nuclear and particle physics 4b physics of the quark gluon plasmaalberica/lectures/kt4_ss15/... ·...

13/04/2016 Alberica Toia 1

Nuclear and Particle Physics 4bPhysics of the

Quark Gluon PlasmaAlberica Toia

Goethe University Frankfurt GSI Helmholtzzentrum für Schwerionenforschung

Lectures and Exercise Summer Semester 2015


Organization● Language: English● Lecture:

● Wednesday 13:00-15:00 ● Phys 01.402

● Marks / examination→ only if required / desired● Seminar presentation → schein ● Oral Exam → grade

● Office hours: tbd on demand


Info: Email and Website● E-Mail:

[email protected]

● Website: https://web-docs.gsi.de/~alberica/lectures/KT4_SS16.html

mailto:[email protected]


Literature


Physics of the Quark Gluon Plasma


Content● 1) Introduction: History and Kinematic variables● 2) Nucleon-nucleon vs nucleus-nucleus● 3) Measurements in heavy ion collisions● 4) QCD and Phase diagram● 5) Strangeness● 6) Hydrodynamics and collective phenomena● 7) Hard Processes● 8) Quarkonia● 9) Dileptons and Photons


Introduction:History and Kinematic Variables

● Motivations: ● QCD at extreme density and temperature● Generation of mass and composition of matter● Evolution of the Universe

● Heavy ion collisions and experiments● SIS/Bevalac● AGS/SPS● RHIC/LHC

● Useful kinematic variables


Composition of matter● The matter we're made of:

● Organs (~10 cm)● Cells (≤0.1 cm)● Molecules (10-7cm)● Atoms (10-8cm)● Nucleus (10-12cm)● Protons

and Neutrons (10-13cm)● Quarks and Gluons

(


The Standard Model● A theory which explains how subatomic particles interact with each

other. The Standard Model is a quantum field theory: the union of quantum chromodynamics (QCD) and the electro-weak theory (does not include gravity!)


QED vs QCDField theory for electromagnetic

interactionsExchange particles (photons) do not

have electric chargeFlux is not confined - U(r) 1/r and

F(r) 1/r2

Field theory for strong (nuclear) interactions

Exchange particles (gluons) do have “color” charge

Flux is confined - U(r) r and F(r) = constant

+ +…


QEDRunning coupling constant:The vacuum behaves like a dielectric:virtual pair e+e- screen the electron charge: the effective charge depends on the distance


QCDAlso in case of QCD there is vacuum polarization.Difference: gluons are color-charged and can interact between themselves. As a consequence, a red charge is surrounded mostly by red charges. A penetrating probe enters in a red-charged region and the amount of charge it feels decreases while getting closer to the charge→ anti-screening


Running coupling and asymptotic freedom

nf: number of quark with mass


ConfinementNo one has ever seen a free quark.QCD is a “confining” gauge theory,with an effective potential: r

V(r)

Color flux restricted in a tube that connects the quark-antiquark pair


ConfinementCrucial feature, but no rigorous theoretical proof exists

For increasing r it becomes energetically favorable to create a quark-antiquark pair and form a new meson


Composition of matter

●The nucleus consists of neutrons (n) and protons (p)●Each n and p is made of 3 quark●Each quark has a mass of only ~ 1% of the mass of n / p (!)●The rest-mass of n / p (and thus our mass) is "frozen energy" from the Big Bang

●We consist of an almost empty room

● 99.9% of the mass of atoms located in the nucleus

● The core is about a trillion(1,000,000,000,000) times smaller than the atom

●Only the lightest Elements (hydrogen and Helium) were created directly after the Big Bang●The rest of us is "Stardust"●All heavy element (eg, carbon and nitrogen) created in stars, eg by Fusion●Explosions: this (early) Star distributed these heavier elements in the universe●


How is the mass generated?

● ~98% of the (light quarks) constituent mass generated dynamically (gluons) in the QCD confining potential

● QCD (χ-symmetry breaking) responsible of the origin of known mass in the universe

● Higgs (EWK-symmetry breaking) gives only the current mass

Mass of the quarks

mN = 938 MeV mq 5 – 10 MeV

• chiral symmetry broken on hadron level

11+ a1 (1270 MeV)

1- (770 MeV)

Mass of the nucleon

The role of chiral symmetry breakingchiral symmetry = fundamental symmetry of QCD for massless quarkschiral symmetry broken on hadron level


The Big Bang● Big Bang model describe the physics of

the Universe from the beginning till now

● ~14 billion years ago the Universe started as a big explosion Energy → mass, kinetic and gravitational energy

● “QUARK EPOCH”Too hot to have quark bound into hadrons. They are massless and freely move in a “deconfined” state

● As temperature drops → Break of Electroweak SymmetryHiggs particles condensing vacuum: leptons and quarks acquire mass→ Break of Chiral Symmetryu,d quark acquire effective massand condense into hadrons“HADRON EPOCH”

Quark-Gluon Plasma

INDIRECT EXPERIMENTAL TEST of BIG BANG:In 1964 Penzias and Wilson casually discover the cosmic background radiation (2.9 K) i.e. “the echo” of the Big Bang: the thermal residual of the initial state of the Universe.

Heavy ion collisions@ LHC


The Big Bang

During the first microseconds of its life, the energy density was so high that hadrons (for example: nucleons) could not form● hadrons are bound states of quark, antiquark and gluoni with no color-charge (colour-singlet)● quark and gluons were therefore deconfined and the Universe was made off a Plasma of Quark and Gluons (QGP)


The Big Bang

When the energy density and the temperature dropped below the critical value● cr≈ 1 GeV/fm

3

● Tcr≈170 MeV ≈ 2 x 1012 K ≈ 100000 x T in the center of the Sun The degrees of freedom connected to the color-charge got confined inside color-neutral objects (color-singlet) with dimensions ~ 1 fm– Formation of hadrons– quark and gluoni are confined inside hadrons


The Big Bang

After 3 minutes, the temperature dropped below the critical value ≈100keV (109 K) and therefore small atomic nuclei can form and survive● This time is called “primordial Nucleo-synthesis”● At this point (after “the first 3 minutes”) the chemical composition of the early Universe is fixed (Chemical freeze-out)● Unstable Hadrons decay and the antiparticles annihilate leaving a small excess of protons, neutrons and electrons The chemical composition of the Universe will change again only after hundreds of millions years, with the formation of stars and the beginning of nuclear fusion processes inside stellar nuclei


The Big Bang

After the primordial nucleo-synthesis the Universe is still ionized and therefore opaque to electromagnetic radiation● ~ 300000 years after the Big Bang, when the temperature drops below 3000 K, electrons and nuclei combine and form atoms (electrically neutral)● At this point the electromagnetic radiation decouple with a blackbody spectrum with T≈3000K (Thermal freeze-out)● Due to the expansion of the universe, this radiation gets a redshift down to a temperature T=2.7 K, (cosmic microwave background)


The Big Bang


Evidence of Big Bang● Expansion of the Universe → Hubble's law (v=Hr)

● Observation of Hubble in 1929 that galaxies move away from us (Red-shift)

● The recessional velocity is proportional to the distance

slope = 75 km/s/Mpc called Hubble's constant


Evidence of Big Bang● Background cosmic radiation

● Foreseen by the Big Bang theory (Gamow) around 3 K and practically isotropic

● Discovered by Penzias and Wilson (1964)● More accurate measurements of anisotropy (due to the density

fluctuations in the early Universe) with satellites COBE (1989) and WMAP (2003)

CO

BE

(198

9)W

AM

P (2

003)


Evidence of Big Bang● Abundance of light elements (H, He, Li)

● the abundance of 3He, 4He, Li and deuterium can be calculated by the Big Bang theory and depend only on one parameter (the baryonic density).

● The Big Bang model is the only one that explains all the measured values (eg the 4He fraction ~ 25% )


Where is QGP produced?

Lattice QCD

Big Bang

Already happened…

Neutron Stars

Do we want to wait for so long...?Heavy Ion Collisions


The QCD Phase transition● QCD calculations indicate that, at a critical temperature ~170 MeV

(T~1.5x1012K) strongly interacting matter undergoes a phase transition to a new state where the quarks and gluons are no longer confined in hadrons

● We can create a system of deconfined quarks and gluons● by heating● by compression

Large increase of energy density atT~Tc


Phase diagram of strongly interacting matter

General term for such phenomena: phase transition examplesVapor → Water → ice -electromagnetic interaction → QED-free Quarks / gluons → proton / neutron nuclei -strong interaction→ QCD


How to study QCDunder these extreme conditions?

● T.D.Lee: “In HEP we have concentrated on experiments in which we distribute a higher and higher amount of energy into a region with smaller and smaller dimensions. In order to study the question of ‘vacuum’, we must turn to a different direction; we should investigate ‘bulk’ phenomena by distributing high energy over a relatively large volume.” [Rev. Mod. Phys. 47 (1975) 267]● Energy density: “Bjorken estimate” (for a longitudinally expanding plasma):

Study how collective phenomena and macroscopic properties of strongly interacting matter emerge from fundamental interactions → HEAVY ION COLLISIONS


Time evolution in lab


CERN Press Release 2000


BNL Press Release 2005


Heavy Ion Experiments


Fixed target experiments at relativistic energy

Beam Energy: 100A MeV → 2A GeV● Pioneer Experiments

● BEVALAC: Plastic Ball and Streamer Chamber (1984 - 1986)● Synchro-Phasotron – Dubna (1975 – 1985)

● Experiments of 2.nd Generation● SIS-GSI: FOPI, KAOS, HADES (1990 – today)● BEVALAC: EOS-TPC, DLS (1990 – 1992)

● Physics:● Collective Effects → Discovery and Investigation of Flow● Equation of State (EOS) → Investigation of compressibility of nuclear

matter● Medium modifications → Kaons, Dileptons with low invariant Mass

● Fundamental Results● Nuclear matter can be compressed and it is possible thereby to achieve

high energy densities.● Prerequisite for the generation of novel phases of strongly interacting

matter.


Fixed target experiments at ultra-relativistic energy

Beam energy: 2A GeV – 200A GeV● 1.st Generation: ,,Not-so-heavy” Ions

● SPS-CERN Projectile: 16O and 32S, Elabmax = 200A GeV, (1986 – 1993)● AGS-BNL Projectile: 28Si, Elabmax = 14.5A GeV, (1986 – 1991)

● 2.nd Generation: ,,really-heavy” Ions● SPS-CERN Projectile: 208Pb, Elabmax = 158A GeV, (1994 – 2002)● AGS-BNL Projectile: 197Au, Elabmax = 11.5A GeV, (1992 – 1994)

● Physics:● Search for the Quark-Gluon Plasma (QGP)● Signatures of the QGP (Strangeness enhancement, J/ψ suppression,...)● Systematic Studies (energy scans) → Threshold-Phenomena?

● Fundamental Results:● Observations are consistent with the QGP● Hypothesis, but not clearly interpretable


Collider experiments at ultra-relativistic energy

● Beam energy: ● RHIC: √sNN = 200 GeV● LHC: √sNN = 2.76 - 5.5 TeV

● Purpose: Search and Studies of the Quark-Gluon Plasma (QGP)● Projectile:

● RHIC: 197Au, Cu (2000 – today)● LHC: 208Pb, Protons

● Physics:● Signatures of the QGP--> detailed studies● New Observables: high-pt suppression, Strong flow Phenomena

● Fundamental results:● Stronger evidence for the existence of a QGP phase● "Strongly coupled QGP" (sQGP), "perfect liquid"


Future planned experiments● Physics-Motivations:

● Systematic Studies of the QCD Phase diagram● Position and Order of the Phase boundary Hadron-Gas → Quark-Gluon

Plasma● Search for Baryonic Matter at extreme density

● Actual Program:● RHIC at low Energy (Au+Au at ~10 GeV ≤ √sNN ≤ 200 GeV)

STAR, PHENIX● NA61 (NA49 continuation) at SPS (Energy- and System-size dependency● FAIR (2020 → )● Beam energy: Elabmax = 30 – 45A GeV (fixed target)● High Beam intensity → rare probes (D-Mesons, J/ψ)

Experiment: CBM / HADES● Other planned Programs: NICA + Nuklotron in Dubna


Future facility FAIRPresent:Z = 1- 92 (proton to Uranium)Up to 2 GeV/ nucleon

Future:100-1000 higher intensityZ = -1- 92 (proton to Uranium, antiproton)Up to 35 GeV/ nucleon


Notations and Conventions


Energy and Momentum conservation

● Consider a reaction: A + B → C + D

● PA,B,C,D

are the energy-momentum 4-vectors of the incoming and outgoing particles

● Energy and momentum conservation is valid in all 4 components

– EA + EB = EC + ED – pA + pB = pC + pD

● Mandelstam Variables● Lorentz invariant Variables

● s = (PA+ P

B)2 = (P

C+ P

D)2

● t = (PA- P

C)2 = (P

B- P

D)2

● u = (PA- P

D)2 = (P

B- P

C)2

→ s + t + u = mA

2 + mB

2+ mC

2+ mD

2 = const.

s: square of the center-of-mass energy (invariant mass) t: square of the four-momentum transfer.


Center of mass system (CMS)

t = momentum transfer in the reaction (square of the 4-momentum transfer)


√s: fixed-target vs colliders

ColliderE

1lab,min = 2m

p


Rapidity


Pseudorapidity

Ultrarelativistic patricles ( → 1, or any massless particle):Pseudorapidity = Rapidity

Pseudorapidity depends only on angle of emission


Example: beam rapidity


Quick overview: kinematic variables


Example: Pseudorapidity distribution


Difference between dN/dy and dN/d in CMS


Luminosity and cross-section


Lorentz invariant phase space element


Invariant cross section


Invariant Mass

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