Low-x Observables at RHIC
(with a focus on PHENIX)
Prof. Brian A Cole
1. Low-x physics of heavy ion collisions
2. PHENIX Et and multiplicity measurements
3. PHOBOS dn/d measurements
4. High-pt hadrons: geometric scaling ??
Relativistic Heavy Ion Collider
Run 1 (2000) : Au-Au @ SNN = 130 GeV
Run 2 (2001-2): Au-Au, p-p @ SNN = 200 GeV
(1-day run): Au+Au @ SNN = 20 GeV
Run 3 (2003): d-Au, p-p @ SNN = 200 GeV
Collision seen in “Target” Rest Frame
Projectile boost 104.
Due to Lorentz contraction
gluons overlap longitudinally
They combine producing
large(r) kt gluons.
Apply uncertainty princ.
E = kt2 / 2Px ~ / 2 t
mid-rapidity x 10-2
Nuclear crossing t ~ 10 fm/c
kt2 ~ 2 GeV2
Gluons with much lower kt
are frozen during collision.
Target simply stimulates
emission of pre-existing gluons
How Many Gluons (rough estimate) ?
Measurements of transverse energy ( Et = E
sin) in “head on” Au-Au collisions give dEt / d ~ 600
GeV (see below).
Assume primordial gluons carry same Et
Gluons created at proper time and rapidity y
appear at spatial z = z = sinh y
So dz = cosh y dy
In any local (long.) rest frame z = y.
dEt / d3x = dEt / d / A (neglecting y, difference)
For Au-Au collision, A = 6.82 150 fm2.
Take = 1/kt , dEt ~ kt dNg
dNg /d3x ~ 600 GeV/ 150 fm2 / 0.2 GeV fm = 20 fm-3
For kt ~ 1 GeV/c, dNg / dA ~ 4 fm-2
Very large gluon densities and fluxes.
“Centrality” in Heavy Ion Collisions
Violence of collision determined by b.
Characterize collision by Npart :
# of nucleons that “participate” or scatter in collision.
Nucleons that don’t participate we call spectators.
A = 197 for Au maximum Npart in Au-Au is 394.
Smaller b larger Npart , more “central” collisions
Use Glauber formalism to estimate Npart for
experimental centrality cuts (below).
Saturation in Heavy Ion Collisions
Kharzeev, Levin, Nardi Model
Large gluon flux in highly boosted nucleus
When probe w/ resolution Q2 “sees”
multiple partons, twist expansion fails
i.e. when >> 1
New scale: Qs2 Q2 at which = 1
Take cross section = s(Q2) / Q2
Gluon area density in nucleus xG(x, Q2) nucleon
Then solve: Qs2 = [constants] s (Qs2) xG(x, Qs2) nucleon
Observe: Qs depends explicitly on nucleon
KLN obtain Qs2 = 2 GeV2 at center of Au nucleus.
But gluon flux now can now be related to Q s
Qs2 / s (Qs2)
Saturation Applied to HI Collisions
Use above approach to determine gluon flux in
incident nuclei in Au-Au collisions.
Assume constant fraction, c, of these gluons are
liberated by the collision.
Assume parton-hadron duality:
Number of final hadrons number of emitted gluons
To evaluate centrality dependence:
nucleon ½ part
Only count participants from one nucleus for Q s
To evaluate energy dependence:
Take Qs s dependence from Golec-Biernat & Wüsthof
Qs(s) / Qs(s0) = (s/s0)/2, ~ 0.3.
Try to describe gross features of HI collisions
e.g. Multiplicity (dN/d), transverse energy (dEt / d)
Low-x Observables in PHENIX
RPC1 = 2.5 m
RPC3 = 5.0 m
REMC = 5.0 m
||<0.38, = (5/8)
Trigger & Centrality
3.0<||<3.9, = 2
|| > 6, |Z|=18.25 m
(not to scale)
PHENIX Centrality Selection
Measure energy (EZDC) EZDC
in spectator neutrons. b
Smaller b smaller EZDC QBBC
Except @ large b neutrons
carried by nuclear fragments.
Measure multiplicity (QBBC)
in nucleon frag. region.
Smaller b larger QBBC EZDC 15%
Make cuts on EZDC vs QBBC
according to fraction of tot 20% 5%
“above” the cut. 10%
State centrality bins by
fractional range of tot
E.g. 0-5% 5% most central QBBC
Charged Particle Multiplicity Measurement
Count particles on statistical basis
Turn magnetic field off.
Form “track candidates” from
hits on two pad chambers.
Require tracks to point to
beamline and match vertex
from beam-beam detector.
Nchg number of such tracks.
Determine background from
false tracks by event mixing Minimum bias
Correct for acceptance, 0-5%
conversions, & hadronic
interactions in material.
Show multiplicity distributions
for 0-5%, 5-10%, 10-15%,
15-20% centrality bins
compared to minimum bias.
PHENIX: Et in EM Calorimeter
Definition: Et = Ei sini Sample M Minv Dist.
Ei = Eitot - mN for baryons
Ei = Eitot +mN for antibaryons
Ei = Eitot for others
Correct for fraction of
100% for , 0, 70 % for
Correct for acceptance
Energy calibration by:
Minimum ionizing part.
electron E/p matching 0
0 mass peak
Plot Et dist’s for 0-5%, 5-10%,
10-15%, 15-20% centrality bins
compared to minimum bias.
Et and Nchg Per Participant Pair
per part. pair
130 GeV 200 GeV
per part. pair
130 GeV 200 GeV
suppressed zero !
Bands (bars) – correlated (total) syst. Errors
Slow change in Et and Nchg per participant pair
Despite 20 change in total Et or Nchg
Et Per Charged Particle
of Et and Nchg very
similar @ 130, 200 GeV. PHENIX preliminary
Take ratio: Et per
Little or no dependence
on beam energy.
Non-trivial given s
dependence of hadron
Nchg determined by
physics of hadronization.
Only one of Nchg, Et can
be saturation observable.
Multiplicity: Model Comparisons
130 GeV 200 GeV
dNchg / d per part. pair
X.N.Wang and M.Gyulassy,
PRL 86, 3498 (2001)
S.Li and X.W.Wang
K.J.Eskola et al,
Nucl Phys. B570, 379 and
Phys.Lett. B 497, 39 (2001)
D.Kharzeev and M. Nardi,
Npart Npart Phys.Lett. B503, 121 (2001)
D.Kharzeev and E.Levin,
Phys.Lett. B523, 79 (2001)
KLN saturation model well describes dN/d vs Npart.
Npart variation due to Qs dependence on part (nucleon).
EKRT uses “final-state” saturation – too strong !!
Mini-jet + soft model (HIJING) does less well.
Improved Mini-jet model does better.
Introduces an Npart dependent hard cutoff (p0)
Ad Hoc saturation ??
Multiplicity: Energy Dependence
Nchg (200) / Nchg (130)
s dependence an important test of saturation
Determined by s dependence of Qs from HERA data
KLN Saturation model correctly predicted the
change in Nchg between 200 and 130 GeV.
And the lack of Npart dependence in the ratio.
Compared to mini-jet (HIJING) model.
dN/d Measurements by PHOBOS
PHOBOS covers large range w/ silicon detectors
=-ln tan /2
Total Nchg (central collision)
5060 ± 250 @ 200 GeV
4170 ± 210 @ 130 GeV
1680 ± 100 @ 19.6 GeV
-5.5 -3 0 +3 +5.5
dN/d Saturation Model Comparisons
Kharzeev and Levin
dN/d per part. pair
Phys. Lett. B523:79-87, 2001
Additional model “input”
x dependence of G(x)
outside saturation region
xG(x) ~ x- (1-x)4
GLR formula for inclusive
To evaluate yield when one
of nuclei is out of saturation.
Assumption of gluon mass
(for y )
M2 = Qs • 1 GeV
Compare to PHOBOS data
at 130 GeV.
Incredible agreement ?!!
Classical Yang-Mills Calculation
Nucl. Phys. A717:268, 2003
Treat initial gluon fields as
classical fields using M-V
initial conditions. x 2.4
Solve classical equations of
motion on the lattice.
At late times, use harm.
osc. approx. to obtain
gluon yield and kt dist.
Results depend on input
saturation scale s.
Re-scaled to compare to data.
No absolute prediction
But centrality dependence of
Nchg and Et reproduced.
But Et /Nchg sensitive to s.
Saturation & Bottom-up Senario
BMSS start from ~ identical
assumptions as KLN but Baier, Mueller, Schiff, and Son
Phys. Lett. B502:51, 2001.
Qs (b=0) 0.8 GeV.
Baier, Mueller, Schiff, and Son
Argue that resulting value Phys. Lett. B539:46-52, 2002
for c, ~ 3, is too large.
Then evaluate what happens
to gluons after emission
In particular, gluon
Nchg no longer directly
proportional to xG(x,Qs)
Extra factors of s
Agrees with (PHOBOS) data.
Faster decrease at low Npart
than in KLN (?)
More reasonable c, c < 1.5
High-pt Hadron Production
PHENIX 0 pt spectra Points: data, lines: theory
High-pt hadron yield predicted to be suppressed in
heavy ion collisions due to radiative energy loss (dE/dx).
Suppression observed in central Au-Au data
x 5 suppression for pt > 4 GeV
Consistent with calculations including dE/dx.
What does this have to do with low x ? …
Geometric Scaling @ RHIC ?
Kharzeev, Levin, McLerran
Geometric scaling (hep-ph/0210332)
extends well above Qs
May influence pt Yield per participant pair
spectra at “high” pt
Compare saturation pQCD
to pQCD at 6, 9 GeV/c
Saturation x3 lower in saturation
Partly responsible for
high-pt suppression ?
Effect½ as large
should be seen in
Data in few months …
Saturation models can successfully describe
particle multiplicities in HI collisions at RHIC.
Withfew uncontrolled parameters: Qs(s0), c.
Closest thing we have to ab initio calculation
They provide falsifiable predictions !
Connect RHIC physics to DIS observables:
sdependence of dN/d saturation in DIS .
Geometric scaling high pt production @ RHIC
Already going beyond simplest description
e.g. bottom-up analysis.
But, there are still many issues (e.g.):
What is the value for Qs ? Is it large enough ?
Is Qs really proportional to part (A1/3)?
How is dn/d related to number of emitted gluons ?
How do we conclusively decide that saturation
applies (or not) to initial state at RHIC ?