Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 2 (2006), 074, 12 pages      hep-ph/0512357      https://doi.org/10.3842/SIGMA.2006.074

Combined Analysis of Two- and Three-Particle Correlations in q,p-Bose Gas Model

Alexandre M. Gavrilik
N.N. Bogolyubov Institute for Theoretical Physics, Kyiv, Ukraine

Received December 29, 2005, in final form October 28, 2006; Published online November 07, 2006

Abstract
q-deformed oscillators and the q-Bose gas model enable effective description of the observed non-Bose type behavior of the intercept (''strength'') λ(2) ≡ C(2)(K,K) - 1 of two-particle correlation function C(2)(p1,p2) 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 λ(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 λ(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).

Key words: 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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References

  1. Avancini S.S., Krein G., Many-body problems with composite particles and q-Heisenberg algebras, J. Phys. A: Math. Gen., 1995, V.28, 685-691.
  2. Perkins W.A., Quasibosons, Internat. J. Theoret. Phys., 2002, V.41, 823-838, hep-th/0107003.
  3. Chang Z., Quantum group and quantum symmetry, Phys. Rep., 1995, V.262, 137-225, hep-th/9508170.
  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, 1995, V.45, 91-139, hep-th/9605204.
  6. Man'ko V.I., Marmo G., Sudarshan E.C.G., Zaccaria F., f-oscillators and nonlinear coherent states, Phys. Scripta, 1997, V.55, 528-541, quant-ph/9612006.
  7. Gavrilik A.M., q-Serre relations in Uq(un), q-deformed meson mass sum rules, and Alexander polynomials, J. Phys. A: Math. Gen., 1994, V.27, L91-L94.
  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., 1998, V.43, 1526-1533, hep-ph/9807559.
  9. Chaichian M., Gomez J.F., Kulish P., Operator formalism of q deformed dual string model, Phys. Lett. B, 1993, V.311, 93-97, hep-th/9211029.
  10. Jenkovszky L., Kibler M., Mishchenko A., Two-parametric quantum deformed dual amplitude, Modern Phys. Lett. B, 1995, V.10, 51-60, hep-ph/9407071.
  11. Gavrilik A.M., Quantum algebras in phenomenological description of particle properties, Nucl. Phys. B (Proc. Suppl.), 2001, V.102, 298-305, hep-ph/0103325.
  12. Gavrilik A.M., Quantum groups and Cabibbo mixing, in Proceedings of Fifth International Conference "Symmetry in Nonlinear Mathematical Physics" (June 23-29, 2003, Kyiv), Editors A.G. Nikitin, V.M. Boyko, R.O. Popovych and I.A. Yehorchenko, Proceedings of Institute of Mathematics, Kyiv, 2004, V.50, Part 2, 759-766, hep-ph/0401086.
  13. Anchishkin D.V., Gavrilik A.M., Iorgov N.Z., Two-particle correlations from the q-Boson viewpoint, Eur. Phys. J. A, 2000, V.7, 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, 2000, V.15, 1637-1646, hep-ph/0010019.
  15. Anchishkin D.V., Gavrilik A.M., Panitkin S., Intercept parameter l of two-pion (-kaon) correlation functions in the q-boson model: character of its pT-dependence, Ukrain. J. Phys., 2004, V.49, 935-939, hep-ph/0112262.
  16. Zhang Q.H., Padula S.S., Q-boson interferometry and generalized Wigner function, Phys. Rev. C, 2004, V.69, 24907, 11 pages, nucl-th/0211057.
  17. Gutierrez T., Intensity interferometry with anyons, Phys. Rev. A, 2004, V.69, 063614, 5 pages, quant-ph/0308046.
  18. Wiedemann U.A., Heinz U., Particle interferometry for relativistic heavy-ion collisions, Phys. Rept., 1999, V.319, 145-230, nucl-th/9901094.
  19. Heinz U., Zhang Q.H., What can we learn from three-pion interferometry? Phys. Rev. C1997, V.56, 426-431, nucl-th/9701023.
  20. Adamska L.V., Gavrilik A.M., Multi-particle correlations in qp-Bose gas model, J. Phys. A: Math. Gen., 2004, V.37, N 17, 4787-4795, hep-ph/0312390.
  21. Csorgö T. et al., Partial coherence in the core/halo picture of Bose-Einstein n-particle correlations, Eur. Phys. J. C, 1999, V.9, 275-281, hep-ph/9812422.
  22. Csanad M. for PHENIX Collab., Measurement and analysis of two- and three-particle correlations, nucl-ex/0509042.
  23. Morita K., Muroya S., Nakamura H., Source chaoticity from two- and three-pion correlations in Au+Au collisions at sNN1/2=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, 2004, V.601, 41-50, nucl-th/0312083.
  25. Arik M., Coon D.D., Hilbert spaces of analytic functions and generalized coherent states, J. Math. Phys., 1976, V.17, 524-527.
  26. Fairlie D., Zachos C., Multiparameter associative generalizations of canonical commutation relations and quantized planes, Phys. Lett. B, 1991, V.256, 43-49.
  27. Meljanac S., Perica A., Generalized quon statistics, Modern Phys. Lett. A, 1994, V.9, 3293-3300.
  28. Chakrabarti A., Jagannathan R., A (p,q)oscillator realization of two-parameter quantum algebras, J. Phys. A: Math. Gen., 1991, V.24, L711-L718.
  29. Macfarlane A.J., On q-analogues of the quantum harmonic oscillator and the quantum group SUq(2), J. Phys. A: Math. Gen., 1989, V.22, 4581-4585.
  30. Biedenharn L.C., The quantum group SUq(2) and a q-analogue of the boson operators, J. Phys. A: Math. Gen., 1989, V.22, L873-L878.
  31. Altherr T., Grandou T., Thermal field theory and infinite statistics, Nucl. Phys. B, 1993, V.402, 195-216.
  32. Vokos S., Zachos C., Thermodynamic q-distributions that aren't, Modern Phys. Lett. A, 1994, V.9, 1-9.
  33. Lavagno A., Narayana Swamy P., Thermostatistics of q deformed boson gas, Phys. Rev. E, 2000, V.61, 1218-1226, quant-ph/9912111.
  34. Daoud M., Kibler M., Statistical mechanics of qp-bosons in D dimensions, Phys. Lett. A, 1995, V.206, 13-17, quant-ph/9512006.
  35. Adler C. et al. [STAR Collab.], Pion interferometry of S(NN)1/2 = 130-GeV Au+Au collisions at RHIC, Phys. Rev. Lett., 2001, V.87, 082301, 6 pages, nucl-ex/0107008.
  36. Adams J. et al. [STAR Collab.], Three-pion HBT correlations in relativistic heavy-ion collisions from the STAR experiment, Phys. Rev. Lett., 2003, V.91, 262301, 6 pages, nucl-ex/0306028.
  37. Aggarwal M.M. et al. [WA98 Collab.], One-, two- and three-particle distributions from 158A GeV/c central Pb+Pb collisions, Phys. Rev. C, 2003, V.67, 014906, 24 pages, nucl-ex/0210002.
  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, 2001, V.517, 25-31, nucl-ex/0102013.
  39. Cheng T.-P., Li L.-F., Gauge theory of elementary particle physics, Oxford, Clarendon Press, 1984.
  40. Odaka K., Kishi T., Kamefuchi S., On quantization of simple harmonic oscillators, J. Phys. A: Math. Gen., 1991, V.24, L591-L596.
  41. Chaturvedi S., Srinivasan V., Jagannathan R., Tamm-Dancoff deformation of bosonic oscillator algebras, Modern Phys. Lett. A, 1993, V.8, 3727-3734.
  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, 2000, V.489, 15-23, hep-ph/0011320.

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