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QCD Phase Diagram, Phase Transition and Fluctuations

QCD Phase Diagram, Phase Transition and Fluctuations. Bedanga Mohanty Physics group, VECC, Kolkata. STAR Preliminary. First observation of anti-hypertriton Relevant to physics of neutron star. QM09 : J. Chen. Heavy Ion Collisions. Experimentally possible. Explore the QCD phase diagram.

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QCD Phase Diagram, Phase Transition and Fluctuations

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  1. QCD Phase Diagram, Phase Transition and Fluctuations Bedanga Mohanty Physics group, VECC, Kolkata

  2. STAR Preliminary First observation of anti-hypertriton Relevant to physics of neutron star QM09 : J. Chen Heavy Ion Collisions Experimentally possible Explore the QCD phase diagram J. D. Bjorken Physical Review D 27 (1983) 140 Supported by theory USA-NSAC 2007 Long-range Plan F. Karsch, Prog. Theor. Phys. Suppl. 153, 106 (2004)

  3. Spontaneous Z3 breaking B = 0 B > 0 Chiral symmetry restored K. Rajagopal and F. Wilczek, Handbook of QCD E. Laerman, O. Philipsen Ann. Rev. Nucl. Part. Sci. 53, 163, 2003 Phase Structure

  4. Higher Moments of Charge Fluctuations in QCD at High Temperature -- C. Miao Non-Gaussian Fluctuations Near the QCD Critical Point -- M. Stephanov Signals of the QCD Critical Point in Hydrodynamic Evolution -- C. Nonaka Critical opalescence - T. Kuihiro Experimental study of the spontaneous strong parity violation -- S. Voloshin Search for the Critical Point of Strongly Interacting Matter in NA49 -- K. Grebieszkow Fluctuations of Conserved Quantities Using Higher Order Moments in STAR Experiment -- T. Nayak Search for QCD critical point .. kurtosis of net proton in STAR experiment - B. Mohanty Probing the QCD Phase Diagram with Chiral Effective Models -- C. Sasaki p/ fluctuations in Au+Au collisions- G. Westfall The Quarkyonic Phase Transition and the FPP-NJL Model in Large and Finite Nc -- L. McLerran p/ fluctuations in Au+Au collisions- J. Tian SPS low-energy scan / FAIR prospects -- C. Hoehne Critical Points in the QCD Phase Diagram with Two Flavors of Quarks -- J. Kapusta The NA61/SHINE Experiment at the CERN SPS - A. Laszlo Bulk properties at 9.2 GeV in STAR - L. Kumar Parity violation in Hot QCD -- D. Kharzeev CBM at FAIR - J. M. Heuser At QM2009 Finite temperature latice QCD : Present status -- P. Petreczky QCD Transition Temperature: Approaching the Continuum on the Lattice -- Z. Fodor Fixed Scale Approach to the Equation of State on the Lattice -- Kazuyuki Kanaya The Chiral Critical Surface of QCD -- O. Philipsen Critical Point in Finite Density Lattice QCD by Canonical Approach -- Shinji Ejiri The Lattice QCD Equation of State and implications for Hydrodynamic Modeling of Heavy Ion Collisions -- R. Soltz Continuum limit of Gloun plasma - S. Gupta QCD critical point using canonical ensemble - A. Li

  5. Part - 1 Lattice QCD results at B ~ 0 Experimental results on fluctuations and charge correlations Before these, few things to keep in mind regarding Lattice results …

  6. a : Lattice spacing N : Sites in imaginary time T : Temperature Reality = continuum limit Smaller “a”, larger Ntat fixed T (B) aNt ~ 1/T Spatial volume also important QM09 : P4 : S. Ejiri Naik and P4 : R. Soltz (C) Lattice Action Smaller Nt - distortions due to cutoff effects EOS computation cost ~ a-11 P. Hegde et al, Eur. Phys. C55, 423 (2008) Different approach by QM09 : K. Kanaya “T integral method” T varied by Nt at fixed “a” (D) Temperature change : Usually fix Ntvary “a” (g : lattice gauge coupling) T. Umeda et al., arXiv : 0809.2842 (E) Setting quark masses Lines of constant Physics - m/m = const Number of quark flavours : 2+1 flavour with mu = md and ms Lattice QCD (A) Quantum statistical ensemble in thermal equilibrium Simulate : Z = Tr exp(-H/T)

  7. 1st order : Peak height ~ V Peak width ~ 1/V Cross over : Peak height ~ const. Peak width ~ const. 2nd order : Peak height ~ V T grows with 6/g2, g : gauge coupling No significant volume dependence (8 times difference in volumes) Phase transition at high T and  = 0 is a cross over Lattice results on electroweak transition in standard model is an analytic cross-over for large Higgs mass K. Kajantie et al., PRL 77, 2887-2890,2006 Order of Phase Transition for B ~ 0 Physical quark masses Continuum limit Simulations along Lines of Constant Physics mK/m = 3.689; fK/m = 1.185 Staggered fermionic action Y. Aoki et al., Nature443:675-678,2006 Relevant to LHC and current RHIC regimes

  8. De-confinement TC ~ 175 (2)(4) - 192 (7)(4) MeV - 185 - 195 MeV Chiral and deconfinement same T or different T ? Transition Temperature Point of sharpest change in temperature dependence chiral susceptibility, the strange quark number susceptibility and the renormalized Polyakov-loop QM09 : Z. Fodor R. Soltz Possible sources of differences : (a) Ambiguity in locating Tc for cross-over; (b) Physical observable used to set the scale (r0, fK); (c ) Preferred renormalization of chiral susceptibilities (d) Use Wilson fermions

  9. Transition Temperature V. G. Bornyakov et al, POS Lat2005, 157 (2005) Y. Maezawa et al, hep-lat/0702005 C. Bernard et al, Phys. Rev. D 71, 034504 (2005) M. Cheng et al, Phys. Rev. D 74, 054507 (2006) Y. Aoki et al, Phys. Lett. B 643, 46 (2006); 0903.4155 • Consequence for heavy-ion phenomenology • both at LHC and RHIC: • ~ T4; Results in ~ 60% in difference energy density at TC F. Karsch : Lattice 2007

  10. Velocity of sound Important for heavy ion phenomenology (T 1/cs2const QM08 :S. Gupta M. Cheng et al., Phys. Rev. D 77, 014511 (2008) 107 Agreement with perturbation theory Consistent with Stefan-Boltzmann limit G. Endrodi et al., PoS LAT2007:228,2007 Lattice : Equation Of State gparton ~ 47.5  ~ g (2/30) g ~ 3 QM09: P. Petreczky R. Soltz 15% deviation from Ideal gas at 4TC Calculations with larger spatial volumes ?

  11. (DpT)2/pT2 ~ (DT)2/T2 = 1/Cv (DN)2/<N> ~ 1/ Fluctuations in particle ratios -- Sensitive to particle numbers at chemical FO not kinetic FO -- Volume effects may cancel S. Jeon, V. Koch, PRL 83, 5435 (1999) Fluctuation in conserved quantities : net charge, net baryon number, net strangeness -- Related to corresponding susceptibilities -- Given strong longitudinal expansion, fluctuations in QGP may be preserved during hadronisation -- Conservation laws limit their dissipation S. Jeon, V. Koch, PRL 85, 2076 (2000) M. Asakawa, U. W. Heinz, B. Muller PRL 85, 2072 (2000) Fluctuation : Deconfinement Transition For a thermodynamic system Fluctuation in experimental observables related to thermodynamic quantities <(DE)2> ~ T2Cv(T) M. Stephanov et al., PRD 60, 114028 (1999) ~ Naively L. Stodolsky, PRL 75,1044 (1995) S. Mrowczynski, PLB 430, 9 (1998) General approach Second moment of event-by-event distributions of multiplicity, mean pT, ET after removing non-dynamical fluctuations.

  12. Fluctuation Measures Dominantly looking at second moment, constructions motivated for removing non-dynamical fluctuations

  13. Ratio Fluctuation Results p/K STAR : arXiv : 0901.1795 p/ K/ QM09 : G. Westfall QM09 : J. Tian QM09 : V. Konchakovski

  14. Conserved Quantity Fluctuation Results Mostly fluctuation in net-charge has been studied PHENIX STAR NA49

  15. Experimental : Possible Deconfinement Observables QM09 : Y. Xu PHENIX : direct photon arXiv:0804.4168 Tinitial > TC (Lattice) initial > C (Lattice) Observables from SPS indicating possible phase transition was discussed in C. Hoehne Plenary Talk

  16. Discussion Why we do not see fluctuations reflecting QGP to hadronic phase transition - One possibility is dissipation of fluctuations Is Relaxation > hadronic This leads to the issue of acceptance needed to measure the primordial fluctuations ymin > ycoll (mean change in rapidity due to collisions) ~ (diffusion coefficient) free (mean free time) M.A. Aziz et al, PRC 70, 034905 (2004) E.V. Shuryak et al, PRC 63, 064903 (2001) B. Mohanty et al, PRC 67, 024904 (2003) What is the expectation for a cross-over phase transition ?

  17. If one observes a difference between NL and NR clear indication of parity violations But how do we experimentally distinguish L.H and R.H quarks (we detect hadrons) Polarization in magnetic field ? For finite volume : Charge difference in upper and lower hemisphere Chiral Magnetic Effect Topological structure of QCD vacuum -- Parity violations in strong interactions Assume quark are mass less : (Helicity/Chirality) R.H quarks & anti-quarks : s and p same direction L.H. quarks & anti-quarks : s and p opposite direction Mass less quarks can change chirality by interacting with gluons. Axial Ward Identity relates chirality to properties (topology) of gluon fields. D.E. Kharzeev et al, NPA 803, 227 (2008) u : Positive charge d : negative charge N L,R : total number of Left/Right handed q+qbar of a particular flavour QM09 : D. Kharzeev

  18. Parity even Physical background QM09 : S. Voloshin Charge asymmetry observed in STAR experiment. Investigations so far indicate they could only be consistent with parity violation effects in strong interactions. De-confined phase needed Chirally symmetric phase needed K. Fukushima et al, PRD 78, 074033 (2008) STARPreliminary Chiral Magnetic Effect Topological structure of QCD vacuum -- Parity violations in strong interactions. Heavy ion collisions : Possibly we have produced a de-confined quark-gluon matter. Large magnetic field in the direction of angular momentum. Charge separation can take place along this direction. Angular momentum is perpendicular to reaction plane. Look for charge asymmetries. S. Voloshin PRC 70, 057901 (2004)

  19. Part - 2 T. Andrews. Phil. Trans. Royal Soc., 159:575, 1869 QCD Critical Point Thermodynamic quantities ~ correlation length Critical exponents, are universal, depend on degrees of freedom in the theory and their symmetry, no dependence on details of interactions. Different physical systems == same universality class T > TC T~TC T < TC Critical Opalescence as observed in CO2 liquid-gas transition For example : Liquid-Gas system critical point and QCD critical point Same universality class : Z2 Long range correlations, density fluctuations

  20. Canonical ensemble used M = 770 MeV Nf = 2 P4-improved staggered quark action First order phase transition for T/Tc < 0.83 and q/T > 2.3 Existence of critical point suggested First Order Phase Transition (B > 0) QM09 : S. Ejiri PRD 78, 074507 (2008) μ∗q /T is the chemical potential that gives a minimum of the effective potential

  21. Critical Points : Linear model with quarks QM09 : C. Sasaki Conventional picture QM09 : J. Kapusta Aim : Study phase diagram of Linear  model coupled to two light flavour quarks of same mass Includes thermal fluctuations of meson and fermion fields Vacuum pion mass varied : 0 to 300 MeV (Can compare to Lattice studies) Studies at non-zero chemical potential No phase transition For m,vac > 321 MeV Constants in the model Pion decay constant f = 92.4 MeV  mass (m)= 700 MeV Mass of quark = 313 MeV m varied : 0 - m/2 Exotic picture Two critical points Phys.Rev.C79:015202,2009

  22. QCD Models : Critical Point Compilation by Mikhail Stephanov QM09 : C. Sasaki Need first principle calculations - Lattice

  23. Lattice : QCD Critical Point Expectation value of an observable M : Dirac Matrix SG : Gluonic action For > 0 the quark determinant becomes complex Issue for non Zero , Det M is not positive definite -- Sign problem • Four approaches • Reweighting : Z = < e -S() det D() / e-S(0) det D(0) >=0 • Taylor expansion of thermodynamic observables in /T about  = 0 • Imaginary chemical potential :  imaginary, fermion determinant positive • Canonical ensemble - predicts existence of QCD critical point (TE ~ 160 MeV and E ~ 600 MeV, m ~ 700 MeV) QM09 : A. Li

  24. Reweighting Taylor Expansion R. Gavai and S. Gupta Phys. Rev. D 78, 14503 (2008) Z. Fodor and S.D. Katz JHEP 0404, 50 (2004) TE = 162 +/- 2 MeV E = 360 +/- 40 MeV TE/TC = 0.94 +/- 0.01 E /TE = 1.8 +/- 0.1 QM09 : Owe Philipsen Imaginary Chemical Potential P. De Forcrand and O. Philipsen PoS LATTICE2008, 208 (2008) c1 > 0 c1 < 0 nf = 2+1 continuum limit ? Spatial volume, stable results for different Nt ? Lattice : QCD critical point

  25. Higher Moments At Critical point < (N)2> ~ 2 < (N)3> ~ 4.5  = Correlation length Value limited in heavy-ion collisions Finite size effects < 6 fm Critical slowing down, finite time effects  ~ 2 - 3 fm (model assumptions) < (N)4> - 3 < (N)2>2 ~ 7 Higher sensitivity as stronger dependence on  M. A. Stephanov, Phys. Rev. Lett. 102, 032301 (2009) Non Gaussian features increase if the system freezes-out closer to QCD Critical point Signature of QCD Critical Point : Higher Moments Challenging to measure B. Berdnikov & K. Rajagopal, Phys. Rev. D 61, 105017 (2000) Stephanov, Rajagopal, Shuryak, Phys. Rev. D 60, 114028 (1999) Experimentally : Look for non-monotonic variation of higher moments of multiplicity distributions and mean pT distributions as a function of beam energy

  26. Q = B/2 + I3 Q ~ (1/VT) < (Q)2> = (1/4) B + I ~ (1/VT) < (Np-pbar)2> Net Proton number fluctuations ~ singularity of the charge and baryon number susceptibility -iso-spin blindness of  field S. Gupta Y. Hatta and M. A. Stephanov, Phys. Rev. Lett. 91, 102003 (2003) Signature of QCD Critical Point : Net protons Equilibrium thermodynamic system Divergence of susceptibilities at Tc Susceptibilities are related to higher moments of multiplicity observables. Also seen in QCD model based calc. B = 0 QM09 : C. Sasaki QM09 :Chuan Miao Net Proton number is sufficient Connection between Lattice and Experimental data possible M. Cheng et al., arXiv: 0811.1006

  27. Experimental Results on Higher Moments QM09 : T.K. Nayak B. Mohanty Net Protons First look at net-protons First look at higher moments Monotonic behavior observed We are probing a small B region STAR Preliminary F2 = (2 - <N>)/<N>2 STAR Preliminary Setting the baseline for the future QCD critical point search program Npart

  28. Signature of QCD Critical Point : pbar/p QM09 : C. Nonaka The presence of a critical point deforms the isoentropic trajectories (S/nB = constant) The critical point serves as an attractor of the hydrodynamical trajectories. pbar/p ~ exp (-2B/T) Below TC : Both T and B decrease for critical point B remains fairly constant for others trajectories Experimentally observable : Drop in pbar/p vs. pT (Coalescence region) Provided nucleons of high pT are chemically frozen out earlier - supported by UrQMD simulations M. Asakawa et al, PRL 101, 122302 (2008)

  29. Experimental Results on pbar/p vs. pT Slope vs. Beam Energy/B Phys. Rev. C73, 044910 (2006) Phys.Rev. C78, 034918 (2008) QM09 : K. Grebieszkow Fitting Procedure : y = a (mT - m) + b No large drop in ratio observed for intermediate pT range STAR STAR : PLB 655, 104 (2007) PRL 97, 152301 (2006)

  30. Signature of QCD Critical Point : Disappearance of Mach Cone QM09 : Teiji Kunihiro Study focused on critical dynamics around QCD critical point with relativistic dissipative hydrodynamics Uses the idea of coupling the density fluctuations to thermal energy Rayleigh peak At the soft mode around QCD critical point is the thermally induced density fluctuations (Rayleigh peak) and the sound modes get suppressed (Brillouin peak) Brillouin peak Brillouin peak Experimentally : Disappearance of mach cone like signals STAR : Phys. Rev. Lett. 102, 052302 (2009)

  31. Critical Point ? B ~ 250 MeV T ~ 178 MeV SPS Fluctuation Results on QCD Critical Point QM09 : K. Grebieszkow Assuming correlation length 3-6 fm and experimental acceptances No signature for energy dependence System size dependence shows a jump Stephanov, Rajagopal, Shuryak, Phys. Rev. D 60, 114028 (1999) Hatta, Ikeda Phts. Rev. D 67, 014028 (2003)

  32. Part - 3 New Phase of QCD New Experimental Programs

  33. New Phase of Matter in Large Colour Limit In the limit of large number of colors (Nc) There could exist three phase of matter Confined phase De-confined phase Quarkyonic phase Matter has and p that of a gas of quarks yet confined. (O(Nc)) QM09 : C. Sasaki QM09 : L. McLerran T Debye Screened Baryons Number N ~ Nc Chiral 2 Quark Gluon Plasma RHIC LHC Critical Point Baryon energy density ~ Meson energy density SPS Confined No Baryons N ~0(1) Not Chiral Confined Baryons N ~ NcNf Chiral FAIR AGS Color Superconductivity Order parameter Baryon number Quarkyonic Matter Confined Matter Liquid Gas Transition Conjectured Phase Diagram for Nc = 3 Experimental signature : Baryon-Baryon correlations to look for nucleation of baryon rich bubbles surrounded by baryon free regions QM09 : P. Sorensen & A. Mocsy

  34. Looking for onset of various observations New Program : Explore QCD phase diagram Pb+Pb 17.3 GeV Au+Au 200 GeV PHENIX : PRL 101, 232301 (2008) Jet quenching WA98 : PRL 100, 242301 (2008) Partonic collectivity Baryon-meson difference meson will play a crucial role QM09 : S. Shi STARPreliminary QM09 : S. Voloshin Chiral Magnetic effect

  35. Cross over QCD critical point QGP 1st order Hadrons R.V. Gavai and S. Gupta, Phys.Rev.D71:114014,2005 New Program : Look for QCD critical point At RHIC Most lattice calculation predicts critical point B > 160 MeV Current studies at RHIC probes B ~ 14 -60 MeV Need a beam energy scan program - but fixed target experiments were there .. The real voyage of discovery consists not in seeking new lands but seeing with new eyes. -- Marcel Proust, French novelist, 1871-1922.

  36. RHIC Critical Point Search Program - Advantage Hadron Mass 200 GeV Beam Energy 62.4 GeV 9.2 GeV Uniform acceptance for different particle species and for different beam energies in the same experimental setup(advantage over fixed traget expt.)

  37. RHIC Critical Point Search Program - Advantage G. Roland Collider experiment : Variation of particle density with beam energy slower. Occupancy in detectors reasonable compared to fixed target experiments at similar collision energy

  38. RHIC - Collider Demonstrated Capabilities All setup worked very well with RF harmonic number 366 Defocusing sextupole reversal and octupole improved blue lifetime by factor 4 ~ 50-60% injection efficiency STAR collisions about 13h after 1st beam and PHENIX about 24h after 1st beam Experiment useful event rates 0.7-1Hz with 56 bunches. Maximum luminosity 3.5 1023 cm-2s-1 Average luminosity 1.2 1023 cm-2 s-1 Factor of 3 increase in luminosity easily achievable

  39. STAR Preliminary RHIC - Experiments Demonstrated Capabilities Results with only 3000 events ! QM09 : L. Kumar These results from the lowest beam energy collisions at RHIC demonstrate experiment’s readiness to take up the proposed Beam Energy Scan Program. Large and uniform acceptance for all beam energies in a collider set up, excellent particle identification (TPC+TOF) and higher statistics will provide ideal data to experimentally measure fluctuations/Kurtosis to locate QCD critical point

  40. RHIC Critical Point Search - Future Plans Experiments have proposed the following plan May a good idea to start with energies common to both experiments Run Number 9071097 First paper from RHIC was based on ~ few thousand events; PHOBOS : PRL 85 (2000) 3100 “The measurements shown here represent the first step toward the development of a full picture of the dynamical evolution of nucleus-nucleus collisions at RHIC energies.” The results shown at QM2009 from RHIC low energy test running : “These measurements shown here could become the first step towards a detailed study of the QCD phase diagram at RHIC”

  41. What is the difference vs. NA49 ? Experimental set up : New spectator calorimeter for centrality selection Forward Time-Of-Flight Beam pipe TPC readout Physics Program : Studying QCD Critical Point and Onset of various observations with varying colliding ion size, collision centrality and having a proper p+p baseline QM09 : A. Laszlo New Program : SPS - SHINE A significant difference between freeze-out and transition temperature can lead to dilution of the signatures of the QCD critical point. One way address this is to vary system size/colliding ion size. F. Becattini et al., PRC 73, 044905

  42. New Program : FAIR - CBM Claudia Hoehne • CBM at SIS 300 will start in 2017 • 10-45A GeV beam energy, high availability of beam (order of 10 weeks per year), interaction rates up to 10 MHz • “CBM light” at SIS 100 in 2015 Au beam up to 11A GeV, p beam up to 30 GeV (multistrange hyperons, charm production in pA) • Assume 10 weeks beam time, 25A Gev Au+Au (minbias), no trigger, 25 kHz interaction (and storage) rate: • “unlimited statistics” of bulk observables, e.g. ~1010-11 kaons, 1010Λ • low-mass di-electrons with high statistics, 106 -mesons (each) • multistrange hyperons with high statistics, 108, 106 QM09 : C. Höhne, J. Heuser High luminosity, rare probes, higher B reach

  43. Current Status Lattice and other QCD based models : B = 0 - Cross-over TC ~ 170-195 MeV B > 160 MeV - QCD critical point Experiments : See distinct signatures that relevant d.o.f are quark and gluons [Tinitial(direct photons) > TC(Lattice)] No signatures of QCD critical point established, possible hints at SPS. New distinct signatures proposed by Lattice and QCD based model calculations. Future program : Exploring the QCD phase diagram needs to be vigorously pursued to know properties of basic constituents of matter under extreme conditions.

  44. Future With the starting of LHC (B~ 0) - we have unique opportunity to understand the properties of matter governed by quark-gluon degrees of freedom at unprecedented initial temperatures achieved in the collisions. To make the QCD phase diagram a reality equal attention needs to be given to high baryon density region. These two complementary programs will make our understanding clearer on • characterization of quark-gluon matter at varying baryon density • finding the QCD critical point and • locating the QCD phase boundary

  45. Thanks Thanks to the Organizers. Thanks to …….. J. Alam, R. Bhalerao, A. Bhasin , X. Dong, K. Grebieszkow, S. Gupta, J. M. Heuser, C. Hoehne, J. Kapusta, T. Kunihiro, L. Kumar, A. Laszlo, M. Lisa, L. Mclerran, T. K. Nayak, C. Nonaka, P. Petercky, C. Pruneau, S. Raniwala, K. Rajagopal, L. Ruan, C. Sasaki, P. Sorensen,M. Stephanov, G. Westfall, N. Xu, Z. Xu, and All other STAR & WA98 Collaborators … for inputs/discussions/suggestions See you at next Quark Matter …

  46. Multiplicity Fluctuation Results WA98 NA49 PHENIX QM09 : K. Grebieszkow

  47. pT Fluctuation/Correlation Results QM09 : K. Grebieszkow CERES STAR PHENIX NA49

  48. Old Program : Fixed Target Hadron Mass NA49 : arXiv : 0808.1237 6.3 GeV 7.6 GeV Beam Energy 8.7 GeV 12.3 GeV 17.3 GeV Non-Uniform acceptance for different particle species and for different beam energies in the same experimental setup

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