The HBT Puzzle at RHIC

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The HBT Puzzle at RHIC
Scott Pratt, Michigan State University
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OUTLINE

• Brief review
• What is the HBT Puzzle?
• Can we blame theorists?
• Can we blame experimentalists?
• Are we leaving something out of the dynamics?
• New HBT Methods Seize the moments !

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Foundation of HBT
GOAL of HBT Invert C(v,q) to obtain g(v,r)
g(v,r) samples relative positions
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Review some vocabulary
Rbeam parallel to beam Rout ? to
beam, parallel to Ppair Rside ? to
beam, ? to Ppair
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Lifetime and Pressure
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HYDRO and RQMD

• Compared to STAR
• Rbeam 80 too large
• Rside 10 too large
• Rout 40 too large

D. Teaney (EOS has phase transition)Similar
conclusionsP. Kolb, P. Huovinen,A.Dumitru,
S.Soff and S. Bass
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GROMITSimple hadronic Boltzmann

• Underpredicts R? !
• Underpredicts ?t? !
• Slightly overpredicts Dt

Similar results Molnar,Humanic, AMPT
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Blast Wave Parameters
F.Retiere,M.Lisa
Unphysical acceleration???
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Essence of the RHIC puzzle
How can the fireball grow from R6 fm to R13
fm in 10 fm/c ?
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Solving the RHIC HBT Puzzle

• Bad Experimental Analysis?
• Bad theory?
• Is something missing from hydro treatments?
• Could EOS be ultra stiff?
• Alternate Measurement of Rout/Rlong/Rside

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Bad Experimental Analysis??

• Experimental Resolution
• Tested with MC
• Experiments are consistent
• Coulomb Correction
• Originally done incorrectly, but only 10 effect

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Bad Theory??
Based on 5 approximations

• Higher-order symmetrization
• Independent emission
• Equal-time approximation
• Smoothness
• Interact only two-at-a-time

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Bad Theory??

• Higher-order symmetrization S.P.
  PLB(93) Only important at qgt200,
  where fmax gt1

Permutation cycle
Cutting cycle diagram yields Gm(p1,p2)
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Bad Theory??

• 2. Independent emission
• Should be good for large sources at moderate pt
• Coherent sources?? (unlikely to extend over large
  V)

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Bad Theory??

• 3. Equal-time approximation
• Not an issue for pure HBT or classical Coulomb

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Bad Theory??

• 4. Smoothness
• Not necessary for Coulomb trajectories
• Not an issue for pure HBT with large
  sourcesS.P., PRC(2000)

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Bad Theory??

• 5. Interact only two-at-a-time
• Assumes Hard Interactions with 3rd body
• Mean Field effects cancel in Glauber
  approximationR.Lednicky et al., PLB(96)

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Shortcomings of Hydro Treatments

• Lack of viscosity
• Underpredicts transverse acceleration
• Underpredicts lifetime (vtherm,z would shrink)
• Assume boost invariance
• Should cut off tails of source at large z
• Neglects longitudinal acceleration
• Emissivity between phases
• Shock wave treatments assume maximum burn rate
• Neglect mass shifts
• Underpredicts phase space density

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Ultra-Stiff Equation of State?

• No Latent Heat
• Not melting vacuum??
• Still difficult to get large Rside and small Rout
  Rlong

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Alternate Measurement of Rout/Rlong/Rside
S.P. and S.Petriconi, PRC(2003)

• Any cos(qqr) dependence in f(q,r,cosq)2
• provides leverage for determining shape

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pK correlations
Rout8 fm, Rside Rbeam 4 fm
1-(me2/q2)lt1/rgt
Classical approximation works well for Q gt 75
MeV/c
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pK correlations
Rout8 fm, Rside Rbeam 4 fm
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pp correlations
Rout8 fm, Rside Rbeam 4 fm
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Moments
Standard formalism
Defining,
Using identities for Ylms,
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Moments

• L0
• L1, M1
• L2, M0,2
• L3, M1,3

Angle-integrated shape
Lednicky offsets
Shape (Rout/Rside, Rlong/Rside)
Boomerang distortion
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Blast Wave Moments

• (z ? -z) CLMeven(q) 0
• (y ? -y) Imag CL,M 0

PRELIMINARY
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SUMMARY

• HBT Puzzle remains elusive
• Theorists must
• Finish checking validity of HBT formalism
• Add features to hydro treatments(viscosity,
  emissivity, non-Bjorken IC)
• Further investigate non-idenctical particles
• Experimentalists should
• Finish analyses of KK interferometry
• Perform shape analyses with non-identical
  particles

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SUMMARY

• Some correlation candidates
• q lt 25 MeV/c (HBT, and scattering length)p?
  p?,K?K?,pp,pK-,pL,KK-,KsKs,K?Ks,LL
• 25 lt q lt 75 MeV/c (Coulomb tails)p?
  p?,K?K?,pp,pK,pp
• Sharp resonancesf(KK-),D(pp),r(pp-),K(Kp),X(X
  p),S(Lp),5Li(pa)
• Coalescenced(pp),L1405(pK)