Experimental Review
of Hard Processes
(mostly at RHIC)
W.A. Zajc
Columbia University
09-Aug-04
Summary

Hard processes:
One in which there exists some scale >> LQCD
 Examples:

 Large
momentum transfer (jets)
 Heavy flavor production
 Direct photons

Preview as summary:

RHIC is an ideal machine for using hard processes
to probe
 Deep
interior of heavy ion collisions (quark-gluon plasma?)
 Gluon, sea-quark contributions to proton spin (G. Bunce)

Measurements to date:
Large momentum transfer (jets): calibrated,
basis for discovery
 Heavy
flavor production: first measurements
 Direct photons: approaching first measurement
09-Aug-04
RHIC Specifications


3.83 km circumference
Two independent rings




120 bunches/ring
106 ns crossing time
Capable of colliding
~any nuclear species
on
~any other species
Energy:
 500 GeV for p-p
 200 GeV for Au-Au
(per N-N collision)

Luminosity


09-Aug-04
Au-Au: 2 x 1026 cm-2 s-1
p-p : 2 x 1032 cm-2 s-1
(polarized)
RHIC’s Experiments
STAR
09-Aug-04
RHIC Achievements to Date

Machine :

Runs 1-4:
Au+Au: operation at 4 energies (19, 62, 130, 200 GeV)
 d+Au comparison run (200 GeV)
 p+p baseline (200 GeV)




Experimental Operations:




Routine operation in excess of twice design luminosity !
First polarized hadron collider !
Routine collection, analysis of 100 Tb datasets
>50 publications in Physical Review Letters
Excellent control of systematics and inter-experiment
comparisons
Experimental Results:



09-Aug-04
Record densities created ~100 times normal nuclear density
New phenomena clearly observed (“jet” quenching)
Strong suggestions of a new state of matter
Run-1 to Run-4 Capsule History
Run
Year
Species s1/2 [GeV ] Ldt
01
2000
Au+Au
130
1 mb-1
10M
0.04 pb-1
3 TB
02 2001/2002 Au+Au
200
24 mb-1
170M
1.0 pb-1
10 TB
p+p
200
03 2002/2003
d+Au
p+p
200
04 2003/2004 Au+Au
Au+Au
0.15 pb-1 3.7G
200
2.74 nb-1
0.35 pb-1
200
62
6.6G
241 mb-1
9 mb-1
Ntot
p-p Equivalent Data Size
0.15 pb-1
1.1 pb-1
5.5G
0.35 pb-1
1.5G
58M
20 TB
46 TB
35 TB
10.0 pb-1
0.36 pb-1
270 TB
10 TB
RHIC Successes (to date) based on ability to deliver physics at ~all scales:
barn
: Multiplicity (Entropy)
millibarn: Flavor yields (temperature)
microbarn: Charm (transport)
nanobarn: Jets (density)
picobarn: J/Psi (deconfinement ?)
09-Aug-04
} This Talk
Why RHIC ?

Different from p-p, e-p colliders
Atomic number A introduces new scale Q2 ~ A1/3 Q02

Different from previous (fixed target) heavy ion facilities
ECM increased by order-of-magnitude
 Accessible x (parton momentum fraction)
decreases by ~ same factor
 Access to perturbative phenomena




x~
2 pT
s
Jets
Non-linear dE/dx
Its detectors are comprehensive
 ~All final state species measured with a suite of detectors
that nonetheless have significant overlap for comparisons

It’s a dedicated facility
 Able to
,
g p, p0, K,
K*0(892), Ks0, h,
p, d, r0, f, D,
L, S*(1385),
L*(1520), X± , W,
D0, D±, J/Y’s,
Perform required baseline and control measurements (+ anti-particles)
…
 Respond rapidly to new opportunities (e.g., 62 GeV Run)

09-Aug-04
Access to Perturbative Phenomena?


Consider measurement of p0’s in p+p
collisions at RHIC.
Compare to pQCD calculation
d  fa / A( xa, m 2 )  fb / B ( xb, m 2 )
•parton distribution functions,
for partons a and b
•measured in DIS, universality

 d  (a  b  c  d )
•perturbative cross-section (NLO)
•requires hard scale
•factorization between pdf and cross
section
 Dh / c ( zh, m 2 )
•fragmentation function
•measured in e+e
Phys. Rev. Lett. 91, 241803 (2003)
09-Aug-04
RHIC Energy Reduces Scale Dependence


The high √s of RHIC


makes contact with rigorous pQCD calculations
minimizes “scale dependence”


Spin program
Providing calibrated probes in A+A
A huge advantage in
PHENIX p+p  p0 + X
-NLO pQCD
F. Aversa et al. Nucl. Phys. B327, 105 (1989)
-CTEQ5M pdf/PKK frag
-Scales m=pT/2, pT, 2pT
m=pT/2
m=2pT
09-Aug-04
Transverse Dynamics

The ability to
access “jet” physics
also clearly
anticipated in RHIC
design manual



(vintage: ISAJET)
a new perturbative
probe of the
colliding matter
Most studies to date
have focused on
single-particle
“high pT” spectra
Please keep in mind:
“High pT” is lower than
you think

09-Aug-04
‘Jets’ at RHIC

Tremendous interest in hard
scattering (and subsequent energy
loss in QGP) at RHIC



Production rate calculable in pQCD
 a superb probe of density
But strong reduction predicted due
to dE/dx ~ path-length
(due to non-Abelian nature of
medium)
However:


“Traditional” jet methodology very
difficult at RHIC
Dominated by the soft background
 Investigate by (systematics of) high-
pT single particles
09-Aug-04
R
Jet
Axis
Predicting pT Distributions at RHIC

Focus on some slice of
collision:


Assume 3 nucleons struck in A,
and 5 in B
Do we weight this contribution
as
Npart ( = 3 + 5) ?
 Ncoll ( = 3 x 5 ) ?


Answer is a function of pT :

Low pT  large cross sections
 yield ~Npart


High pT  small cross sections
 yield ~Ncoll

09-Aug-04
Soft, non-perturbative,
“wounded nucleons”, ...
Hard, perturbative,
“binary scaling”,
point-like, A*B, ...
Systematizing our Knowledge

All four RHIC experiments have
carefully developed techniques
for determining




the number of participating
nucleons NPART in each collision
(and thus the impact parameter)
The number of binary nucleonnucleon collisions NCOLL as a
function of impact parameter
Spectators
Participants
Spectators
Binary Collisions
This effort has been essential in
making the QCD connection

Soft physics ~ NPART

Hard physics ~ NCOLL
Often express impact
parameter b in terms of
“centrality”, e.g., 10-20% most
09-Aug-04
Participants
b (fm)
Luminosity

Consider collision of ‘A’ ions per bunch
with
‘B’ ions per bunch:
Cross-sectional
area ‘S’

A
Luminosity
B
A B
L~
S
09-Aug-04
Change scale by ~ 109

Consider collision of ‘A’ nucleons per nucleus
with
‘B’ nucleons per nucleus:
Cross-sectional
area ‘S’
A

‘Luminosity’
B
A B
L~
~ N Coll  A  B
S
not
09-Aug-04
N Part  A  B
Provided:
No shadowing
Small
cross-sections
An example of Ncoll ~ A*B scaling



Small cross section
processes scale as
though scattering
occurs incoherently
off nucleons in
nucleus
scale as
A1.0 in m+A
scale as
Ncoll ~A*B in A+B
09-Aug-04
7.2 GeV muons on various targets.
M. May et al., Phys. Rev. Lett. 35, 407,1975)
(
Ncoll Scaling in d+Au

09-Aug-04
PHENIX PRELIMINARY
3
-2
1/T
1/T
ABABEdN/dp [mb GeV ]
PHENIX PRELIMINARY
PHENIX PRELIMINARY
PHENIX PRELIMINARY
3
-2
1/T
ABEdN/dp [mb GeV ]
1/TAB
1/T
EdN/dp3 [mb GeV-2]
1/T
AB AB
1/TABEdN/dp3 [mb GeV-2]
1/TABEdN/dp3 [mb GeV-2]
1/T
AB
PHENIX PRELIMINARY
single electrons from non-photonic sources agree well
with pp fit and binary scaling

09-Aug-04
1/TAA
1/TABEdN/dp3 [mb GeV-2]
AA
3
-2
1/TABEdN/dp
1/T [mb GeV ]
AA
3 3 GeV
-2] -2]
GeV
1/T1/T
ABEdN/dp
ABEdN/dp
1/T [mb[mb
EdN/dp3 [mb GeV-2]
1/T1/T
AA AB
1/TAAABEdN/dp3 [mb GeV-2]
1/T
Ncoll Scaling in Au+Au
Again, good agreement of electrons from charm with Ncoll
Ncoll Scaling for Charm
0.906 <  < 1.042
dN/dy = A (Ncoll)

binary collision scaling of pp result works VERY WELL for
non-photonic electrons in d+Au, Au+Au open charm is a
good CONTROL, similar to direct photons
09-Aug-04
Ncoll Scaling for Direct Photons


Ncoll scaling works to
describe the direct photon
yield in Au+Au, starting from
NLO description of
measured p+p yields
N.B. This method of analysis
(double ratio of g/p0) shows
Ncoll scaling after
accounting for observed
suppression of p0 yields in
Au+Au collisions
(to be discussed next)
09-Aug-04
PHENIX Preliminary
Vogelsang
NLO
Another Example of Ncoll Scaling


PHENIX (Run-2) data on p0 production
in peripheral collisions:
Excellent agreement
between
PHENIX measured p0’s
in p+p
and
PHENIX measured p0’s
in Au-Au peripheral
collisions scaled by
the number of collisions
over ~ 5 decades
09-Aug-04
PHENIX Preliminary
Central Collisions Are Profoundly Different
Q: Do all processes that should scale like A*B do just that?
A: No!
Central collisions
are different .
(Huge deficit at high pT)
 This is a clear discovery
of new behavior at RHIC
 Suppression
of
low-x gluons in
the initial state?
 Energy loss in

a new state of matter?
PHENIX Preliminary
09-Aug-04
Systematizing Our Expectations
Describe in terms of scaled ratio
Yield in Au  Au Events

RAA A  B Yield in p  p Events
= 1 for “baseline expectations”
> 1 “Cronin” enhancements (as in proton-nucleus)
< 1 (at high pT) “anomalous” suppression
no effect 
09-Aug-04
Ratio: Au+Au / ( p+p Expectation )
09-Aug-04
Is The Suppression Always Seen at RHIC?


NO!
Run-3: a crucial control measurement via d-Au collisions
d+Au results from
presented at a press conference
at BNL on June, 18th, 2003
09-Aug-04
Is The Suppression Unique to RHIC?
Yes- all previous

nucleus-nucleus
measurements see
enhancement,
not suppression.
SPS 17 GeV
Effect at RHIC is
qualitatively new physics
made accessible by RHIC’s
ability to produce

ISR 31 GeV


RHIC 200 GeV
Demonstrates importance of
in situ measurement of
requisite baseline physics!
09-Aug-04
(copious) perturbative
probes
(New states of matter?)
Run-2 results show that this
effect persists (increases) to
the highest available
transverse momenta

Describe in terms of
scaled ratio RAA


Yield in Au  Au Events
A  B Yield in p  p Events 
= 1 for “baseline expectations”
First Conclusion

The combined data from Runs 1-3 at RHIC on
p+p, Au+Au and d+Au collisions establish that
a new effect (a new state of matter?)
is produced in central Au-Au collisions
Au + Au Experiment
Final Data
09-Aug-04
d + Au Control Experiment
Preliminary Data
High pT Particle Production in A+A
h
AB
2
dN
 K   dxa dxb  d 2k a d 2k b
dyd pT
abcd
 f a / A ( xa , Q 2 ) f b / B ( xb , Q 2 )
 g (k a ) g (k b )
0
h/c
*
c
2
c
D (z ,Q )
pzc
09-Aug-04
Parton Distribution Functions
Intrinsic kT , Cronin Effect
 S A ( xa , Qa2 ) S B ( xb , Qb2 )
d

(ab  cd )
dtˆ
1
zc*
  dP( )
0
zc
(Slide courtesy of K. Filimonov)
Shadowing, EMC Effect
Hard-scattering cross-section
c
Partonic Energy Loss
a
Fragmentation Function
b
d
09-Aug-04
Energy Loss of Fast Partons

Many approaches
1983: Bjorken

1991: Thoma and Gyulassy (1991)






dE 3 30 2
 4 ET 
 4 ET 
2

 S  ln 2  ~  S T 2 ln 2 
dx
4
 M 
 M 

 E
dE 4p
2

C F S T 2 ln 
dx
3
 mD
1993: Brodsky and Hoyer (1993)
1997: BDMPS- depends on path length(!)
1998: BDMS

dE

dx
DkT




2
2
2
 L
dE
CR mD

 S
L ln  
 
dx
8 g
 g

N
dE
 s C
dx
4
DkT
2
2
Numerical values range from


09-Aug-04
~ 0.1 GeV / fm (Bj, elastic scattering of partons)
~several GeV / fm (BDMPS, non-linear interactions of gluons)
QCD Analog of the LPM Effect
Q When can a gluon be considered radiated?
A When it’s about a wavelength away from source
(LPM = Landau-Pomeranchuk-Migdal)
E0  E  

 Coherent (reduced!) emission when
k
E0

E
second scatter occurs “before”
gluon is radiated
  1
d
lcoh      d
 kT  kT
  E0
 Gyulassy-Wang obtained for a parton
dE C2 s 2  C A E 
crossing a series of



q ln 
 
dz
p
static scattering centers
 CR m d 
 But!
Baier-Dokshitzer-Mueller-Peigne-Schiff (BDMPS) noted:
T
QCD  non-Abelian
 Gluon FSI  LESS destructive interference
 m2 
dE

 L   DE ~ L2
 Non-linear energy loss
dz
d 

(Slide
courtesy
of
M.
Chiu)
09-Aug-04

Exceedingly High Densities?
Both


Au+Au suppression (I. Vitev and M. Gyulassy, hep-ph/0208108)
d+Au enhancement (I. Vitev, nucl-th/0302002 )
understood in an approach that combines multiple
scattering with absorption in a dense partonic medium
 Our
high pT probes
have been
25%
calibrated
(50% ?)
dNg/dy ~ 1100
 > 100 0 (!)
09-Aug-04
d+Au
Au+Au
Current Status (Runs 1-3)

Established:
 p+p:
p+p
 Quantitative
description of
perturbative probes
 d+Au:
Role of
 initial
state effects
 multiple scattering
d+Au
 Au+Au:
 (Strong)
role of final state effects
 Quantitative measure of parton
energy loss in a dense
(expanding) medium
Au+Au

To do:
Develop same quantitative
understanding of
 Angular
time
09-Aug-04
correlations
of jet partners
 Flavor composition of “jets”
Further Evidence

STAR azimuthal
correlation
function shows
~ complete
absence of
“away-side” jet
G
O
N
E
G
O
N
E
Pedestal&flow subtracted
C2 (Au  Au)  C2 (p  p)  A *(1 2v 22 cos(2Df ))
Df

09-Aug-04
 Surface emission only (?)
 That is, “partner” in hard scatter
is absorbed in the dense medium
Path-Length (L) Effects?
pTtrigger=4-6 GeV/c, 2<pTassociated<pTtrigger, |h|<1
p/4
Out-of-plane
3p/4
y
x
in-plane
-3p/4
-p/4
Back-to-back suppression out-of-plane stronger than in-plane
Effect of path length on suppression is experimentally accessible
09-Aug-04
Baryons Are Different

Results from



09-Aug-04
PHENIX (protons and anti-protons)
STAR (lambda’s and lambda-bars)
indicate little or no suppression of baryons in the
range ~2 < pT < ~5 GeV/c
One explanation: quark recombination
(next slide)
Recombination


The (normal) in vacuo
fragmentation
of a high momentum quark
to produce hadrons
competes with the (new)
in medium recombination
of lower momentum quarks
to produce hadrons
Example:

Fragmentation: Dq→h(z)


produces a 6 GeV/c p
from a 10 GeV/c quark
Recombination:
produces a 6 GeV/c p
from two 3 GeV/c quarks
 produces a 6 GeV/c proton
from three 2 GeV/c quarks

Fries, et al, nucl-th/0301087
Greco, Ko, Levai, nucl-th/0301093
...requires the assumption of a thermalized
parton phase... (which) may be appropriately
called a quark-gluon plasma
Fries et
al., nucl-th/0301087
Lepez,
Parikh,
Siemens, PRL 53 (1984) 1216
09-Aug-04
Recombination Extended
The complicated observed flow pattern in v2(pT) for hadrons
d2n/dpTdf ~ 1 + 2 v2(pT) cos (2 f)
is predicted to be simple at the quark level under
pT → pT / n , v2 → v2 / n , n = (2, 3) for (meson, baryon)
if the flow pattern is established at the quark level
Compilation
courtesy of H.
Huang
09-Aug-04
Further Extending Recombination



New PHENIX Run-2 result on v2 of p0’s:
New STAR Run-2 result on v2 for X’s:
ALL hadrons measured to date
obey quark recombination systematics(!)
PHENIX Preliminary
X
p0
STAR Preliminary
09-Aug-04
Recombination Challenged

Successes:



Accounts for pT
dependence of
baryon/meson yields
Unifies description of
v2(pT) for baryons and
mesons
Challenged by


09-Aug-04
“Associated emission”
at high pT
Can the simple appeal of
Thermal-Thermal
correlations survive
extension to
Jet-Thermal ?
Does charm flow?
PHENIX PRELIMINARY




09-Aug-04
Is partonic flow
realized?
v2 of non-photonic
electrons indicates
non-zero charm flow
in Au+Au collisions
Uncertainties are
large
Definite answer:
Au+Au Run-04 at
RHIC!
(on tape)
J/Y Measurements To Date

p+p results:


~comparable
to other hadron facilities
(especially at low pT)
Au+Au results:



09-Aug-04
A limit only
To be addressed in Run-4
(on tape)
An entire program of
charmonium physics is just
getting underway
Run-3 J/Y’s in d+Au

2.7 nb-1 d+Au




SOUTH ARM
Provides
clear J/Y signals
With modest
discrimination
power to test
shadowing models
A clear indication
of the much greater
x2 range made
available
by RHIC
A clear need for



20 nb-1
: shadowing
200 nb-1 : Y’, Drell-Yan
>200 nb-1 : U’s
 Measurements beyond ~20 nb-1
require RHIC II luminosities
09-Aug-04
NORTH ARM
Vogt, PRL 91:14
2301,2003
Kopeliovich, NP A696:669,2001
Direct photons: centrality dependence
 direct photons are not inhibited by hot/dense medium
rather shine through consistent with pQCD
PHENIX Preliminary
Preliminary PbGl
PbGl // PbSc
PbSc Combined
Combined
PHENIX
50-60%
40-50%
30-40%
Central
200
GeV
60-70%
Central
AuAu
200
GeV
0-10%
Central
200
GeV
AuAu
80-92%
Central
AuAu
200
GeV
10-20%
CentralAuAu
200
GeV
AuAu
70-80%
20-30%
Central
AuAu
200
GeV
1 + (g pQCD x Ncoll) / g phenix backgrd Vogelsang NLO
++ (g
(g pQCD
x Ncoll
) / g phenix
Vogelsang NLO
NLO
pQCD
backgrd
111 +
pQCD x Ncoll
coll) / g phenix
phenix backgrd
backgrd Vogelsang
pQCD
coll
phenix
backgrd
Vogelsang
 thermal photons: reduction of
09-Aug-04
systematic uncertainties is essential
CGC + Hydro + Jets

A beautiful example of the convergence between





CGC as a description of the initial state
Hydrodynamics as a description of the bulk matter evolution
Jets as a probe of same
T. Hirano and Y. Nara, nucl-th/0404039:
What measurements can we perform at RHIC to test the assumptions
of CGC initial state?
(p+A measurements)
09-Aug-04
A Striking Connection


We’ve yet to understand
the discrepancy between
lattice results and StefanBoltzmann limit:
The success of naïve
hydrodynamics requires
very low viscosities
viscosity
h
  ~ 0.1
entropy density s

Both are predicted from
~gravitational phenomena
in N=4 supersymmetric
theories: h  1
4p

3

 SB 4
s
09-Aug-04
Summary


Evidence for bulk behavior (flow, thermalization): unequivocal
Evidence for high densities (high pT suppression): unequivocal
(Control measurement of d+Au essential supporting piece of evidence)

The same


initial state conditions
time evolution of density
t0
L
h
needed to explain hydrodynamic flow
are obtained by measurements with perturbative probes

OUR FIRST TENTATIVE STEPS TOWARD “CONCORDANCE”

Strong suggestions of recombination at the (bulk!) quark level:
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scaling of v2 based on quark content
pT dependence of meson/baryon ratios
Again, perturbative probes may prove critical test of the model
What remains?
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(Much) more robust quantitative understanding
Quantitative understanding of “failures” (e.g., HBT)
Direct evidence for deconfiment leading to
COMPLETE CHARACTERIZATION
OF THE NEW STATE OF MATTER FORMED AT RHIC
09-Aug-04
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