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πΞ Correlations in Heavy Ion Collisions and Ξ (1530) Puzzle. P. Chaloupka (NPI ASCR, Czech Republic), B. Kerbikov (ITEP, Russia), R. Lednicky (JINR & NPI ASCR), Malinina (JINR & SINP MSU), and M. Š umbera (NPI ASCR, Czech Republic)  PowerPoint PPT Presentation
πΞ Correlations in Heavy Ion Collisions and Ξ(1530) Puzzle
P. Chaloupka(NPI ASCR, Czech Republic), B. Kerbikov (ITEP, Russia),R. Lednicky (JINR & NPI ASCR), Malinina (JINR & SINP MSU), and M. Šumbera (NPI ASCR, Czech Republic)
V Workshop on Particle Correlations and Femtoscopy 1417 Octobre, 2009, CERN
nuclth 0907.0617
Outline
Motivation for femtoscopy with Ξ
Current experimental results of πΞ
FSI calculations
Comparison with data
Conclusions
Evolution of matter in HI collisions
t
~ fm/c
CGC (?)
Mixed phase
Hadron gas
Thermal freezeout
Chemical freezeout
Prethermal partonic state ~ fm/c
~ 7fm/c
GLP’60: enhanced ++ ,  vs + at small opening angles – interpreted as BE
enhancement
Kopylov and Podgortsky ’7175: settled basics of correlation femtoscopy
Analogy in Astronomy: Hanbury Brown and Twiss (HBT effect)
Correlation femtoscopy : measurement of spacetime characteristics R, c ~fm of particle production using
particle correlations due to the effects of QS and FSI
FEMTOSCOPY: Momentum correlations
q = p1 p2 , x = x1 x2
out transverse pair velocity vt
side
long beam
The corresponding correlation widths are usually parameterized in terms of the Gaussian correlation radii R_i:
We choose as the reference frame the longitudinal comoving system (LCMS)
The idea of the correlation femtoscopy with the help of identical particlesis based on an impossibility to distinguish between registered particles emitted from different points
Correlation strength or chaoticity
CF=1+exp(Ro2qo
2 –Rs2qs
2 Rl
2ql2
2Rol
2qoql)
Weights for QS only: P12=C(q)=1+(1)Scos qx >
( )
( )inv
inv
S QCF N
B Q
Final State Interaction
CF nnpp
Coulomb only
FSI is sensitive to source size and scattering amplitude. It complicates CF analysis but makes possible:
Femtoscopy with nonidentical particles:K,, p,, Ξ ...Study of the “exotic” scatterings: , K,, KK,, , p,Ξ , ..
Study of the relative spacetime asymmetries C+/C: Lednicky, Lyuboshitz et al. PLB 373 (1996) 30
Spherical harmonics method: Danielewicz, P. and Pratt, S., Phys. Rev C75 03490 (2007) Z.Chajevski and M.Lisa, PRC78 064903 A.Kisiel and D.A. Brown (2009) 0901.3527
k*=q/2
CF of identical particles sensitive to terms even in k*r* ( cos 2k*r*>) measures only dispersion of the components of relative separation r* = r1* r2* in pair cms
CF of nonidentical particles sensitive also to terms odd in k*r* measures also relative spacetime asymmetries  shifts <r*>
+  K+ K K0S p p
p
p
K0S
K
K+

+
What particle systems provide us with most interesting and direct information on dynamics of heavy ion collisions ?
Why πΞ ?models predict an early decoupling of multistrange
hadrons like Ξ (ΔS=2) dueto their small interaction cross section
They provide us with footprints of the early stages of evolution.
A window on πΞ scatteringlength
Experimental data (STAR) on πΞ correlations
Coulomb and strong ( Ξ*1530 ) final state interaction effects are present.
Ξ* (1530), P13 I(J)=1/2(3/2+), Γ=9.1 MeV
Centrality dependence is observed, particularly strong in the Ξ* region
M
mmMmmMk
2
])([])([ 2/1222/122*
*(1530)
200 GeV AuAu
Braz.J.Phys.37:925932,2007
M.Sumbera
Braz.J.Phys.37:925932,2007
M.Sumbera
πΞ model comparisonAnalysis of P. Chaloupka and M. Sumbera (Braz.J.Phys.37:925932,2007) :
Used FSI model:S. Pratt, S. Pertricioni Phys.Rev. C68, 054901 (2003)
+ Emission points from hydroinspired Blastwave constrained by ππHBT
Discrepancy in Ξregion, over predicts A
00 and A
11
Coulomb part in qualitative agreement
R = (6.7±1.0) fm ∆rout
= (5.6±1.0) fm
∆out
<0 Ξ emitted more on the outside –agrees with the flow Ξ scenario
Spherical decomposition
Z. Chajecki , T.D. Gutierrez ,
M.A. Lisa and M. LópezNoriega,
nuclex/0505009 )
A00 monopole – size 
A11 dipole  shift in outdirection 
Spherical decomposition
, Z. Chajecki , T.D. Gutierrez
,M.A. Lisa and M. LópezNoriega
( nuclex/0505009
A00  monopole – size
A11  dipole  shift in outdirection
The factors which have to be taken into account in π+Ξ FSI calculations:
 The superposition of strong and Coulomb interactions
 The presence of Ξ*(1530) resonance
 The spin structure of w.f. including spin flip
 The fact that π+Ξ state is a superposition of I=1/2
and I=3/2 isospin states and π+Ξ is coupled in π0Ξ0 and that the thresholdes of the two channels are nondegenerate
 The contribution from inner potential region
where the structure of the strong interaction is unknown.
1
1/2
( ) *1 1
1
( , ) ~ ( cos )iik r
ik r ii i i
ek r e f
r
The outgoing multichannel wave functions of π+Ξ system enter as a building block into CF
i=14, π+Ξ,
2 2( ) ( )( ) ( ) ( , ) ( ) ( , )i i i
i i
C k d rS r k r d rS r k r
k is a relative momentum of the pair
The outstate w.f.’s have the asymptotic form
π0Ξ0 without and with spin flip
Coulomb
Ξ*(1530)π0Ξ0 π+Ξ
EStrong S wave Strong P wave
Pwave is dominated by Ξ*(1530)
Ξ*(1530)
πΞ Ξ*(1530)The low energy region of interaction up to the resonance is dominated by S and Pwaves.
Therefore the w.f. contains 2 phase shifts with I = 1/2, 3/2 for Swave and 4 phase shifts with I = 1/2, 3/2 and J = 1/2, 3/2 for Pwave (J = L ± 1/2 is the total momentum).
To reduce the number of parameters we have assumed that the dominant interaction in Pwave occurs in a state with J = 3/2, I = 1/2 containing Ξ*(1530) resonance. Since the parameters of Ξ*(1530) are known from the experiment we are left with two Swave phase shifts which are expressed in terms of the two scattering lengths a1/2 and a3/2 with isospin I=1/2 and I=3/2 correspondingly.
The structure of π+Ξ Wave Function
The wave function
here is the pure Coulomb w.f., k1 and k2 are the c.m. momenta in and π0Ξ0 channels;spherical harmonics correspond to the reversed direction of the vector k,
2224( ) * 0 0 1*
0 0 0 1 1 1 1 1 11
22
0 0 1*20 0 0 1 1 1 1 1 1
1
2 2( , ) ( , )
33
2 2
33
Couli
k r k r T Y T Y T Y
kR Y R Y R Y
k
Coulπ+Ξ
( , )m ml lY Y
1
1
( ) ( )1 1 1 1 1
( )1/2 ( )1 2 1 2 2
( ln 2 /2)( )
( , ) 4 ( ) ( , ) /
( , ) ( / ) 4 ( ) (0, ) /
( , )
l
l
l
ill l
ill i l
i ll
i e H
i e H
H e
combination of the regular and singular Coulomb functions Fl and Gl
ρ1 =k1r, ρ2 =k2r, η =(a1k1) 1, a1=214 fm is a Bohr radius of the π+Ξ
system taking into account the negative sign of the Coulomb repulsion.
The wave function2224
( ) * 0 0 1*0 0 0 1 1 1 1 1 1
1
22
0 0 1*20 0 0 1 1 1 1 1 1
1
2 2( , ) ( , )
33
2 2
33
Couli
k r k r T Y T Y T Y
kR Y R Y R Y
k
1/21 1 2
1 10 0
1 2 1 2
/ 2 ( ) / 2,
/ 2 / 2
, 2 / 3, / 3
T RE E i E E i
The quantities
contain the elastic 1 → 1 and inelastic 1 → 2 scattering amplitudes fl{J;11} and fl
{J;21}. For the Swaves (l=0, J=1/2), they are expressed through the scattering lengths a±1/2 and a±3/2 in a similar way as in pionnucleon scattering.
For the resonance Pwave
;11* ;21*1 1 2, ( )J J
l l l lT k f R k k f
Ξ*(1530)
= 2 Γ/3, Γ2=Γ/3
The inner region correctionThe above expression describes the region r > ε ~ 1~fm where the strong potential is assumed to vanish.In the inner region r < ε , we substitute by and take into account the effect of strong interaction in a form of a correction which depends on the strong interaction time (expressed through the phase shift derivatives) and can be calculatedwithout any new parameters unless the Swave effective radii are extremely large. It is important that the complete CF does not depend on ε provided the sourcefunction is nearly constant in the region r< ε . (MC procedure was checked using exact calculations within Mathematica)
2
Coul
Without introduction of the correction, the resonance region exhibits clear interference of Coulomb and strong interactions,which is not observed in the data !
How to calculate CF numerically
3/2 3 1 2 2( ) (8 ) exp( / 4 )S r R r R
2) HYDJET++ http://cern.ch/lokhtin/hydjet++ I.Lokhtin, L.Malinina, S.Petrushanko, A.Snigirev, I.Arsene, K.Tywoniuk, eprint arXiv:0809.2708, Comput.Phys.Commun.180:779799,2009. The soft part of HYDJET++ event represents the "thermal" hadronic state FASTMC: Part I: N.S. Amelin et al, PRC 74 (2006) 064901; Part II: N.S. Amelin, et al. PR C 77 (2008) 014903
1) source is approximated with Gaussian in PRF
3) Standard UrQMD (v2.2) output of freezeout particles http://www.th.physik.unifrankfurt/~urqmd
FSI code Richard Lednicky's code for calculation of the two particle
correlations due to QS and FSI
Source models:
πΞ FSI model comparison
The influence of Swave scattering lengths parameters on CF in Coulomb region.
source is approximated with Gaussian in PRF
Ro = Rs = Rl = 7 fm
At present experimental errors, the CF at R > 7 fm is practically independent of the Swave scattering parameters.
Ro = Rs = Rl = 2 fm
source is approximated with Gaussian
πΞ FSI model comparison
Similarly to the FSI model S. Pratt's (PRC68, 054901(2003) )our calculations are in agreement with he data in the lowk Coulomb region. Contrary to this model, they are however much closer to the experimental peak in the Ξ*(1530) region though, they still somewhat overestimate this peak (at R=7 fm. Exp. ~1.05, Model ~1.2)The predicted peak is however expected to decrease due to a strong angular asymmetry of a more realisticsource function obtained from Blastwave like simulations.
Angular asymmetry in Blastwavelike model HYDJET++
Consider Source model: Gaussian in PRF (at R=7 fm. Exp. ~1.05, Model ~1.2, m, Model with angular dependence ~ 1.05)
πΞ FSI model comparison
– HYDJET++– UrQMD (v2.2)
Conclustions & Plans•Using a simple Gaussian model for the source function, we have reasonably described the experimental πΞ CF.
•Estimated the emission source radius (~7fm) and tested the sensitivity to the low energy parameters of the strong interaction.
•The predicted peak is however expected to decrease due to a strong angular asymmetry of a more realistic source function obtained from the Blastwave like simulations.
•Blastwave like model HYDJET++ (soft part) allows to get the
reasonable description of the πΞ CF in the whole k* region.
•UrQMD 2.2 model also provides reasonable description of CF.
•Spherical harmonic method will be applied to extract spacetime shifts.
Additional slides
Reason of differences withS. Pratt, S. Petriconi (PRC68, 054901(2003) )
1. The approach is of course the same, the resulting CF formula coincides with ours if corrected for misprints.
2. So there is likely a bug in the PrattPetriconi code. As for our calculations, they have been checked with the help of MATHEMATICA. Criterium of correcteness is independence of ε
Boost to pair rest frame
Particle 1source
Particle 2Source
Separation between particle1 and 2 andBoost to pairRest frame
r*out = T (rout – T t)
2 free parameters in the Gaussian approximationWidth of the distribution in pair rest frameOffset of the distribution from zero
(slide from F.Retiere QM05)
SpaceTime shifts in pair rest frame πΞ, πK, πp, KpπΞ, πK, πp, Kp
Within HYDJET++ model the combined freezeout scenario
describes better the observed in experiment πΞ πΞ spacetime differences;
π, K, p π, K, p freezeout atfreezeout at TTthth=100 MeV =100 MeV
HYDJET++: hydro + part related to the partonic states The soft part of HYDJET++ event represents the "thermal" hadronic state FASTMC: Part I: N.S. Amelin, R. Lednisky, T.A. Pocheptsov, I.P. Lokhtin, L.V. Malinina, A.M. Snigirev, Yu.A. Karpenko, Yu.M. Sinyukov, Phys. Rev. C 74 (2006) 064901; Part II: N.S. Amelin, R. Lednisky, I.P. Lokhtin, L.V. Malinina, A.M. Snigirev, Yu.A. Karpenko, Yu.M. Sinyukov, I.C. Arsene, L. Bravina, Phys. Rev. C 77 (2008) 014903 http://uhkm.jinr.ru
The hard, multipartonic part of HYDJET++ event is identical to the hard part of Fortranwritten HYDJET (PYTHIA6.4xx + PYQUEN1.5) : I.P.Lokhtin and A.M.Snigirev, Eur. Phys. J. C 45, 211 (2006), http://cern.ch/lokhtin/pyquen, http://cern.ch/lokhtin/hydro/hydjet.html
Official version of HYDJET++ code and webpage with the documentation: http://cern.ch/lokhtin/hydjet++
The complete manual: I.Lokhtin, L.Malinina, S.Petrushanko, A.Snigirev, I.Arsene, K.Tywoniuk, eprint arXiv:0809.2708, Comput.Phys.Commun.180:779799,2009.
HYDJET++ is capable of reproducing the bulk properties of multiparticle system created in heavy ion collisions at RHIC (hadron spectra and ratios, radial and elliptic flow, momentum correlations), as well as the main highpTobservables.
The 2particle momentum CF is defined as a normalized ratio of correspondingtwo and single particle distributions.
CF q , k = γN 2 p i , p j
N 1 p i N 2 p j
CF p1 , p2 =1 λ exp −R out2 qout
2 −R side2 q side
2 −Rlong2 q long
2 −2R out , long2 qout q long
q= pi− p j
k=1/2 pi p j CF ∞=1
1D CF Most simple parametrization:CF q ,k =1 λ k exp−Rinv
2 qinv2
q inv2 =−q2
strength of correlations
Decompose q into components:QlongLong : in beam directionQoutOut : in direction of pair transverse momentumQsideSide : qLong & qOut
Parametrizations of CF
CF= γA2 pi , p j B 2 p i , p j
Z. Chajecki , T.D. Gutierrez , M.A. Lisa and M. LópezNoriega, nuclex/0505009 Z. Chajecki , T.D. Gutierrez , M.A. Lisa and M. LópezNoriega, nuclex/0505009
200GeV AuAu different centralities
Ξ
Spherical decomposition – accessing emission shift
Different Alm
coefficients correspond to different symmetries of the source
A00  monopole – size
A11  dipole  shift in outdirection
A11
≠ 0  shift in the average emission point between and
Simplified idea of CF asymmetry(valid for Coulomb FSI)
x
x
v
v
v1
v2
v1
v2
k*/= v1v2
Ξ
Ξ
k*x > 0v > vp
k*x < 0v < vp
Assume emitted later than Ξ or closer to the center
Ξ
Ξ
Longer tint
Stronger CF
Shorter tint Weaker CF
CF
CF
Modified slide of R.Lednicky
flow
CFasymmetry for charged particlesAsymmetry arises mainly from Coulomb FSI
CF Ac() exp(ik*r*)F(i,1,i)2
=(k*a)1, =k*r*+k*r*F 1+r*/a+k*r*/(k*a)r*a
k*1/r* Bohr radius
}
±226 fm for p±214 fm for Ξ
CF+x/CFx 1+2 <x* /ak* 0
x* = x1*x2* rx* Projection of the relative separation r* in pair cms on the direction x
In LCMS (vz=0) or x  v: x* = t(x  vtt)
CF asymmetry is determined by space and time asymmetries
Modified slide of R.Lednicky
Shift <x in out direction is due to collective transverseflow & higher thermal velocity of lighter particles
y
X
1
2
Source
For QS only: P12=C(q)=1+(1)Scos qx>
pp
Momentum correlations of identical particles QS only
K1
xb
Two planewaves:
ππ
1/R
C q =N 2 k 1 , k 2
N 1 k 1 N 2 k 2 q=k 1−k 2
C ∞ =1
The 2particle correlation function C(q) is defined as a normalized ratio of the corresponding two and single particle distributions.
K2K1
K2
Out: direction of the mean transverse momentum of the pairSide: orthogonal to outLong: beam direction
The corresponding correlation widths are usually parameterized in terms of the Gaussian correlation radii:
The above wave function corresponds to r> R< 1 fm. Can we say anything about without knowning the small distance dynamics ? Luders and Wigner solved the problem for us:
We know δ for Ξ*(1530):
Then
The Explanation:
kr
kdk
dRdr
R
(2sin2
11
0
2
2)( )( Rr
0
2/
EEarctg
RrRr
rqrdSrqrSrdqC2)(2)( ),()0(),()()(
4/)(
2/~
220
EE
And see the last figure
à la LW