Introduction to QCDLayoutEssential ingredientsA brief history ...Energy scalesQuantum ChromodynamicsConfinementAsymptotic freedom - effective chargeAsymptotic freedom - the coupling “constant”Asymptotic freedom - summaryQuark deconfinement - medium effectsDebye screeningDebye screening in nuclear matterChiral symmetryChiral symmetry explained ?Estimating the critical parameters, Tc and ecThe MIT bag modelBag model resultsPhase transition phenomenologyEstimates of the critical parametersThe quark-hadron phase diagramLattice QCDSummary of lecture 1Introduction to QCDadopted from Peter G. JonesTHE UNIVERSITYOF BIRMINGHAM1.2Peter G. JonesLayout•Phase transitions in the earlier universe–The sequence of events t = 10-43-10-5 s after the Big Bang–Phase transitions in the early universe–The QCD phase transition is the most recent of these–It defines the moment when the strong interaction became STRONG–Is it possible to study this phase transition in the laboratory ?•Features of QCD–Confinement of quarks (r ~ 1 fm)–Asymptotic freedom (r  0)–Quark masses and chiral symmetry•Phase transition phenomenology–MIT bag model•Lattice QCD–Estimates of the critical parameters1.3Peter G. JonesEssential ingredients•The structure of matter•Fundamental constituents of the Standard Modelelectronnucleus nucleonsproton neutrongluons quarks1500 MeV150 MeVud sc tbeeQuarksLeptons5 MeV10 MeV 5000 MeV180000 MeVProton (uud)Neutron (udd)Table of “bare” quark masses, leptons and gauge bosonsGaugebosonsGluonW±,Z0PhotonGraviton ?1.4Peter G. JonesA brief history ...Temperature (oK)Time after the Big Bang (seconds)10-910-610-31 103106109101210151018110310610910121015Quark-Gluon PlasmaHadronizationNucleosynthesisAtoms FormedNowAccelerators1.5Peter G. JonesEnergy scales•The beginningThe universe is a hot plasma of fundamental particles … quarks, leptons, force particles (and other particles ?)10-43 s Planck scale (quantum gravity ?) 1019 GeV10-35 s Grand unification scale (strong and electroweak) 1015 GeVInflationary period 10-35-10-33 s10-11 s Electroweak unification scale 200 GeV•Micro-structure10-5 s QCD scale - protons and neutrons form 200 MeV3 mins Primordial nucleosynthesis 5 MeV3105 yrs Radiation and matter decouple - atoms form 1 eV•Large scale structure1 bill yrs Proto-galaxies and the first stars3 bill yrs Quasars and galaxy spheroids5 bill yrs Galaxy disksToday Life !1.6Peter G. JonesQuantum ChromodynamicsImportant 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 mass1.7Peter G. JonesConfinement•The strong interaction potential–Compare the potential of the strong and electromagnetic interaction–Confining term arises due to the self-interaction property of the colour fieldVemq1q240rcrVsc r krc, c , k constants eme240hc in MKS units h= c =1 natural units001 Heaviside- Lorentz unitsQED QCDCharges electric (2) colour (3)Gauge boson (1) g (8)Charged no yesStrengtheme241137s0.1  0.2q1q2q1q2a) QED or QCD (r < 1 fm)b) QCD (r > 1 fm)r1.8Peter G. Jones•Influence of the “vacuum”–In relativistic quantum mechanics, vacuum fluctuations are possible.–Need to consider interaction with virtual antiparticle-particle pairs.–Analogy with electric charge in a dielectric medium.–Introduces the concept of an effective charge.•Effect in QED–The “vacuum” is also a polarisable medium.–Charges are surrounded by virtual e+e- pairs.–Observed charge increases when r < d.–Where d is given by the electron Compton wavelength. Asymptotic freedom - effective chargeq+-+-+-+-+-+-+-qd ~ molecular spacing Et ~ ht ~ h/ mc2DCct h/ mcdielectric1.9Peter G. Jones•It is more usual to think of coupling strength rather than charge–and the momentum transfer squared rather than distance.•In both QED and QCD the coupling strength depends on distance.–In QED the coupling strength is given by: where  = (Q2  0) = e2/4 = 1/137–In QCD the coupling strength is given by: which decreases at large Q2 provided nf < 16.Asymptotic freedom - the coupling “constant”2MQ2 W2 M2M initial state mass energy transferW final state mass Q momentum transferemQ2 13 ln Q2m2  sQ2 s2 1 s2 33  2nf 12ln Q22 Q2»m2Q2 = -q2e  e1.10Peter G. JonesAsymptotic 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.1.11Peter G. JonesQuark 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: 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