Download presentation
Presentation is loading. Please wait.
Published byJunior Perry Modified over 9 years ago
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 ?
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.