1. Low-x Observables at RHIC (with a focus on PHENIX) Prof. Brian A Cole Columbia University Outline 1.Low-x physics of heavy ion collisions 2.PHENIX E t and multiplicity measurements 3.PHOBOS dn/d  measurements 4.High-p t hadrons: geometric scaling ?? 5.Summary

2. Relativistic Heavy Ion Collider STAR  Run 1 (2000) : Au-Au @  S NN = 130 GeV  Run 2 (2001-2): Au-Au, p-p @  S NN = 200 GeV  (1-day run): Au+Au @  S NN = 20 GeV  Run 3 (2003):d-Au, p-p @  S NN = 200 GeV

3. Collision seen in “Target” Rest Frame  Projectile boost   10 4. u Due to Lorentz contraction gluons overlap longitudinally u They combine producing large(r) k t gluons.  Apply uncertainty princ. u  E = k t 2 / 2Px ~  / 2  t  Some numbers: u mid-rapidity  x  10 -2 u Nuclear crossing  t ~ 10 fm/c  k t 2 ~ 2 GeV 2  Gluons with much lower k t are frozen during collision.  Target simply stimulates emission of pre-existing gluons

4. How Many Gluons (rough estimate) ?  Measurements of transverse energy (E t =  E sin  ) in “head on” Au-Au collisions give dE t / d  ~ 600 GeV (see below).  Assume primordial gluons carry same E t  Gluons created at proper time  and rapidity y appear at spatial z =   z  =  sinh y u So dz =  cosh y dy u In any local (long.) rest frame  z =   y.  dE t / d 3 x = dE t / d  / A  (neglecting y,  difference) u For Au-Au collision, A =  6.8 2  150 fm 2.  Take  = 1/k t, dE t ~ k t dN g  dN g /d 3 x ~ 600 GeV/ 150 fm 2 / 0.2 GeV fm = 20 fm -3  For k t ~ 1 GeV/c, dN g / dA ~ 4 fm -2  Very large gluon densities and fluxes.

5. “Centrality” in Heavy Ion Collisions  Violence of collision determined by b.  Characterize collision by N part : u # of nucleons that “participate” or scatter in collision. u Nucleons that don’t participate we call spectators. u A = 197 for Au  maximum N part in Au-Au is 394.  Smaller b  larger N part, more “central” collisions  Use Glauber formalism to estimate N part for experimental centrality cuts (below). Spectators Impact parameter (b)

6. Kharzeev, Levin, Nardi Model  Large gluon flux in highly boosted nucleus  When probe w/ resolution Q 2 “sees” multiple partons, twist expansion fails u i.e. when  >> 1 u New scale: Q s 2  Q 2 at which  = 1  Take cross section  =   s (Q 2 ) / Q 2  Gluon area density in nucleus   xG(x, Q 2 )  nucleon  Then solve: Q s 2 = [constants]  s (Q s 2 ) xG(x, Q s 2 )  nucleon u Observe: Q s depends explicitly on  nucleon  KLN obtain Q s 2 = 2 GeV 2 at center of Au nucleus.  But gluon flux now can now be related to Q s u   Q s 2 /  s (Q s 2 ) Saturation in Heavy Ion Collisions

7. 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: u Number of final hadrons  number of emitted gluons  To evaluate centrality dependence: u  nucleon  ½  part u Only count participants from one nucleus for Q s  To evaluate energy dependence: u Take Q s s dependence from Golec-Biernat & Wüsthof  Q s (s) / Q s (s 0 ) = (s/s 0 ) /2, ~ 0.3.  Try to describe gross features of HI collisions u e.g. Multiplicity (dN/d  ), transverse energy (dE t / d  )

8. Low-x Observables in PHENIX Charged Multiplicity Pad Chambers: R PC1 = 2.5 m R PC3 = 5.0 m |  |<0.35,  =  Transverse Energy Lead-Scintillator EMCal: R EMC = 5.0 m |  |<0.38,  = (5/8)  Trigger & Centrality Beam-Beam Counters: 3.0<|  |<3.9,  = 2  0º Calorimeters: |  | > 6, |Z|=18.25 m Collision Region (not to scale)

9. PHENIX Centrality Selection b N ch ETET E ZDC Q BBC E ZDC Q BBC  Zero-degree calorimeters: u Measure energy (E ZDC ) in spectator neutrons. u Smaller b  smaller E ZDC u Except @ large b neutrons carried by nuclear fragments.  Beam-beam counters: u Measure multiplicity (Q BBC ) in nucleon frag. region. u Smaller b  larger Q BBC  Make cuts on E ZDC vs Q BBC according to fraction of  tot “above” the cut.  State centrality bins by fractional range of  tot u E.g. 0-5%  5% most central 5% 10% 15% 20%

10. 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.  N chg  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. 0-5% Minimum bias

11. PHENIX: E t in EM Calorimeter  Definition: E t =  E i sin  i u E i = E i tot - m N for baryons u E i = E i tot +m N for antibaryons u E i = E i tot for others  Correct for fraction of deposited energy u 100% for ,  0, 70 % for    Correct for acceptance  Energy calibration by: u Minimum ionizing part. u electron E/p matching u  0 mass peak  Plot E t dist’s for 0-5%, 5-10%, 10-15%, 15-20% centrality bins compared to minimum bias.  0  Sample M  M inv Dist.

12. E t and N chg Per Participant Pair  Bands (bars) – correlated (total) syst. Errors  Slow change in E t and N chg per participant pair u Despite  20 change in total E t or N chg N part dE t /d  (GeV) per part. pair dN chg /d  (GeV) per part. pair 130 GeV 200 GeV Beware of suppressed zero ! PHENIX preliminary

13. E t Per Charged Particle  Centrality dependence of E t and N chg very similar @ 130, 200 GeV.  Take ratio: E t per charged particle. u  perfectly constant u Little or no dependence on beam energy.  Non-trivial given  s dependence of hadron composition.  Implication: u E t / N chg determined by physics of hadronization. u Only one of N chg, E t can be saturation observable. PHENIX preliminary

14. Multiplicity: Model Comparisons  KLN saturation model well describes dN/d  vs N part. u N part variation due to Q s dependence on  part (  nucleon ).  EKRT uses “final-state” saturation – too strong !!  Mini-jet + soft model (HIJING) does less well. u Improved Mini-jet model does better.  Introduces an N part dependent hard cutoff (p 0 )  Ad Hoc saturation ?? 200 GeV130 GeV dN chg / d  per part. pair N part HIJING X.N.Wang and M.Gyulassy, PRL 86, 3498 (2001) Mini-jet S.Li and X.W.Wang Phys.Lett.B527:85-91 (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)

15. Multiplicity: Energy Dependence  s dependence an important test of saturation u Determined by s dependence of Q s from HERA data  KLN Saturation model correctly predicted the change in N chg between 200 and 130 GeV. u And the lack of N part dependence in the ratio.  Compared to mini-jet (HIJING) model. N part N chg (200) / N chg (130)

16. dN/d  Measurements by PHOBOS  PHOBOS covers large  range w/ silicon detectors Total N chg (central collision)  5060 ± 250 @ 200 GeV  4170 ± 210 @ 130 GeV  1680 ± 100 @ 19.6 GeV 0+3 -3 +5.5 -5.5 simulation  =-ln tan  /2  

17. dN/d  Saturation Model Comparisons Additional model “input”  x dependence of G(x) outside saturation region u xG(x) ~ x - (1-x) 4  GLR formula for inclusive gluon emission: u To evaluate yield when one of nuclei is out of saturation.  Assumption of gluon mass (for y   ) u M 2 = Q s 1 GeV  Compare to PHOBOS data at 130 GeV.  Incredible agreement ?!! Kharzeev and Levin Phys. Lett. B523:79-87, 2001 dN/d  per part. pair dN/d 

18. Classical Yang-Mills Calculation  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 k t dist.  Results depend on input saturation scale  s. u Re-scaled to compare to data. u No absolute prediction u But centrality dependence of N chg and E t reproduced.  But E t /N chg sensitive to  s. Krasnitz,Nara,Venugopalan Nucl. Phys. A717:268, 2003 x 2.4 x 1.1

19. Saturation & Bottom-up Senario  BMSS start from ~ identical assumptions as KLN but u Q s (b=0)  0.8 GeV. u Argue that resulting value for c, ~ 3, is too large.  Then evaluate what happens to gluons after emission u In particular, gluon splitting, thermalization. u N chg no longer directly proportional to xG(x,Q s )  Extra factors of  s  Agrees with (PHOBOS) data. u Faster decrease at low N part than in KLN (?)  More reasonable c, c < 1.5 Baier, Mueller, Schiff, and Son Phys. Lett. B502:51, 2001. Baier, Mueller, Schiff, and Son Phys. Lett. B539:46-52, 2002

20. High-p t Hadron Production  High-p t hadron yield predicted to be suppressed in heavy ion collisions due to radiative energy loss (dE/dx).  Suppression observed in central Au-Au data u  x 5 suppression for p t > 4 GeV  Consistent with calculations including dE/dx.  What does this have to do with low x ? … No dE/dx with dE/dx Ratio: Measured/expected Points: data, lines: theory Expected Observed PHENIX  0 p t spectra

21. Geometric Scaling @ RHIC ? Argument  Geometric scaling extends well above Q s  May influence p t spectra at “high” p t  Compare saturation to pQCD at 6, 9 GeV/c u Saturation x3 lower in central collisions. u Partly responsible for high-p t suppression ?  Testable prediction: u Effect ½ as large should be seen in d-Au collisions. u Data in few months … Kharzeev, Levin, McLerran (hep-ph/0210332) pQCD saturation Yield per participant pair

22. Summary  Saturation models can successfully describe particle multiplicities in HI collisions at RHIC. u With few uncontrolled parameters: Q s (s 0 ), c. u Closest thing we have to ab initio calculation  They provide falsifiable predictions !  Connect RHIC physics to DIS observables: u  s dependence of dN/d   saturation in DIS. u Geometric scaling  high p t production @ RHIC  Already going beyond simplest description u e.g. bottom-up analysis.  But, there are still many issues (e.g.): u What is the value for Q s ? Is it large enough ? u Is Q s really proportional to  part (A 1/3 )? u 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 ?