tjh: saturation, low-x, qcd workshop villaggio guglielmo, july 2-18, 2007 1 saturation, low-x, and...
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TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 20071
Saturation, Low-x, and QCDat RHIC, Part 1
T. Hallman
Villaggio Guglielmo, Italy
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 20072
Plan of these lectures
• Overview of (relevant) physics and experimental tools at RHIC
• Experimental results to date– Low-x– Ultra-Peripheral Collisions– Tagged Forward Proton Studies
• New physics reach in place or coming soon• Future possibilities• Conclusions
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 20073
Thanks in advance to:
Les Bland, Romiro Debbe, Wlodek Guryn, Spencer Klein, Janet Seger, Carl Gagliardi, Hiromi Okada
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 20074
Relativistic Heavy Ion Collider
RHIC
STARPHENIX
PHOBOSBRAHMS
2005 Configuration
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 20075
Relativistic Heavy Ion Collider
RHIC
STARPHENIX
BRAHMS
2006 Configuration
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 20076
Relativistic Heavy Ion Collider
RHIC
STARPHENIX 2007 Onward
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 20077
Relativistic Heavy Ion Collider
RHIC
STARPHENIX 2011 EBIS Source in operation; HITL, HTB gone
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 20078
Relativistic Heavy Ion Collider
STAR
PHENIX
PHOBOS BRAHMS
RHIC
Design Performance Au + Au (Now) p + p
(Now @ 200)
Max snn 200 GeV 500 GeV
L [cm-2 s -1 ] 2 x 1026 (3.6 x 1027 ) 1.4 x 1031 (3.5 x 1031 )
Interaction rates 1.4 khz ( 36 khz) 300 khz ( 750 khz)
Two Concentric Superconducting Rings
Ions: A = 1 ~ 200, pp, pA, AA, AB
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 20079
Relativistic Heavy Ion Collider
STAR
PHENIX
PHOBOS BRAHMS
RHIC
Design Performance Au + Au (Now) p + p
(Now @ 200)
Max snn 200 GeV 500 GeV
L [cm-2 s -1 ] 2 x 1026 (3.6 x 1027 ) 1.4 x 1031 (3.5 x 1031 )
Interaction rates 1.4 khz ( 36 khz) 300 khz ( 750 khz)
Two Concentric Superconducting Rings
Ions: A = 1 ~ 200, pp, pA, AA, AB
Most important for the physics of this workshop
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200710
The Science of RHIC• RHIC’s original science mission:
– Discovery of a new state of matter (quark-gluon plasma) in central heavy ion collisions ( ) (elliptic flow (v2), jet quenching, ε 3-5 GeV/fm3 from hydro, jet quenching, and dET/d )
– Detailed unfolding of the spin structure of the nucleon (new results on ΔG, AN, Sivers functions for quarks and gluons)
• “Value added” physics: – Low x structure of hadrons– Fundamental tests of QCD– Search for new exotics
Forward inclusive spectra and correlationsTagged forward proton studiesUltra-peripheral collisions
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200711
Low-x structure of hadrons:
forward inclusive spectra and correlations
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200712
INEL
2.47<<5.29
The data at forward rapidities were collected with FS at 4º ( ~3) and 2.3º (~3.4)
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200713
Particle Identification in Forward Spectrometer with BRAHMS RICH
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200714
FPD
Top-view=0
=2
= 1
+z beam -z beam
FPD++
East-side West-side
ppcos
2tanln
z
• Inclusive 0 in forward region: 4<<3 (FPD), 2.5<<4 (FPD++)
• Di-jet results: 1<<2 (Barrel EMC, Endcap EMC, 2)
STAR Run6 Configuration
xz
y
Wine Country New York City
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200715
From p+p to Au+Au in the STAR TPC
p+p jet+jet (STAR@RHIC)
Au+Au X (STAR@RHIC)
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200716
zx
y
South: Left North: Right
FPD++ (Forward Pion Detector) , West side
STARSTAR
Inclusive Inclusive 00
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200717
zx
y
South: Left North: Right
FPD++ (Forward Pion Detector) , West side
STARSTAR
Inclusive Inclusive 00
FPD
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200718
Acceptance of FPDSTARSTAR
Inclusive Inclusive 00
Strong xF and pT correlation because of limited acceptance.
FPD
xF0 0.2 0.4 0.6 0.8
4
5
0
2
3
1
6p T
GeV
/c
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200719
Acceptance of FPD and FPD++
STARSTAR
Inclusive Inclusive 00
Study of the pT dependence needs large acceptance.
FPD++
FPD
xF0 0.2 0.4 0.6 0.8
4
5
0
2
3
1
6p T
GeV
/c
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200720
STAR Forward Meson Spectrometer
• FMS increases areal coverage of forward EMC from 0.2 m2 to 4 m2
• Addition of FMS to STAR provides nearly continuous EMC from -1<<+4
FMS will span this entire acceptance—no gap
It will also extend the coverage to smaller η, providing even higher pT reach at a given xF.
Inset shows invariant mass spectrum for 2-photon events with 4 < pT < 5 GeV/c,
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200721
STAR Forward Meson Spectrometer
• FMS increases areal coverage of forward EMC from 0.2 m2 to 4 m2
• Addition of FMS to STAR provides nearly continuous EMC from -1<<+4
South half of FMS arrayon movable trolley ready forpositioning near beamline
FMS will span this entire acceptance—no gap
It will also extend the coverage to smaller η, providing even higher pT reach at a given xF.
Inset shows invariant mass spectrum for 2-photon events with 4 < pT < 5 GeV/c,
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200722
PHOBOS Experiment Philosophy:
– Global phenomena large spatial sizes small momenta
– Minimimum number of technologies:
• All Si-strip tracking• Si multiplicity detection• PMT-based TOF
– Unbiased global look at very large number of collisions (~109)
•
“Table-top” Spectrometer
• Charged Hadrons • Particle Correlations
TOF
Magnet Dipole
Spectrometer Arm
Silicon pad ring counters
VPD
Somewhat unique capability at RHIC (so far) for dN/d, v2 over 4
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200723
PHENIX
PHENIX
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200724
Energy and momentum conservation
xL = xa - xb =(2MT/√s)sinh y
ka + kb = k
xaxb = MT2/s
A solution to this system is:
xa = (MT/√s) ey
xb = (MT/√s) e-y
where y is the rapidity of the (xL,, k) system
In a 2->2 interaction where both partons are measured at rapidities y1 and y2,
Ysystem=1/2(y1+y2)
y*=1/2(y1-y2)
Leading order kinematics
(Sudakov variables)
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200725
Why does the relevant instrumentation focus on measurements at high rapidity: Parton Distribution Functions
X2 range X1 range
Measurements at high rapidity set the dominant parton type:
Projectile (x1 ~1) mostly valence quarks.
Target (x2<0.01) mainly gluons.
Endpoint at RHIC depends on partondynamics at play
Sensitive to xg 10-3 in pQCD picture
Sensitive to xg 10-4 in CGC picture
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200726
• Question
– At low-x in the previous plot, the gluon distribution continues to grow exponentially
– But, it can not grow indefinitely without bound
– What happens at when x becomes very small ?
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200727
= Q2R02(x)
Transverse size of the color dipole is set equal to 1/Q where Q2 is the virtuality of the exchanged photon.
“Geometric Scaling” at HERA (A. Staśto, K. Golec-Biernat et al. PRL
86 2001)
R0 “saturation radius” ~ x ( 0.3)
defines a scale: for values of Q2
such that for 1/Q ≥ R0
the growth in the cross section saturates
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200728
= Q2R02(x)
Transverse size of the color dipole is set equal to 1/Q where Q2 is the virtuality of the exchanged photon.
“Geometric Scaling” at HERA (A. Staśto, K. Golec-Biernat et al. PRL
86 2001)
R0 “saturation radius” ~ x ( 0.3)
defines a scale: for values of Q2
such that for 1/Q ≥ R0
the growth in the cross section saturates
Suggestion from change in slope for < 1 is that perhaps we already see a “hint” of saturation at HERA
Caveat No. 1: Why for consistent with Q2 >>> greater than Q2s does this
scaling still seem to work?
Caveat No.2 if one takes examines this relationship for x > .01 for all Q2– a pretty 1 parameter scaling does not seem to work
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200729
Quantum Evolution
gluon radiation gluon fusion
Y
dN/d(ln1/x) = s (2N - N2)
RdA = (dpA/d2kdy)/(Adpp/d2kdy)
For k >> Qs :RdA< 1 increasing with k approaching 1 from below.
For Qs < k < kgeom : RdA e-1.65 y << 1
For k Qs : RdA exp (4 y(1-√1+lnA1/6/2 y) ) < 1
At high energy/ rapidity it becomes constant RdA A-1/6
Kharzeev, Kovchegov and Tuchin Phys. Rev. D 68, 094013
Suppression at all k, suppression even stronger for higher A !
dP/dY s
U. Wiedemann et al. Phys. Rev. D 68, 054009
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200730
ln 1x related to rapidity of
produced hadrons.
As y grows
Attempt at a semi-classical, effective field approach: conceptual expectation for a Color Glass Condensate
D. Kharzeev, hep-ph/0307037
Iancu and Venugopalan, hep-ph/0303204
Is there evidence for gluon saturation at RHIC energies?
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200731
CGC Initial Condition at RHIC not “crazy”19.6 GeV 130 GeV 200 GeV
Charged hadron pseudo-rapidity
1) High number of Nch indicates initial high density;2) Mid-y, Nch Npart parton scattering not entirely incoherent;3) Saturation model works (Kharzeev et al)
Initial high parton density at RHICPRL 85, 3100 (00); 91, 052303 (03); 88, 22302(02); 91, 052303
(03)
PHOBOS Collaboration
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200732
BRAHMS d+Au results as function of rapidity and centrality
BRAHMS, PRL 93, 242303
RdAu= YielddAu
NcollYieldpp
Normalized ratio of previously measured dN/d
Calculated from spectraRcp ratios are constructed in wide bins and with data from same run period
NuclearModificationFactor
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200733
First RHIC (BRAHMS) results in the context of CGC?
Similar saturation effects had already been seen at HERA, and the multiplicity densities in A+A at RHIC show coherence that hint to the onset of saturation. The rapidity and centrality dependence of the BRAHMS results could then be the result of “quantum evolution” of an already saturated Au wave function.
These results came just after the effects of the onset of the Color Glass Condensate at RHIC energies were predicted and a qualitative description of its effects in high rapidity particle production was offered.
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200734
Q = 2 GeV5 GeV
10 GeV
Leading twist gluon shadowing, e.g.:
• Gerland, Frankfurt, Strikman, Stocker & Greiner (hep-ph/9812322)
• phenomenological fit to DIS & DY data, Eskola, Kolhinen, Vogt hep-ph/0104124
• and many others
Iancu and Venugopalan hep-ph/0303204
Shadowing or formation of a CGC ?
Amount of gluon shadowing differs by up to a factor of three between different models →
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200735
Q = 2 GeV5 GeV
10 GeV
Leading twist gluon shadowing, e.g.:
• Gerland, Frankfurt, Strikman, Stocker & Greiner (hep-ph/9812322)
• phenomenological fit to DIS & DY data, Eskola, Kolhinen, Vogt hep-ph/0104124
• and many others
Iancu and Venugopalan hep-ph/0303204
Shadowing or formation of a CGC ?
Amount of gluon shadowing differs by up to a factor of three between different models →
Phenomenological fits diverge below x 0.02 (where data ends)
Requires solution of BK and JIMWLK equations
The answer remains a question for experiment
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200736
Two very different possibilities at low x
Kharzeev, Levin, McLerran gives physics picture (NPA748, 627)
d+Au: Mono-jet?
PT is balanced by many gluons
Dilute parton system
(deuteron)
Dense gluon
field (Au)
Color glass condensate predicts that the back-to-back correlation from p+p should be suppressed
p+p: Di-jet
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200737
2cos2 vx
y
p
patan
Anisotropic Flow
x
yz
px
py
A Short Excursion: Elliptic Flow in Heavy Ion Collisions
Peripheral Collisions
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200738
Comparison of elliptic flow and predictions of hydro potentially provide evidence for local thermalization and an EOS with a soft point
- Minimum bias data! At low pT, model result fits mass hierarchy well!- Details do not work, need more flow in the model!
P. H
uo
vi ne
n, p
r ivate
com
mu
nica
t i on
s, 20
04
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200739
Constituent quark scaling
Constituent quark DOF.
(Deconfinement)
solid: STARopen: PHENIX PRL91(03)
v2 appears to scale with number of constituent quarks. quark coalescence.
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200740
KET/n scaling across collision centralities
KET/n scaling observed across centralities
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200741
A remarkable scaling of the fine structure of elliptic flow is observed at RHIC
At midrapidity v2 (pt,M,b,A)/n = F(KET/n)*ε(b,A)
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200742
Why bring this up? (for completeness): hypothesis of hadronization by recombination
Hadronization by recombination of thermal density of soft partons and shower partons
The decrease in RCP as increases is related to the depletion of the thermal density (dN/d) of soft partons.
R. Hwa et al. Phys. Rev C71 024902 (2005)
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200743
Relevance of the answer to the QGP: v2 and the hydro limit— Glauber vs Color Glass Condensate
• Do we have Glauber matter distribution + perfect liquid, or Color Glass Condensate distribution + viscous matter?
• Understanding the initial state is crucial to understand what we are seeing in the final state
CGC Glauber
Hirano et al, PLB 636, 299
CGC: Treats the nucleus as a saturated gluon field
Effects initial eccentricityof the overlap zone
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200744
In fact there is a strong coupling to understandingthe story at mid-rapidity:
Answers are (urgenetly) needed to:
Understand the initial state conditions for relativistic heavy nuclei at RHICand confirm our understanding of multiplicities and rapidity dependence
Understand how thermalization appears to be established so quickly at RHIC
Understand whether we have really reached the hydro limit for v2
Understand mid-rapidity particle production at the LHC in the future
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200745
A. Dumitru et al Nucl.Phys.A765:464-482,2006
Forward hadron production and the Color Glass Condensate
Projectile: collection of quarks and gluons subject to DGLAP evolution.
Target: CGC subject to quantum evolution.
Impressive, but forcomparable STAR 0
data (coming up) a k factor of 0.9 mustbe assumed
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200746
BRAHMS p+p identified spectra at high rapidity
Red : positive
Blue empty: negative
Built with data from 4 and 2.3 degrees and up to six magnetic field settings.
Geometrical acceptance corrections applied as well as absorption and decay in flight.
Trigger bias (~20%) is also corrected. Normalization to total inelastic cross-section (40 mb)
To appear in PRL online 22 June
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200747
What do we know where we think we should know something: comparison of measurement and NLO pQCD calculations
The frag. functions differ by the amount of gluon fragmentation into ’s. The data points toward a dominance of gluon-gluon and gluon-quark below 10 GeV/c
NLO pQCD can reproduce the data at RHIC energies. This is a strong indication that it gives a correct description of these
neutral pions at y=0
S.S. Adler et al. PRL 91 241803 (2003)
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200748
What do we know where we think we should know something: comparison of measurement and NLO pQCD calculations
The frag. functions differ by the amount of gluon fragmentation into ’s. The data points toward a dominance of gluon-gluon and gluon-quark below 10 GeV/c
NLO pQCD can reproduce the data at RHIC energies. This is a strong indication that it gives a correct description of these
neutral pions at y=0
S.S. Adler et al. PRL 91 241803 (2003)
hep-ex/0704.3599
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200749
√s=23.3GeV √s=52.8GeV
NLO-pQCD can reproduce y~0 hadron production at ISR but fails at higher rapidities.
Neutral pion production at small angles
at ISR
Lloyd et al.PRL 45 89
(1980)
Bourrely and Soffer Eur. Phys. J. C36 371-374 (2004)
xF xF
Ed
3 d
p3 [b
/GeV
3 ]
Ed
3 d
p3 [b
/GeV
3 ]
Data-pQCD difference at pT=1.5GeV
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200750
BRAHMS NLO pQCD comparisons to data
Calculations done by W. Vogelsang. Only one scale =pT and the same fragmentation functions as used for the PHENIX comparison.
The KKP does a better job compared to Kretzer, can we extend the conclusion about gg and gq dominance at these rapidities?
KKP has only 0 frag. Needed some modification for charged pions
y = 2.95
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200751
NLO pQCD for proton+anti-proton compared to data
A recent update of the KKP fragmentation function is used here: AKK where g->p has increased relevance.
The AKK function does well at y=0 (STAR p+p-) where the ratio anti-p/p~1 can be seen as consistent with dominance of gg or gq processes
J. Adams et al. Phys. Lett. B 637 (2006) 161
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200752
d+Au analysis
These spectra are still preliminary but one can already see that the yields change is small for different centrality samples.
The analysis of the d+Au data is underway, this time will include particle identification (RICH) in the full spectrometer FS
BRAHMS Preliminary
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200753
Nuclear modification factors with pid
As expected there is a difference between positive and negative pions driven by a “suppression” of negative pions in p+p (isospin)
Red:positive
Open blue: negative
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200754
Similar effects measured by PHENIX and PHOBOSPRL 94, 082302
PRC 70, 061901(R)
Suppression in the d direction and enhancement in the Au frag. region
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200755
STAR 0 at high rapidity in p+p
FPD: Lead-glass arrays 3.4<<4.0 on both sides of collision.
Spectra at 3.3 and 3.8 obtained with a smaller FPD
J. Adams et al. PRL 97 152302 (2006)
KKP frag. func. has higher gluon fragmentation into ’s than Kretzer
Good agreement for pT > 1.8 GeV/c
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200756
STAR Forward 0 from d+Au collisions
Inclusive 0 cross section per binary collision from d+Au at <> =4
CGC calculation is the closest to data; use of Kretzer FF will improve agreement.
CGC:A. Dumitru et al., Nucl. Phys. A765, 464 (2006)
MS: I. Vitev et al. PRL 93 262301 (2004)
NLO: W. Vogelsang
Same calculation as for BRAHMSK factor of 1.6
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200757
STAR Nuclear Modification Factor at high rapidity
BRAHMS published result consistent with new STAR once an isospin suppression of h- in p+p is taken into account (factor of 2/3).
Calculations that do not include mod. of Au wave function cannot reproduce data.
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200758
Summary so far:• At low-x expect some type of saturation of the gluon
distribution
• Two possibilities: same 2→2 QCD type scattering but reduced or coherent scattering off semi-classical field
• No conclusion yet from theory despite a lot of work
• Data consistent with both pictures (and others as well)
• Need a more discriminating measure
TJH: Saturation, Low-x, QCD Workshop Villaggio Guglielmo, July 2-18, 200759
A better way to tell what is going on: back-to-back azimuthal correlations
(Kharzeev, Levin, and McLerran, NP A748, 627)
The emission of gluons (pT~Qs) between the jets makes the correlations disappear.
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