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the approach initiated in: Anchishkin, Gavrilik, Iorgov, Eur. J .Phys. A , 2000 ;

Intercepts of multi-pion correlation functions within different deformed Bose gas models A. Gavrilik (BITP, Kiev) in collab. with Anastasiya Rebesh.

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the approach initiated in: Anchishkin, Gavrilik, Iorgov, Eur. J .Phys. A , 2000 ;

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  1. Intercepts of multi-pion correlation functionswithin different deformed Bose gas modelsA. Gavrilik(BITP, Kiev)in collab. with Anastasiya Rebesh

  2. based on:A.Gavrilik, SIGMA, 2, paper 74, p.1-12, 2006 [hep-ph/0512357] A.G., A.Rebesh, Mod. Phys. Lett. A, 2008 A.G., I.Kachurik, A.Rebesh, J. Phys. A, 2010 A.G., A.Rebesh, arXiv: 1007.5187 [quant-ph/0512357] the approach initiated in: Anchishkin, Gavrilik, Iorgov, Eur. J .Phys. A, 2000; Mod. Phys. Lett. A, 2000 Anchishkin, Gavrilik, Panitkin, Ukr. J. Phys. A, 2004 Some next steps in: L.Adamska, A.Gavrilik, J. Phys. A, 2004 [hep-ph/0312390] A.Gavrilik, SIGMA, 2, paper 74, p.1-12, 2006 [hep-ph/0512357] Q.Zhang, S.Padula, Phys. Rev. C, 2004

  3. Data on π+π+andπ–π–correlations ( B.I.Abelev et al.(STAR collab.)., PR C80:024905 (2009); arXiv:0903.1296 Pion Interferometry in Au+Au and Cu+Cu Collisions at √sNN=62.4 and200 GeV ) NB!”thetrend”is seen: 1) Monotonic increasing; 2) Concavity upwards; 3) Saturation by a constant < 1 (= case of Bosons)

  4. -- Fibonacci oscillators, with property of en.levels: En+1= λEn + ρEn-1 -- quasi-Fibonacci oscillators, with property of en. levels: OUR GOLE:● use deformed oscillators(DOs)(=deformed bosons), develop corresp. version of deformed Bose gas – – and try tomodel the above “trend”● we examine a number of variants of DOs from two verydifferent classes: En+1= λn En+ ρn En-1 Typical:p,q-oscillators, for whichλ=p+q, ρ= -pq Typical: μ-oscillator, for whichλn=λ(n,μ),ρn=ρ(n,μ) with definite A.G., I.Kachurik, A.Rebesh, J. Phys. A, 2010

  5. Why deformed q-oscillators, and(ideal) q-Bose gas models? • (a)finite proper volume of particles; • (b)substructure of particles; • (c)memory effects; • (d)particle-particle, or particle-medium interactions • (i.e, non-ideal pion or Bose gas); • (e) possible existence of non-chaotic (partially coherent) components of • emitting sources;effects from long-lived resonanses (e.g., put in the • core-halo picture); • • (g) non-Gaussian (effects of) sources; • (h) fireball -- short-lived, highly non-equilibrium, complicated system. • If we use 2-parameter say q,p-deformed Bose gas model, then: • 1) It gives formulae for 1-param. versions (AC,BM,TD,…) as special cases; • 2)q,p-Bose gas model accounts jointly for any two independent reasons (to • q-deform)from the above list. • About items (b)& (d) --- on next slide Important also in other contexts

  6. (b) QUASIBOSONS VSdeformed oscillators: It is shown(e.g. S.Avancini, G.Krein, J.Ph.A1995)that algebra of quasiboson (composite boson) operators, realized in terms of constituent’s fermionic operators, indeed modifies: If: , (a,a†,b,b† -- fermionic) then: where and Δαβcan be made using deformed oscillator! (more detailed analysis: A.G. & Yu.Mishchenko, in preparation) (d) Account ofinterparticle interactions in deformation, then: non-idealBose gas ideal deformedBose gas (e.g.,A.Scarfone, P.Narayana Swamy, J.Ph.A 2008);

  7. Deformedoscillators of “Fibonacci class” --- q,p-oscillator: (q,p-bracket) ---q-oscillators: 1) ifp=1-AC (Arik-Coon) type, 2)ifp=q.-1-BM (Bied.-Macfarlane) type, 3)ifp=q-TD (Tamm-Dancoff) type, and many others in this class: 4)…),e.g.,ifp = exp (½(q-1)) (A.G., A.Rebesh, Mod.Phys.Lett.A 2008) .

  8. n-Particlecorrelationsinq,p-Bose gas model. Ideal gas of q,p-bosons: thermal averages, one-particledistribution: (q,p-Bose) (AC type q-Bose) Bose AC type q-Bose BM q-Bose q,p-Bose →

  9. Intercepts of 2-particlecorrel. Functions & their asymptotics (BM type, q=exp(iθ)) NB: Asymptotics (βω→∞)of intercepts isgiven solely bythe deformation parameter(s)q orq,p

  10. Intercepts of3-particlecorrel. functions & their asymptotics (BM type, q=exp(iθ)) NB: Asymptotics (βω→∞)of intercepts aregiven solely bythe deformation parameter(s)q orq,p

  11. Intercept (maxim.value) ofn-particle correlation function for thep,q-Bosegasmodel General formula:L.Adamska,A.Gavrilik, J. Phys. A (2004) Asymptotics(βω→∞) of interceptis given byq(orq & p): q,p

  12. Interceptsin pq-Bose gas model VSexper.data on pion correlations (NA44at CERN: I.G.Bearden et al., Phys.Lett. B, 2001) pure Bose value section 2 Equating our f-las for λ(2) & λ(3) to exper.values yields two surfaces βω section 1 (A.Gavrilik, SIGMA, 2 (2006), paper 74,1-12, [hep-ph/0512357] )

  13. Two sections: 1) set • 2) set • λpq(2) NB: we have 1σ contours λpq(3) section 1 section 2 Csanad (for PHENIX), NP A774 (2006) nucl-ex/0509042 2 phenom. param.

  14. Deformedoscillators of “quasi-Fibonacci” class --- μ-oscillator:structure f-n (μ-bracket) ---(μ;p,q)-oscillators: 1) μ-AC type, 2)μ-BM type, 3)μ-TDtype, (A.G., I.Kachurik,A.Rebesh, J.Ph. A2010)

  15. Interceptλμ(2)of 2-pion correl. function VS mean momentum, with a s y m p t o t i c s: 0.8306 0.8332 0.7566 0.7680 Intercepts of momentum correlation functions inμ-Bose gas model and their asymptotics, arXiv: 1007.5187 A. Gavrilik, A.Rebesh,

  16. Behaviour of , μ-Bose gas λ(3) Interceptλμ(3)of 3-pion correl. functionVS particle mean momentum KT: 3.6097 3.0083 Asymptotics is given as: μ=0.1 μ=0.15 (to μ3 ) (to μ5 ) Intercepts of momentum correlation functions inμ-Bose gas model and their asymptotics, arXiv: 1007.5187 A. Gavrilik, A.Rebesh,

  17. Characteristic function r(3)(KT) made from λ(2) &λ(3): π/30 (U.Heinz, Q.Zhang, PRC 1997) Also, it has sense of cos Φ – spec. phase (H.Heiselberg, A.Vischer, nucl-th/9707036) π/4 BM typeq-Bose gas μ-Bose gas

  18. Data- Theory NB: centrality (left) temperature (right)

  19. SUMMARY • The explored models, even from different classes (Fibo. or quasi-Fibo.), provide KT dependence, and naturally mimic ’thetrend’ • We have explicit f-las for 2-,3-,…,n-particle correlation intercepts λp,q(n)(K,T), λμ(n)(K,T) & rp,q(3)(K,T) or rμ(3)(K,T) (exact in p,q-case, approximate in μ-case) • Basic fact: asymptotics is given in terms of deform. parameters solely: λp,q(n),asymp. =f(p,q); λμ(n),asymp. =g(μ), etc. • Having fixed deform. parameter (from asymptotics, using high KT bins), the temperature is fixedfrom lowerKT bins • So, we await much more experim. data! (see next.slide)

  20. What isneeded from experiment. side,to make choisefromamong many models: • More data onπ±π± correl. inters. λ(2)(for higher & lowerKT) • Data onπ±π±π±correl. inters.λ(3)(for wide range ofKT) • Data on the functionr(3)(KT)(for wide range ofKT ) THANK YOU!

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