The HBT Puzzle at RHIC Scott Pratt, Michigan State University.
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Transcript of 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 !
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
Foundation of HBT
23 ),(),(),( rqrvgrdqvC
GOAL of HBT: Invert C(v,q) to obtain g(v,r)
g(v,r) samples relative
positions
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
Review some vocabulary
Rbeam : parallel to beamRout: to beam, & parallel to Ppair
Rside: to beam, & to Ppair
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
Lifetime and Pressure
thermalbeam
sideout
vRvRR
//)( 2222
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
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
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
GROMITSimple hadronic
Boltzmann
• Underpredicts R !
• Underpredicts !
• Slightly overpredicts
STAR
Similar results: Molnar,Humanic, AMPT …
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
Blast Wave Parameters
Unphysical acceleration???
F.Retiere,M.Lisa…
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
Essence of the RHIC puzzle
How can the fireball grow from R=6 fm to R=13 fm in ~ 10 fm/c ?
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
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
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
Bad Experimental Analysis??
1. Experimental Resolution• Tested with MC• Experiments are consistent
2. Coulomb “Correction”• Originally done incorrectly,
but only 10% effect
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
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
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
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)
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
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
|);();(|
|),;,(|
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
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
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
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
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
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)
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
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
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
Ultra-Stiff Equation of State?
No Latent Heat• Not melting vacuum??
• Still difficult to get large Rside and small Rout & Rlong
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
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)
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
pK+ correlations Rout=8 fm, Rside = Rbeam = 4 fm
Classical approximation works well for Q > 75 MeV/c
~1-(e2/q2)<1/r>
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
pK+ correlations Rout=8 fm, Rside = Rbeam = 4 fm
Ratio ~ (Rout/Rside)2
Independent of Qinv for large Q
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
p+ correlations Rout=8 fm, Rside = Rbeam = 4 fm
Positive for qside
Negative forqout
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
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
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
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
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
Blast Wave Moments
• (z -z) CL+M=even(q) = 0
• (y -y) Imag CL,M = 0
PRELIMINARY
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
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
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
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)