the hbt puzzle at rhic scott pratt, michigan state university
TRANSCRIPT
![Page 1: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/1.jpg)
The HBT Puzzle at RHIC
Scott Pratt, Michigan State University
![Page 2: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/2.jpg)
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 !
![Page 3: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/3.jpg)
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
![Page 4: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/4.jpg)
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
![Page 5: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/5.jpg)
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
Lifetime and Pressure
thermalbeam
sideout
vRvRR
//)( 2222
![Page 6: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/6.jpg)
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
![Page 7: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/7.jpg)
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
GROMITSimple hadronic
Boltzmann
• Underpredicts R !
• Underpredicts !
• Slightly overpredicts
STAR
Similar results: Molnar,Humanic, AMPT …
![Page 8: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/8.jpg)
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
Blast Wave Parameters
Unphysical acceleration???
F.Retiere,M.Lisa…
![Page 9: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/9.jpg)
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 ?
![Page 10: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/10.jpg)
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
![Page 11: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/11.jpg)
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
![Page 12: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/12.jpg)
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
![Page 13: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/13.jpg)
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)
![Page 14: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/14.jpg)
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
|);();(|
|),;,(|
![Page 15: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/15.jpg)
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
![Page 16: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/16.jpg)
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
![Page 17: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/17.jpg)
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)
![Page 18: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/18.jpg)
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
![Page 19: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/19.jpg)
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
![Page 20: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/20.jpg)
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)
![Page 21: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/21.jpg)
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>
![Page 22: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/22.jpg)
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
![Page 23: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/23.jpg)
SCOTT PRATT MICHIGAN SCOTT PRATT MICHIGAN STATE UNIVERSITYSTATE UNIVERSITY
p+ correlations Rout=8 fm, Rside = Rbeam = 4 fm
Positive for qside
Negative forqout
![Page 24: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/24.jpg)
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
![Page 25: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/25.jpg)
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
![Page 26: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/26.jpg)
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
![Page 27: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/27.jpg)
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
![Page 28: The HBT Puzzle at RHIC Scott Pratt, Michigan State University](https://reader030.vdocuments.site/reader030/viewer/2022032723/56649d0d5503460f949e15cc/html5/thumbnails/28.jpg)
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)