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Residual correlations and photon interferometry at CBM

K. Mikhaylov, A. Stavinskiy, ITEP, Moscow. Residual correlations and photon interferometry at CBM. Outlook Introduction gg correlations g p and Λ p correlations Conclusions. 8.CBM Collaboration Meeting. Strasbourg, September, 2006. K.Mikhaylov, Moscow, ITEP. 2.

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Residual correlations and photon interferometry at CBM

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  1. K. Mikhaylov, A. Stavinskiy, ITEP, Moscow Residual correlations and photon interferometry at CBM • Outlook • Introduction • gg correlations • gpandΛpcorrelations • Conclusions

  2. 8.CBM Collaboration Meeting. Strasbourg, September, 2006. K.Mikhaylov, Moscow, ITEP 2 Particle interferometry in heavy ion collisions  direct /p0 ratio; space-time structure (r,) p; p  Parameters of 0p interaction

  3. 8.CBM Collaboration Meeting. Strasbourg, September, 2006. K.Mikhaylov, Moscow, ITEP 3 Method: Residual correlations • The residual correlation is the correlation between decay products due to combination of both small relative velocity correlations between parents and small decay momenta of products • 00 correlations  (e.g. WA-98) • 0p correlations  p; p High multiplicity of 0 and 0  importance of residual correlations

  4.  π0 } residual correlation π0   • Distance between 0 25 million Fermis • No  interference , but correlation! 8.CBM Collaboration Meeting. Strasbourg, September, 2006. K.Mikhaylov, Moscow, ITEP 4 RESIDUAL CORRELATIONS The correlation function of -pair: C() = Nreal*C()/Nmixed , where C() is the correlation function of 00 which usually parametrized: C() = 1+exp(-Q2R2) For the present simulations of  correlationsthe source radius (R) of 0 was the same as 's source radius (5 fm). The spectra of pions and gammas were in exponential form with slope ~ 200 MeV.

  5. gg residual correlation function 8.CBM Collaboration Meeting. Strasbourg, September, 2006. K.Mikhaylov, Moscow, ITEP 5 • The region of Qinv [70MeV-mp] is free of direct photons correlation • The value of CF linearly depends on yield of gdirect/po at 70< Qinv <mp One can extract the yield of gdirect

  6. New method to extract yield of direct photons 8.CBM Collaboration Meeting. Strasbourg, September, 2006. K.Mikhaylov, Moscow, ITEP 6 study the region between direct photons correlation peak and p0 peak Cmeasured = Cg(p0)g(p0) + Cg(direct)g(p0) + Cg(direct)g(direct), Cg(p0)g(p0) - the residual correlation of g's from p0 decay [0-mp] Cg(direct)g(p0) =1 – the correlations of direct g and g's from p0 decay, Cg(direct)g(direct) – the correlations of direct g's [0-70MeV] If the number of direct g pairs is small with comparison of the number of gdirectgp0and gp0gp0 pairs, and the yield of direct gammas: gdirect/gp0 (Cmeasured-1)/(Csim -1) [70-mp], Csim=Cg(p0)g(p0)simulated with experimental spectum of p0 We need better then 9% energy resolution of ECAL to study the region between direct photons correlation peak and p0peak

  7. p0 correlation function 8.CBM Collaboration Meeting. Strasbourg, September, 2006. K.Mikhaylov, Moscow, ITEP 7 • Analytical model with Strong FSI [Stoks, Rejken, PRC 59(1999) 3009: fs0=6fm, ds0=3.3fm,ft0=0.3, dt0=-20.7fm] • Enhancement at small k*

  8. Residual correlation in pgsystem 8.CBM Collaboration Meeting. Strasbourg, September, 2006. K.Mikhaylov, Moscow, ITEP 8 • Visible effect • Depends on source size • If source size is known  extract unknown parameters of strong interaction ofpS0

  9. Procedure to extract signal for pgSo 8.CBM Collaboration Meeting. Strasbourg, September, 2006. K.Mikhaylov, Moscow, ITEP 9 • Choose system of particles [p1] [p2+p-+g] • First proton p1 is not from decay of strange particle • g does not have partner from p0 mass region. • Reconstruction of L ( mp+ mp- = mL ) • mg+mL = mS0 • System [p1] [p2+p-+g] at low relative momentum • Other cuts (pT region?)

  10. Residual correlation in pLsystem 8.CBM Collaboration Meeting. Strasbourg, September, 2006. K.Mikhaylov, Moscow, ITEP 10 • Purely comparablewithpSo • If purity of L is not 100% we have to take into account residual correlations

  11. ComparisonpL andpLSo 8.CBM Collaboration Meeting. Strasbourg, September, 2006. K.Mikhaylov, Moscow, ITEP 11 • The shape and the value of both correlation functions are close • In practice we measure mixed of both and the purity of pLdepends on the yieldS0/L

  12. Conclusions The new method of direct photons yield was shown The resolution of ECAL is important for this new method. The feasibility of gamma-proton correlation is shown Parameters of strong interaction of p0 can be extracted from pcorrelation function The purity of particles is very important for correlation study in heavy ion collision

  13. Back up

  14. 8.CBM Collaboration Meeting. Strasbourg, September, 2006. K.Mikhaylov, Moscow, ITEP 14 gg residual correlation function (UrQMD) • The region of QINV 70MeV-mp is free of direct photons correlation • Low statistics to show how to extract yield of direct gammas

  15. 8.CBM Collaboration Meeting. Strasbourg, September, 2006. K.Mikhaylov, Moscow, ITEP 15 Correlation function • The correlation function of two particles (C): where σ12is two particle production cross section, • σ1 and σ2single particle production cross section • Gaussian parametrization: where invis the strength of correlation, Qinv - invariant relative momentum, Rinv – radius parameter • Experimental correlation function: where Nreal(Qinv) is the pair distribution for particle-pairs from the same event, and Nmixed(Qinv) is the corresponding distribution for pairs of particles taken from different events. C2 normalized to unity at large Qinv. Mixing procedure[G.I.Kopylov, PL 50B(1974)p.472] C=σ12 / σ1 σ2 C=1+invexp(-Q2invR2inv) C=Nreal(Qinv)/Nmixed(Q)

  16. 8.CBM Collaboration Meeting. Strasbourg, September, 2006. K.Mikhaylov, Moscow, ITEP 16 Analytical model to relate CF R.Lednicky,V.Lyuboshitz,Sov.J.Nucl.Phys,35(1982)770 • The correlation function is calculated as the square of the wave function average over the total spin S and over the distribution of relative distance (r*) of particle emission points in the pair rest frame: C(k*)=<|S-k* (r*)|> where k* is the momentum of one of the particle in the pair rest frame • S-wave part of wave function: S-k* (r*)=e-ik*r*+ fS(k*)eik*r*/r* • The effective range approximation for s-wave scattering amplitude: fS(k*)=(1/fS0 + 1/2dS0k*2 - ik*)-1 where fS0 is scattering length and dS0 is the effective radius for given total spin S=0 or S=1 • Assuming a Gaussian distribution for particle source: d3N/d3r* ~ exp(-r*2/4r20) where r0 is the radius of the source

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