# Presentation: 741978

## HBT

- Dan Magestro, The Ohio State University

**Overview of HBT interferometry **
**The SPS & RHIC HBT program**
**Recent “standard” HBT results**
**The RHIC HBT puzzle**
**New directions: ******** dependence, pp vs. AuAu, non-Id, ******** HBT**

## Hanbury Brown-Twiss interferometry

**Hanbury Brown-Twiss interferometry**

**Two-particle interferometry: p-space separation ******** space-time separation**

## The HBT program at SPS and RHIC

**Technique: Study interferometry as **_**differentially**_** as possible**

**RHIC: Fertile ground for correlations studies**

| beam energy | onset effects, transition phenomena |
| --- | --- |
| transverse momentum (kT) | dynamics, collective expansion |
| particle species | differences in emission |
| collision system | origins of correlations, phase space  |
| azimuthal angle | spatial anisotropies, constrain system evolution |

**HBT in HI collisions: Explore space-time evolution of system**
- Geometry: spatial distribution of emission points
- Dynamics: hot & dense early stages reflected in freeze-out pattern
- Lifetime: sensitive to nature of phase transition

##  HBT excitation function

**STAR, PRL 87 (2001) 082301**

## The kT (mT) dependence

**x-p correlations arise mostly due to collective expansion**
- Radial flow pushes higher-pT particles more at surface

**Analytical expressions**
- System lifetime (Sinyukov)

- Transverse flow velocity, system size

- expansion duration

- transverse rapidity

**Little difference from SPS to RHIC**
- Consistent lifetimes: f ~ 8-10 fm/c

**m****T**** scaling ~ holds up to 1 GeV at SPS**

## HBT at √s = 200 GeV

**PHENIX ********-HBT: k****T**** , centrality dependence at 200 GeV****(nucl-ex/0401003)**
- New Coulomb treatment causes ~ 10-15% change in Rout/Rside

**STAR ********-HBT:**** ****k****T**** , centrality and ********  dependence at 200 GeV (later)****(nucl-ex/0312009)**
- Sufficient statistics for triple-differential analysis!

## A highlight from this week

**Burt Holzman, PHOBOS**

## The RHIC HBT Puzzle - 1

**Hydrodynamics at RHIC**
- Can describe soft pT spectra and v2 consistently, for several particle species
- Fast thermalization in partonic phase (~1⁄2 fm/c), lives for ~15 fm/c
- Underpredicts Rside and its kT dependence
- Overpredicts Rout and Rlong by factor ~2

**Hydro doesn’t work. Why is this a puzzle?**
- Expanding fireball, undergoing phase transition, should _at least_ cause Rout > Rside

## The RHIC HBT Puzzle - 2

**The RHIC HBT Puzzle - 2**

**Default initial conditions (fit p****T**** & v****2****)**

- Kolb & Heinz, QGP3 (nucl-th/0305084)

- √s = 130 GeV

- STAR

- PHENIX

- 4

- 8

- 0.2

- 0.4

- 0.6

- 0.8

- kT (GeV/c)

**Thermalize faster, or initialize Hydro with non-zero flow**

**Freeze-out directly at hadronization**
- Conflicts with fits to particle spectra

_**Can HBT puzzle be resolved in Hydro? **_

**Hydro + partial chemical equilibrium**Hirano and Tsuda, PRC 66 (2002) 054905
- Chemical potentials maintain proper abundances through hadronic evolution
- Smaller Rlong, but fails Rout , Rside

- Rout (fm)

- Rside (fm)

- Rlong (fm)

## The RHIC HBT Puzzle - 3

**The RHIC HBT Puzzle - 3**

**Parton cascade with opacity**Molnar and Gyulassy, nucl-th/0211017
- Pion freeze-out distribution sensitive to transport opacity 

- √s = 130 GeV

- STAR

- PHENIX

- 4

- 8

- 0.2

- 0.4

- 0.6

- 0.8

- kT (GeV/c)

**Positive x****o****-t correlation ?!**Lin, Ko and Pal, PRL 89 (2002) 152301

_**Alternative approaches **_

- Rout (fm)

- Rside (fm)

- Rlong (fm)

## The RHIC HBT Puzzle - 4

**The RHIC HBT Puzzle - 4**

**Blast-wave parametrization**Retiere and Lisa, nucl-th/0312024
- Longitudinal boost invariance
- Relative particle abundances not fixed
- Constant parameters at freeze-out

- √s = 130 GeV

- STAR

- PHENIX

- 4

- 8

- 0.2

- 0.4

- 0.6

- 0.8

- kT (GeV/c)

**Buda-Lund Hydro parameterization**Csorgo et al, nucl-th/0311102
- Not boost invariant (Hubble flow)
- Freeze-out smeared in temperature

_**Hinting at the solution **_

- Rout (fm)

- Rside (fm)

- Rlong (fm)

| Tf | 104  3 MeV |
| --- | --- |
| f | 8.9  0.3 fm/c |

| To | 214  7 MeV |
| --- | --- |
| f | 6.0  0.2 fm/c |

## Azimuthally sensitive  HBT

**Azimuthally sensitive ******** HBT**

**HBT(********): probe spatial anisotropy at freeze-out**Wiedemann, PRC 57 (1998) 266
- Freeze-out shape probes nature & timescale of system evolution
- How much (if any) initial spatial deformation survives system expansion?

- Initial geometry → aniosotropies in pressure gradients

- 

- 

- Preferential in-plane expansion → decreases spatial anisotropy

- 

- Freeze-out source shape via HBT → measure of pressure, expansion time

- (model-dependent)

- _late rescattering_

- _hydrodynamic expansion_

- time

**x**

- _beam into screen_

- Rside2

## HBT(): Centrality & kT dependence

- STAR Collaboration, nucl-ex/0312009

## Fourier coefficients of HBT() oscillations

**0****th****-order FC: centrality & k****T**** dependence mirrors ********-integrated analyses; quantitatively consistent**
**Relative amplitudes increase from central to peripheral collisions**

- means

- relative amplitudes

**STAR Collaboration, nucl-ex/0312009**

## Fourier coefficients of HBT() oscillations

******initial**** = ********final**

**STAR Collaboration, nucl-ex/0312009**

**Out-of-plane sources at freeze-out**
- Pressure and/or expansion time was not sufficient to quench initial shape
**From v****2**** we know...**
- Strong in-plane flow → significant pressure build-up in system

-  **Short expansion time plays dominant role****     in out-of-plane freeze-out source shapes**

**Evolution of eccentricity ****→ consistent with ******** ~ 9 fm from R****long**** Sinyukov fit**

## Universal pion freeze-out

- Use HBT radii to estimate freeze-out volume Vf

**CERES proposed a simple ansatz to investigate if critical mean free path for pions ********f**** drives freeze-out**

**Does this work for lighter systems?**

## HBT in p+p collisions at RHIC

**HBT in p+p collisions at RHIC**

**RHIC: HBT for 3 very different systems at same c.m. energy & with same detector**
**k****T**** dependence of HBT radii presumably arises in different ways **

**T. Gutierrez for STAR Coll, poster**

- Rout

- Rside

- Rlong

**p+p**

## p+p → d+Au → Au+Au

- All three systems exhibit similar kT dependence (?!)
- Systematic study underway to assess “Gaussian-ness” of correlation

**T. Gutierrez for STAR Coll, poster**

- preliminary

## Same universal freeze-out in p+p, d+Au ?

**V****f**

**N******

**CERES, PRL 90 (2003) 022301**

******f**** ~ 1 fm seems to hold for light systems as well (!)**
**Why are p+p, d+Au and Au+Au so similar?**

**Check CERES’ ansatz using dN/dy’s and HBT radii for p+p and d+Au**
- dN/dy’s taken from power-law fits to STAR pT spectra (nucl-ex/0309012)

## Non-identical particle correlations

**Study emission asymmetries with final-state interactions**
- Strong radial flow induces species-dependent x-p correlations

- _Case 1_Particle emitted closer to center is _**slower**_

- _Case 2_Particle emitted closer to center is _**faster**_

- Effective interaction time _larger_
- Stronger correlation

- Effective interaction time _shorter_
- Weaker correlation

**The two cases can be discriminated**
- Two correlation functions: “lighter particle faster”, “lighter particle slower”
- Compare correlation strength of two CF’s

## Non-identical particle correlations

**“****pion faster” shows stronger correlation**
-  pions on average emitted nearer to source center
- Arises naturally in collective expansion picture
**Similar studies are underway for many particle combinations**
- Exotic correlations like - can yield information about nature of  flow

**pion faster**

**PRELIMINARY**

**pion slower**

**A. Kisiel for STAR**

- Au+Au, √s = 200 GeV

## HBT of direct photons

**Photon interferometry in heavy ion collisions**
- Probes initial state, not final-state interactionsSrivastava and Kapusta; Timmerman *et al*; Peressounko PRC 67 (2003) 014905
- A major challenge experimentally!
- Low relative direct photon yield
- Many sources of small-Qinv pairs: photon conversions, 0 HBT, mis-id ’s, resonance decays, etc.

**WA98: First ********-HBT in R.H.I.C. **
- Rinv quantitatively similar to  HBT in same kT region
- → Soft photons arise in latestages of collision

## Conclusions

**Identical-meson HBT interferometry**
- HBT is _the_ observable that doesn’t fit into dynamic picture at low pt
- p+p, d+Au and Au+Au exhibit similar kT dependence, similar freeze-out pion mean free path
**Azumithally sensitive HBT**
- Evidence for out-of-plane extended sources at freeze-out
- Short-lived system “remembers” its initial spatial anisotropy
**Non-identical particle correlations**
- Lighter particles emitted closer to center
**Direct photon interferometry**
- Similar Rinv for - and -HBT; access to low-pT direct photon yield

- “HBT brings us from enlightenment to tragedy, and back to enlightenment, on a time scale of four years.”
- Reinhard Stock

- The HBT puzzle is three years old.  2004 is looking promising!

**BACK-UPS**

## Recent “standard” HBT results - SPS 

**NA44:  High m****T**** ********- and p-HBT ****(**nucl-ex/0305014)

## Recent “standard” HBT results - SPS 

**NA49:  Kaon HBT ****(**Phys.Lett. B 557 (2003) 157)
- Less influence from resonances & feeddown

**New results shown this week**
- HBT @ 20, 30, 40, 80, 158 AGeV (!)

- T = 120  12 MeV → f ~ 9.5  1 fm, T ~ 0.55

## A highlight from this week

## Refined Coulomb treatment

**Final-state interactions (Coulomb, strong) influence correlation signal**
**Traditionally, all pairs in CF corrected for Coulomb**

- This over-corrects the CF → increases width, decreases radii

## Collision timescale

**Collision timescale**

- 0

- 5

- 10

- 15

- Evolution time (fm/c)

- Hydrodynamical model

- Blast-wave fit

- Rlong Sinyukov fit

- c

- eq

- HBT()

- Buda-Lund

## HBT() predictions from hydrodynamics

**HBT(********) predictions from hydrodynamics**

**Hydro: Freeze-out shape sensitive to lifetime, initial conditions**
- kT dependence probes different regions of space-time source
- Realistic hydro parameters: Source orientation reflected in HBT() oscillations

**Heinz & Kolb, PLB 542 (2002) 216**

- Hydro calculations initialized with fits to RHIC spectra & v2

## HBT() experimental technique

**Construct correlation functions for discrete bins w.r.t. reaction plane angle**** **
**Apply HBT formalism to extract R****ij****2**** vs. ******
- Additional out-side cross-term

**Oscillations of R****ij****2**** reflect spatial anisotropies in system**
- Oscillations governed by geometrical symmetries

- Rside2

- Out-of-plane

- In-plane

-  = 0°

-  = 90°

- Rside (large)

- Rside (small)

## A simple estimate – 0 from init and final 

- BW → X, Y @ F.O.  (X > Y)
- hydro: flow velocity grows ~ t
- From RL(mT): 0 ~ 9 fm/c
- consistent picture
- Longer or shorter evolution times
-  inconsistent
- toy estimate: 0 ~ 0(BW)~ 9 fm/c