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

The HBT Puzzle at RHIC

Scott Pratt, Michigan State University

SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY

OUTLINEOUTLINE

• 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 !


Foundation of HBT

23 ),(),(),( rqrvgrdqvC

GOAL of HBT: Invert C(v,q) to obtain g(v,r)

g(v,r) samples relative

positions


Review some vocabulary

Rbeam : parallel to beamRout: to beam, & parallel to Ppair

Rside: to beam, & to Ppair


Lifetime and Pressure

thermalbeam

sideout

vRvRR

//)( 2222


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 conclusions:P. Kolb, P. Huovinen,A.Dumitru, S.Soff and S. Bass

STAR


GROMITSimple hadronic

Boltzmann

• Underpredicts R !

• Underpredicts !

• Slightly overpredicts

STAR

Similar results: Molnar,Humanic, AMPT …


Blast Wave Parameters

Unphysical acceleration???

F.Retiere,M.Lisa…


Essence of the RHIC puzzle

How can the fireball grow from R=6 fm to R=13 fm in ~ 10 fm/c ?


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


Bad Experimental Analysis??

1. Experimental Resolution• Tested with MC• Experiments are consistent

2. Coulomb “Correction”• Originally done incorrectly,

but only 10% effect


Bad Theory??

1. Higher-order symmetrization

2. Independent emission

3. Equal-time approximation

4. Smoothness

5. Interact only two-at-a-time

23 ),(),(),( rqrvgrdqvC

Based on 5 approximations


Bad Theory??1. Higher-order symmetrization S.P. PLB(93)

Only important at q>200, where fmax >1

Permutation cycle

Cutting cycle diagram yields Gm(p1,p2)


Bad Theory??2. Independent emission

• Should be good for large sources at moderate pt

• Coherent sources?? (unlikely to extend over large V)

ba

baff

bfafba

fbafba

pxTpxTxdxd

ppxxTxdxd

221

44

221

44

|);();(|

|),;,(|


Bad Theory??

3. Equal-time approximation

• Not an issue for pure HBT or classical Coulomb

),(),;,( 2/)(21

frame, mass ofcenter In

barelttiM

ba xxqeppxxU bainv


Bad Theory??4. Smoothness

• Not necessary for Coulomb trajectories• Not an issue for pure HBT with large sources

S.P., PRC(2000)

),(),(),(),(

)2/()2/(),( *4

baba

f

xipff

xpSxpSxqpSxqpS

exxTxxTxdxpS


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)


Shortcomings of Hydro Treatments

1. Lack of viscosity• Underpredicts transverse acceleration

• Underpredicts lifetime (vtherm,z would shrink)

2. Assume boost invariance• Should cut off tails of source at large z• Neglects longitudinal acceleration

3. “Emissivity” between phases• Shock wave treatments assume maximum burn rate

4. Neglect mass shifts• Underpredicts phase space density

Help explain small

Help explain small <>

Help explain small size


Ultra-Stiff Equation of State?

No Latent Heat• Not melting vacuum??

• Still difficult to get large Rside and small Rout & Rlong


Alternate Measurement of Rout/Rlong/Rside

Any cos(qr) dependence in |(q,r,cos)|2

provides leverage for determining shape

For r outside interaction range ,

),(1)(cos)12(1

),(),( 20 rqePi

qrrqrq ini

S.P. and S.Petriconi, PRC(2003)

Phase shifts determine (even for small r)


pK+ correlations Rout=8 fm, Rside = Rbeam = 4 fm

Classical approximation works well for Q > 75 MeV/c

~1-(e2/q2)<1/r>


pK+ correlations Rout=8 fm, Rside = Rbeam = 4 fm

Ratio ~ (Rout/Rside)2

Independent of Qinv for large Q


p+ correlations Rout=8 fm, Rside = Rbeam = 4 fm

Positive for qside

Negative forqout


Moments

),()(4)(

)(cos1)cos,,(421

),(

),()()(),(1)()(

)(1)cos,,(1)(

,2

,

22

,,

,,

23

rqFrgdrrqC

PrqdrrrqF

YrgdrgYqCdqC

rgrqrdqC

mm

qrqr

rmrm

qmqm

qr

Standard formalism:

Defining,

Using identities for Ylms,

Simple correspondence! Danielewicz and Brown


Moments

• L=0

• L=1, M=1

• L=2, M=0,2

• L=3, M=1,3

Angle-integrated shape

Lednicky offsets

Shape (Rout/Rside, Rlong/Rside)

Boomerang distortion


Blast Wave Moments

• (z -z) CL+M=even(q) = 0

• (y -y) Imag CL,M = 0

PRELIMINARY


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


SUMMARY

• Some correlation candidates:

– q < 25 MeV/c (HBT, and scattering length),KK,pp,pK-,p,KK,KsKs,KKs,

– 25 < q < 75 MeV/c (Coulomb tails),KK,pp,pK+,p

– Sharp resonances(K+K-),(p),(),K*(K),*(p),*(),5Li(p)

– Coalescenced(pp),1405(pK)

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

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