Transcript Cosmology
Quantum Chromodynamics (QCD) Main features of QCD Confinement At large distances the effective coupling between quarks is large, resulting in confinement. Free quarks are not observed in nature. Asymptotic freedom At short distances the effective coupling between quarks decreases logarithmically. Under such conditions quarks and gluons appear to be quasi-free. (Hidden) chiral symmetry Connected with the quark masses When confined quarks have a large dynamical mass - constituent mass In the small coupling limit (some) quarks have small mass - current mass Confinement The strong interaction potential Compare the potential of the strong & e.m. interaction Vem q1q2 c 4 0 r r Vs c kr r c, c, k constants Confining term arises due to the self-interaction property of the colour field q1 q2 a) QED or QCD (r < 1 fm) r q1 b) QCD (r > 1 fm) q2 Charges Gauge boson Charged Strength QED QCD electric (2) g(1) no e2 1 em 4 137 colour (3) g (8) yes s 0.1 0.2 Asymptotic freedom - the coupling “constant” It is more usual to think of coupling strength rather than charge and the momentum transfer squared rather than distance. 2M Q2 W 2 M 2 M initial state mass energy transfer W final state mass Q momentum transfer In both QED and QCD the coupling strength depends on distance. e e In QED the coupling strength is given by: em Q2 1 3 lnQ 2 m 2 Q2»m2 where = (Q2 0) = e2/4 = 1/137 In QCD the coupling strength is given by: s Q 2 33 2n f 2 1 ln Q s 2 2 s 12 2 which decreases at large Q2 provided nf < 16. Q2 = -q2 Asymptotic freedom - summary Effect in QCD Both q-qbar and gluon-gluon loops contribute. + The quark loops produce a screening effect analogous to e e loops in QED But the gluon loops dominate and produce an anti-screening effect. The observed charge (coupling) decreases at very small distances. The theory is asymptotically free quark-gluon plasma ! “Superdense Matter: Neutrons or Asymptotically Free Quarks” J.C. Collins and M.J. Perry, Phys. Rev. Lett. 34 (1975) 1353 Main points Observed charge is dependent on the distance scale probed. Electric charge is conveniently defined in the long wavelength limit (r ). In practice em changes by less than 1% up to 1026 GeV ! In QCD charges can not be separated. Therefore charge must be defined at some other length scale. In general s is strongly varying with distance - can’t be ignored. Quark deconfinement - medium effects Debye screening In bulk media, there is an additional charge screening effect. At high charge density, n, the short range part of the potential becomes: r 1 1 1 V(r) exp where rD 3 r r n rD and rD is the Debye screening radius. Effectively, long range interactions (r > rD) are screened. The Mott transition In condensed matter, when r < electron binding radius an electric insulator becomes conducting. Debye screening in QCD Analogously, think of the quark-gluon plasma as a colour conductor. Nucleons (all hadrons) are colour singlets (qqq, or qqbar states). At high (charge) density quarks and gluons become unbound. nucleons (hadrons) cease to exist. Debye screening in nuclear matter High (color charge) densities are achieved by Colliding heaving nuclei, resulting in: 1. Compression. 2. Heating = creation of pions. Under these conditions: 1. Quarks and gluons become deconfined. 2. Chiral symmetry may be (partially) restored. The temperature inside a heavy ion collision at RHIC can exceed 1000 billion degrees !! (about 10,000 times the temperature of the sun) Chiral symmetry Chiral symmetry and the QCD Lagrangian Chiral symmetry is a exact symmetry only for massless quarks. In a massless world, quarks are either left or right handed The QCD Lagrangian is symmetric with respect to left/right handed quarks. Confinement results in a large dynamical mass - constituent mass. chiral symmetry is broken (or hidden). When deconfined, quark current masses are small - current mass. chiral symmetry is (partially) restored Example of a hidden symmetry restored at high temperature Ferromagnetism - the spin-spin interaction is rotationally invariant. Below the Curie temperature the underlying rotational symmetry is hidden. Above the Curie temperature the rotational symmetry is restored. In the sense that any direction is possible the symmetry is still present. Chiral symmetry explained ? Red’s rest frame Lab frame Chiral symmetry and quark masses ? a) blue’s velocity > red’s Red’s rest frame b) red’s velocity > blue’s Lab frame Blue’s handedness changes depending on red’s velocity Modelling confinement: The MIT bag model Modelling confinement - MIT bag model Based on the ideas of Bogolioubov (1967). Neglecting short range interactions, write the Dirac equation so that the mass of the quarks is small inside the bag (m) and very large outside (M) Wavefunction vanishes outside the bag if M and satisfies a linear boundary condition at the bag surface. Solutions Inside the bag, we are left with the free Dirac equation. The MIT group realised that Bogolioubov’s model violated E-p conservation. Require an external pressure to balance the internal pressure of the quarks. The QCD vacuum acquires a finite energy density, B ≈ 60 MeV/fm3. New boundary condition, total energy must be minimised wrt the bag radius. B Confinement Represented by Bag Model Bag Model of Hadrons Comments on Bag Model Bag model results Refinements Several refinements are needed to reproduce the spectrum of low-lying hadrons e.g. allow quark interactions Fix B by fits to several hadrons Estimates for the bag constant Values of the bag constant range from B1/4 = 145-235 MeV Results Shown for B1/4 = 145 MeV and s = 2.2 and ms = 279 MeV T. deGrand et al, Phys. Rev. D 12 (1975) 2060 Summary of QCD input QCD is an asymptotically free theory. In addition, long range forces are screened in a dense medium. QCD possess a hidden (chiral) symmetry. Expect one or perhaps two phase transitions connected with deconfinement and partial chiral symmetry restoration. pQCD calculations can not be used in the confinement limit. MIT bag model provides a phenomenological description of confinement. Still open questions in the Standard Model K*-(892) Resonances are: Luis Walter Alvarez 1968 Nobel Prize for “ resonance particles ” discovered 1960 • Excited state of a ground state particle. • With higher mass but same quark content. • Decay strongly short life time (~10-23 seconds = few fm/c ), width = natural spread in energy: = h/t. Breit-Wigner shape 0 2 4 Number of events 10 8 6 Chirality: Why Resonances ? 640 680 720 760 800 840 880 920 Invariant mass (K0+) [MeV/c2] minv E1 E2 2 p1 p 2 K* from K-+p collision system K p K*p K0 • Broad states with finite and t, which can be formed by collisions between the particles into which they decay. 2 Why Resonances?: • Surrounding nuclear medium may change resonance properties • Chiral symmetry breaking: Dropping mass -> width, branching ratio Bubble chamber, Berkeley M. Alston (L.W. Alvarez) et al., Phys. Rev. Lett. 6 (1961) 300. Strange resonances in medium Short life time [fm/c] K* < *< (1520) < 4 < 6 < 13 < 40 Rescattering vs. Regeneration ? Medium effects on resonance and their decay Red: before chemical freeze out products before (inelastic) and after chemical Blue: after chemical freeze out freeze out (elastic). Electromagnetic probes - dileptons q Dilepton production in the QGP The production rate (and invariant mass distribution) depends on the momentum distribution of q-qbar in the plasma. g* l+ l- q The momentum distributions f(E1) and f(E2) depend on the thermodynamics of the plasma. The cross-section for the sub-process (M) is calculable in pQCD. Reconstruct the invariant mass, M, of the dilepton pair’s hypothetical parent. Nf dN e 2 3 3 f d p1d p2 Nc N 2f 6 f E1 f E2 M v12 e 2 dtd x f 1 l l 3 Dilepton production from hadronic mechanisms 1. Drell-Yan 2. Annihilation and Dalitz decays 3. Resonance decays 4. Charmed meson decays qq l l l l l l g , , and J/ D l X high Mass low Mass discrete low Mass CERES low-mass e+e– mass spectrum Almost final results from the 2000 run Pb+Au at 158 GeV per nucleon comparison to the hadron decay cocktail Enhancement over hadron decay cocktail for mee > 0.2 GeV: 2.430.21 (stat) for 0.2 GeV<mee< 0.6 GeV: 2.80.5 (stat) • Absolutely normalized spectrum • Overall systematic uncertainty of normalization: 21% NA60 Low-mass dimuons Superb data!!! Mass resolution: 23 MeV at the position , and even peaks clearly visible in dimuon channel Net data sample: 360 000 events Deconfinement at Initial Temperature Matsui & Satz (1986): (Phys. Lett. B178 (1986) 416) Color screening of heavy quarks in QGP leads to heavy resonance dissociation. RHIC s = 200 GeV J/Ycc-bar) e+ +e, (bb-bar) e+ +e, + + Thermometer for early stages: Tdis(Y(2S)) < Tdis((3S))< Tdis(J/Y) Tdis((2S)) < Tdis((1S)) Total bottom / charm production Melting at SPS Decay modes: c J/Y + g b + g Lattice QCD: SPS TI ~ 1.3 Tc RHIC TI ~ 2 Tc The suppression of heavy quark states signature of deconfinement at QGP. J/ suppression Charmonium production The J/ is a c-cbar bound state (analogous to positronium) Produced only during the initial stages of the collision qq cc Thermal production is negligible due to the large c quark mass mc 1500MeV TQGP Charmonium suppression (Debye screening) Semi-classically (E = T + V) E(r) 2 r / rD p e s 2 r p2 ~ 1 r 2 mc 2 Differentiate with respect to r to find minimum (bound state) Find there is no bound state if 1 rD 0.84 s rD pQCD 2 1 9 s T For s = 0.52 and T = 200 MeV, rD(pQCD) = 0.36 fm Compare with rBohr = 0.41 fm (setting rD above) Conclusion: the J/ is not bound in the plasma under these conditions Onium physics – the complete program Melting of quarkonium states (Deconfinement TC) Tdiss(Y’) < Tdiss((3S)) < Tdiss(J/Y) Tdiss((2S)) < Tdiss((1S)) Future Measurements: Resonance Response to Medium Resonances below and above Tc: Temperature partons Shuryak QM04 Quark Gluon Plasma hadrons Hadron Gas Baryochemical potential (Density) Gluonic bound states (e.g. Glueballs) Shuryak hepph/0405066 Deconfinement: Determine range of T initial. J/and state dissociation Chiral symmetry restoration Mass and width of resonances ( e.g. leptonic vs hadronic decay, chiral partners and a1) Hadronic time evolution Hadronisation (chemical freeze-out) till kinetic freeze-out. Deconfinement: Melting of J/Y RHIC SPS J/Y normal nuclear absorption curve J abs 4.18 0.35mb Interaction length Projectile J/ L Target J/ suppression at SPS and RHIC are the same Strong signal for deconfinement in QGP phase RHIC has higher initial temperature Expect stronger J/ suppression Partonic recombination of J/ cent Npa Nco rt ll 0 10% 339 104 9 10 20% 222 590 Chiral Symmetry Restoration Vacuum At Tc: Chiral Restoration Data: ALEPH Collaboration R. Barate et al. Eur. Phys. J. C4 409 (1998) Measure chiral partners Near critical temperature Tc (e.g. and a1) a1 + Ralf Rapp (Texas A&M) J.Phys. G31 (2005) S217S230 Resonance Reconstruction in STAR TPC Energy loss in TPC dE/dx End view STAR TPC K- p p dE/dx (1520) (1385) K e momentum [GeV/c] p K(892) (1020) (1520) (1385) X1530 +K K+K p +K + X+ • Identify decay candidates (p, dedx, E) • Calculate invariant mass Invariant Mass Reconstruction in p+p Invariant mass: (1520) STAR Preliminary (1520) minv E1 E2 2 p1 p 2 2 — original invariant mass histogram from K- and p combinations in same event. — normalized mixed event histogram from K- and p combinations from different events. (rotating and like-sign background) Extracting signal: After Subtraction of mixed event background from original event and fitting signal (Breit-Wigner). Resonance Signal in p+p collisions STAR Preliminary STAR Preliminary p+p K(892) ΦK+K- Statistical error only X STAR Preliminary (1385) Δ++ STAR Preliminary p+p Invariant Mass (GeV/c2) Resonance Signal in Au+Au collisions STAR Preliminary *0 K + K(892) K*0 Au+Au minimum biaspT 0.2 XX *± +*± GeV/c |y| 0.5 (1520) (1020) STAR Preliminary STAR Preliminary Estimating the critical parameters, Tc and c Mapping out the Nuclear Matter Phase Diagram Perturbation theory highly successful in applications of QED. In QCD, perturbation theory is only applicable for very hard processes. Two solutions: 1. Phenomenological models 2. Lattice QCD calculations Lattice QCD Quarks and gluons are studied on a discrete space-time lattice Solves the problem of divergences in pQCD calculations (which arise due to loop diagrams) There are two order parameters 1. The Polyakov Loop 2. The Chiral Condensate 0.5 4.5 15 35 L ~ Fq ~ mq 75 GeV/fm3 /T4 Lattice Results Tc(Nf=2)=1738 MeV Tc(Nf=3)=1548 MeV (F. Karsch, hep-lat/9909006) T = 150-200 MeV ~ 0.6-1.8 GeV/fm3 T/Tc Lattice QCD: the latest news (critical parameters at finite baryon density) Phenomenology I: Phase transition The quark-gluon and hadron equations of state The energy density of (massless) quarks and gluons is derived from Fermi-Dirac statistics and Bose-Einstein statistics. p 3dp g 2 bp 2 e 1 1 q 1 g p3 dp 2 2 e b p 1 2T 4 30 7 2T 4 2 T 2 4 q q 2 120 4 8 where is the quark chemical potential, q = - q and b = 1/T. Taking into account the number of degrees of freedom TOT 16 g 12 q q Consider two extremes: 1. High temperature, low net baryon density (T > 0, B = 0). B = 3 q 2. Low temperature, high net baryon density (T = 0, B > 0). Phenomenology II: critical parameters High temperature, low density limit - the early universe Two terms contribute to the total energy density For a relativistic gas: For stability: Low temperature, high density limit - neutron stars Only one term contributes to the total energy density By a similar argument: qg 37 2 30 T4 1 Pqg qg 3 Pnet Pqg B 0 14 90 Tc 2 B 37 q 3 2 100 170 MeV 4 q 2 c 2 2 B 14 300 500 MeV ~ 2-8 times normal nuclear matter density given pFermi ~ 250 MeV and ~ 23/32 How to create a QGP ? energy = temperature & density = pressure