1. π-Ξ 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 14-17 Octobre, 2009, CERN nucl-th 0907.0617

2. Outline Motivation for femtoscopy with Ξ Current experimental results of π-Ξ FSI calculations Comparison with data Conclusions

3. Evolution of matter in HI collisions t  ~  fm/c CGC (?)‏ Mixed phase Hadron gas Thermal freeze-out Chemical freeze-out Prethermal partonic state  ~  fm/c  ~ 7  fm/c GLP’60: enhanced  +  +,  -  - vs  +  - at small opening angles – interpreted as BE enhancement Kopylov and Podgortsky ’71-75: settled basics of correlation femtoscopy Analogy in Astronomy: Hanbury Brown and Twiss (HBT effect)‏ Correlation femtoscopy : measurement of space-time characteristics R, c  ~fm of particle production using particle correlations due to the effects of QS and FSI

4. 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 co-moving system (LCMS)‏ The idea of the correlation femtoscopy with the help of identical particles is based on an impossibility to distinguish between registered particles emitted from different points Correlation strength or chaoticity CF=1+ exp(-R o 2 q o 2 –R s 2 q s 2 -R l 2 q l 2 -2R o l 2 q o q l )‏ Weights for QS only: P 12 =C(q)=1+(-1) S  cos q  x >

5. Final State Interaction CFCF n p 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 space-time 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 space-time asymmetries - shifts

6. What particle systems provide us with most interesting and direct information on dynamics of heavy ion collisions ? Why π-Ξ ? models predict an early decoupling of multi-strange hadrons like Ξ (ΔS=2) due to their small interaction cross section They provide us with footprints of the early stages of evolution. A window on π-Ξ s cattering length

7. Experimental data (STAR) on π-Ξ 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  *(1530)‏ 200 GeV AuAu Braz.J.Phys.37:925-932,2007 M.Sumbera Braz.J.Phys.37:925-932,2007 M.Sumbera

8. π-Ξ model comparison A nalysis of P. Chaloupka and M. Sumbera (Braz.J.Phys.37:925-932,2007) : Used FSI model: S. Pratt, S. Pertricioni Phys.Rev. C68, 054901 (2003) + Emission points from hydro-inspired Blastwave constrained by π-π  HBT Discrepancy in Ξ  region, over predicts A 00 and A 11 Coulomb part in qualitative agreement R = (6.7±1.0) fm ∆r out = (-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. López-Noriega, nucl-ex/0505009 )‏ A 00 - monopole – size A 11 - dipole - shift in out-direction Spherical decomposition Z. Chajecki, T.D. Gutierrez, M.A. Lisa and M. López-Noriega, nucl-ex/0505009 )‏ A 00 - monopole – size A 11 - dipole - shift in out-direction

9. 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 π 0 Ξ 0 and that the thresholdes of the two channels are non- degenerate - The contribution from inner potential region where the structure of the strong interaction is unknown.

10. The outgoing multichannel wave functions of π + Ξ - system enter as a building block into CF i=1-4, π + Ξ -, k- is a relative momentum of the pair The out-state w.f.’s have the asymptotic form π 0 Ξ 0 without and with spin flip

11. Coulomb Ξ*(1530)‏ π0Ξ0π0Ξ0 π+Ξ-π+Ξ- E Strong S wave Strong P- wave P-wave is dominated by Ξ*(1530)‏ Ξ*(1530)‏ πΞπΞ The low energy region of interaction up to the resonance is dominated by S and P-waves. Therefore the w.f. contains 2 phase shifts with I = 1/2, 3/2 for S-wave and 4 phase shifts with I = 1/2, 3/2 and J = 1/2, 3/2 for P-wave (J = L ± 1/2 is the total momentum). To reduce the number of parameters we have assumed that the dominant interaction in P-wave 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 S-wave phase shifts which are expressed in terms of the two scattering lengths a 1/2 and a 3/2 with isospin I=1/2 and I=3/2 correspondingly. The structure of π + Ξ - Wave Function

12. The wave function here is the pure Coulomb w.f., k 1 and k 2 are the c.m. momenta in and π 0 Ξ 0 channels; spherical harmonics correspond to the reversed direction of the vector k, π+Ξ-π+Ξ- combination of the regular and singular Coulomb functions Fl and Gl ρ 1 =k 1 r, ρ 2 =k 2 r, η =(a 1 k 1 ) -1, a 1 =-214 fm is a Bohr radius of the π + Ξ - system taking into account the negative sign of the Coulomb repulsion.

13. The wave function The quantities contain the elastic 1 → 1 and inelastic 1 → 2 scattering amplitudes f l {J;11 } and f l {J;21 }. For the S-waves (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 pion-nucleon scattering. For the resonance P-wave Ξ*(1530)‏ = 2 Γ /3, Γ2=Γ /3

14. The inner region correction The 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 calculated without any new parameters unless the S-wave effective radii are extremely large. It is important that the complete CF does not depend on ε provided the source function is nearly constant in the region r< ε. (MC procedure was checked using exact calculations within Mathematica) Without introduction of the correction, the resonance region exhibits clear interference of Coulomb and strong interactions, which is not observed in the data !

15. How to calculate CF numerically 2) HYDJET++ http://cern.ch/lokhtin/hydjet++ I.Lokhtin, L.Malinina, S.Petrushanko, A.Snigirev, I.Arsene, K.Tywoniuk, e-print arXiv:0809.2708, Comput.Phys.Commun.180:779-799,2009. 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 freeze-out particles http://www.th.physik.uni-frankfurt/~urqmd FSI code Richard Lednicky's code for calculation of the two particle correlations due to QS and FSI Source models:

16. π-Ξ FSI model comparison The influence of S-wave 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 S-wave scattering parameters. Ro = Rs = Rl = 2 fm

17. source is approximated with Gaussian π-Ξ FSI model comparison Similarly to the FSI model S. Pratt's (PRC68, 054901(2003) )‏ our calculations are in agreement with he data in the low-k 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 realistic source function obtained from Blast-wave like simulations.

18. Angular asymmetry in Blastwave-like 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)

19. π-Ξ FSI model comparison – HYDJET++ – UrQMD (v2.2)‏

20. Conclustions & Plans Using a simple Gaussian model for the source function, we have reasonably described the experimental π-Ξ 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 Blast-wave like simulations. Blast-wave like model HYDJET++ (soft part) allows to get the reasonable description of the π-Ξ CF in the whole k* region. UrQMD 2.2 model also provides reasonable description of CF. Spherical harmonic method will be applied to extract space-time shifts.

21. Additional slides

22. Reason of differences with S. 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 Pratt-Petriconi code. As for our calculations, they have been checked with the help of MATHEMATICA. Criterium of correcteness is independence of ε

23. Boost to pair rest frame Particle 1 source Particle 2 Source Separation between particle 1 and 2 and Boost to pair Rest frame  r* out =  T (  r out –  T  t) ‏ 2 free parameters in the Gaussian approximation Width of the distribution in pair rest frame Offset of the distribution from zero (slide from F.Retiere QM05)‏

24. πΞ, πK, πp, Kp Space-Time shifts in pair rest frame πΞ, πK, πp, Kp πΞ Within HYDJET++ model the combined freeze-out scenario describes better the observed in experiment πΞ space-time differences; π, K, p freeze-out at T th =100 MeV

25. HYDJET++: h ydro + 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 http://uhkm.jinr.ru The hard, multi-partonic part of HYDJET++ event is identical to the hard part of Fortran-written 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 http://cern.ch/lokhtin/hydro/hydjet.html Official version of HYDJET++ code and web-page with the documentation: http://cern.ch/lokhtin/hydjet++ The complete manual: I.Lokhtin, L.Malinina, S.Petrushanko, A.Snigirev, I.Arsene, K.Tywoniuk, e-print arXiv:0809.2708, Comput.Phys.Commun.180:779-799,2009. HYDJET++ is capable of reproducing the bulk properties of multi-particle system created in heavy ion collisions at RHIC (hadron spectra and ratios, radial and elliptic flow, momentum correlations), as well as the main high-p T observables.

26. The 2-particle momentum CF is defined as a normalized ratio of corresponding two and single particle distributions. 1D CF Most simple parametrization: strength of correlations Decompose q into components: QlongLong: in beam direction QoutOut : in direction of pair transverse momentum QsideSide :  q Long & q Out Parametrizations of CF

27. Z. Chajecki, T.D. Gutierrez, M.A. Lisa and M. López-Noriega, nucl-ex/0505009 200GeV AuAu different centralities ΞΞ Spherical decomposition – accessing emission shift Different A lm coefficients correspond to different symmetries of the source A 00 - monopole – size A 11 - dipole - shift in out-direction A 11 ≠ 0 - shift in the average emission point between p and X

28. Simplified idea of CF asymmetry (valid for Coulomb FSI)‏ x x v v v1v1 v2v2 v1v1 v2v2 k*/  = v 1 -v 2   Ξ Ξ k* x > 0 v  > v p k* x < 0 v  < v p Assume  emitted later than Ξ or closer to the center Ξ   Ξ Longer t int Stronger CF  Shorter t int Weaker CF   CF  CF  Modified slide of R.Lednicky flow

29. CF-asymmetry for charged particles Asymmetry arises mainly from Coulomb FSI CF  A c (  ) |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 /CF  x  1+2 <  x*  /a k*  0  x* = x 1 *-x 2 *  r x *  Projection of the relative separation r* in pair cms on the direction x In LCMS ( v z =0) or x || v :  x* =  t (  x - v t  t)‏  CF asymmetry is determined by space and time asymmetries Modified slide of R.Lednicky Shift <  x  in out direction is due to collective transverse flow & higher thermal velocity of lighter particles

30. For QS only: P 12 =C(q)=1+(-1) S  cos q  x> pp Momentum correlations of identical particles QS only K1K1 xbxb Two plane-waves: ππ 1/R The 2-particle correlation function C(q) is defined as a normalized ratio of the corresponding two and single particle distributions. K2K2 K1K1 K2K2 Out: direction of the mean transverse momentum of the pair Side: orthogonal to out Long: beam direction The corresponding correlation widths are usually parameterized in terms of the Gaussian correlation radii:

31. 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: And see the last figure à la L-W