Low-x 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 STAR • Run 1 (2000) : Au-Au @ SNN = 130 GeV • Run 2 (2001-2): Au-Au, p-p @ SNN = 200 GeV • (1-day run): Au+Au @ SNN = 20 GeV • Run 3 (2003): d-Au, p-p@ SNN = 200 GeV

3. 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 • Violence of collision determined by b. • Characterize collision by Npart: • # of nucleons that “participate” or scatter in collision. • Nucleons that don’t 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). Spectators Impact parameter (b)

6. 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  >> 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 GeV2at center of Au nucleus. • But gluon flux now can now be related to Qs •   Qs2 / s (Qs2)

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: • 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)

8. Low-x Observables in PHENIX Charged Multiplicity Pad Chambers: RPC1 = 2.5 m RPC3 = 5.0 m ||<0.35, = Transverse Energy Lead-Scintillator EMCal: REMC = 5.0 m ||<0.38,  = (5/8) Trigger & Centrality Beam-Beam Counters: 3.0<|h|<3.9, = 2 0º Calorimeters: |h| > 6, |Z|=18.25 m Collision Region (not to scale)

9. PHENIX Centrality Selection ET EZDC b QBBC Nch • Zero-degree calorimeters: • Measure energy (EZDC) in spectator neutrons. • Smaller b  smaller EZDC • Except @ 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% 20% 5% 10% QBBC

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. • 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%

11. PHENIX: Et in EM Calorimeter • Definition: Et =  Ei sini • Ei = Eitot - mNfor 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 dist’s for 0-5%, 5-10%, 10-15%, 15-20% centrality bins compared to minimum bias. Sample M Minv Dist. 0

12. Et and Nchg Per Participant Pair 200 GeV 130 GeV dEt/d (GeV) per part. pair 200 GeV 130 GeV dNchg/d (GeV) per part. pair Npart Npart • Bands (bars) – correlated (total) syst. Errors • Slow change in Et and Nchg per participant pair • Despite 20 change in total Et or Nchg PHENIX preliminary PHENIX preliminary Beware of suppressed zero !

13. Et Per Charged Particle • Centrality dependence of Et and Nchg very similar @ 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

14. Multiplicity: Model Comparisons 130 GeV 200 GeV dNchg / d per part. pair Npart Npart • 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 Npartdependent hard cutoff (p0) • Ad Hoc saturation ?? 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 Nchg (200) / Nchg (130) Npart • 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.

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

17. dN/d Saturation Model Comparisons • 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 ?!! Kharzeev and Levin Phys. Lett. B523:79-87, 2001 dN/d per part. pair dN/d

18. Classical Yang-Mills Calculation x 2.4 x 1.1 • 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. Krasnitz,Nara,Venugopalan Nucl. Phys. A717:268, 2003

19. Saturation & Bottom-up Senario • BMSS start from ~ identical assumptions as KLN but • Qs (b=0)  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 < 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-pt Hadron Production • 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 > 4 GeV • Consistent with calculations including dE/dx. • What does this have to do with low x ? … Ratio: Measured/expected Points: data, lines: theory PHENIX 0 pt spectra No dE/dx Expected with dE/dx Observed

21. Geometric Scaling @ 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

22. 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 @ 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 ?