F. Low, Ref. 13, and Phys. Rev. Dg,
21.
S. Nussinov,
163 (1975).
Phys. Rev. Letters 34, 1286 (1973).
D. E. Soper, UC-Davis preprint M. K. Gaillardand
See also J. F. Gunion and
(1976).
22.
J. Ellis,
G. C. Ross, Nucl. Phys. Bill,
23.
E. G. Floratos,
24.
T. De Grand, Y. J. Ng, and S. -H. H. Tye, to be published.
25.
D. Sivers and R. Cutler,
26.
S. J. Brodsky,
.27.
S. Brodsky,
C. Carlson,
S. Brodsky,
J. F. Gunion, and R. Jaffe, Phys. Rev. D 5, 2487 (1972).
CERN preprint
and R. Horgan, in preparation.
and R. Suaya, Phys. Rev. D 2,
28.
D. R. Yennie, S. C. Frautshi,
29.
J. Dash, hlarseille
30.
For a recent discussion,
31.
J. M. Cornwall (1976). Tblisi
TH-2261 (1976).
to be published.
W. Caswell,
eastern University
preprint
(1976) and J. Frenkel
379 (1961).
(1977). and Y. Srivastava,
North-
(1976).
and G. Tiktopoulos, et al.,
2264 (1976).
and H. Suura, Ann. Phys. 2,
see G. Pancheri-Srivastava
preprint
J. C. Taylor
253 (1976).
UCLA preprints
XVIII International et al.,
TEP 2 (1976) and TEP 10
Conference on High Energy Physics,
Oxford preprint
(1976).
- 22 32.
Of course there is also the less interesting orders in perturbation
theory (unlike QED) resembles
where the final state multiplicity thank J. Bjorken for conversations 33.
34.
possibility
that the result in QCD to all thermodynamic
has little to do with the initial
models
process.
I wish to
on this point.
S. Berman,
J. Bjorken,
and J. Kogut, Phys. Rev. D&, 3788 (1971).
J. Bjorken,
Phys. Rev. D S, 3098 (1973).
See M. Benecke, XII Rencontre de hIoriond (1977); and M. Benecke, A. Bialas, S. Pokorski,
Nucl. Phys. BllO,
488 (1976).
I wish to thank M. Benecke for discus-
sions on this point. 35.
For an alternative Moriond
(1977).
method,
and
see W. Ochs and L. Stodolsky, XII Rencontre de
