Lowx Observables at RHIC with a focus on PHENIX

1
Low-x Observables at RHIC (with a focus on
PHENIX)

• Prof. Brian A Cole
• Columbia University

• Outline
• Low-x physics of heavy ion collisions
• PHENIX Et and multiplicity measurements
• PHOBOS dn/d? measurements
• High-pt hadrons geometric scaling ??
• Summary

2
Relativistic Heavy Ion Collider

• Run 1 (2000) Au-Au _at_ ?SNN 130 GeV
• Run 2 (2001-2) Au-Au, p-p _at_ ?SNN 200 GeV
• (1-day run) AuAu _at_ ?SNN 20 GeV
• Run 3 (2003) d-Au, p-p _at_ ?SNN 200 GeV

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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
• Some numbers
• 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

4
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.

5
Centrality in Heavy Ion Collisions
Spectators
Impact parameter (b)

• Violence of collision determined by b.
• Characterize collision by Npart
• of nucleons that participate or scatter in
  collision.
• Nucleons that dont 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).

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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 ?? gtgt 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 Qs
• ? ? Qs2 / ?s (Qs2)

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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 Qs
• 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?)

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Low-x Observables in PHENIX
Charged Multiplicity Pad Chambers RPC1 2.5
m RPC3 5.0 m ?lt0.35, ??? Transverse
Energy Lead-Scintillator EMCal REMC 5.0
m ?lt0.38, ?? (5/8)? Trigger Centrality
Beam-Beam Counters 3.0lthlt3.9, ?? 2? 0º
Calorimeters h gt 6, Z18.25 m
Collision Region (not to scale)
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PHENIX Centrality Selection

• Zero-degree calorimeters
• Measure energy (EZDC) in spectator
  neutrons.
• Smaller b ? smaller EZDC
• Except _at_ large b neutrons carried by nuclear
  fragments.
• Beam-beam counters
• Measure multiplicity (QBBC) in nucleon frag.
  region.
• Smaller b ? larger QBBC
• Make cuts on EZDC vs QBBC according to fraction
  of ?tot above the cut.
• State centrality bins by fractional range of
  ?tot
• E.g. 0-5 ? 5 most central

EZDC
15
5
20
10
QBBC
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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
• Correct for acceptance, ?
  conversions, hadronic interactions in material.
• Show multiplicity distributions for
  0-5, 5-10, 10-15, 15-20
  centrality bins compared to minimum
  bias.

Minimum bias
0-5
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PHENIX Et in EM Calorimeter
Sample M?? Minv Dist.

• Definition Et ? Ei sin?i
• Ei Eitot - mN for baryons
• Ei Eitot mN for antibaryons
• Ei Eitot for others
• Correct for fraction of deposited energy
• 100 for ?, ?0, 70 for ??
• Correct for acceptance
• Energy calibration by
• Minimum ionizing part.
• electron E/p matching
• ?0 mass peak
• Plot Et dists for 0-5, 5-10, 10-15,
  15-20 centrality bins compared to minimum bias.

?0???
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Et and Nchg Per Participant Pair
PHENIX preliminary
PHENIX preliminary
Beware of 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

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Et Per Charged Particle

• Centrality dependence of Et and Nchg very
  similar _at_ 130, 200 GeV.
• Take ratio Et per charged particle.
• ? perfectly constant
• Little or no dependence on beam energy.
• Non-trivial given ?s dependence of hadron
  composition.
• Implication
• Et / Nchg determined by physics of hadronization.
• Only one of Nchg, Et can be saturation
  observable.

PHENIX preliminary
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Multiplicity Model Comparisons
HIJING X.N.Wang and M.Gyulassy, PRL 86, 3498
(2001) Mini-jet S.Li and X.W.Wang
Phys.Lett.B52785-91 (2002) EKRT K.J.Eskola et
al, Nucl Phys. B570, 379 and Phys.Lett. B 497,
39 (2001) KLN D.Kharzeev and M. Nardi, 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 ??

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Multiplicity Energy Dependence

• ?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.

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dN/d? Measurements by PHOBOS

• PHOBOS covers large ? range w/ silicon detectors

h-ln tan q/2
simulation

• Total Nchg (central collision)
• 5060 250 _at_ 200 GeV
• 4170 210 _at_ 130 GeV
• 1680 100 _at_ 19.6 GeV

?
?
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dN/d? Saturation Model Comparisons
Kharzeev and Levin Phys. Lett. B52379-87, 2001

• Additional model input
• x dependence of G(x) outside saturation region
• xG(x) x-? (1-x)4
• GLR formula for inclusive gluon emission
• 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 ?!!

dN/d? per part. pair
dN/d?
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Classical Yang-Mills Calculation
Krasnitz,Nara,Venugopalan Nucl. Phys. A717268,
2003

• Treat initial gluon fields as classical fields
  using M-V initial conditions.
• 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.

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Saturation Bottom-up Senario

• BMSS start from identical assumptions as KLN
  but
• Qs (b0) ? 0.8 GeV.
• Argue that resulting value for c, 3, is too
  large.
• Then evaluate what happens to gluons after
  emission
• In particular, gluon splitting, thermalization.
• 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 lt 1.5

Baier, Mueller, Schiff, and Son Phys. Lett.
B50251, 2001. Baier, Mueller, Schiff, and Son
Phys. Lett. B53946-52, 2002
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High-pt Hadron Production
Ratio Measured/expected Points data, lines
theory
PHENIX ?0 pt spectra
No dE/dx
Expected
with dE/dx
Observed

• 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 gt 4 GeV
• Consistent with calculations including dE/dx.
• What does this have to do with low x ?

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Geometric Scaling _at_ RHIC ?

• Argument
• Geometric scaling extends well above Qs
• May influence pt spectra at high pt
• Compare saturation to pQCD at 6, 9 GeV/c
• Saturation x3 lower in central collisions.
• Partly responsible for high-pt suppression ?
• Testable prediction
• Effect ½ as large should be seen in d-Au
  collisions.
• Data in few months

Kharzeev, Levin, McLerran (hep-ph/0210332)
Yield per participant pair
pQCD
saturation
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Summary

• Saturation models can successfully describe
  particle multiplicities in HI collisions at RHIC.
• With few uncontrolled parameters Qs(s0), c.
• Closest thing we have to ab initio calculation
• They provide falsifiable predictions !
• Connect RHIC physics to DIS observables
• ?s dependence of dN/d? ? saturation in DIS .
• Geometric scaling ? high pt production _at_ 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 ?