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Systematics of global observables in relativistic heavy ion collisions
23c
Nuclear Physics A.525 (1991) 23c-38~ North-Holland, Amsterdam
SYSTEMATICS OF GLOBAL OBSERVABLES IN RELATIVISTIC
1.
Johanna
STACHEL
Physics
Department,
of
particles
heavy
is
to
particles.
which
any
event.
given
indicators tool
USA*
comparison
to
density
achieved
spatial
observables
are
the
Then By
particle
are
angle
sine
of
integrating well
over as
its
amount
of
angles
and is
Supported
of
one the
polar
all
detector
by the National
to
of
sensitive
Science
to
be
as
a
latter
enters
via
model
as well
of
the
predictions as
the energy
the this the
particles
of
the
cell
transverse dEt/dn.
and
stopping
power
and the A.P.Sloan
0 1991 - Elsevier Science Publishers B.V. (North-Holland)
or
the
charged into
a
cell
obtains,
after
Et=C[eisin(f3i)]
quantity
incident
number
a detector
energy
This the
therefore,
emitted
in
global
experimental is
energy
as well
pseudorapidity
for here
detector
of
the
particle
measured
the nuclear
Foundation
of
these
4 and,
0 or
energy
direction
and do/dE
events
discussed
Instead
dependence the
the
and
angle
angle
charged
elements,
from
to
understanding
many
azimuthal polar
to
dN,/dn.
angle
are a most
target
du/dN
over
measurement
observable
weighs
are
systematics
to
variables
the
The
restricted
our
power
in
collision.
of
to
discussed.
frequently
therefore
the
function
density
shifted
stopping
space
energy, the
for
phase
respect
their
where
The
identified
They
kinetic
basis
integral
respect
pseudo-rapidity
energy
037.59474/91/$03.50
a
study
them.
of
distributions
with
observables
nuclear
the
spatial
the number
by
of
kinematics.
also
the
E carried
instance
Averaging
experimental
pseudo-rapidity solid
as
their
parameter,
distributions.
with
can
are
spectroscopy fraction
and
these
stage
study
to
projectile
provide
on the
usually
the
one
comparing
constant
is and
the
they
energy
for
the
impact
an early
-ln(tan(WZ))
given
the
distributions
multiplicity reasons
But
experiments
their
=
or
at
and
dynamics
as
observables
limited
variables
such
can be obtained
Typically,
the
contrast
a very
reaction
collision.
models.
in
characterization,
variables
mechanism.
information
only
event
masses,
reaction
global
global
and
here
samples
global
the
of
projectile
as
Such the
of
function
as
NY 11794,
relevant
a collision
be understood
for
centrality
in
physics
typically
for
useful
ion
N emitted
term global
by
Brook,
INTRODUCTION
In relativistic
n
SUNY, Stony
HEAVY ION COLLISIONS
measures beam
to
as well
Foundation
the
larger as the
24c
J. StacheE / Global obsetvables in relativistic heavy ion collisions
amount
of
thermalization
Ideally, avoids
measurements
extrapolations
More
frequently,
systems, detail
Another
a
fraction
observables
cover
comparisons of
4n
of is
in mind possible
Bsd.
Since
ignores
nucleons
that
ion
the
full
different
covered
solid
angle
systems
and,
kinematic
the
comparing
shifts
which
unambiguous. different
as discussed
in more
three at
Section
Transverse
energy
will
be
is
not
here
to
will
contain
is
the
energy
called
enitted
of
1 msr only,
inelastically
of
into
zero-degree
the order
or
elastic
2.
of
will
in
scattered
the number of
collisions,
leading
to
be
extent
the
its 3.
of
and
considered relevant
experiments
observables
The
projectile
therefore
the
as in
the
on initial
context
of
densities.
and/or
energy are will
4.
and
be
to evidence
in general
chapter
the
distributions
zero-degree
density
In will
stopping
they
of
accelerators,
above
nuclear
observables,
energy
both
amount
experiments.
in addition or
as baryons
global
at
multiplicity
of
There,
relativistic
pseudo-rapidity to
question
as well
the
a large
introduced
particles
4.
of
detector
transverse
baryons
start
CERN SPS,
connection
chapter
like
some remarks
from
charged
and
the the
electronic
global
address
subject
after
AGS and
and
chapter
of
years
available
emulsion
observables
distributions Although
a half
production
the
global
particles
only
the
of
as a measure
Brookhaven
systematics
discussed
transparency from
it
is beam,
small,
produced
no or
and the
from
discussed.
context
incident
usually
and takes
observables
results the
is
of
this
the
collision.
program
following,
in
of
angle
undergone
about
on global
including
cone
quantity
have
of
By now,
used
direction
contribution
this
centrality
the the
the
to
heavy
frequently
around
nucleons
2.
makes
to keep
variable
cone
energy
data
reaction.
below.
a small
one
the
global
and only
one has
in of
gained also
t
introduced. be
Finally,
discussed section
5
temperature.
CHARGEDPARTICLE PSEUDO-RAPIDITY DENSITY
Charged
particle
technique,
proportional
pseudo-rapidity all
cases
Lorentz have
target and
by
y and &,
displayed
described
=
S,
streamer are
It
and projectile equating for
tube
been arrays
is
of
the
measured
The
generally as
rapidity
the
and
and charged
nmax
r
particle
1,2.
centroid
well
relevant
using
and Silicon-pad
shown in Figures
Ap and At participating
SpApYpi(At+ApYp>
the values
have
by a Gaussian.
by kinematics.
of
emission
or
distributions
well
determined volume
distributions
arrays.
The overall of
the
reproduced center
the
of
projectile
Using and
Ycm = cosh-I(Ycm), pseudo-rapidiy
the
momentum for
pseudo-rapidity.
target In density
Typical
shape
Gaussian
by using
emulsion
the
is
overlap particle standard
nucleons Figure at
in
nmax is
we
3 are the
25c
Fig. 1: Charged particle pseudo-rapidity density for central Si collisions from
-1
-2
0
1
3
2
4
Pseudorapidity
maximum as system.
a function
Joined
those
by
coresponding
and
trigger
that,
to
cross
in
of
is
cm energy
lines
are
identical
or
sections.
compatible
energy
dN,/dQ
with
a common and plausible
intercept
of
1.9
production
ceases
mass of
the
constant
of
the
hand,
centrality
of and
third
the
is
Figure
4
Gaussians
collision
and
variance to
shown
the
values
obtained “0 to experimental
by
for
similar
systems.
for
0-
S-projectiles
open
and
in moderately
corresponding geometric systematic
to cross
uncertainties
200
EMU0
1
A GeV
40
the
30
the
depend
20
In
for
the
fitting
10
distributions shown (closed with
central about
160+Em
on
energy.
Points
colliding
symbols)
targets
also cm
namely
combinations
The of
the
and projectile
the
combination.
on
are
variance
on
found
logarithmically
The
depends,
strongly
the
nucleon-nucleon
comparable,
the
particles.
projectile
variable,
Gaussian
equals
proportionality
the
be
P
50
particle
4s
two colliding
other
target
when
in
should
target
(at
\qnax) m 1nJs
GeV ;
calculated that
finds
beam with
ds,
points
similar
One
the
general,
dependence
the
dashed
are and
heavy
collisions 10%
section. the data
of
the Within are
0
-2
0
2
4
6
8
ri
Fig. 2: Charged particle pseudorapidity density distribution from EMU01 (ref.2) for two different trigger conditions corresponding to about 11 % ogeom.
26c
J. Stachel / Global observables in relativistic heavy ion collisions
I
”
I”“1
Pseudo-Rapidity
I
x ,” ,?, I’ _
,’ I ,’’ ,I0,’ ,’ ,, ,f’ ,,’ ,“’ ;’ !’ ,’ I’ J5 ,’ ,’ ,’ ,’ 9’,’ >’,’ ,,’ ,’ ,’ ,’ ,’ o,,’ ,‘ ,’ ,A,’ ,‘,’ ,,’ d’ ,’ ,*’4* ,_-,‘,’ ,I 0” ,,* ,‘,*’ ,,’ ,*’ ,,I ,;, ,, ,*’ ,?I ,;r x’p*,__ ’ ,’ ,_’ _,__,m*+ ,:, ,*‘,, , ,,_*,:’ ,‘,;_,* ,_F_ _ _
100
50
0
1.0
I
Density
1
2
10
1.G
1.4
b’ 1.2
.0
20
J/s 5,Gpv,
3: Beam energy dependence of the charged particle pseudorapidity density. Points are obtained fitting Gaussians to the data of refs. 3-8, points representing comparable systems are connected by dashed lines.
Fig. 4: Width of charged particle pseudo-rapidity distributions for central collisions corresponding to 10% ugeom using 0- and S-beams (closed s mbols1~2~g and open symbols7p2(p10).
Fig.
described
by
systematic
target
in
figs.
in
a quadratic
i.e.
on
the
target
in The
of
slowing
only
of
about
down of
The
bottom
however,
not
peak
the
of
relative
to
any
the
distributions
of
energy
emitted effects
with
There
5 shows
transverse
quantitative
increasing
is
central
energy; conclusions
the
a small
coverage
the
backward above,
of
hand,
but
systematic
panel
between
dN/dn Et
appears decrease
(central
particular
since for
participating
other
correlation this
collision
discussed
the
collisions
charged
the
into
number on
a strong
on lnds,
characterizing
kinematic
distribution,
results
multiplicity
centrality
no shown
is
slides
plot taken in
of
charged does, at
the
acceptance
peak. of
charged
6 (bottom). power
the
particle
parameters
with
and very
while
of
available,
The information
the
the
fig.
and
distribution
scaling
Figure
of
presently
found.
transverse
cm motion
peripheral
allow
the
the
of
shape
how the
illustrates the
panel
data is
charged
vary
on centrality.
multiplicity
particle
by
variance
depend
10% between
fig.5).
5, panel
all
Gaussian total
5 illustrates
fig.
The
weakly
the the
densities
top
nucleons.
to
possible
Figure
Inspecting
mass dependence
with
pseudo-rapidiy
characterized,
The
projetile
dependence
NC m ln*J.s.
hemisphere.
in
0.531nds.
3 and 4 together
particle
i.e.
c or
law
particle
The display dependence
multiplicity
with
target
is
double
logarithmic
dN/dn
m Ata.
Experimental
in
mass order
points
is
displayed
to
test
are
for
for
a
0 and
S/Si
beams
of
various
minimum bias
to very
solid
lines
for
lines
for
200
values of
tiO.4
beam
energy
beams
(solid
target
based
mass
a=O.33
comparison or
value of
is
experimental
at of
the
to the
two curves is
nucleon obtained
study
the
2.75 2.5
1
1 A
2.25
0
0
are
25
25
of
respect
instance in ref.5). indicate
OLsimply
ways
to study
the
that
models models.
The fact the
that
presence
only
cuts
reflect
or
heavier
in
string
integrated For
the
Typical
to note
expected
shown
of
that
and
the
interesting
that
dotted
seen
data.
for
could
the
by
to centrality
larger
for
here
be
dependence
than
density.
values
more direct
is
and
can
set
from
connected
meaningful
at
a constant
the
kinematics
this.
‘3
I 75
I 50
1 100
I 125
I 150
I 175
:
50
75
75
50
E,
100
(-0.1
(-0.1
125
150
175
200
CTC2.9)
100
125
<7<2.9)
150
(Ge”)’
(GeV)
175
(GeV)
200
of
multiplicity
a . .
E,
0
It
either
pseudo-rapidity
E, (-0.1<7<2.9)
0
noted
made for
resulting
and there
with
as
larger
be
is
law each
somewhat
calculations
should
It
stronger
collisions,
e.g.
scaling
of
fig.6).
systematically
instance,
be
ranging are
60 GeV/nucleon
power
trend
to in
nucleon
It At
a
systematically
(see is
maximum of
reaction
1 25
values
dependence
value
n ,for
1.25 c 0
but
for
right
no systematic
and top
effects.
rescattering
NC
found
with
tend
sections
respectively.
the
to
cross
be comparable
lines
energy,
given
obtained,
lines
trigger should
consistent
a are
on individual
There, the
are
is
incident
are
for
for that
dashed
GeV/nucleon,
results
resulting
the
central.
14.6
and Values
GeV/nucleon
experimental
values
energies
Fig. 5: Characteristics of charged particle pseudorapidity distributions as a function of centrality for Ag (squares) and W targets (circles) as measured* by HELIOS. Open and closed symbols are for 60 and 200 GeV/nucleon incident energy.
28c
3.
.I. Stachel / Global observables in relativistic heavy ion collisions
TRANSVERSE ENERGY PRODUCTION
energy
Transverse calorimeters
these
Typical
targets
are
target
and
nucleons
for
leading
to
nucleus
with
pseudo-rapidity
to
In
A=400. a
in
by
It
e.g.,
completely 8 the
effect
of
the
should
be
noted
covering
distributions
of
of
to
the nuclear
transverse
ratio
equivalent the
essentially energy
data16 the are
and
shape
of
of The
parameters
where
participating
deformation
an axis
of
NA35 and WA80 at
and understood.
impact number
distribution that
types
and CERN energies
geometry
with
various
The characteristic
due
and
nucleus
tail
measurement
and by NA34,
collision
is,
using
Brookhaven
7 and 8.
the
a prolate the
measured
for
Figures
targets
fig.
U target,
Et values
correspond
heavy overlap
little.
the
in
dominated
for
projectile
varies
clearly
do/dEt
displayed is
developing
been
Brookhaven 11-13
distributions
distributions
shoulder
have
by El302 and E814 at
CERN14-20. various
distributions
of
can
be seen
about
.8/1.2
to a spherical shown
in
full
solid
angle.
fig.
very
similar
in
8 The
shape
500 Fig. 6: Target mass dependence of charged particle pseudo-rapidity density (bottom) and transverse energy production (top). Data in the bottom graph are from refs. 1,5,8,9,10; solid, dashed and dotted lines connect points for 14.6, 60 and 200 GeV/nucleon incident energy. Data in the top graph are from
r
k!
;;; 200 r T !g
_ ,&
I..
50
200
~~f~,le6~~“,;f~,~~,erd’ electromagnetic energy and open circles16 to total Et integrated over n. Coefficients o?, given to the right, correspond to Ata behavior.
100
jis 100 c2 r
50
< 5 20
10
10
20
50
100
AT
200
500
29~
J. Stachel / Global observables in relativistic heavy ion collisions
and
characteristics
particle discussed Figure
above.
the
As an example,
typical
and
follow dN,/dn The
Gaussian
width same
(see
e.g.
top
of
target
the
beams.
The
charged (bottom
of
fraction
for
of
that
one
should
but
total
from
of
with
WA80 and the the
about keep energy
ratio
y=2-4, 7.5:1
is
0
for
for
fraction of 7:l
obtained
by NA35 (see
ref.
energy20p18e
28.5*3X,
of
the
covering
22-253 in
of
mind
for
the
that
mesons. to
of
number in
NA35 have
electromagnetic
transverse
central
of
from
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(or
15
20
is
measure
of (also
positive) crude,
and negative
A very
energy
pion
pion
is
25
kinetic
.15
measured18 to
estimate rapidity
estimate
by baryons. energy
and nucleon about
for
transverse
GeV one would for
StS
protons, is
find
that
electromagnetic
rough
carried
pions this
S+Au they
energy
rapidity.
that
Et
very
ET[oevl
200 GeV/nucleon
calorimeters
electromagnetic
10
transverse
a common temperature
S+S.
18).
For
total
transverse
Assuming
5
Fig. 7: Transverse energy distributions from E814 measured12p l3 over two different regions of acceptance. Data are not unfolded for leakage and resolution. Solid lines: Landau fireballz5. Dashed and solid lines with diamonds: HIJET withoutz6 and with27 rescattering.
values
indicative
correspond the
very
densities
(pseudo-)rapidities
spectra
solid
a are
6)
respectively
gives
open NA34
effects.
measured
25+2X,
the from
rapidity
Experiments also
peak of
obtained
possibly
rescattering
200 open
full
was
fig.
.40
40
of
the
the
particle
around
at
while
what
0
asterisks
coefficients
to
IO-’
Shown
The
results over
similar
1o-3
the
for
the
to values
integrated
4 4
as
shows
results
Gaussian,
angle.
6
and
are
lo-*
Gaussians
dependence
experimental
circles
with
production.
S
B ;
refs.14,15,21).
energy
correspond
shape
7
can
systematics
mass
triangles
one
the
figure
GeV/nucleon
in
shown as
by kinematics. of
the
transverse
the
are
determined
Height
charged
densities
by WA80. Again,
centroids
are
the
9 distributions
obtainedzO see
to
pseudo-rapidity
nucleons momentum conclude
by NA35) averaged
close
distributions
to
then Here,
the
that over ratio
reported
3oc
.I. Stachel / Global observables in relativistic heavy ion collisions
Comparing
dNc/dn
energy
per
= 0.55
GeV for
not
charged
change
energy has
For
the
target-projectile
significant
rise
collisions:
for
the
three
not
explained
Et/NC
by
event about
a change
in
the
source
of
such to
backward and n = 1.
quantity
the
present,
for (see
or
however,
GeV/nucleon
This
first
in not
trend
on
is
and
central
surprising a
E814 give
rather
be
the
data
are
Et/NC
$0 c t
I,, \d
Tr~tltverse du/dE, 200
energy differential in
-0.1
GeV/nuc.
<
7
<
3-nucleus
cross-s-;+ion
5.5
for
collisions
$
10
IO
IO-
CO-
Id
Id
GeV and
therein).
could
experimental
from
show a
and 0.75
where
spectra
found.
data
10 and refs.
enough
data22
dependence is
0.58
instance,
pt
beam
200
central
ref. the
or
S+W at
these
are
does
collaboration
collision
values
Et/NC
value
collision
significant the
transverse
this
S+Em and
moderately
IRIS,
ratio
14.6
no
used.
: nucleon at
At
like
the
pseudo-rapidity
for
predicted
of
of
respective
GeV is
that
O+Em,
again
of
the
WA80 finds
Helios-Emulsion
for
centrality
generators
pion
interesting
The
angles
compute
B-interval.
centrality
combinations
0.55
an effect, decide.
is
mass,
a function
target-projectile
of
available
as
towards
value
It
n = 1.4-3. or
can
a given
GeV/nucleon). this
interval
n = 2-3
in
target
200
combination however,
for
and
investigatedlO
GeV/nucleon.
Inspecting,
with
60
one
distributions,
evaluated and 0 beams5.
significantly
(comparing
constant
dEt/dn
n = 2.-4.2
recently
Both
and
particle,
Fig. 8: Transverse enefgy distributions measured over a very large solid angle.
=
J. Stachel / Global observables in relativistic heavy ion collkions
0.41
Nvcieus
A GeV I90 +
200
for
GeV
lower
value
results
is
in
mind
Si+Au as
are
GeV,
as
at
n = 0.8.
compared
not
that
pions
31c
too
to
surprising
numbers
of
comparable by
rapidity
and
that,
central
rapidity,
CERN
keeping
nucleons
for
shown23
The
the
and
Si+Au at
E802,
at
14.6
central
backwards
of even
nucleons
dominate. Another
interesting
explored
information
2.5
3.0
3
5
4.0
4.6
8.0
6.5
discussion
has Only
Sarcevic. simulations the trivial
initiated
two
of
fluctuations
simulations25 kind
of
are
more
relevant.
do/dEt
for
shown
in
ii)
There
are
shown in
respectively.
hemisphere without
While
(top
parameters
Et
experimental fact
something
(see
to
this do
of
is is
same
the
surrounding
chance
of
secondaries
for
come
very
Et
are
pursue
the
to
targets
target
spectator Indeed, in
heavy
in
also of
more
4r,
tail
Si+Pb
the
with the
as are in
targets. and
forward
several
models the
shape
same
of
the
the distribution.
suggests nueleons
calculations
reproducing
the
a wide
for
by
tail
only
be from E814,
spectra
and
in
the
covering
calculationsz5)
lighter
close
will
reproduced
sample fireball
is
from E824 and NA34 for
severely
collisions.
To data
at least
fireball
broader
this
if
rather
Landau
contributing
systems
underpredicted
with
rescattering
effect
7,10)
case
and soon
hemisphere,
Landau
the
du/dEt.
that,
particles
the where
24 experimental
not
first
angle,
emitted
and
Monte-Carlo
solid
tail
8)
schematic
from
is
effects
Friedman
full
lines),
fig.
tail
This
Baym,
show
the
in
the
system
the
is
in
Very
ref.
significantly
participate
by
in
the
the
that
to
figs.
e.g.
backward
spectrum that
(solid
7 and 10 data
for
sections
difficulty
way
in This
by experimental
a hot
the
the
backward
figs.
of
instance,
10
course,
fluctuations*
i)
from
for
may be another the
here:
unusual,
production.
study24
from
7 and
suggested
covering
leakage
part
now16 from NA34 (see
data
like earlier
only
seen,
figs.
dominated
place
already be
not
emission
contributing
available
As an example
o+w,
arise can
fluctuations
they
in
covers
This
fluctuation
interesting
are
an
particle
set-up
space.
by
comments
statistical
experimental
phase
The
been
dependence production20.
be the
contains
energy
of
assumes,
Fig. 9: Pseudo-rapidity of transverse energy
of
fluctuations
transverse
rl
to
tail
possibly
on,
event-to-event 20
the
distributions
da/dEt
o
question
whether
is,
that
this
has
do
not
that that
these
data.
include As an
.I. Stachel/ Globai observables in ~ela~~~~tic heavy ion col&ions
32c
example
are
rescattering the
latter
shown
in
(dashed
figs. and
calculation
does
equivalent
calculations
and
obviously,
there,
practically
not
7,lO
solid
the
In
visible).
rescattering
effects
have
qualitatively)
the
conclusions
effect
to
be seen
substantial.
It
fluctuations
not
4~ data
is
published the of
is
still model
data the
in
the not
clear
outstanding. calculations
by covering
Et spectrum
only at
been
at
in
into
the
while
there
although
fall
short
in
two27
respectively
in
top
of
at
Brookhaven
by
Werner
systems from
the
fig.
10
energies
and
Koch28
generator
comparatively
differences is
statistics
for
to note as
below
are
additional
comparison
amusing
decades
and, little
backward
need
a detailed
somewhat
however,
with27r13
both
Results
shown
is
the
whether
models
and for
VENUS event
There
same:
present
clearly one28
are (and
publication
hemisphere,
and
satisfactorily.
hemisphere
the
is,
without26
diamonds)
much smaller
included
these It
data
recent
are
forward
contained
is a
open
the
forward
effect
calculations
with
reproduce
for the
HIJET
lines
that
compared the
with the to
shoulder
200 GeV/nucleon.
NA34 -.l
10
Fig. 10: Experimental transverse energy distributions (solid dots) from WA80 (ref.19) and NA34 (ref.14). Meaning of the curves: same as in figure 7.
0°’u1,,,,1_,,,, 0
50
100 150 ET [GeV]
ll-i-d2
800
250
J. Stachel / Global observables in relativisticheavy ion collisions
33c
4. NUCLEAR STOPPING Frequently the amount of stopping (and thermalization) in a heavy ion collision is judged from the amount of transverse energy observed for a given system. Information is arrived at by comparing the amount of experimentally observed Et to what is predicted by a model, which assumes, for instance, complete stopping. As discussed e.g. in ref. 29 the answer obtained this way is by no means model independent. The only model independent result to be obtained this way is a lower limit for stopping fraction by comparing the experimental value to the kinematic limit in which all stopped energy is emitted into 90' in the cm frame. A better contraint can be put on this number by, in addition, measuring the energy Rad going into a small cone around the beam axis. By demanding that a model from which information concerning stopping is derived simultaneously describe the transverse energy and Rsd one puts a tighter constraint on the kinematics30 and some models, like the isotropic fireball, are ruled out that way. From studying that correlation it was concluded in ref. 30 in an analysis using the Landau fireball model, that for O+Au at 200 GeVfnucleon there is still about 85% stopping (for a definition of the number see refs. 25,30). Figures 11 and 12 show such data at 14.6 and 200 GeV/nucleon. In figure 11 instead Et the charged particle multiplicity is plotted but because of the tight correlation between the two quantities, as discussed 200 A GeV “0
0
BOO
,500
+ 197Au
2400
3200
EZDC (GW Fig. 11: Charged particle multiplicity measuredg*22 bv E814 over ij il0.9-3.9 versus energy emitted into a forward 0.8" cone. Due to the pretrigger there is a cutoff at N,rZO.
Fig. 12: Correlation of Et in a midrapidity calorimeter (n=2.4-5.5) and forward enery from WA80 (refs. 19,20).
J. Stachel / Global observables in relativistic heavy ion collisions
34c
the
above,
interpretation
clearly
see
many
collisions
observed
in
fig.
12
the
most
the
central
stopping
that
that
even
particle
this
interpretation
l-2
in
by noting
with
E814
where cone
leading of
is
corresponding drastically Displayed target Fermi integral
0.8O
Since
for
of
multiplicity
still
is
out
of
fairly
is
no
still
400
this
do/dEt
it
In
but
left
for
in
beam
nucleons
one
through
a statement
On the
at AGS energies,
for energy
transmitted to
can
growing.
GeV
and dEt/dn
system30.
one
two quantities
16 are
One relates
undisputed
12
GeV/nucleon
by beam rapidity
incident
thermalized
Et)
the
about
carried the
and
resolution,
(and
between
is
energy
a
around
the
beam
and neutrons about
rapidity
nuclei. motion
14.6
Et distributions
from
the
spectra
decreases in Figure
11
At
experimental
collion.
the
figs.
reactions.
are
about
consistent
other
hand,
is
unambiguous
not
while
collisions.
cone protons
about
this
that
the
there
nucleons
emission
the
the
Comparing
two
correlation
a central
200 GeV/nucleon In
but
a clear
collisions
Assuming
conclude target
for
also
same. the
within
is,
beam direction is
the
between
there
there
direction. would
is
a difference
with
13 is there
y = 3.0-3.85.
is
beam axis
and
one can
identify
(in This
some the
for
forward
in
for
rapidity
200 GeV/N
In
component
which
and various
expected this
just plot
due
shows
expectations
‘*S + =S +
-I--
a
the
energy.
neutrons
with
in
13,31).
transverse
nucleus)
consistent
detected
(refs.
or
spectrometer
are
a beam rapidity
Si projectile is
a
y > 1.6
component
smearing
interval
of
Nucleons
centrality
beam rapidity
is
part
identified.
increasing
this
the neutrons
axis
are
to the
from
PROTONS
0
0
i
Fig. 13: Average multiplicity of beam rapidity neutrons (y=3.0-3.85, pt<.2 GeV/c) as a function of Et into -0.5
~f~;,~~t,5~~r~:3;a~~~~~~d from
NA35 streamer chamber data positively and negatively charged tracks for central __. . collisions.
on S+S
.I. Stachel / Global observables in relativistic healy ion collisions
fragmentation
models
remarkable
feature
nucleons
(results
corresponding
a
reflect
nucleon
the
supports
values
smaller
from
target
stopping
rapidity
comes
from
carefully
Figure
14
the
full
can
be
of
65% for
The
for
seen
know whether
to
allow
the
the
of
of
be of
the
the
fact
rapidity this
energy
the
is
gets
therefore
best
a streamer
density
chamber
is
of that
a
etc.
displayed
in
practically
distributions,
proton
the
and
Kaons
covers
A and anti-A
over
information
from Lambdas,
shift
that
one
and
stopping
the
based.
the
Landau try
EfCm
the An
thus
the
fraction
is
numerator
/
base Vf.
achieved
large to
energy
the
this
still
validity
of
and
the
low,
obviously
reproduces
an energy
density
There
denotes
sf the
energy
the
estimate the
that
the
taken
this
is
no
on which that
experimental on
to
as from
there
fact
stopping
deposited
(area)
as well
assumption,
uses
central
longitudinal
grounds
so
scaling
approach
mode134
size
the
assumption
too
enough
at
transverse
ion like
estimate
Shuryak-Bjorken
on dimensional
from
are
to
is
then
One method
pseudo-rapidity
alternative
corresponds
the
in heavy
One would
transverse
Here at
arises
mode135
and sf
the
stopping
are
in
a unknown constant,
beam energies
confirming
to
connects
of
present.
transition.
scaling
dn/dz.
+ Uncertainty
is
can
EL =
on the
amount at
densities
phase
related
term
and is
present
of
based is
the
energy
(dEt/dn),,,
1 fm-l
plateau
Therefore,
in
the
available
reactions
last
system
section
deconfinement
density
The
order
previous
these
densities
estimate
kinematics
and
in
system.
extent
by
strongly
nucleons
The
distribution
concludes
beam energies
by eSB = l/at
the
This
rapidity
analysis18,33
the
at
expected
energy
rapidity
average
observation
identified
rapidity
considering
on top
reflected
reaction.
in
large
to
where
This
tracks
proton
sits
as
and
CONDITIONS
is
initial
the
of
contributions
S+S.
also
with
section
component
midrapidity.
negative
system
and,
deduce
at
for
Si+Pb
consistent
energies.
measurement
deduced
symmetric range
particular
As we have collisions
and
difference
a central
cross
This
here)
in
midrapidity
Brookhaven
shown
are
scattering
23,32,31).
for
l/300 targets
The
beam rapidity
data
beam rapidity
especially
positive
stopping.
INITIAL
and
about
towards
(refs.
no direct
resulting
the
to
this
is
this
rapidity
amount
5.
comparing
used
E814
interval
33,18).
This rises
resolution. for
neutron
Cu and Al
inelastic
thickness.
there
correcting
(refs.
or
interpretation
At CEEN energies a large
path
and
the of
for
detector
multiplicity
with
probability
continuously
E810
account small
agree
observed
free
that
E802, the
protons
mean
a distribution
data
into very
a transmission
The larger
common
of
the
for
to
collision.
taking observed
and
is
35c
the data.
mode125p30
fraction
(stopped)
and in
the
36c
J. Stachel / Global observables in relativistic heavy ion collisions
overlap
volume
defining
this
however,
Vf
that
the
S+W, are only
the 2.7
be
what
the in
transition. time
determined
future
the
rapidity
size
density
/fm3,
is
which address
Combining trigger
temperature energy
of
the
this
the
one
of
degrees irrelevant other with major
in
has
to the
contribution
Si+Pb This
at
by
estimate
above
assume
estimates
ideal
system
have
large
is
of
course, that
The
for is
but
For
small
the The
results
in
related
drops
which
out
the
of
makes
it
pions
or also
how to
While
this
perturbance
here
number
point just
open.
same
initial
quantity
also
is a
the
the
The question
instance,
it
at
directly the
with
does
formed.
T = &/(2.7n).
latter
dealing
degeneracies.
nucleons,
is
g T3 (/fm3).
or Vf)
behavior,
out.
one
estimate
S+W data
note
200
nR = 5 and 8
deduce
temperature
(dn/dz
gas
drops
stage
AGS energies
is,
For
n = 15.9
the
One should
particle
entropy-density.
while for
to
volume.
(measured
and 200 GeV/nucleon
above. the
to
go
A = 30 but
state.
behavior,
energy-
g T4 (GeV/fm3),
initial
part
carried
of
gas
to
charged
above,
final
stage clearly
accelerators.
a naive
the
densities
ideal
ratio
cases.
for
the
and particle
as
the
needed
this is
around
unit
such
in
at
both the
per
Obviously,
observed
is
This
still
two models
g and one obtains
at
in at
which
entropy
the
discussed
freedom
mesons, the
is
both
still
whether
as
GeV/nucleon
Et/N,
same
assuming
E = 42.9
to arrive
while
energy
system
GeV in
quantity
was difficult and,
for
14.6
the
estimates
at
from
pions
and can that
advantageous
are
can,
of
number.
one can,
system
to
T = 0.16-0.17
using
these
rough
probably
it
system
to note
maintained.
makes
give
similar
very
one
be available one
number
when a pion.
one has
of
Applying
to
the
density
degeneracy
arguments
a large
section)
that
the
estimates
very
are
is
are
and
the
order
in
ESB and EL. At 200
encouraging
question
densities
At present
the
question
the estimates cross
critical
A = 200 will
obtains,
certainly
the
the
of
in
note,
dn/dz
both
for
for
is
arises
One should
defining
estimates
certainly
difficulty
GeV Si+Pb
case
these
system
of
estimate
S+W one
this
as
GeV/fm3
it
possible.
lines
GeV/nucleon
not
the
14.6
In any case,
more
beams with
same
in
the
be evaluated?
same
For
1.0
energy
of
projectiles
near
Along
the
the
and 1.1
and
such
to
gets
Clearly,
The
scale
by
heaviest the
large
Here
it
is
values,
GeV/fm3.
are
is
energies.
as an indication.
a phase
over
these
and one
corresponding
values
time
uncertainty
at
and 8.3
taken
resulting for
model
and projectile.
at what
basic
same result
GeV/nucleon
target
e.g.
the
Shuryak-Bjorken nearly
between
volume,
deal is
at
a
200
GeV/nucleon. While arrived that
the at
we
densities have
been
preceeding
from are
quite
discussion different
dealing
where, altered.
with
almost
systems
certainly,
Whether
is view
the
rather points of
the systems
qualitative it
is
certainly
and
presented high
properties
of
studied
have
presents
here energy
normal actually
to
numbers illustrate
and
(nuclear)
particle matter
undergone,
at
J. Stachel / Global observables in relativistic heavy ion collisions
37c
least locally, a phase transition, is not clear and needs further experimental study and, especially, the use of heavier beams in order to produce extended systems of high density and temperature.
ACKNOWLEDGEMENT Thanks are due to all my experimental collegues from the current experiments at BNL and CERN for providing me their, in part unpublished, data without which the current review would have been impossible. I also would like to thank Peter Braun-Munzinger for many clarifying discussions.
RERERENCES
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.I. Stachel / Global observables in relativistic heavy ion collisions
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Nuclear Physics A.525 (1991) 23c-38~ North-Holland, Amsterdam
SYSTEMATICS OF GLOBAL OBSERVABLES IN RELATIVISTIC
1.
Johanna
STACHEL
Physics
Department,
of
particles
heavy
is
to
particles.
which
any
event.
given
indicators tool
USA*
comparison
to
density
achieved
spatial
observables
are
the
Then By
particle
are
angle
sine
of
integrating well
over as
its
amount
of
angles
and is
Supported
of
one the
polar
all
detector
by the National
to
of
sensitive
Science
to
be
as
a
latter
enters
via
model
as well
of
the
predictions as
the energy
the this the
particles
of
the
cell
transverse dEt/dn.
and
stopping
power
and the A.P.Sloan
0 1991 - Elsevier Science Publishers B.V. (North-Holland)
or
the
charged into
a
cell
obtains,
after
Et=C[eisin(f3i)]
quantity
incident
number
a detector
energy
This the
therefore,
emitted
in
global
experimental is
energy
as well
pseudorapidity
for here
detector
of
the
particle
measured
the nuclear
Foundation
of
these
4 and,
0 or
energy
direction
and do/dE
events
discussed
Instead
dependence the
the
and
angle
angle
charged
elements,
from
to
understanding
many
azimuthal polar
to
dN,/dn.
angle
are a most
target
du/dN
over
measurement
observable
weighs
are
systematics
to
variables
the
The
restricted
our
power
in
collision.
of
to
discussed.
frequently
therefore
the
function
density
shifted
stopping
space
energy, the
for
phase
respect
their
where
The
identified
They
kinetic
basis
integral
respect
pseudo-rapidity
energy
037.59474/91/$03.50
a
study
them.
of
distributions
with
observables
nuclear
the
spatial
the number
by
of
kinematics.
also
the
E carried
instance
Averaging
experimental
pseudo-rapidity solid
as
their
parameter,
distributions.
with
can
are
spectroscopy fraction
and
these
stage
study
to
projectile
provide
on the
usually
the
one
comparing
constant
is and
the
they
energy
for
the
impact
an early
-ln(tan(WZ))
given
the
distributions
multiplicity reasons
But
experiments
their
=
or
at
and
dynamics
as
observables
limited
variables
such
can be obtained
Typically,
the
contrast
a very
reaction
collision.
models.
in
characterization,
variables
mechanism.
information
only
event
masses,
reaction
global
global
and
here
samples
global
the
of
projectile
as
Such the
of
function
as
NY 11794,
relevant
a collision
be understood
for
centrality
in
physics
typically
for
useful
ion
N emitted
term global
by
Brook,
INTRODUCTION
In relativistic
n
SUNY, Stony
HEAVY ION COLLISIONS
measures beam
to
as well
Foundation
the
larger as the
24c
J. StacheE / Global obsetvables in relativistic heavy ion collisions
amount
of
thermalization
Ideally, avoids
measurements
extrapolations
More
frequently,
systems, detail
Another
a
fraction
observables
cover
comparisons of
4n
of is
in mind possible
Bsd.
Since
ignores
nucleons
that
ion
the
full
different
covered
solid
angle
systems
and,
kinematic
the
comparing
shifts
which
unambiguous. different
as discussed
in more
three at
Section
Transverse
energy
will
be
is
not
here
to
will
contain
is
the
energy
called
enitted
of
1 msr only,
inelastically
of
into
zero-degree
the order
or
elastic
2.
of
will
in
scattered
the number of
collisions,
leading
to
be
extent
the
its 3.
of
and
considered relevant
experiments
observables
The
projectile
therefore
the
as in
the
on initial
context
of
densities.
and/or
energy are will
4.
and
be
to evidence
in general
chapter
the
distributions
zero-degree
density
In will
stopping
they
of
accelerators,
above
nuclear
observables,
energy
both
amount
experiments.
in addition or
as baryons
global
at
multiplicity
of
There,
relativistic
pseudo-rapidity to
question
as well
the
a large
introduced
particles
4.
of
detector
transverse
baryons
start
CERN SPS,
connection
chapter
like
some remarks
from
charged
and
the the
electronic
global
address
subject
after
AGS and
and
chapter
of
years
available
emulsion
observables
distributions Although
a half
production
the
global
particles
only
the
of
as a measure
Brookhaven
systematics
discussed
transparency from
it
is beam,
small,
produced
no or
and the
from
discussed.
context
incident
usually
and takes
observables
results the
is
of
this
the
collision.
program
following,
in
of
angle
undergone
about
on global
including
cone
quantity
have
of
By now,
used
direction
contribution
this
centrality
the the
the
to
heavy
frequently
around
nucleons
2.
makes
to keep
variable
cone
energy
data
reaction.
below.
a small
one
the
global
and only
one has
in of
gained also
t
introduced. be
Finally,
discussed section
5
temperature.
CHARGEDPARTICLE PSEUDO-RAPIDITY DENSITY
Charged
particle
technique,
proportional
pseudo-rapidity all
cases
Lorentz have
target and
by
y and &,
displayed
described
=
S,
streamer are
It
and projectile equating for
tube
been arrays
is
of
the
measured
The
generally as
rapidity
the
and
and charged
nmax
r
particle
1,2.
centroid
well
relevant
using
and Silicon-pad
shown in Figures
Ap and At participating
SpApYpi(At+ApYp>
the values
have
by a Gaussian.
by kinematics.
of
emission
or
distributions
well
determined volume
distributions
arrays.
The overall of
the
reproduced center
the
of
projectile
Using and
Ycm = cosh-I(Ycm), pseudo-rapidiy
the
momentum for
pseudo-rapidity.
target In density
Typical
shape
Gaussian
by using
emulsion
the
is
overlap particle standard
nucleons Figure at
in
nmax is
we
3 are the
25c
Fig. 1: Charged particle pseudo-rapidity density for central Si collisions from
-1
-2
0
1
3
2
4
Pseudorapidity
maximum as system.
a function
Joined
those
by
coresponding
and
trigger
that,
to
cross
in
of
is
cm energy
lines
are
identical
or
sections.
compatible
energy
dN,/dQ
with
a common and plausible
intercept
of
1.9
production
ceases
mass of
the
constant
of
the
hand,
centrality
of and
third
the
is
Figure
4
Gaussians
collision
and
variance to
shown
the
values
obtained “0 to experimental
by
for
similar
systems.
for
0-
S-projectiles
open
and
in moderately
corresponding geometric systematic
to cross
uncertainties
200
EMU0
1
A GeV
40
the
30
the
depend
20
In
for
the
fitting
10
distributions shown (closed with
central about
160+Em
on
energy.
Points
colliding
symbols)
targets
also cm
namely
combinations
The of
the
and projectile
the
combination.
on
are
variance
on
found
logarithmically
The
depends,
strongly
the
nucleon-nucleon
comparable,
the
particles.
projectile
variable,
Gaussian
equals
proportionality
the
be
P
50
particle
4s
two colliding
other
target
when
in
should
target
(at
\qnax) m 1nJs
GeV ;
calculated that
finds
beam with
ds,
points
similar
One
the
general,
dependence
the
dashed
are and
heavy
collisions 10%
section. the data
of
the Within are
0
-2
0
2
4
6
8
ri
Fig. 2: Charged particle pseudorapidity density distribution from EMU01 (ref.2) for two different trigger conditions corresponding to about 11 % ogeom.
26c
J. Stachel / Global observables in relativistic heavy ion collisions
I
”
I”“1
Pseudo-Rapidity
I
x ,” ,?, I’ _
,’ I ,’’ ,I0,’ ,’ ,, ,f’ ,,’ ,“’ ;’ !’ ,’ I’ J5 ,’ ,’ ,’ ,’ 9’,’ >’,’ ,,’ ,’ ,’ ,’ ,’ o,,’ ,‘ ,’ ,A,’ ,‘,’ ,,’ d’ ,’ ,*’4* ,_-,‘,’ ,I 0” ,,* ,‘,*’ ,,’ ,*’ ,,I ,;, ,, ,*’ ,?I ,;r x’p*,__ ’ ,’ ,_’ _,__,m*+ ,:, ,*‘,, , ,,_*,:’ ,‘,;_,* ,_F_ _ _
100
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Density
1
2
10
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1.4
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.0
20
J/s 5,Gpv,
3: Beam energy dependence of the charged particle pseudorapidity density. Points are obtained fitting Gaussians to the data of refs. 3-8, points representing comparable systems are connected by dashed lines.
Fig. 4: Width of charged particle pseudo-rapidity distributions for central collisions corresponding to 10% ugeom using 0- and S-beams (closed s mbols1~2~g and open symbols7p2(p10).
Fig.
described
by
systematic
target
in
figs.
in
a quadratic
i.e.
on
the
target
in The
of
slowing
only
of
about
down of
The
bottom
however,
not
peak
the
of
relative
to
any
the
distributions
of
energy
emitted effects
with
There
5 shows
transverse
quantitative
increasing
is
central
energy; conclusions
the
a small
coverage
the
backward above,
of
hand,
but
systematic
panel
between
dN/dn Et
appears decrease
(central
particular
since for
participating
other
correlation this
collision
discussed
the
collisions
charged
the
into
number on
a strong
on lnds,
characterizing
kinematic
distribution,
results
multiplicity
centrality
no shown
is
slides
plot taken in
of
charged does, at
the
acceptance
peak. of
charged
6 (bottom). power
the
particle
parameters
with
and very
while
of
available,
The information
the
the
fig.
and
distribution
scaling
Figure
of
presently
found.
transverse
cm motion
peripheral
allow
the
the
of
shape
how the
illustrates the
panel
data is
charged
vary
on centrality.
multiplicity
particle
by
variance
depend
10% between
fig.5).
5, panel
all
Gaussian total
5 illustrates
fig.
The
weakly
the the
densities
top
nucleons.
to
possible
Figure
Inspecting
mass dependence
with
pseudo-rapidiy
characterized,
The
projetile
dependence
NC m ln*J.s.
hemisphere.
in
0.531nds.
3 and 4 together
particle
i.e.
c or
law
particle
The display dependence
multiplicity
with
target
is
double
logarithmic
dN/dn
m Ata.
Experimental
in
mass order
points
is
displayed
to
test
are
for
for
a
0 and
S/Si
beams
of
various
minimum bias
to very
solid
lines
for
lines
for
200
values of
tiO.4
beam
energy
beams
(solid
target
based
mass
a=O.33
comparison or
value of
is
experimental
at of
the
to the
two curves is
nucleon obtained
study
the
2.75 2.5
1
1 A
2.25
0
0
are
25
25
of
respect
instance in ref.5). indicate
OLsimply
ways
to study
the
that
models models.
The fact the
that
presence
only
cuts
reflect
or
heavier
in
string
integrated For
the
Typical
to note
expected
shown
of
that
and
the
interesting
that
dotted
seen
data.
for
could
the
by
to centrality
larger
for
here
be
dependence
than
density.
values
more direct
is
and
can
set
from
connected
meaningful
at
a constant
the
kinematics
this.
‘3
I 75
I 50
1 100
I 125
I 150
I 175
:
50
75
75
50
E,
100
(-0.1
(-0.1
125
150
175
200
CTC2.9)
100
125
<7<2.9)
150
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(GeV)
175
(GeV)
200
of
multiplicity
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E,
0
It
either
pseudo-rapidity
E, (-0.1<7<2.9)
0
noted
made for
resulting
and there
with
as
larger
be
is
law each
somewhat
calculations
should
It
stronger
collisions,
e.g.
scaling
of
fig.6).
systematically
instance,
be
ranging are
60 GeV/nucleon
power
trend
to in
nucleon
It At
a
systematically
(see is
maximum of
reaction
1 25
values
dependence
value
n ,for
1.25 c 0
but
for
right
no systematic
and top
effects.
rescattering
NC
found
with
tend
sections
respectively.
the
to
cross
be comparable
lines
energy,
given
obtained,
lines
trigger should
consistent
a are
on individual
There, the
are
is
incident
are
for
for that
dashed
GeV/nucleon,
results
resulting
the
central.
14.6
and Values
GeV/nucleon
experimental
values
energies
Fig. 5: Characteristics of charged particle pseudorapidity distributions as a function of centrality for Ag (squares) and W targets (circles) as measured* by HELIOS. Open and closed symbols are for 60 and 200 GeV/nucleon incident energy.
28c
3.
.I. Stachel / Global observables in relativistic heavy ion collisions
TRANSVERSE ENERGY PRODUCTION
energy
Transverse calorimeters
these
Typical
targets
are
target
and
nucleons
for
leading
to
nucleus
with
pseudo-rapidity
to
In
A=400. a
in
by
It
e.g.,
completely 8 the
effect
of
the
should
be
noted
covering
distributions
of
of
to
the nuclear
transverse
ratio
equivalent the
essentially energy
data16 the are
and
shape
of
of The
parameters
where
participating
deformation
an axis
of
NA35 and WA80 at
and understood.
impact number
distribution that
types
and CERN energies
geometry
with
various
The characteristic
due
and
nucleus
tail
measurement
and by NA34,
collision
is,
using
Brookhaven
7 and 8.
the
a prolate the
measured
for
Figures
targets
fig.
U target,
Et values
correspond
heavy overlap
little.
the
in
dominated
for
projectile
varies
clearly
do/dEt
displayed is
developing
been
Brookhaven 11-13
distributions
distributions
shoulder
have
by El302 and E814 at
CERN14-20. various
distributions
of
can
be seen
about
.8/1.2
to a spherical shown
in
full
solid
angle.
fig.
very
similar
in
8 The
shape
500 Fig. 6: Target mass dependence of charged particle pseudo-rapidity density (bottom) and transverse energy production (top). Data in the bottom graph are from refs. 1,5,8,9,10; solid, dashed and dotted lines connect points for 14.6, 60 and 200 GeV/nucleon incident energy. Data in the top graph are from
r
k!
;;; 200 r T !g
_ ,&
I..
50
200
~~f~,le6~~“,;f~,~~,erd’ electromagnetic energy and open circles16 to total Et integrated over n. Coefficients o?, given to the right, correspond to Ata behavior.
100
jis 100 c2 r
50
< 5 20
10
10
20
50
100
AT
200
500
29~
J. Stachel / Global observables in relativistic heavy ion collisions
and
characteristics
particle discussed Figure
above.
the
As an example,
typical
and
follow dN,/dn The
Gaussian
width same
(see
e.g.
top
of
target
the
beams.
The
charged (bottom
of
fraction
for
of
that
one
should
but
total
from
of
with
WA80 and the the
about keep energy
ratio
y=2-4, 7.5:1
is
0
for
for
fraction of 7:l
obtained
by NA35 (see
ref.
energy20p18e
28.5*3X,
of
the
covering
22-253 in
of
mind
for
the
that
mesons. to
of
number in
NA35 have
electromagnetic
transverse
central
of
from
negative Although proton
(or
15
20
is
measure
of (also
positive) crude,
and negative
A very
energy
pion
pion
is
25
kinetic
.15
measured18 to
estimate rapidity
estimate
by baryons. energy
and nucleon about
for
transverse
GeV one would for
StS
protons, is
find
that
electromagnetic
rough
carried
pions this
S+Au they
energy
rapidity.
that
Et
very
ET[oevl
200 GeV/nucleon
calorimeters
electromagnetic
10
transverse
a common temperature
S+S.
18).
For
total
transverse
Assuming
5
Fig. 7: Transverse energy distributions from E814 measured12p l3 over two different regions of acceptance. Data are not unfolded for leakage and resolution. Solid lines: Landau fireballz5. Dashed and solid lines with diamonds: HIJET withoutz6 and with27 rescattering.
values
indicative
correspond the
very
densities
(pseudo-)rapidities
spectra
solid
a are
6)
respectively
gives
open NA34
effects.
measured
25+2X,
the from
rapidity
Experiments also
peak of
obtained
possibly
rescattering
200 open
full
was
fig.
.40
40
of
the
the
particle
around
at
while
what
0
asterisks
coefficients
to
IO-’
Shown
The
results over
similar
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the
for
the
to values
integrated
4 4
as
shows
results
Gaussian,
angle.
6
and
are
lo-*
Gaussians
dependence
experimental
circles
with
production.
S
B ;
refs.14,15,21).
energy
correspond
shape
7
can
systematics
mass
triangles
one
the
figure
GeV/nucleon
in
shown as
by kinematics. of
the
transverse
the
are
determined
Height
charged
densities
by WA80. Again,
centroids
are
the
9 distributions
obtainedzO see
to
pseudo-rapidity
nucleons momentum conclude
by NA35) averaged
close
distributions
to
then Here,
the
that over ratio
reported
3oc
.I. Stachel / Global observables in relativistic heavy ion collisions
Comparing
dNc/dn
energy
per
= 0.55
GeV for
not
charged
change
energy has
For
the
target-projectile
significant
rise
collisions:
for
the
three
not
explained
Et/NC
by
event about
a change
in
the
source
of
such to
backward and n = 1.
quantity
the
present,
for (see
or
however,
GeV/nucleon
This
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trend
on
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and
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surprising a
E814 give
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Tr~tltverse du/dE, 200
energy differential in
-0.1
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<
7
<
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5.5
for
collisions
$
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IO-
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Id
Id
GeV and
therein).
could
experimental
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show a
and 0.75
where
spectra
found.
data
10 and refs.
enough
data22
dependence is
0.58
instance,
pt
beam
200
central
ref. the
or
S+W at
these
are
does
collaboration
collision
values
Et/NC
value
collision
significant the
transverse
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S+Em and
moderately
IRIS,
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14.6
no
used.
: nucleon at
At
like
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predicted
of
of
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GeV is
that
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WA80 finds
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for
centrality
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pion
interesting
The
angles
compute
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centrality
combinations
0.55
an effect, decide.
is
mass,
a function
target-projectile
of
available
as
towards
value
It
n = 1.4-3. or
can
a given
GeV/nucleon). this
interval
n = 2-3
in
target
200
combination however,
for
and
investigatedlO
GeV/nucleon.
Inspecting,
with
60
one
distributions,
evaluated and 0 beams5.
significantly
(comparing
constant
dEt/dn
n = 2.-4.2
recently
Both
and
particle,
Fig. 8: Transverse enefgy distributions measured over a very large solid angle.
=
J. Stachel / Global observables in relativistic heavy ion collkions
0.41
Nvcieus
A GeV I90 +
200
for
GeV
lower
value
results
is
in
mind
Si+Au as
are
GeV,
as
at
n = 0.8.
compared
not
that
pions
31c
too
to
surprising
numbers
of
comparable by
rapidity
and
that,
central
rapidity,
CERN
keeping
nucleons
for
shown23
The
the
and
Si+Au at
E802,
at
14.6
central
backwards
of even
nucleons
dominate. Another
interesting
explored
information
2.5
3.0
3
5
4.0
4.6
8.0
6.5
discussion
has Only
Sarcevic. simulations the trivial
initiated
two
of
fluctuations
simulations25 kind
of
are
more
relevant.
do/dEt
for
shown
in
ii)
There
are
shown in
respectively.
hemisphere without
While
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parameters
Et
experimental fact
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to
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of
is is
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the
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for
come
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are
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to
targets
target
spectator Indeed, in
heavy
in
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more
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tail
Si+Pb
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with the
as are in
targets. and
forward
several
models the
shape
same
of
the
the distribution.
suggests nueleons
calculations
reproducing
the
a wide
for
by
tail
only
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spectra
and
in
the
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calculationsz5)
lighter
close
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sample fireball
is
from E824 and NA34 for
severely
collisions.
To data
at least
fireball
broader
this
if
rather
Landau
contributing
systems
underpredicted
with
rescattering
effect
7,10)
case
and soon
hemisphere,
Landau
the
du/dEt.
that,
particles
the where
24 experimental
not
first
angle,
emitted
and
Monte-Carlo
solid
tail
8)
schematic
from
is
effects
Friedman
full
lines),
fig.
tail
This
Baym,
show
the
in
the
system
the
is
in
Very
ref.
significantly
participate
by
in
the
the
that
to
figs.
e.g.
backward
spectrum that
(solid
7 and 10 data
for
sections
difficulty
way
in This
by experimental
a hot
the
the
backward
figs.
of
instance,
10
course,
fluctuations*
i)
from
for
may be another the
here:
unusual,
production.
study24
from
7 and
suggested
covering
leakage
part
now16 from NA34 (see
data
like earlier
only
seen,
figs.
dominated
place
already be
not
emission
contributing
available
As an example
o+w,
arise can
fluctuations
they
in
covers
This
fluctuation
interesting
are
an
particle
set-up
space.
by
comments
statistical
experimental
phase
The
been
dependence production20.
be the
contains
energy
of
assumes,
Fig. 9: Pseudo-rapidity of transverse energy
of
fluctuations
transverse
rl
to
tail
possibly
on,
event-to-event 20
the
distributions
da/dEt
o
question
whether
is,
that
this
has
do
not
that that
these
data.
include As an
.I. Stachel/ Globai observables in ~ela~~~~tic heavy ion col&ions
32c
example
are
rescattering the
latter
shown
in
(dashed
figs. and
calculation
does
equivalent
calculations
and
obviously,
there,
practically
not
7,lO
solid
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In
visible).
rescattering
effects
have
qualitatively)
the
conclusions
effect
to
be seen
substantial.
It
fluctuations
not
4~ data
is
published the of
is
still model
data the
in
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outstanding. calculations
by covering
Et spectrum
only at
been
at
in
into
the
while
there
although
fall
short
in
two27
respectively
in
top
of
at
Brookhaven
by
Werner
systems from
the
fig.
10
energies
and
Koch28
generator
comparatively
differences is
statistics
for
to note as
below
are
additional
comparison
amusing
decades
and, little
backward
need
a detailed
somewhat
however,
with27r13
both
Results
shown
is
the
whether
models
and for
VENUS event
There
same:
present
clearly one28
are (and
publication
hemisphere,
and
satisfactorily.
hemisphere
the
is,
without26
diamonds)
much smaller
included
these It
data
recent
are
forward
contained
is a
open
the
forward
effect
calculations
with
reproduce
for the
HIJET
lines
that
compared the
with the to
shoulder
200 GeV/nucleon.
NA34 -.l
10
Fig. 10: Experimental transverse energy distributions (solid dots) from WA80 (ref.19) and NA34 (ref.14). Meaning of the curves: same as in figure 7.
0°’u1,,,,1_,,,, 0
50
100 150 ET [GeV]
ll-i-d2
800
250
J. Stachel / Global observables in relativisticheavy ion collisions
33c
4. NUCLEAR STOPPING Frequently the amount of stopping (and thermalization) in a heavy ion collision is judged from the amount of transverse energy observed for a given system. Information is arrived at by comparing the amount of experimentally observed Et to what is predicted by a model, which assumes, for instance, complete stopping. As discussed e.g. in ref. 29 the answer obtained this way is by no means model independent. The only model independent result to be obtained this way is a lower limit for stopping fraction by comparing the experimental value to the kinematic limit in which all stopped energy is emitted into 90' in the cm frame. A better contraint can be put on this number by, in addition, measuring the energy Rad going into a small cone around the beam axis. By demanding that a model from which information concerning stopping is derived simultaneously describe the transverse energy and Rsd one puts a tighter constraint on the kinematics30 and some models, like the isotropic fireball, are ruled out that way. From studying that correlation it was concluded in ref. 30 in an analysis using the Landau fireball model, that for O+Au at 200 GeVfnucleon there is still about 85% stopping (for a definition of the number see refs. 25,30). Figures 11 and 12 show such data at 14.6 and 200 GeV/nucleon. In figure 11 instead Et the charged particle multiplicity is plotted but because of the tight correlation between the two quantities, as discussed 200 A GeV “0
0
BOO
,500
+ 197Au
2400
3200
EZDC (GW Fig. 11: Charged particle multiplicity measuredg*22 bv E814 over ij il0.9-3.9 versus energy emitted into a forward 0.8" cone. Due to the pretrigger there is a cutoff at N,rZO.
Fig. 12: Correlation of Et in a midrapidity calorimeter (n=2.4-5.5) and forward enery from WA80 (refs. 19,20).
J. Stachel / Global observables in relativistic heavy ion collisions
34c
the
above,
interpretation
clearly
see
many
collisions
observed
in
fig.
12
the
most
the
central
stopping
that
that
even
particle
this
interpretation
l-2
in
by noting
with
E814
where cone
leading of
is
corresponding drastically Displayed target Fermi integral
0.8O
Since
for
of
multiplicity
still
is
out
of
fairly
is
no
still
400
this
do/dEt
it
In
but
left
for
in
beam
nucleons
one
through
a statement
On the
at AGS energies,
for energy
transmitted to
can
growing.
GeV
and dEt/dn
system30.
one
two quantities
16 are
One relates
undisputed
12
GeV/nucleon
by beam rapidity
incident
thermalized
Et)
the
about
carried the
and
resolution,
(and
between
is
energy
a
around
the
beam
and neutrons about
rapidity
nuclei. motion
14.6
Et distributions
from
the
spectra
decreases in Figure
11
At
experimental
collion.
the
figs.
reactions.
are
about
consistent
other
hand,
is
unambiguous
not
while
collisions.
cone protons
about
this
that
the
there
nucleons
emission
the
the
Comparing
two
correlation
a central
200 GeV/nucleon In
but
a clear
collisions
Assuming
conclude target
for
also
same. the
within
is,
beam direction is
the
between
there
there
direction. would
is
a difference
with
13 is there
y = 3.0-3.85.
is
beam axis
and
one can
identify
(in This
some the
for
forward
in
for
rapidity
200 GeV/N
In
component
which
and various
expected this
just plot
due
shows
expectations
‘*S + =S +
-I--
a
the
energy.
neutrons
with
in
13,31).
transverse
nucleus)
consistent
detected
(refs.
or
spectrometer
are
a beam rapidity
Si projectile is
a
y > 1.6
component
smearing
interval
of
Nucleons
centrality
beam rapidity
is
part
identified.
increasing
this
the neutrons
axis
are
to the
from
PROTONS
0
0
i
Fig. 13: Average multiplicity of beam rapidity neutrons (y=3.0-3.85, pt<.2 GeV/c) as a function of Et into -0.5
~f~;,~~t,5~~r~:3;a~~~~~~d from
NA35 streamer chamber data positively and negatively charged tracks for central __. . collisions.
on S+S
.I. Stachel / Global observables in relativistic healy ion collisions
fragmentation
models
remarkable
feature
nucleons
(results
corresponding
a
reflect
nucleon
the
supports
values
smaller
from
target
stopping
rapidity
comes
from
carefully
Figure
14
the
full
can
be
of
65% for
The
for
seen
know whether
to
allow
the
the
of
of
be of
the
the
fact
rapidity this
energy
the
is
gets
therefore
best
a streamer
density
chamber
is
of that
a
etc.
displayed
in
practically
distributions,
proton
the
and
Kaons
covers
A and anti-A
over
information
from Lambdas,
shift
that
one
and
stopping
the
based.
the
Landau try
EfCm
the An
thus
the
fraction
is
numerator
/
base Vf.
achieved
large to
energy
the
this
still
validity
of
and
the
low,
obviously
reproduces
an energy
density
There
denotes
sf the
energy
the
estimate the
that
the
taken
this
is
no
on which that
experimental on
to
as from
there
fact
stopping
deposited
(area)
as well
assumption,
uses
central
longitudinal
grounds
so
scaling
approach
mode134
size
the
assumption
too
enough
at
transverse
ion like
estimate
Shuryak-Bjorken
on dimensional
from
are
to
is
then
One method
pseudo-rapidity
alternative
corresponds
the
in heavy
One would
transverse
Here at
arises
mode135
and sf
the
stopping
are
in
a unknown constant,
beam energies
confirming
to
connects
of
present.
transition.
scaling
dn/dz.
+ Uncertainty
is
can
EL =
on the
amount at
densities
phase
related
term
and is
present
of
based is
the
energy
(dEt/dn),,,
1 fm-l
plateau
Therefore,
in
the
available
reactions
last
system
section
deconfinement
density
The
order
previous
these
densities
estimate
kinematics
and
in
system.
extent
by
strongly
nucleons
The
distribution
concludes
beam energies
by eSB = l/at
the
This
rapidity
analysis18,33
the
at
expected
energy
rapidity
average
observation
identified
rapidity
considering
on top
reflected
reaction.
in
large
to
where
This
tracks
proton
sits
as
and
CONDITIONS
is
initial
the
of
contributions
S+S.
also
with
section
component
midrapidity.
negative
system
and,
deduce
at
for
Si+Pb
consistent
energies.
measurement
deduced
symmetric range
particular
As we have collisions
and
difference
a central
cross
This
here)
in
midrapidity
Brookhaven
shown
are
scattering
23,32,31).
for
l/300 targets
The
beam rapidity
data
beam rapidity
especially
positive
stopping.
INITIAL
and
about
towards
(refs.
no direct
resulting
the
to
this
is
this
rapidity
amount
5.
comparing
used
E814
interval
33,18).
This rises
resolution. for
neutron
Cu and Al
inelastic
thickness.
there
correcting
(refs.
or
interpretation
At CEEN energies a large
path
and
the of
for
detector
multiplicity
with
probability
continuously
E810
account small
agree
observed
free
that
E802, the
protons
mean
a distribution
data
into very
a transmission
The larger
common
of
the
for
to
collision.
taking observed
and
is
35c
the data.
mode125p30
fraction
(stopped)
and in
the
36c
J. Stachel / Global observables in relativistic heavy ion collisions
overlap
volume
defining
this
however,
Vf
that
the
S+W, are only
the 2.7
be
what
the in
transition. time
determined
future
the
rapidity
size
density
/fm3,
is
which address
Combining trigger
temperature energy
of
the
this
the
one
of
degrees irrelevant other with major
in
has
to the
contribution
Si+Pb This
at
by
estimate
above
assume
estimates
ideal
system
have
large
is
of
course, that
The
for is
but
For
small
the The
results
in
related
drops
which
out
the
of
makes
it
pions
or also
how to
While
this
perturbance
here
number
point just
open.
same
initial
quantity
also
is a
the
the
The question
instance,
it
at
directly the
with
does
formed.
T = &/(2.7n).
latter
dealing
degeneracies.
nucleons,
is
g T3 (/fm3).
or Vf)
behavior,
out.
one
estimate
S+W data
note
200
nR = 5 and 8
deduce
temperature
(dn/dz
gas
drops
stage
AGS energies
is,
For
n = 15.9
the
One should
particle
entropy-density.
while for
to
volume.
(measured
and 200 GeV/nucleon
above. the
to
go
A = 30 but
state.
behavior,
energy-
g T4 (GeV/fm3),
initial
part
carried
of
gas
to
charged
above,
final
stage clearly
accelerators.
a naive
the
densities
ideal
ratio
cases.
for
the
and particle
as
the
needed
this is
around
unit
such
in
at
both the
per
Obviously,
observed
is
This
still
two models
g and one obtains
at
in at
which
entropy
the
discussed
freedom
mesons, the
is
both
still
whether
as
GeV/nucleon
Et/N,
same
assuming
E = 42.9
to arrive
while
energy
system
GeV in
quantity
was difficult and,
for
14.6
the
estimates
at
from
pions
and can that
advantageous
are
can,
of
number.
one can,
system
to
T = 0.16-0.17
using
these
rough
probably
it
system
to note
maintained.
makes
give
similar
very
one
be available one
number
when a pion.
one has
of
Applying
to
the
density
degeneracy
arguments
a large
section)
that
the
estimates
very
are
is
are
and
the
order
in
ESB and EL. At 200
encouraging
question
densities
At present
the
question
the estimates cross
critical
A = 200 will
obtains,
certainly
the
the
of
in
note,
dn/dz
both
for
for
is
arises
One should
defining
estimates
certainly
difficulty
GeV Si+Pb
case
these
system
of
estimate
S+W one
this
as
GeV/fm3
it
possible.
lines
GeV/nucleon
not
the
14.6
In any case,
more
beams with
same
in
the
be evaluated?
same
For
1.0
energy
of
projectiles
near
Along
the
the
and 1.1
and
such
to
gets
Clearly,
The
scale
by
heaviest the
large
Here
it
is
values,
GeV/fm3.
are
is
energies.
as an indication.
a phase
over
these
and one
corresponding
values
time
uncertainty
at
and 8.3
taken
resulting for
model
and projectile.
at what
basic
same result
GeV/nucleon
target
e.g.
the
Shuryak-Bjorken nearly
between
volume,
deal is
at
a
200
GeV/nucleon. While arrived that
the at
we
densities have
been
preceeding
from are
quite
discussion different
dealing
where, altered.
with
almost
systems
certainly,
Whether
is view
the
rather points of
the systems
qualitative it
is
certainly
and
presented high
properties
of
studied
have
presents
here energy
normal actually
to
numbers illustrate
and
(nuclear)
particle matter
undergone,
at
J. Stachel / Global observables in relativistic heavy ion collisions
37c
least locally, a phase transition, is not clear and needs further experimental study and, especially, the use of heavier beams in order to produce extended systems of high density and temperature.
ACKNOWLEDGEMENT Thanks are due to all my experimental collegues from the current experiments at BNL and CERN for providing me their, in part unpublished, data without which the current review would have been impossible. I also would like to thank Peter Braun-Munzinger for many clarifying discussions.
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