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Low-x Observables at RHIC (with a focus on PHENIX) Prof. Brian A Cole Columbia University Outline 1. 2. 3. 4. 5. Low-x physics of heavy ion collisions PHENIX Et and multiplicity measurements PHOBOS dn/d measurements High-pt hadrons: geometric scaling ?? Summary 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 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: x 10-2 Nuclear crossing t ~ 10 fm/c mid-rapidity kt2 ~ 2 GeV2 Gluons with much lower kt are frozen during collision. Target simply stimulates emission of pre-existing gluons 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. “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 A that don’t participate we call spectators. = 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). 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 GeV2 at center of Au nucleus. But gluon flux now can now be related to Qs Qs2 / s (Qs2) 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 Only ½ part 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) 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<||<3.9, = 2 0º Calorimeters: || > 6, |Z|=18.25 m Collision Region (not to scale) PHENIX Centrality Selection Zero-degree calorimeters: ET Measure energy (EZDC) in spectator neutrons. Smaller EZDC b b smaller EZDC QBBC Nch Except @ large b neutrons carried by nuclear fragments. Beam-beam counters: 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 Measure 15% 20% 5% 10% QBBC 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% PHENIX: Et in EM Calorimeter Definition: Et = Ei sini Sample M Minv Dist. 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 electron 0 ionizing part. E/p matching mass peak Plot Et dist’s for 0-5%, 5-10%, 10-15%, 15-20% centrality bins compared to minimum bias. 0 dNchg/d (GeV) per part. pair dEt/d (GeV) per part. pair Et and Nchg Per Participant Pair Beware of suppressed zero ! 200 GeV 130 GeV PHENIX preliminary 200 GeV 130 GeV PHENIX preliminary Npart Bands (bars) – correlated (total) syst. Errors Slow change in Et and Nchg per participant pair Despite 20 change in total Et or Nchg Npart 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 Multiplicity: Model Comparisons dNchg / d per part. pair 130 GeV HIJING 200 GeV 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 Npart Npart 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 ?? Nchg (200) / Nchg (130) Multiplicity: Energy Dependence 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. dN/d Measurements by PHOBOS PHOBOS covers large range w/ silicon detectors =-ln tan /2 simulation Total Nchg (central collision) 5060 ± 250 @ 200 GeV 4170 ± 210 @ 130 GeV 1680 ± 100 @ 19.6 GeV -5.5 -3 0 +3 +5.5 Kharzeev and Levin Phys. Lett. B523:79-87, 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 dN/d per part. pair dN/d Saturation Model Comparisons Classical Yang-Mills Calculation Krasnitz,Nara,Venugopalan Nucl. Phys. A717:268, 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. x 2.4 x 1.1 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 High-pt Hadron Production PHENIX 0 pt spectra Ratio: Measured/expected Points: data, lines: theory No dE/dx Expected Observed with dE/dx 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 ? … 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 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 ?