HBT in STAR
advertisement
HBT in STAR Mike Lisa*, Ohio State University • “Traditional” HBT results: 200 GeV vs 130 GeV Au+Au collisions • New experimental developments • Bowler/Sinyukov Coulomb correction • Pushing the systematics – azimuthally-sensitive HBT • Results from 130, 200 GeV • Interpreting asHBT results • Hydro, Hydro+RQMD, BlastWave • Conclusions * Work of: Mercedes López-Noriega, Dan Magestro, Randy Wells STAR HBT 13 February 2003 Winter Workshop - Breckenridge CO 1 Reminder: p-space observables reproduced by dynamical models, x-space not STAR HBT 13 February 2003 Heinz & Kolb, hep-ph/0204061 Winter Workshop - Breckenridge CO 2 “Standard” HBT:130 vs 200 GeV • Essentially identical analysis carried out for 200 GeV data as published 130 GeV 130 GeV 200 GeV STAR, QM02 • (exact centrality definition, etc, being finalized) • New: centrality dependence of pT dependence • mostly an overall scaling of R • Little change with increased energy • Transverse size slightly bigger @ low pT? • Similar pT-dependence • Ro/Rs problem persists • Longitudinal radius: no change • Sinyukov fit R L 0 mT : T 0cent 10 fm / c, 0periph 7.5 fm / c • Lower-energy RHIC run needed STAR HBT 13 February 2003 Winter Workshop - Breckenridge CO 3 Recent analysis developments I • RHIC analyses used “standard” Coulomb correction, used by previous experiments • “apples-to-apples” extension of systematics A (q ) N (1 exp(R ij2qiq j )) B(q) K coul (q) f 177c (2002) STAR, QM01; NPA698, • Effects of “diluting” CC (resonances, etc) explored & reported @ QM01 • Ro affected most K coul (q) 1 f (K coul (q) 1) 0 f 1 • Y2 data: dilution effect vs pT, centrality • RO/RS ~ 10-15% increase when f = ≈ 0.5 • More correct CC method of Bowler (’91) & Sinyukov (’98), used by CERES (’02) • Similar effect on radii as dilution with f = No Coulomb CC “Standard” Coulomb CC In “right” direction, but does not solve RO/RS problem A (q ) N 1 K coul (q) 1 exp(R ij2qiq j 1 B(q) STAR HBT 13 February 2003 Winter Workshop - Breckenridge CO 4 “Traditional” HBT results ~ stable • So what’s the problem with theory? – Timescale too long? – Hadronic phase overestimated? – HBT technique not understood? • Can (HBT and other) data be consistently understood? – What are characteristics of freezeout source @ RHIC? • Parameterization of freezeout • Explore with further systematics– non-central collisions – Azimuthally-sensitive HBT STAR HBT 13 February 2003 Winter Workshop - Breckenridge CO 5 Noncentral collision dynamics hydro evolution • hydro reproduces v2(pT,m) (details!) @ RHIC for pT < ~1.5 GeV/c • system response EoS • early thermalization indicated • Dynamical models: • x-anisotropy in entrance channel p-space anisotropy at freezeout • magnitude depends on system response to pressure STAR HBT 13 February 2003 Heinz & Kolb, hep-ph/01110756 Winter Workshop - Breckenridge CO Effect of dilute stage hydro evolution later hadronic stage? • hydro reproduces v2(pT,m) (details!) @ RHIC for pT < ~1.0 GeV/c • system response EoS • early thermalization indicated • dilute hadronic stage (RQMD): • little effect on v2 @ RHIC STAR HBT 13 February 2003 Winter Workshop - Breckenridge Teaney, Lauret, & CO Shuryak, nucl-th/0110037 7 Effect of dilute stage hydro evolution later hadronic stage? • hydro reproduces v2(pT,m) (details!) @ RHIC for pT < ~1.5 GeV/c • system response EoS • early thermalization indicated hydro only hydro+hadronic rescatt • dilute hadronic stage (RQMD): • little effect on v2 @ RHIC • significant (bad) effect on HBT radii STAR HBT 13 February 2003 STAR PHENIX calculation: Winter Workshop - Breckenridge COSoff, Bass, Dumitru, PRL 2001 8 Effect of dilute stage hydro evolution later hadronic stage? • hydro reproduces v2(pT,m) (details!) @ RHIC for pT < ~1.5 GeV/c • system response EoS • early thermalization indicated • dilute hadronic stage (RQMD): • little effect on v2 @ RHIC • significant (bad) effect on HBT radii • related to timescale? - need more info STAR HBT 13 February 2003 Winter WorkshopTeaney, - Breckenridge CO& Shuryak, nucl-th/0110037 9 Lauret, Effect of dilute stage hydro evolution later hadronic stage? • hydro reproduces v2(pT,m) (details!) in-planeextended @ RHIC for pT < ~1.5 GeV/c • system response EoS • early thermalization indicated • dilute hadronic stage (RQMD): • little effect on v2 @ RHIC • significant (bad) effect on HBT radii • related to timescale? - need more info • qualitative change of freezeout shape!! • important piece of the puzzle! STAR HBT 13 February 2003 out-of-plane-extended Winter WorkshopTeaney, - Breckenridge CO& Shuryak, nucl-th/0110037 10 Lauret, Indirect indications of x-space anisotropy @ RHIC STAR, PRL 87 182301 (2001) • v2(pT,m) globally well-fit by hydro-inspired “blast-wave” T (MeV) dashed solid 135 20 100 24 0(c) 0.52 0.02 0.54 0.03 a (c) 0.09 0.02 0.04 0.01 S2 STAR HBT 0.0 13 February 2003 0.04 0.01 temperature, radial flow consistent with fits to spectra anisotropy of flow boost spatial anisotropy (out-of-plane extended) Winter Workshop - Breckenridge CO 11 Possible to “see” via HBT relative to reaction plane? fp=90° • for out-of-plane-extended source, expect • large Rside at 0 2nd-order • small Rside at 90 oscillation Rside (small) Rside (large) fp=0° 2 Rs [no flow expectation] fp STAR HBT 13 February 2003 Winter Workshop - Breckenridge CO 12 Need a model of the freezeout- BlastWave BW: hydro-inspired parameterization of freezeout • longitudinal direction • infinite extent geometrically • boost-invariant longitudinal flow • Momentum space • temperature T • transverse rapidity boost (r , f ) ~ r cos( 2f ) s 0 a RY b RX • coordinate space • transverse extents RX, RY • freezeout in proper time • evolution duration 0 • emission duration 7 parameters describing freezeout 0 2 dN ~ exp 2 d 2 STAR HBT 13 February 2003 Winter Workshop - Breckenridge CO 13 BlastWave fits to published RHIC data • pT spectra constrain (mostly) T, 0 central midcentral peripheral • (traditional) HBT constrains R, 0, – (fit to STAR-HBT only) • v2(pT,m) constrains a, RX/RY Central Midcentral Peripheral T (MeV) 108 3 106 2 95 3 0 0.88 0.01 0.87 0.01 0.81 0.02 a 0.06 0.01 0.05 0.01 0.04 0.01 RX (fm) 12.9 0.4 10.2 0.5 8.0 0.1 RY (fm) 12.8 0.4 11.8 0.6 10.0 0.2 0 (fm/c) 8.9 0.3 7.4 0.7 6.5 0.4 (fm/c) 0.0 9.0 0.8 1.8 0.09 0.6 2 / ndf 80.5 / 101 153.7 / 92 74.3 / 68 STAR HBT 13 February 2003 Winter Workshop - Breckenridge CO 14 Minbias observations at 130 GeV “raw” • flat within errors • Significant (& “allowed”) oscillations observed in HBT radii • RP/binning correction* significant • produces RL2 oscillation from “nowhere”? – is it real? preliminary 2 RO after RP/binning correction R S2 2 R OS (*) [Heinz, Hummel, MAL, Wiedemann PRC 044903 (2002)] STAR HBT 13 February 2003 - Breckenridge CO R. Wells,Winter PhD Workshop thesis, Ohio State, 2002 R 2L 15 asHBT versus BlastWave • Minbias asHBT well-reproduced with same BlastWave from minbias v2(pT,m) • Ry = 11.4 fm s2 = 0.045 • Rx = 10.8 fm • 0 = 8.3 fm/c • = 0 ( → ~1.5 fm/c w/ Bowler CC)) • Consistent picture – convincing argument for flow scenario • Saturation ???? Au+Au 130 GeV minbias • asHBT: geometry dominates dynamics • Source out-of-plane extended STAR HBT 13 February 2003 Winter Workshop - Breckenridge CO 16 Azimuthal HBT: hydro predictions RHIC (T0=340 MeV @ 0=0.6 fm) • Out-of-plane-extended source (but flips with hadronic afterburner) • flow & geometry work together to produce HBT oscillations • oscillations stable with KT (note: RO/RS puzzle persists) STAR HBT 13 February 2003 & Kolb, hep-ph/0204061 Winter Workshop - Breckenridge Heinz CO 17 Azimuthal HBT: hydro predictions RHIC (T0=340 MeV @ 0=0.6 fm) • Out-of-plane-extended source (but flips with hadronic afterburner) • flow & geometry work together to produce HBT oscillations • oscillations stable with KT “LHC” (T0=2.0 GeV @ 0=0.1 fm) • In-plane-extended source (!) • HBT oscillations reflect competition between geometry, flow • low KT: geometry • high KT: flow STAR HBT sign flip 13 February 2003 & Kolb, hep-ph/0204061 Winter Workshop - Breckenridge Heinz CO 18 Further systematics in Au+Au 200 GeV Centrality cuts kT-integrated 12 f bins kT cuts Mid-central 4 f bins • Oscillation phases: out-of-plane extended source • Source size increases, oscillations decrease with increasing centrality • 0th and 2nd harmonics only • Average size (0th harmonic) falls with kT • Mild evolution of 2nd harmonic with kT STAR HBT 13 February 2003 Winter Workshop - Breckenridge CO 19 “Grand summary” Fourier Coefficients n=0 n=2 • Centrality- and kT- dependence of the f-dependence summarized concisely by Fourier coefficients 2 R pT ,f cosnf R ,n pT 2 R p ,f sin nf T 2 o, s, l os central midcentral peripheral STAR HBT 13 February 2003 Winter Workshop - Breckenridge CO 20 “Grand summary” Fourier Coefficients n=0 n=2 • Centrality- and kT- dependence of the f-dependence summarized concisely by Fourier coefficients 2 R pT ,f cosnf R ,n pT 2 R p ,f sin nf T 2 o, s, l os • Hydro predictions (*): b = 6 fm “RHIC” source “LHC” (IPES) source central midcentral peripheral • Scale of homogeneity lengths off • Phase/magnitude of oscillations from “RHIC” source in the ballpark • significance ? STAR HBT& Kolb, (*) Heinz hep-ph/0204061 13 February 2003 Winter Workshop - Breckenridge CO 21 Evolution of spatial anisotropy • Extraction of full freezeout scenario underway • Timescales short, flow dominant • Out-of-plane-extended freezeout geometry for all centralities – further constraint on evolution timescale (and dynamic models!!) STAR HBT 13 February 2003 Winter Workshop - Breckenridge CO 22 • HBT systematics from 200 GeV similar to 130 GeV – New, more correct CC ~ 10-15% effect on Ro • Dynamic models (hydro, hydro+RQMD) – soft p-space signals – soft x-space signals X – worse agreement with hadronic stage included • BlastWave – toy model, but… – consistent framework to extract main features of freezeout – can initial state effects describe all signals as consistently? – in particular, short timescales 0, -- perhaps the problem • asHBT STAR HBT – probes details of anisotropic geometry/flow interplay – consistent w/ BW expectations (& further constrains f.o. picture) • (ditto for non-identical particle correlations) – f.o. source out-of-plane extended • (model-dependent in principle, but robust in fact) • another constraint on evolution duration – detailed systematics from 200 GeV run • hydro suggests this can reveal important physics • tighter model constraints • 2003 new level of presentation (FCs) for asHBT 13 February Winter Workshop - Breckenridge CO 23 Backups follow STAR HBT 13 February 2003 Winter Workshop - Breckenridge CO 24 Next slides • Show Fabrice’s BW fits of published data • Show BW vs Randy’s stuff – Rx=Ry and rho_a = 0 cases too • Show Dan’s 3 centrality bins with 12 phi bins – 2nd order harmonics only • Show Dan’s centrality/kT dependence • Show “1-page summary,” with Heinz/Kolb on top • Show Dan’s figure 4 STAR HBT 13 February 2003 Winter Workshop - Breckenridge CO 25 Symmetries of the emission function I. Mirror reflection symmetry w.r.t. reactionplane (for spherical nuclei): S( x, y, z, t ;Y , KT , ) S( x, y, z, t ;Y , KT ,) ~ x ~ x (Y , KT , ) 1 ~ x ~ x (Y , KT ,) with 1 (1) 2 2 II. Point reflection symmetry w.r.t. collision center (equal nuclei): S( x, y, z, t ;Y , KT , ) S( x, y, z , t ;Y , KT , ) ~ x ~ x (Y , KT , ) 2 ~ x ~ x (Y , KT , ) with STAR HBT 2 (1) 13 February 2003 0 0 Winter Workshop Breckenridge CO Heinz, Hummel, MAL, -Wiedemann, PRC66 044903 (2002) 26 Fourier expansion of HBT radii @ Y=0 Insert symmetry constraints of spatial correlation tensor into Wiedemann relations and combine with explicit -dependence: Rs2 (f) Rs2,0 2 n 2, 4,6,... Rs2, n cos(nf) Ro2 (f) Ro2,0 2 n 2, 4,6,... Ro2, n cos(nf) 2 2 n 2, 4,6,... Ros , n sin( nf) 2 Ros (f) Rl2 (f) Rl2,0 2 n 2, 4,6,... Rl2,n cos(nf) Rol2 (f) 2 n 1,3,5,... Rol2 , n cos(nf) Rsl2 (f) 2 n 1,3,5,... Rsl2 , n sin( nf) Note: These most general forms of the Fourier expansions for the HBT radii are preserved when averaging the correlation function over a finite, symmetric window around Y=0. Relations between the Fourier coefficients reveal interplay between flow and STAR geometry, and can help disentangle space and time HBT 13 February 2003 Winter Workshop Breckenridge CO Heinz, Hummel, MAL, -Wiedemann, PRC66 044903 (2002) 27 Bowler CoulombCorrection vs +Work in progress: finalizing resolution effects, etc. Low kT STAR HBT 13 February 2003 High kT Winter Workshop - Breckenridge CO 28 “Traditional HBT” - cylindrical sources C(qo , qs , ql ) 1 e Decompose q into components: qLong : in beam direction qOut : in direction of transverse momentum qSide : qLong & qOut K q o2 R o2 q s2 R s2 q l2 R l2 ~2 K ~ x out t 2 2 ~ R s K x side K ~2 2 Rl K ~ x long l t R o2 K K x out , x side x, y Rout Rside (beam is into board) STAR HBT 13 February 2003 ~ xx x d 4 x S( x, K ) f ( x ) f 4 d x S( x, K ) Winter Workshop - Breckenridge CO 29 Anisotropic sources Six HBT radii vs f side •Source in b-fixed system: (x,y,z) •Space/time entangled in pair system (xO,xS,xL) R s2 ~2 ~2 y K fp x x sin f y cos f ~ x~y sin 2f 2 out 2 b ~ ~ ~ R o2 ~ x 2 cos2 f ~y 2 sin 2 f 2 t 2 2 ~ x t cosf 2 ~y t sin f ~ x~y sin 2f ~ ~ R l2 ~z 2 2L ~z t 2L t 2 ~ ~ 2 R os ~ x~y cos 2f 12 ( ~y 2 ~ x 2 ) sin 2f ~ x t sin f ~y t cosf ~ ~ ~ ~ 2 R ol ( ~ x~z L ~ x t ) cosf ( ~y~z L ~y t ) sin f ~z t L t 2 ~ ~ R sl2 ( ~y~z L ~y t ) cosf ( ~ x~z L ~ x t ) sin f • explicit and implicit (xx(f)) dependence on f STAR HBT ! 13 February 2003266 (1998). Winter Workshop - Breckenridge CO Wiedemann, PRC57 ~ xx x d 4 x f ( x, K ) q( x ) q 4 d x f ( x, K)30 Recent analysis developments II Quick slide on pT vs kT cuts if Mercedes gets me a plot… Otherwise, forget it.. Not that important STAR HBT 13 February 2003 Winter Workshop - Breckenridge CO 31 Need a model of the freezeout- BlastWave BW: hydro-inspired parameterization of freezeout • longitudinal direction • infinite extent geometrically • boost-invariant longitudinal flow • Momentum space • temperature T • transverse rapidity boost (r , f ) ~ r cos( 2f ) s 0 a RY b RX • coordinate space • transverse extents RX, RY 2 • freezeout in proper time f 2 r cos f r sin s 0 s • ~revolution duration RY RXduration • emission 7 parameters describing freezeout 1 2 1 exp (~ r 1)/ as 0 dN ( ~ r) ~ exp 2 d 2 STAR HBT 13 February 2003 Winter Workshop - Breckenridge CO 32
