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Combined Analysis of Two- and Three-Particle Correlations in $q,p$-Bose Gas Model
Symmetry, integrability and geometry: methods and applications, Tome 2 (2006) Cet article a éte moissonné depuis la source Math-Net.Ru

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$q$-deformed oscillators and the $q$-Bose gas model enable effective description of the observed non-Bose type behavior of the intercept (“strength”) $\lambda^{(2)}\equiv C^{(2)}(K,K)-1$ of two-particle correlation function $C^{(2)}(p_1,p_2)$ of identical pions produced in heavy-ion collisions. Three- and $n$-particle correlation functions of pions (or kaons) encode more information on the nature of the emitting sources in such experiments. And so, the $q$-Bose gas model was further developed: the intercepts of $n$-th order correlators of $q$-bosons and the $n$-particle correlation intercepts within the $q,\!p$-Bose gas model have been obtained, the result useful for quantum optics, too. Here we present the combined analysis of two- and three-pion correlation intercepts for the $q$-Bose gas model and its $q,\!p$-extension, and confront with empirical data (from CERN SPS and STAR/RHIC) on pion correlations. Similar to explicit dependence of $\lambda^{(2)}$ on mean momenta of particles (pions, kaons) found earlier, here we explore the peculiar behavior, versus mean momentum, of the 3-particle correlation intercept $\lambda^{(3)}(K)$. The whole approach implies complete chaoticity of sources, unlike other joint descriptions of two- and three-pion correlations using two phenomenological parameters (e.g., core-halo fraction plus partial coherence of sources).
Keywords: $q$- and $q,p$-deformed oscillators; ideal gas of $q,p$-bosons; $n$-particle correlations; intercepts of two and three-pion correlators. 
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     author = {Alexandre M. Gavrilik},
     title = {Combined {Analysis} of {Two-} and {Three-Particle} {Correlations} in $q,p${-Bose} {Gas} {Model}},
     journal = {Symmetry, integrability and geometry: methods and applications},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a73/}
}
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Alexandre M. Gavrilik. Combined Analysis of Two- and Three-Particle Correlations in $q,p$-Bose Gas Model. Symmetry, integrability and geometry: methods and applications, Tome 2 (2006). http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a73/

[1] Avancini S. S., Krein G., “Many-body problems with composite particles and $q$-Heisenberg algebras”, J. Phys. A: Math. Gen., 28 (1995), 685–691 | DOI | MR | Zbl

[2] Perkins W. A., “Quasibosons”, Internat. J. Theoret. Phys., 41 (2002), 823–838 ; hep-th/0107003 | DOI | MR | Zbl

[3] Chang Z., “Quantum group and quantum symmetry”, Phys. Rep., 262 (1995), 137–225 ; hep-th/9508170 | DOI | MR

[4] Kibler M. R., Introduction to quantum algebras, hep-th/9409012

[5] Mishra A. K., Rajasekaran G., “Generalized Fock spaces, new forms of quantum statistics and their algebras”, Pramana, 45 (1995), 91–139 ; hep-th/9605204 | DOI

[6] Man'ko V. I., Marmo G., Sudarshan E. C. G., Zaccaria F., “$f$-oscillators and nonlinear coherent states”, Phys. Scripta, 55 (1997), 528–541 ; quant-ph/9612006 | DOI | MR

[7] Gavrilik A. M., “$q$-Serre relations in $U_q(u_n)$, $q$-deformed meson mass sum rules, and Alexander polynomials”, J. Phys. A: Math. Gen., 27 (1994), L91–L94 | DOI | MR | Zbl

[8] Gavrilik A. M., Iorgov N. Z., “Quantum groups as flavor symmetries: account of nonpolynomial $SU(3)$-breaking effects in baryon masses”, Ukrain. J. Phys., 43 (1998), 1526–1533 ; hep-ph/9807559 | MR

[9] Chaichian M., Gomez J. F., Kulish P., “Operator formalism of $q$-deformed dual string model”, Phys. Lett. B, 311 (1993), 93–97 ; hep-th/9211029 | DOI | MR

[10] Jenkovszky L., Kibler M., Mishchenko A., “Two-parametric quantum deformed dual amplitude”, Modern Phys. Lett. B, 10 (1995), 51–60 ; hep-ph/9407071 | DOI | MR | Zbl

[11] Gavrilik A. M., “Quantum algebras in phenomenological description of particle properties”, Nucl. Phys. B (Proc. Suppl.), 102 (2001), 298–305 ; hep-ph/0103325 | DOI | MR | Zbl

[12] Gavrilik A. M., “Quantum groups and Cabibbo mixing”, Proceedings of Fifth International Conference “Symmetry in Nonlinear Mathematical Physics”, Proceedings of Institute of Mathematics, Part 2 (June 23–29, 2003, Kyiv), 50, eds. A. G. Nikitin, V. M. Boyko, R. O. Popovych and I. A. Yehorchenko, Kyiv, 2004, 759–766 ; hep-ph/0401086 | MR | Zbl

[13] Anchishkin D. V., Gavrilik A. M., Iorgov N. Z., “Two-particle correlations from the $q$-Boson viewpoint”, Eur. Phys. J. A, 7 (2000), 229–238 ; nucl-th/9906034

[14] Anchishkin D. V., Gavrilik A. M., Iorgov N. Z., “$q$-Boson approach to multiparticle correlations”, Modern Phys. Lett. A, 15 (2000), 1637–1646 ; hep-ph/0010019 | DOI

[15] Anchishkin D. V., Gavrilik A. M., Panitkin S., “Intercept parameter $\lambda$ of two-pion (-kaon) correlation functions in the $q$-boson model: character of its $p_T$-dependence”, Ukrain. J. Phys., 49 (2004), 935–939; hep-ph/0112262

[16] Zhang Q. H., Padula S. S., “$Q$-boson interferometry and generalized Wigner function”, Phys. Rev. C, 69 (2004), 24907, 11 pp., ages ; nucl-th/0211057 | DOI

[17] Gutierrez T., “Intensity interferometry with anyons”, Phys. Rev. A, 69 (2004), 063614, 5 pp., ages ; quant-ph/0308046 | DOI

[18] Wiedemann U. A., Heinz U., “Particle interferometry for relativistic heavy-ion collisions”, Phys. Rept., 319 (1999), 145–230 ; nucl-th/9901094 | DOI

[19] Heinz U., Zhang Q. H., “What can we learn from three-pion interferometry?”, Phys. Rev. C, 56 (1997), 426–431 ; nucl-th/9701023 | DOI

[20] Adamska L. V., Gavrilik A. M., “Multi-particle correlations in $qp$-Bose gas model”, J. Phys. A: Math. Gen., 37:17 (2004), 4787–4795 ; hep-ph/0312390 | DOI | MR | Zbl

[21] Csorgö T. et al., “Partial coherence in the core/halo picture of Bose–Einstein $n$-particle correlations”, Eur. Phys. J. C, 9 (1999), 275–281 ; hep-ph/9812422

[22] Csanad M. for PHENIX Collab., Measurement and analysis of two- and three-particle correlations

[23] Morita K., Muroya S., Nakamura H., Source chaoticity from two- and three-pion correlations in Au+Au collisions at $\sqrt{s_{NN}}=130$ GeV, nucl-th/0310057

[24] Biyajima M., Kaneyama M., Mizoguchi T., “Analyses of two- and three-pion Bose–Einstein correlations using Coulomb wave functions”, Phys. Lett. B, 601 (2004), 41–50 ; nucl-th/0312083 | DOI

[25] Arik M., Coon D. D., “Hilbert spaces of analytic functions and generalized coherent states”, J. Math. Phys., 17 (1976), 524–527 | DOI | MR

[26] Fairlie D., Zachos C., “Multiparameter associative generalizations of canonical commutation relations and quantized planes”, Phys. Lett. B, 256 (1991), 43–49 | DOI | MR

[27] Meljanac S., Perica A., “Generalized quon statistics”, Modern Phys. Lett. A, 9 (1994), 3293–3300 | DOI | MR

[28] Chakrabarti A., Jagannathan R., “A $(p,q)$ oscillator realization of two-parameter quantum algebras”, J. Phys. A: Math. Gen., 24 (1991), L711–L718 | DOI | Zbl

[29] Macfarlane A. J., “On $q$-analogues of the quantum harmonic oscillator and the quantum group $SU_q(2)$”, J. Phys. A: Math. Gen., 22 (1989), 4581–4585 | DOI | MR

[30] Biedenharn L. C., “The quantum group $SU_q(2)$ and a $q$-analogue of the boson operators”, J. Phys. A: Math. Gen., 22 (1989), L873–L878 | DOI | MR | Zbl

[31] Altherr T., Grandou T., “Thermal field theory and infinite statistics”, Nucl. Phys. B, 402 (1993), 195–216 | DOI

[32] Vokos S., Zachos C., “Thermodynamic $q$-distributions that aren't”, Modern Phys. Lett. A, 9 (1994), 1–9 | DOI

[33] Lavagno A., Narayana Swamy P., “Thermostatistics of $q$ deformed boson gas”, Phys. Rev. E, 61 (2000), 1218–1226 ; quant-ph/9912111 | DOI | MR

[34] Daoud M., Kibler M., “Statistical mechanics of $qp$-bosons in $D$ dimensions”, Phys. Lett. A, 206 (1995), 13–17 ; quant-ph/9512006 | DOI | MR | Zbl

[35] Adler C. et al. [STAR Collab.], “Pion interferometry of $\sqrt{S(NN)}=130$ GeV Au+Au collisions at RHIC”, Phys. Rev. Lett., 87 (2001), 082301, 6 pp., ages ; nucl-ex/0107008 | DOI

[36] Adams J. et al. [STAR Collab.], “Three-pion HBT correlations in relativistic heavy-ion collisions from the STAR experiment”, Phys. Rev. Lett., 91 (2003), 262301, 6 pp., ages ; nucl-ex/0306028 | DOI

[37] Aggarwal M. M. et al. [WA98 Collab.], “One-, two- and three-particle distributions from 158$A$ GeV/$c$ central Pb+Pb collisions”, Phys. Rev. C, 67 (2003), 014906, 24 pp., ages ; nucl-ex/0210002 | DOI

[38] Bearden I. G. et al. [NA44 Collab.], “One-dimensional and two-dimensional analysis of 3 pi correlations measured in Pb+Pb interactions”, Phys. Lett. B, 517 (2001), 25–31 ; nucl-ex/0102013 | DOI

[39] Cheng T.-P., Li L.-F., Gauge theory of elementary particle physics, Clarendon Press, Oxford, 1984 | MR | Zbl

[40] Odaka K., Kishi T., Kamefuchi S., “On quantization of simple harmonic oscillators”, J. Phys. A: Math. Gen., 24 (1991), L591–L596 | DOI | MR | Zbl

[41] Chaturvedi S., Srinivasan V., Jagannathan R., “Tamm–Dancoff deformation of bosonic oscillator algebras”, Modern Phys. Lett. A, 8 (1993), 3727–3734 | DOI | MR | Zbl

[42] Heiselberg H., Vischer A. P., The phase in three-pion correlations, nucl-th/9707036

[43] Csorgo T., Szerzo A. T., “Model independent shape analysis of correlations in 1, 2 or 3 dimensions”, Phys. Lett. B, 489 (2000), 15–23 ; hep-ph/0011320 | DOI