tjh: saturation, low-x, qcd workshop villaggio guglielmo, july 2-18, 2007 1 saturation, low-x, and...

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


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


Thanks in advance to:

Les Bland, Romiro Debbe, Wlodek Guryn, Spencer Klein, Janet Seger, Carl Gagliardi, Hiromi Okada


Relativistic Heavy Ion Collider

RHIC

STARPHENIX

PHOBOSBRAHMS

2005 Configuration



RHIC

STARPHENIX

BRAHMS

2006 Configuration



RHIC

STARPHENIX 2007 Onward



RHIC

STARPHENIX 2011 EBIS Source in operation; HITL, HTB gone



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



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


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


Low-x structure of hadrons:

forward inclusive spectra and correlations


INEL

2.47<<5.29

The data at forward rapidities were collected with FS at 4º ( ~3) and 2.3º (~3.4)


Particle Identification in Forward Spectrometer with BRAHMS RICH


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


From p+p to Au+Au in the STAR TPC

p+p jet+jet (STAR@RHIC)

Au+Au X (STAR@RHIC)


zx

y

South: Left North: Right

FPD++ (Forward Pion Detector) , West side

STARSTAR

Inclusive Inclusive 00


zx

y

South: Left North: Right

FPD++ (Forward Pion Detector) , West side

STARSTAR


FPD


Acceptance of FPDSTARSTAR


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


Acceptance of FPD and FPD++

STARSTAR


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


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,


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,


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


PHENIX

PHENIX


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)


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


• 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 ?


= 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


= 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


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


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?


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


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


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.


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 →


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


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


2cos2 vx

y

p

patan

Anisotropic Flow

x

yz

px

py

A Short Excursion: Elliptic Flow in Heavy Ion Collisions

Peripheral Collisions


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


Constituent quark scaling

Constituent quark DOF.

(Deconfinement)

solid: STARopen: PHENIX PRL91(03)

v2 appears to scale with number of constituent quarks. quark coalescence.


KET/n scaling across collision centralities

KET/n scaling observed across centralities


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)


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)


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


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


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


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


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)


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


√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


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


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


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


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


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


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


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


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.


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


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.

tjh: saturation, low-x, qcd workshop villaggio guglielmo, july 2-18, 2007 1 saturation, low-x, and...

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forward spectrometer

forward region

rhicau au x star

areal coverage of forward

star tpcp p jet jet

m2 addition of fms

khz300 khz

jet quenching