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 XXth August 2017 Outline of Lectures • Lecture 1: The Basics • Lecture 2: ALICE exp. • Aims of H.I. physics • Event characterisation • The quark model – Energy density • The strong interaction – Temperature – Size of system • The Quark-Gluon Plasma – (QGP) Liquid or gas ? • Selected probes • MIT Bag Model – Strangeness • How to make a QGP – Jet/high pT suppression – Quarkonium suppression • ALICE upgrade (if time) 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 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 +2/3 U -1/3 U -1/3 d d +2/3 -1/3 U d Elementary Particles Actually, a proton or neutron, with any energy will probably look more like this. Full of sea-quarks and anti-quarks 5 Family of Particles So, there is a family of particles: Up quark (u) Down quark (d) Electron (e-) Electron neutrino (e) Mass ~ 0.003 ~ 0.006 ~ 0.0005 < 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 BUT…. Nature supplies us with two extra families that are very much heavier: up charm top quarks down strange bottom e leptons e 7 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 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: 휶 푽 = − 풆풎 풓 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 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) 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) The Strong Force Free quarks are not observed experimentally Potential energy between quarks: V = - (4s / 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 b g i.e. made of 3 quarks: Baryon (e.g. proton) r Or quark & anti-quark: Meson (e.g. pion) b b Theory of strong interactions is called Quantum ChromoDynamics (QCD) 12 Quark Mass +2/3 U -1/3 +2/3 +2/3 -1/3 d Proton U U d +2/3 U Mass: 0.003 + 0.003 + 0.006 1 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 The Quark-Gluon Plasma Soup of free quarks – Normal hadronic matter 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 Natural Units • Most constants in formulae are there due to the arbitrary system of units used. • Hence we find the constants 푐, ℎ, 푘퐵 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 풄 = 풉 = 풌푩 = ퟏ 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 퐸 = 훾푚 and 2 2 2 퐸 = 푝 + 푚 ℎ 1 • 푝 = → 푝 = De Broglie’s equation • K.E. of particle with temperature T: 퐸 ≈ 푘푇 → 퐸 ≈ 푇 Natural Units Hence • Energy has units of GeV • Mass has units of GeV/c2 • 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 kB = 1 but measure distance in terms of Fermi’s: (1 fm = 10-15 metres) Hence we also measure time in fm (note 1 fm is the time taken for light to travel 10-15 m i.e. traverse a proton) 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. 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 QCD Vacuum 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. 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 (MeV4 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 non- interacting and massless. Hence, they may be described as a relativistic gas of massless particles. Energy of Bag • The total energy of the bag is given by: 푬 = 푬풓 + 푩푽 [eq. 1] • where Er 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. ퟏ • In a gas of particles of negligible mass the pressure is 풑 = 푬 /푽 ퟑ 풓 1 • So equilibrium requires: B = 퐸 /푉 → 푬 = 3BV [eq. 2] 3 푟 풓 • From eqs. 1 and 2 we get 푬 = ퟑ푩푽 + 푩푽 = ퟒ푩푽 [eq. 3] • The mass of light hadrons and their resonances may be used to extract a value for B ퟏ • Various fits give values of between 푩ퟒ ≈ ퟏퟓퟎ − ퟐퟎퟎ 푴풆푽 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: Ng = 2(spin) x 8(colour) = 16 Quarks: Nq = 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. Energy Density due to Gluons Energy density due to gluons: ∞ 푝2푑푝 푝 휋2푇4 휀 = 4휋 = (see online notes) 0 (2휋)3 푒푝/푇−1 30 Where p is the momentum of the gluons and 4p2p/(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. Energy Density due to quarks Energy density due to quarks: ∞ 푝2푑푝 푝 휀 = 4휋 (see online notes) 푞 0 (2휋)3 푒(푝−휇)/푇+1 And energy density due to anti-quarks: ∞ 푝2푑푝 푝 휀 = 4휋 푞 0 (2휋)3 푒(푝+휇)/푇+1 Putting them together gives: 7휋2푇4 휇2푇2 휇4 휀 + 휀 = + + 푞 푞 120 4 8휋2 Total Energy Density Taking into account the degrees of freedom, the total energy density of a QGP is: 37휋2푇4 3휇4 휀 = 16휀 + 12 휀 + 휀 = + 3휇2푇2 + 푞 푞 30 2휋2 The above equation assumes no interactions.