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Home , Down quark, Gluon, Plasma (physics), Up quark

Heavy- Lecture 1: QCD and the - 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 – • The – – Size of system • The Quark-Gluon Plasma – (QGP) or ? • Selected probes • MIT Bag Model – Strangeness • How to make a QGP – /high pT suppression – suppression • ALICE upgrade (if time)

Aims of Ultra-Relativistic Heavy Ion Physics

 Study strongly interacting at extreme energy densities over large and long time-scales.  Study the role of chiral symmetry in the generation of mass in (accounts for over 98% of mass of nuclear matter).  Study the of quark confinement.  Study the QCD transition from hadronic matter to a deconfined state of and - The Quark-Gluon Plasma.  Study the physics of the Quark-Gluon Plasma (QCD under extreme conditions).

3 Elementary

and are made from two types of quarks: Up (u) and Down (d).

 u-quarks have +2/3 while d-quarks have charge –1/3 ( has electric charge -1 in these units).

+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) (d) Electron (e-) Electron

(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   e   7 Virtual Particles & the

The forces between fundamental particles are mediated by virtual carrier particles. For example, the electromagnetic interaction between two charged particles (say two ) is understood to be due to the exchange of virtual . A virtual is one that violates , but only for a short of time (t < ħ/E) – it ‘borrows’ energy using the Heisenberg uncertainty principle. 8 The Electro-Magnetic

Electromagnetic Force  1 electric charge (& its opposite charge)  Mediated by photons (Of course, photons do not have electric charge themselves) between charges, a distance r apart goes as: 휶 푽 = − 풆풎 풓  The electric 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 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 = - (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 b g i.e. made of 3 quarks: (e.g. proton) r

Or quark & anti-quark: (e.g. ) 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 and/or densities nuclear matter ‘melts’ into a plasma of free quarks and gluons. This would have existed up to about 10 millionths of a second after the , and could be

created in the core of collapsing neutron . 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 and have no units i.e.  = v/c • Einstein’s equations simplify to 퐸 = 훾푚 and 퐸2 = 푝2 + 푚2 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 • 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 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 , 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 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 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 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() x 8(colour) = 16 Quarks: Nq = 2(spin) x 3 (colour) x 2(flavour) = 12

We treat the gluons as an ideal relativistic and the quarks (anti-quarks) as an ideal relativistic , both of temperature T. Energy Density due to Gluons

Energy density due to gluons:

∞ 푝2푑푝 푝 휋2푇4 휀 = 4휋 = (see online notes) 𝑔 0 (2휋)3 푒푝/푇−1 30

Where p is the momentum of the gluons and 4p2p/(2)3 is the 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 + 𝑔 푞 푞 30 2휋2

The above equation assumes no interactions. To includes interactions the above is modified as follows:

37휋2 11휋 2 2 3휇4 휀 = − 훼 푇4 + 1 − 훼 3휇2푇2 + 1 − 훼 30 3 푠 휋 푠 휋 푠 2휋2

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 Tc, we obtain the relation:

ퟑퟕ흅ퟐ ퟏퟏ흅 ퟐ ퟐ 흁ퟐ B = − 휶 푻ퟒ + ퟏ − 휶 흁ퟐ푻ퟐ + ퟏ − 휶 풄 ퟗퟎ ퟗ 풔 풄 흅 풔 풄 풄 흅 풔 ퟐ흅ퟐ

See phase diagram on next slide

In context of the Bag Model, 퐵1/4 = 200 MeV corresponds to an energy density of: 3 -1 QGP  0.8 GeV/fm (QGP = 4B and 1 fm = 5.07 GeV ) Phase Diagram / Eq of State

 Dotted line: 1/4  B = 150 MeV, s = 0  Broken line: 1/4  B = 250 MeV, s = 0  line: 1/4  B = 250 MeV, s = 0.5 CERN SPS • Simple model gives a (late 80s early 90s) critical temperature in the range 100-200 MeV. • Probably more realistic values of B1/4

= 200 MeV, s = 0.5 (not shown) give a Tc ~ 150 MeV

Phases of Strongly Interacting Matter

colour

27 Phases of Strongly Interacting Matter Lattice QCD, B = 0 Both statistical and lattice QCD predict that nuclear matter will undergo a at a temperature of,

HotQCD Collaboration: Phys. Rev. D90 (2014) 094503

T ~ 150 - 170 MeV and energy density,  ~ 1 GeV/fm3. 28 Heavy Ion Create QGP by colliding ultra-relativistic heavy

Requires a

Accelerators used over past 30 years: Colliders: AGS, SPS, RHIC, LHC

SNN (GeV) = 5.4 19 200 2760 5500

29 CERN

Deep underground, we have built the World’s largest machine

French Alps

Geneva

The Large Collider (LHC) Which accelerates sub-atomic particles to 0.999999991 the speed of light …. LHC Tunnel LHC - Facts

• 27 km circumference • Each proton (or lead ) 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 ). • Vacuum as low as interplanetary space (10-13 atm)

What Happens when Lead Nuclei Smash Together?

• A super-hot, sub- atomic fireball is created. • Quark-Gluon Plasma is formed and lasts for about 10-22 seconds • Then thousands of particles are produced We have to study the QGP from this! Space-time Evolution of A+A Collisions HISTORY OF HEAVY ION COLLISIONS Heavy-ion collisions produce Space-time picture‘ quasi-thermal’ QCD matter Dominated by soft partons Evolution described byp ~r eT l~a t1i0v0is-3t0ic0 MeV hydrodynamic models, which Tkin T chem neFered einzeiti-oalu ct oHadronsndHitiaordns-sca ast tienripnugt.s produce ‘quasi-free’ partons Tcrit Þ Initial-state production known from pQCD Simplest case: SÞym Promebter imec dium through energy loss Phacseoll itsraionnsiTskint i(on no elliUpsetic ftlhoew )st, reidenaglth of pQCD to explore QCD matter gas equatioHadronn of sta Gaste (b ag model), Sensitive to medium density, transport properties only lonTgchemitud inal expansion (1D, Mixed QGPB &j oerxpkeannT)sicrito n Phase?

QGP Pre-equilibrium

Initial state

Hadronisation Htemperatureumboldt Kolleg, Kitzb uTehcritel | 0≈1.0 7155.2016 |MeV Michael W(fromeber (SMI LQCD), Vienna) 5

Chemical freezeout temperature, Tchem ≤ Tcrit, fixes hadron yields 34 Kinetic freezeout temperature, Tkin < Tchem, fixes momentum distributions J. Stachel. K. Reygers | QGP physics SS2015 | 6. Space-time evolution of the QGP 2 Observables

Jets 35 Open charm, beauty The ALICE Experiment Size: 16 x 26 metres Weight: 10,000 tonnes Detectors: 18

Collaboration: > 1300 Members > 120 Institutes > 35 countries

Birmingham-built Central Trigger Processor Electronic Brain of the detector. SpringSpring The2008 2002 ALICE Detector

Ready for Physics

ALICE in December 07 – photo by Simon Hadley, Birmingham 37Post First Pb-Pb Collisions Sunday 7th November 2010

• ‘Mini Big Bangs’ created • All worked very well • No killer produced

38 High Energy Collisions

• First high energy collisions (3.5 TeV + 3.5 TeV) at about 12pm on 31st March 2010. • Phase I - 2010 to 2013 - great success • LHC upgrade 2013 to 2015 – almost doubling of energy. • Phase II – started Easter Sunday 2015 – high energy collisions (6.5 TeV + 6.5 TeV) started beginning of June 2015. – High energy lead collisions took place in Nov 2015

39 Early

Recreate conditions similar to those some 10-6 seconds after the Big Bang Learn about the evolution of the very early Universe 40 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 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 between 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 )  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 oC ?

42