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The Golden Ratio:

Reviewing the existing results of

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The Golden Ratio:

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  1. Bedanga Mohanty VECC, Kolkata  mesons in High Energy Nuclear Collisions Outline  meson in High Energy Collisions Review of existing results Strangeness Enhancement Partonic Collectivity Recombination and hints of Thermalization Probing QCD Phase Boundary  : v2 measurement Thanks to Nu Xu, Jinhui Chen, Zhangbu Xu, Huan Huang, Guoliang Ma and STAR for discussions QGP Meet 2008 : Bedanga Mohanty

  2. First seen in bubble chamber experiments at Brookhaven in 1962 in the reactions K- + p L + K+K K- + p L + K++K- Mass 1020 MeV, G<<20 MeV Quantum numbers JPC = 1--  mesons - Discovery STAR @ RHIC, BNL High signal for the decay to KK, at the edge of the kinematically allowed region, rp decay suppressed STAR : QM2008 QGP Meet 2008 : Bedanga Mohanty

  3.  mesons QGP Meet 2008 : Bedanga Mohanty

  4. Golden ratio meson in high energy collisions Remark A goldentool which can be used to address various aspect of heavy-ion collisions Next :  meson and Strangeness Enhancement QGP Meet 2008 : Bedanga Mohanty

  5. P. Koch, B. Muller,J. Rafelski Phys. Rep. 88 (1982) 331 Phys. Rev. Lett. 48 (1982) 1066 Phys. Rep. 142 (1986) 167 Canonical Effect in p+p collisions : Quantum Numbers exactly conserved J. Cleymans, A. Muronga, K. Redlich, A. Tounsi, et al. Suppression causes : -Strangeness ordering -Beam energy dependence Phys. Lett. B. 388 (1996) 401 Phys. Rev. C 58 (1997) 2747 Phys. Rev. C 57 (1998) 3319 Phys. Lett. B. 486 (2000) 61 Eur. Phys. J. C 24 (2002) 589 hep-ph/0111159 QGP scenario : Strangeness Enhancement Copious production of s and sbar pairs Strangeness enhancement relative to p+p collisions Stronger effect for multi-strange hadrons and increases with strangeness content QGP Meet 2008 : Bedanga Mohanty

  6. arXiv:0810.4979  mesons and Strangeness Enhancement Strangeness enhancement observed -- Dense partonic medium formation in A+A ? -- Canonical suppression in p+p ? Statistical model predictions -- Enhancement increases with strange-quark content -- Enhancement higher for lower beam energy at RHIC energies: -- Not canonically suppressed -- Does not follow number of strange-quark ordering -- Enhancement(62.4) < Enhancement(200) STAR Preliminary • enhancement between K-() and  ? STAR :arXiv:0804.4363 : J.Phys.G35:044031,2008 Possible Issues : If formed by KK coalescence can be subjected to Canonical suppression. Is production OZI suppressed in p+p collisions ? QGP Meet 2008 : Bedanga Mohanty

  7.  Production from KK Coalescence Naively from KK Coalescence If formed by KK Coalescence -- K- ratio will change with collision centrality/Beam energy/System size -- Width of rapidity distribution : 1/ ~ 1/K- + 1/K+ --- Inverse Slope of transverse momentum distribution : T~ 2 TK --- and K v2 measurements (discussed later) --- Constraints due to the spin quantum number (K are spin 0 and is spin 1) production not from KK coalescence at RHIC energies Observed strangenessenhancement not due to Canonical suppression effects RMS rapidity dist. STAR : Phys. Rev. Lett. 99 (2007) 112301 Phys. Lett. B 612 (2005) 181 arXiv:0809.4737 NA49 : arXiv:0806.1937 Phys. Rev. Lett. 96 (2005) 052301

  8. Violations of OZI rule observed in p+p collisions. - u d Phys. Lett. B 59 (1975) 88 arXiv: nucl-th/9907059 K - s or c s d for J/y 0 R()=tan2()= 4.2 X10-3: deviation from ideal mixing angle f s or c d s Phys. Lett. B 60 (1976) 371 Phys. Lett. B 353 (1995) 319 Phys. Lett. B 592 (2004) 1 u K+ d + OZI suppressed Not OZI suppressed Phys. Lett. 5 (1963) 165 CERN Report Nos. TH-401 and TH-412 (1964) (unpublished) Prog. Theor. Phys. 35 (1966) 1061 Okubo Zweig Iizuka Suppression of Suppression of interaction with nucleons, non-strange mesons and resonances At high colliding energies at RHIC -- OZI suppression could be lifted Observed enhancement not due to OZI suppression in p+p collisions

  9. Golden ratio  meson in high energy collisions Remark A goldentool which can be used to address various aspect of heavy-ion collisions Strangeness enhancement in heavy-ion collisions at RHIC is due to formation of a dense partonic medium and not alone due to Canonical Suppression effects STAR Preliminary  meson Strangeness Enhancement Next meson - Partonic Collectivity, Recombination and Thermalization QGP Meet 2008 : Bedanga Mohanty

  10. y  2v2 dN/df dN/df 0  2p 0 f 2p Collectivity Pressure gradiant Initial spatial anisotropy x INPUT Spatial Anisotropy Interaction among produced particles OUTPUT Momentum Anisotropy QGP Meet 2008 : Bedanga Mohanty

  11. STAR : Phys. Rev. Lett. 99 (2007) 112301 PHENIX : Phys. Rev. Lett. 99 (2007) 052301 Partonic collectivity at RHIC Substantial v2 measured for mesons v2 similar to other mesons Constituent Quark Scaling observed Reflects partonic collectivity : Heavier s quarks flows as lighter u and d quarks To further strengthen the idea of partonic collectivity --not formed from KK coalescence (already discussed) --  likely decouples early in interactions and does not participate strongly in hadronic interactions QGP Meet 2008 : Bedanga Mohanty

  12. Au+Au ~ 3  ~ 3.5  frezee-out at RHIC just after Tc from Lattice QCD ~ 2.6  ~ 4  ~ 2.1  Van Hecke, Sorge, Xu (98) No decay b=2.0fm arXiv:nucl-th/0509061 STAR : Nucl. Phys. A 757 (2005) 102 arXiv:nucl-th/0606044 STAR : Phys. Lett. B 612 (2005) 181  possibly decouples early ~ 10 mb  <pT> is almost independent of centrality unlike anti-protons Indicates possibly  decouples early in the interaction decouples from the system early at RHIC energies

  13. STAR preliminary Au+Au@200GeV Cu+Cu@200GeV Recombination and Hints of Thermalization Clear change in spectral shape -- Exponential (~thermal) for central collisions -- Power law type (~ hard process) at high pT in peripheral collisions Monotonic rise of  ratio at low pT -- Good agreement with models based on  and production by thermal s-quark coalescence STAR : Phys. Rev. Lett. 99 (2007) 112301 arXiv: nucl-th:0406072 arXiv:0809.4737 QGP Meet 2008 : Bedanga Mohanty

  14. Golden ratio  meson in high energy collisions Remark A goldentool which can be used to address various aspect of heavy-ion collisions Strangeness enhancement in heavy-ion collisions at RHIC is due to formation of dense partonic medium and not alone due to Canonical Suppression effects STAR Preliminary  meson Strangeness Enhancement  meson : Partonic Collectivity and Thermalization The collectivity observed in heavy-ion collisions at RHIC is due to partonic interactions. Hints of formation of some kind of thermalized (partial?) system Next meson as a probe for QCD phase boundary QGP Meet 2008 : Bedanga Mohanty

  15.  : Probe QCD phase diagram • Supporting observations from previous • discussions - • -- Primordial production ~ 100% • - Decouples early from the system ~ TC • - Not formed from KK Coalescence • - Hadronic interactions small/OZI suppressed • -- ss structure and Strangeness enhancement • due to dense partonic matter formation • -- Substantial v2 observed in Au+Au 200 GeV • -- NCQ Scaling NA49 Key observable : v2 of  meson RHIC data suggests - collectivity observed in  due to partonic interactions Absence/reduction of collectivity and NCQ scaling of  could indicate system in Hadronic phase QGP Meet 2008 : Bedanga Mohanty

  16. Wu Kejun v2 expectation from AMPT Default setting, ~ 10 mb No NCQ Scaling observed Large v2 ofcould bedue to KK contributions Partonic Coalescence NCQ scaling observed QGP Meet 2008 : Bedanga Mohanty

  17. Golden ratio  meson in high energy collisions Remark A goldentool which can be used to address various aspect of heavy-ion collisions Strangeness enhancement in heavy-ion collisions at RHIC is due to formation of a dense partonic medium and not alone due to Canonical Suppression effects  meson Strangeness Enhancement  meson : Partonic Collectivity, Recombination and Thermalization The collectivity observed in heavy-ion collisions at RHIC is due partonic interactions. Hints of formation of some kind of thermalized (partial?) system  meson as a probe for QCD phase boundary Large Collectivity and Number of Constituent Quark Scaling of v2 -- clear indication matter went through partonic phase QGP Meet 2008 : Bedanga Mohanty

  18.  mesons : Summary QGP Meet 2008 : Bedanga Mohanty

  19. Highlights STAR Preliminary Strangeness enhancement at RHIC Due to formation of dense partonic medium Collectivity at RHIC Developed due to partonic interactions QCD phase boundary Small v2 andabsence of NCQ scaling - Hadronic phase Large  v2 and NCQ scaling - Partonic phase QGP Meet 2008 : Bedanga Mohanty

  20. b a De Divina Proportione Normal Human Heart Beats in rhythm  •  p-p+p0is suppressed compared to K-K+ (which is actually kinematically suppressed) "Feynman taught me that in strong interaction physics everything that can possibly happen does, and with maximum strength,only conservation laws suppress reactions. Here was a reaction that was allowed but did not proceed.” -- Zweig = 1.61803.. The Golden Ratio is a universal law : in which is contained the ground-principle of all formative striving for beauty and completeness in the realms of both nature and art, and which permeates, as a paramount spiritual ideal, all structures, forms and proportions, whether cosmic or individual, organic or inorganic, acoustic or optical; which finds its fullest realization, however, in the human form. -- Adolf Zeising QGP Meet 2008 : Bedanga Mohanty

  21. Back up QGP Meet 2008 : Bedanga Mohanty

  22. Hadronic matter Small v2 - Support from Models J.Phys.G32:1121-1130,2006 URQMD partonic Supporting arguments for small  v2 for hadronic matter -- v2 large only if there is partonic interactions Largev2 from KK coalescence, but  production unlikely from KK coalescence Hence small v2 expected if matter went through hadronic phase only QGP Meet 2008 : Bedanga Mohanty

  23. STAR : Phys. Rev. Lett. 99 (2007) 112301 High pT probing partonic matter STAR Preliminary STAR : arXiv:0809.4737 Observations : Suppression in 200 GeV Au+Au collisions No suppression in 200 GeV d+Au collisions Interpretation : Dense medium formed in 200 GeV Au+Au collisions Turn-off of suppression may indicate hadronic matter Advantage over other hadrons : Production likely via parton coalescence Understand difference in quark vs. gluon energy loss arXiv:0705.0953 QGP Meet 2008 : Bedanga Mohanty

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