Heavy-Ion Physics Lecture 1: QCD and the Quark-Gluon Plasma

Transcription

1 Heavy-Ion Physics Lecture 1: QCD and the Quark-Gluon Plasma Professor David Evans The University of Birmingham Nuclear Physics Summer School Queen s University, Belfast XX th August 2017

2 Outline of Lectures Lecture 1: The Basics Aims of H.I. physics The quark model The strong interaction The Quark-Gluon Plasma (QGP) MIT Bag Model How to make a QGP Lecture 2: ALICE exp. Event characterisation Energy density Temperature Size of system Liquid or gas? Selected probes Strangeness Jet/high p T suppression Quarkonium suppression ALICE upgrade (if time)

3 Aims of Ultra-Relativistic Heavy Ion Physics Study strongly interacting matter at extreme energy densities over large volumes and long time-scales. Study the role of chiral symmetry in the generation of mass in hadrons (accounts for over 98% of mass of nuclear matter). Study the nature of quark confinement. Study the QCD phase transition from hadronic matter to a deconfined state of quarks and gluons - The Quark-Gluon Plasma. Study the physics of the Quark-Gluon Plasma (QCD under extreme conditions). 3

4 Elementary Particles Protons and neutrons are made from two types of quarks: Up (u) and Down (d). u-quarks have electric charge +2/3 while d-quarks have charge 1/3 (electron has electric charge -1 in these units). Proton Neutron +2/3 U -1/3 d +2/3 U -1/3 d +2/3 U -1/3 d

5 Elementary Particles Actually, a proton or neutron, with any energy will probably look more like this. Full of sea-quarks and anti-quarks 5

6 Family of Particles So, there is a family of particles: Up quark (u) Down quark (d) Electron (e - ) Electron neutrino ( e ) Mass ~ ~ ~ < 10-8? (relative to the mass of a single proton) All visible matter (the whole Periodic Table) is made up of the first three particles. 6

7 BUT. Nature supplies us with two extra families that are very much heavier: leptons quarks up down e e charm strange top bottom 7

8 Virtual Particles & the Forces The forces between fundamental particles are mediated by virtual carrier particles. For example, the electromagnetic interaction between two charged particles (say two electrons) is understood to be due to the exchange of virtual photons. A virtual particle is one that violates conservation of energy, but only for a short period of time ( t < ħ/ E) it borrows energy using the Heisenberg uncertainty principle. 8

9 The Electro-Magnetic Force Electromagnetic Force 1 electric charge (& its opposite charge) Mediated by photons (Of course, photons do not have electric charge themselves) Potential energy between charges, a distance r apart goes as: V em = α r The electric field lines spread out from the electric charges. So the force between electrically charged objects gets weaker as the objects are moved apart 9

10 The Strong Force Strong Force 3 colour charges (red, green, blue) anti-quarks carry anti-colour charge ( red, green, blue) Mediated by gluons 8 types of gluons gluons carry colour themselves (so can interact with each other as well) So rather than spreading out, the strong field forms a string of gluons between coloured objects (quarks)

11 The Strong Force Strong Force 3 colour charges (red, green, blue) anti-quarks carry anti-colour charge ( red, green, blue) Mediated by gluons 8 types of gluons gluons carry colour themselves (so can interact with each other as well) So rather than spreading out, the strong field forms a string of gluons between coloured objects (quarks)

12 The Strong Force Free quarks are not observed experimentally Potential energy between quarks: V = - (4 s / 3r) + kr Linear term need infinite energy to have a free object with colour. (k ~ 1 GeV/fm) Free particles must have no net colour i.e. made of 3 quarks: Baryon (e.g. proton) b r g Or quark & anti-quark: Meson (e.g. pion) Theory of strong interactions is called Quantum ChromoDynamics (QCD) b b 12

13 Quark Mass +2/3 U +2/3 U -1/3 d +2/3 U +2/3 U -1/3 d Proton Mass: Quarks have a much higher effective mass when confined in particles. Only account for ~ 2% of proton mass Rest due to the strong force So, 98% of your mass actually comes from the strong force. 13

14 The Quark-Gluon Plasma Normal hadronic matter Soup of free quarks Quark-Gluon Plasma At extreme temperatures and/or densities nuclear matter melts into a plasma of free quarks and gluons. This state of matter would have existed up to about 10 millionths of a second after the Big Bang, and could be created in the core of collapsing neutron stars. 14

15 Natural Units Most constants in formulae are there due to the arbitrary system of units used. Hence we find the constants c, h, k B all over the place just because of the system of units we are using. It is possible to setup a self-consistent system of units where c = h = k B = 1 and simplify life for all of us! In this case, all speeds are just measured as a fraction of the speed of light and have no units i.e. = v/c Einstein s equations simplify to E = γm and E 2 = p 2 + m 2 De Broglie s equation p = h p = 1 K.E. of particle with temperature T: E kt E T

16 Natural Units Hence Energy has units of GeV Mass has units of GeV/c 2 Momentum has units of GeV/c Temperature has units of GeV Distance has units of GeV -1 (as p = 1/ ) Time has units of GeV -1 (as distance = speed x time) Experimentalists will often only have c and k B = 1 but measure distance in terms of Fermi s: (1 fm = metres) Hence we also measure time in fm (note 1 fm is the time taken for light to travel m i.e. traverse a proton)

17 Tools to Study QCD and the QGP Two basic approaches to calculating properties of QCD Lattice Gauge Theories Field theory is formulated and solved on a discrete lattice of space-time points using powerful computers Phenomenological Models E.g. the Bag Model which may be used to calculated some of the properties of a QCD without the intense numerical calculations needed for lattice QCD.

18 MIT Bag Model Concept is that if quarks are placed in the QCD vacuum, the vacuum will expel the colour field of the quarks isolating them into a bag. Energy and momentum are conserved at the bag surface by introducing an external pressure at the boundary to balance the internal pressure of the confined quarks. General notion of the MIT bag model is that the true QCD vacuum is destroyed inside the bag by the presence of quarks so that coloured particles are allowed unlike in the QCD vacuum which only supports excitations of colour singlets. QCD Vacuum

19 The MIT Bag Model For reasons of Lorentz invariance the exterior pressure due to the QCD vacuum must be characterised by a scalar constant B, known as the bag constant. B has dimensions of energy density (MeV 4 in natural units). We can work out the total energy of the bag by assuming the partons confined in the bag (of volume V) are noninteracting and massless. Hence, they may be described as a relativistic gas of massless particles.

20 Energy of Bag The total energy of the bag is given by: E = E r + BV [eq. 1] where E r is the internal energy of the gas and B the bag constant For equilibrium the radiation pressure inside the bag has to balance the pressure exerted by the QCD vacuum. In a gas of particles of negligible mass the pressure is p = 1 3 E r/v So equilibrium requires: B = 1 3 E r/v E r = 3BV [eq. 2] From eqs. 1 and 2 we get E = 3BV + BV = 4BV [eq. 3] The mass of light hadrons and their resonances may be used to extract a value for B Various fits give values of between B MeV

21 Using the MIT Bag Model to calculate conditions for QGP formation Consider only two light u and d quarks Assume them to be massless Neglect all interactions among constituents (for now) i.e. s = 0. We can work out the energy density of QGP due to gluons, quarks, and anti-quarks. Note degrees of freedom: Gluons: N g = 2(spin) x 8(colour) = 16 Quarks: N q = 2(spin) x 3 (colour) x 2(flavour) = 12 We treat the gluons as an ideal relativistic Bose gas and the quarks (anti-quarks) as an ideal relativistic Fermi gas, both of temperature T.

22 Energy Density due to Gluons Energy density due to gluons: ε g = 4π 0 p2 dp (2π) 3 p e p/t 1 = π2 T 4 30 (see online notes) Where p is the momentum of the gluons and 4 p 2 p/(2 ) 3 is the phase space factor. For the quarks one has to introduce a chemical potential to allow for a surplus of quarks over anti-quarks.

23 Energy Density due to quarks Energy density due to quarks: ε q = 4π 0 p2 dp (2π) 3 p e (p μ)/t +1 (see online notes) And energy density due to anti-quarks: ε q = 4π 0 p2 dp (2π) 3 p e (p+μ)/t +1 Putting them together gives: ε q + ε q = 7π2 T μ2 T μ4 8π 2

24 Total Energy Density Taking into account the degrees of freedom, the total energy density of a QGP is: ε = 16ε g + 12 ε q + ε q = 37π2 T μ 2 T 2 + 3μ4 2π 2 The above equation assumes no interactions. To includes interactions the above is modified as follows: ε = 37π π 3 α s T π α s 3μ 2 T π α s 3μ 4 2π 2

25 Equation of State The QGP phase is expected to be stable if P = /3 B, equality giving the boundary of stability. Calling and T on the boundary critical values, c and T c, we obtain the relation: B = 37π π 9 α s T c π α s μ c 2 T c π α s μ c 2 2π 2 See phase diagram on next slide In context of the Bag Model, B 1/4 = 200 MeV corresponds to an energy density of: QGP 0.8 GeV/fm 3 ( QGP = 4B and 1 fm = 5.07 GeV -1 )

26 Phase Diagram / Eq of State Dotted line: B 1/4 = 150 MeV, s = 0 Broken line: B 1/4 = 250 MeV, s = 0 Solid line: B 1/4 = 250 MeV, s = 0.5 Simple model gives a critical temperature in the range MeV. Probably more realistic values of B 1/4 = 200 MeV, s = 0.5 (not shown) give a T c ~ 150 MeV CERN SPS (late 80s early 90s)

27 Phases of Strongly Interacting Matter colour 27

28 Phases of Strongly Interacting Matter Lattice QCD, B = 0 Both statistical and lattice QCD predict that nuclear matter will undergo a phase transition at a temperature of, HotQCD Collaboration: Phys. Rev. D90 (2014) T ~ MeV and energy density, ~ 1 GeV/fm 3. 28

29 Heavy Ion Collisions Create QGP by colliding ultra-relativistic heavy ions Requires a particle accelerator Accelerators used over past 30 years: Colliders: AGS, SPS, RHIC, LHC S NN (GeV) =

30 CERN Deep underground, we have built the World s largest machine French Alps Geneva The Large Hadron Collider (LHC) Which accelerates sub-atomic particles to the speed of light.

31 LHC Tunnel

32 LHC - Facts 27 km circumference Each proton (or lead nucleon) goes around the 27km ring over 11,000 times a second. 300 trillion protons in the beam Energy of proton beam in LHC > 0.3 GJ (freight train travelling at 100 mph) Energy stored in magnets > 1 GJ Super-conducting magnets cooled to ~ 1.9 K (colder than Outer Space). Vacuum as low as interplanetary space (10-13 atm)

33 What Happens when Lead Nuclei Smash Together? A super-hot, subatomic fireball is created. Quark-Gluon Plasma is formed and lasts for about seconds Then thousands of particles are produced We have to study the QGP from this!

34 Space-time collision picture TORY OF HEAVY ION COLLISIONS Heavy-ion quasi-the Domina p ~ T T kin T chem T crit Freeze-out T kin Phase transition Use the s Hadron Gas Sensitive T chem T crit QGP & expansion Hadrons Hard-scat Þ Initial-s Þ Probe m Mixed Phase? Pre-equilibrium QGP Initial state Hadronisation temperature T crit 155 MeV (from LQCD) Humboldt Kolleg, Kitzbuehel Michael Weber (SMI, Vienna) 5 Chemical freezeout temperature, T chem T crit, fixes hadron yields Kinetic freezeout temperature, T kin < T chem, fixes momentum distributions 34

35 Observables Jets Open charm, beauty 35

36 Size: 16 x 26 metres Weight: 10,000 tonnes Detectors: 18 The ALICE Experiment Collaboration: > 1300 Members > 120 Institutes > 35 countries Birmingham-built Central Trigger Processor Electronic Brain of the detector.

37 The ALICE Detector Spring Spring Ready for Physics ALICE in December 07 photo by Simon Hadley, Birmingham 37 Post

38 First Pb-Pb Collisions Sunday 7 th November 2010 Mini Big Bangs created All worked very well No killer strangelets produced 38

39 High Energy Collisions First high energy collisions (3.5 TeV TeV) at about 12pm on 31 st March Phase I to great success LHC upgrade 2013 to 2015 almost doubling of energy. Phase II started Easter Sunday 2015 high energy collisions (6.5 TeV TeV) started beginning of June High energy lead collisions took place in Nov

40 Early Universe Recreate conditions similar to those some 10-6 seconds after the Big Bang Learn about the evolution of the very early Universe 40

41 Lecture 1 Summary QCD predicts a phase transition from nuclear matter to a de-confined state of quarks, anti-quarks, and gluons quark-gluon plasma (QGP). Happens at energy densities of ~ 1 GeV/fm Temperatures of ~ 150 MeV Can create a QGP using ultra-relativistic heavy-ion collisions Recreate the conditions existing ~ 1 micro-second after Big Bang 41

42 Discussion Points If there were not 3 generations of particles but only one, what implications would this have? i.e. what process could not happen? If 98% of nuclear mass comes from QCD, where does the other 2% come from? The nuclear force between nucleons can not be mediated by gluons as coloured objects can not exist outside bound states (e.g. protons). It must therefore be mediated by a virtual colourless state. What is this state (i.e. what is the virtual particle) If ħ = 197 MeV/fm, calculate the approx. range of the nuclear force (if you use a calculator you should be ashamed!) Approx. what does a temperature of 200 MeV equate to in o C? 42