Quark-Gluon Plasma

Sijbo-Jan Holtman

Overview

• Introduction

• Phases of nuclear matter

• Thermodynamics

• Experiments

• Conclusion

IntroductionResearch of quark-gluon plasma important to understand early universe and center of neutron stars

phase transition!

The Phases of Nuclear matter• Normal nuclei : density ρ0 , temperature T=0

• Gas: peripheral collision between gold nuclei

Phases of Nuclear matter

• Central collision • N + N = Δ + N , new degree of freedom • dynamical equilibrium between πN and Δ • Boltzmann distribution

dN / dE = cst e -E / kT (E is kinetic energy)• kT< 150 MeV

Hadronic matter

Phases of nuclear matter

Central collision between gold nuclei

Phases of nuclear matterQuark-gluon plasma (QGP) or Quark soup

• ρ0 = (6 fm3) -1 volume of nucleon is 10 / ρ0

• For T > 200 MeV enough energy for nucleon-nucleon interaction to increase collision frequency very much

• The disintegration of nucleons and pions into quarks and gluons

Hadron gas

QGP

Phases of nuclear matterPhase diagram

Big Bang

Normal nuclear matter

Neutron stars

Thermodynamics

Derivation of the equation of state

• Gluons, u and d quarks massless

• all interactions neglected

• degrees of freedom Gluons: Ng = 2(spin) × 8(colour) = 16 Quarks: Nq =

2(spin) × 3(colour) × 2(flavour) = 12• energy density in each degree of freedom

Thermodynamics

εq = (dp) p (e(βp-μ)+1) -1 x= (βp-μ)

= T4 /2π2 dx (x+βμ)3 (e x+1) -1

εq = (dp) p (e(βp+μ)+1) -1 x= (βp+μ)

= T4 /2π2 dx (x-βμ)3 (e x+1) -1

εq + εq = 7π4 T4/120 + μ2 T4/4 + μ4/8 π2

Quarks and anti-quarks

εg = (dp)p(eβp-1) -1= π2T4 / 30

Gluons

Thermodynamics

The total energy density for μ=0 (same amount of quarks as anti-quarks)

ε = 16 εg + 12 (εq + εq) = (T/160 MeV)4 GeV/fm3

Compare with

εnuc = 125 MeV/fm3 ε of nuclear matter

εN=300-500 MeV/fm3 ε inside nucleon

Thermodynamics

Determining a physically realistic μ with the baryonic density

nb = 1/3 12 (nq – nq); nq = (dp) (e(βp-μ)+1) -1

nb = 2 μT2/3 + 2μ3/3π2

Consequences:

• High temperature μ ~ T-2/3

• nb = 4/3 dε/dμ (also valid with interactions)

ThermodynamicsIn the same way

P=1/3 ε; s = 1/3 dε/dT

Range of stability of QGP:

P can balance B the external vacuum pressure

B = π2Tc4[(37/90-11αs/9π)+(1-2αs/π)(xc

2+1/2 xc4)]

μ c=xcπTc

ε = (T/160 MeV)4 GeV/fm3

εc = ½-2 GeV/fm3

Thermodynamics

Phase diagram according to the calculation

Only 10-15 percent difference between interaction included and interaction excluded

Experiments

• J/Ψ suppression because colour screening hinders the quarks from binding

• Strangeness and charm enhancement

Perturbative Vacuum

cc

Color Screening

cc

Experiments

Jet quenching

• Hard scatterings (HS) produce jets of particles

• In a colour deconfined medium the partons strongly interact and loose energy by gluon radiation

• HS near the surface can give a jet in one direction, while the other side is quenched

Experiments

Search for QGP done at Relativistic Heavy Ion Collider (RHIC) on Long Island, New York

ExperimentsPHENIX: Pionering High Energy Nuclear Interaction

eXperiment

Au+Au till 100 GeV, d+Au and p+p till 250 GeV

Experiments

• Au+d similar to peripheral Au+Au

Escaping Jet“Near Side”

Lost Jet“Away Side”

d+Aud+Au Au+AuAu+Au

NearNear Away Away

Experiments

• Au+d similar to peripheral Au+Au• Away side strongly suppressed in Au+Au

Escaping Jet“Near Side”

Lost Jet“Away Side”

NearNear Away Away

d+Aud+Au Au+AuAu+Au

Experiments

Central collision simulation

Conclusion

• QGP not yet experimentally verified

• Problems remain: T=0, high ρ (neutron stars) and high T, low ρ experimentally difficult to realize