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25/10/2017 Alberica Toia 1

Nuclear and Particle Physics 4aElectromagnetic Probes

Alberica ToiaGoethe University Frankfurt

GSI Helmholtzzentrum für Schwerionenforschung

Lectures and Exercise Winter Semester 2017-18


Organization● Language: English● Lecture:

● Wednesday 09:00-11:00 ● 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/KT4a_WS1718.html

mailto:[email protected]


Literature


Content● 1) 25.10 Introduction: general picture of Heavy Ion Physics● 2) 01.11 Detectors● 3) 15.11 Dielectrons: low energy● 4) 22.11 Dielectrons: intermediate energy● 5) 29.11 Dielectrons: high energy● 6) 06.12 Theory I● 7) 13.12 Theory II● 6) 10.01 J/psi and quarkonia● 7) 17.01 Photons● 8) 24.01 ElectroWeak Probes● 9) 31.01 Dark Matter● 10) 07.02 Students presentations


Introduction:general picture of Heavy Ion Physics

● 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

● Typical measurements in heavy ion physics


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!)

strong interaction:- binds quarks into hadrons- binds nucleons into nucleidescribed by QCD:- interaction between particles carrying colour charge (quarks,gluons)- mediated by strong force carriers(gluons)very successful theory!… but with outstan ding puzzles!


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


Confinement- No one has ever seen a free quark.- Quarks seem to be permanently confined within protons, neutrons, pions and other hadrons- It looks like half of the fundamental fermions are not directly observableHow come?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


Deconfinement- What if we compress/heat matter so much that the individual hadrons start to interpenetrate?

- Lattice QCD predicts thatif a system of hadrons is brought to sufficiently largedensity and/or temperaturea deconfinement phasetransition should occur- In the new phase, calledQuark-Gluon Plasma (QGP),quarks and gluons are nolonger confined withinindividual hadronshadrons, but arefree to move around over alarger volume


The QCD Phase transition● In Lattice QCD non-perturbative problems are treated by discretization on a space-

time lattice. As a result, ultraviolet (large momentum scale) divergencies can be avoided

● lQCD calculations indicate that, at a critical temperature ~170 MeV (T~2000 billion K) 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


Restoration of bare masses● Confined quarks acquire an additional mass (~ 350 MeV) dynamically, through the

confining effect of strong interactions

● M(proton) ≈ 938 MeV; m(u)+m(u)+m(d) == 10÷15 MeV● Deconfinement is expected to be accompanied by a restoration of the masses to the

“bare” values they have in the Lagrangian

● As quarks become deconfined, the masses go back to the bare values;eg :

● m(u,d): ~ 350 MeV → a few MeV● m(s): ~ 500 MeV → ~ 150 MeV

● This effect is usually referred to as “ Partial Restoration of Chiral Symmetry Symmetry”.

● Chiral Symmetry: fermions and antifermions have opposite helicity. The symmetry is exact only for massless particles, therefore its restoration here is only partial


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


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


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"


Typical Measurements in heavy ion collisions

● Global Properties

● Multiplicity → Energy Density

● Femtoscopy → System size

● Bulk medium

● Momentum, azimuthal distribution → radial, ellitpic, … flow

● Hard probes

● Interaction of partons with medium

● Jets → higher pT

● Heavy flavor → hierarchy in energy loss

● Quarkonia

● Screening / (re)generation

● Comparison pp to AA → control experiments

● pA

● Electroweak probes


Heavy Ion Collisions● Proton-proton collisions: elementary collisions

● Heavy-ion collisions:depending upon the impact parameter between the nuclei:

● Some nucleons participate in the collision → participants● Some do not → spectators

● This characterization of shape & size of overlap region is called centrality


Glauber Model● Glauber model: geometrical picture of AA collision

● Straight−line nucleon trajectories● N-N cross−section independent of the number of

collisions the nucleons have undergone before● Nuclear density profile: Woods−Saxon (2pF)

determined via e–nucleus scattering

– ρ0 is a normalization factor: the charge density, integrated over the infinite volume, must give the charge of the nucleus.

– R Radius: width at half height– a skin depth: distance over which the density

falls from 90% (r1) to 10% (r2) of its maximum value → characterizes the thickness of the diffuse surface layer of the nucleus.

– Additional parameter w to account for non-spherical shape of nucleus

– Intra-nucleon distance

R


Glauber Model● Glauber model: geometrical picture of AA collision

● Straight−line nucleon trajectories● N-N cross−section independent of the number of

collisions the nucleons have undergone before

● Inelastic nucleon-nucleon cross section measured in pp, ppbar experimentsVan der Meer scan


Analytical Calculation● “Projectile” B + “Target” A

● Thickness function TA:

probability per unit volume for finding the nucleon at given location

● Product of TAT

B then gives the

joint probability per unit area of nucleons being located in the respective overlapping flux tubes

● Integrating this product over all values of s defines nuclear overlap function effective overlap area of specific nucleons in A and B

● Probability of single NN interaction (multiplying by the NN)

● All possible NN collisions independent and with same NN→ Probability of n such NN interactions from binomial distribution

→ total inelastic cross section → number of collisions → number of the participants


Glauber Monte Carlo● Simple approach to Glauber calculations

● Nucleons have straight-line trajectories σ independent of previous interactions

● Nucleons distributed in 3D space according to Woods-Saxon

● Impact parameter drawn at random from dσ/db = 2πb → Orientation

● Collision happens if distance between nucleons < √(σinel

NN/π)

● If collision → increment Npart, Ncoll


Results of Glauber Model● Determines Npart, Ncoll for any impact parameter b

● Divide in centrality classes according to impact parameter distribution

● Obtain mean values of Npart, Ncoll, TAA


Centrality experimentally

“Spectators”

Zero-degreeCalorimeter

“Spectators”

Many things scale with Npart:• Transverse Energy• Particle Multiplicity• Particle Spectra

“Participants”

Detectors at 90o

The collision geometry (i.e. the impact parameter) determines the number of nucleons that participate in the collision

Zero-degreeCalorimeter

Only ZDCs ”measure” Npart N part=A−N spec

However the production of nuclear fragments breaks such a direct relationship in the *measured* variables


Relating Glauber to real collisions● Npart & Ncoll not measured directly

● Observables (e.g. dN/dNch

) mapped to these quantities

● Number of ancestors (source of particle) given by fN

part + (1-f)N

coll

● Each ancestor emits particles according to Negative Binomial Distribution()

● Fit multiplicity calculated with NBD x Glauberto experimental one

● For each class defined by cuts in the experimental multiplicity there is a corresponding class in the simulated multiplicity.For this one, we know Npart, Ncoll.


The ZDC measurement

Zero Degree Calorimeter measures spectators→ anti-correlated with multiplicity measurements

● Central (high multiplicity): no spectators

● Peripheral (low multiplicity): many spectators

However, due to fragmentation, spectators recombine→ They escape detection→ decrease of forward energy in peripheral collisions:response no longer monotonic


Multiplicity

●Energy dependence fitted with power-law function asb:● pp: b = 0.103(2)● Pb-Pb: b = 0.155(4)

● x 2.5 pp or pPb collision at the same energy● Much stronger energy dependence ● not solely related to the multiple collisions undergone by the participants (e.g. proton in pA collisions).

ALICE PRL 116 (2016) 222302

Global properties of the systemMultiplicity ~ energy density

Evolution with energy and system size?

The average yield per participant pair is strongly dependent on collision centrality● Similar trend seen at √sNN=2.76 TeV→ Energy- (and system-) scaling ● Yield in peripheral collisions close to the one measured in p-Pb and pp collisions● Most of the models fairly describe the data (except HIJING).


Transverse Energy

Centrality dependence similar to RHIC (PHENIX)

PRC71:034908 (2005)PRC70:054907 (2004)

● ET

had from charged hadrons directly measured by the tracking detectors

● ftotal

from MC to convert into total ET

● From RHIC to LHC● ~2.5 increase

dET/d/ (0.5*N

part)

● Energy density (Bjorken)

● ~ 16 GeV/(fm2c)RHIC: =5.4±0.6 GeV/(fm2c)

(GeV

)


Basic models for heavy-ion collisions● Statistical models:

basic assumption: the system is described by a (grand) canonical ensemble of noninteracting fermions and bosons in thermal and chemical equilibrium

[ -: no dynamics]

● (Ideal-) hydrodynamical models:basic assumption: conservation laws + equation of state; assumption of local thermal and chemical equilibrium

[ -: - simplified dynamics]

● Transport models:based on transport theory of relativistic quantum many-body systems -off-shell Kadanoff-Baym equations for the Green-functions S


Basic models for heavy-ion collisions


Thermal model for heavy-ion collisionsStarting point: grand-canonical partition function for a relativistic ideal quantum gas of hadrons

describes the statistical properties of a system in thermodynamic equilibrium.→ all other thermodynamic quantities:

Conservation Laws:Baryon number conservation:Initial system has no charm or strangeness:Third component of isospin:→ iterative calculation:Compare calculated particle yields with data�2-minimization in (T, μ

B) plane (thermal fit).


From the thermal model to the QCD phase diagramChemical freeze-out line

By colliding nuclei with different center of mass energies, different regions of the phase diagram are explored.• Thermal model fits to the experimental data define the chemical freeze-out line in the QCD phase diagram. A priori, a thermal model description is not

related to the QGP itself. It describes a hadron gas. However, the chemical freeze-out line determined by thermal fits coincides with the phase boundary calculated by lattice QCD above top SPS energies!However, collision rates and timescales of fireball expansion imply that equilibrium cannot be reached in the hadronic phase…

Do multi-particle collisions near TC equilibrate the system? [1]: A rapid change in density near the phase transition can explain this.[2]Alternatively, the system is ‘born into equilibrium’ by the filling of phase space during hadronization.


pt- Distributions

● High pT (>>1 GeV/c):● Particle production

mechanisms are hard● The dN/pTdpT distributions

depart from the exponential trend and follow a power-law

transverse momentum (pT) distributions of particles produced in the collisions allow to extract important information on the system created in the collision

● Low pT (


Blast-wave modelThermal models cannot describe the differential spectra – e.g. pT or rapidity spectra of hadrons

● One needs to account for the collective flow!●The simplest way: Blast-wave model(P..J.. Siiemens and J..O.. Rasmussen,, Phys.. Lett.. 42 (1979) 880)

● add a collective velocity which is common for all hadrons!● all particle spectra are described by a universal formula with common thermal freeze-out

parameters:● a temperature T of the fireball and a radial-flow velocity b

● E, p: total energy and momentum of the particle I while A are normalization factors

•Blast-wave fit parameters

•Centrality

•STAR pp √s=200 GeV


Chemical and Thermal Freeze-out

Thermal Freeze out - Stop elastic interactions- Dynamics of particle (“momentum spectra”) frozenTfo (RHIC/LHC) ~ 100-130 MeV

Chemical Freeze-out - Stop inelastic interactions- Particle abundance (“chemical composition”) forzen Tch (RHIC/LHC) ~ 170 MeV


Anisotropic flow

Initial spatial anisotropy of the overlap region of colliding nuclei→ anisotropy in momentum space via interactions of produced particles.Sensitive to:• initial collision geometry• transport mechanism→ provides a measurement of collectivity(properties of deconfined medium)

y

Quantified by the Fourier decomposition

v1: directed flowv2: elliptic flowv3: triangular flow...

Systemexpansion

Coordinatespace

Momentumspace

ALICE PRL 116 (2016) 132302

Ultra-cold Li explode into

vacuum

SCIENCE Vol: 298 2179 (2002)

Collectivity of the system?


Anisotropic flow Anisotropic flow measurements usingtwo- and multi-particle cumulants●Elliptic flow results show very similarvalues to the ones seen at √sNN=2.76 TeV

●Higher harmonics (v3,v4) are alsounchanged with energy●v3 becomes larger than v2 atpT>2GeV/c in central collisions

●pT-integrated v2, v3 and v4 indicate amild increase with collisions energyattributed to the increase in ●Good agreement with hydrodynamicalcalculations●Measurements support a low valuefor the shear viscosity to entropyratio (η/s)

ALICE PRL 116 (2016) 132302

Collectivity of the system?


Hard Probes

penetrating beam(jets or heavy particles) absorption or scattering pattern

QGP

●Hard processes are those processes with high momentum transfer →short distances →Time Scale short ●Experimental observables connected to hard processes are:

● Hadrons with high pT Jets● Hadrons from open heavy flavour (charm and beauty)● Quarkonia (J/, ’, , ’, ”)

●In pp collisions calculable with pQCD techniques using universality (of PDF and FF) and factorization theorem●In AA collisions hard processes are expected to scale with the number of elementary nucleon-nucleon collisions●The nuclear modification factor is defined as:

●Rutherford experiment atom discovery of nucleusSLAC electron scattering e proton discovery of quarks

RAA < 1

RAA = 1

RA

A


High pT Particles: pp●pT distribution measured in 0.15 < pT < 20 GeV/c and ||


High pT Particles: Pb-Pb

● Spectra measured for 0.15 GeV/c < pT < 40 GeV/c● Compared to pp-reference (measurement!)scaled by TAA● Reconstruction and track selection improved wrt. Run 1 → Reduced systematic uncertainties.● Larger statistics recorded for Pb–Pb and pp. Currently under reconstruction

Centrality Sys (TAA) Ncoll0-5% 26.27 0.93 1840

5-10% 20.48 0.74 1430

10-20% 14.30 0.46 1001

20-40% 6.76 0.27 473

40-60% 1.95 0.10 136

60-80% 0.40 0.032 28


High pT Particles: Pb-PbStrong modification of the spectra shape ● minimum at pT ≈ 6-7 GeV/c● strong rise in 6 < pT < 50 GeV/c● strong centrality dependence for pT


Heavy Flavor: Pb-PbExpectations of HierarchyRadiative Energy loss decreases wrt light quarks(Casimir factor and dead cone effect)Eradg > Eradcharm > Eradbeauty→ RAA (U,D) < RAA (D) < RAA (B)

● Comparison between D and secondary J/ (from B decays) for central collisions

● RAAcharm < RAAbeauty → expected hierarchy

●Suppression of D mesons in central collisions ● High pT: the suppression for D and is similar

→ explained by softer fragmentation and pT spectrum of gluons w.r.t. c-quarks

● Low pT: indications of RAAD > RAAπ

ALICE JHEP 03 (2016) 081

Non Prompt J/ψ: CMS-PAS-HIN-12-014JHEP: 1511(2015)205

D vs light hadronsEg > Ec?

Charm vs beautyEc > Eb?


Heavy Flavor in Pb-Pb: v2

-Significant non-zero elliptic flow observed, v2(D) ~ v2 (charged particles)-Models which implement strong collisional energy loss and hadronisation viacoalescence agree with the data

ALICE arXiv: 1606.00321

Charm thermalizein QGP?

Does heavy flavour thermalize in the QGP and consequently flows ?-Heavy flavour elliptic flow sensitive to transport properties of QGPDue to the large mass, b and c quarks should take longer time to be influenced by the collective expansion of the medium


Quarkonia

Suppression (Debye screening) → Sequential meltingColor charge of one quark masked by surrounding quarks.Prevents qq binding in the QGP.Debye screening radius (λD) vs quarkonium radius (r).λD < r the quarks are effectively masked from each other. → depending on the binding energies of the quarkonium states

Recombination Increasing the collision energy the cc pair multiplicity increases (RHIC: ~10; LHC: ~100).Regeneration of J/ψ pairs from independently cc.Leads to an enhancement of J/ψ (or less suppression).No/small regeneration is expected for bottomonia.

Digal,Petrecki,Satz PRD 64(2001) 0940150

Bound states of charm or beauty quark and its anti-quarkHeavy and tightly boundHeavy quark pairs produced in the initial hard partonic collisions.

P. Braun-Munzinger,J. Stachel, PLB 490(2000) 196 R. Thews et al, Phys.Rev.C63:054905(2001)


Quarkonia RAA

Different RAA ALICE vs RHIC → recombination- Weaker centrality dependence- Smaller suppression than at RHICRegeneration is higher at higher √sNN- High-pT J/ψ are suppressed more than low pTRegeneration is higher at low pT.(bulk of cc production)

ALICE 2.5


Control Experiment● various observables measured in “cold” nuclei (p–Pb):ALICE - N

ch, EPJC 74 (2014) 3054

- heavy flavor, PRL 113 (2014) 232301 - Jets, EPJC 76 (2016) 5, 271 ● Electroweak probesCMS- , PLB 710 (2012) 256- W±, PLB 715 (2012) 66- Z0, PRL 106 (2011) 212301,CMS-PAS-HIN-13-004

→ Ncoll binary scaling

...provide experimental demonstration that suppression in Pb-Pb is due to parton energy loss in a hot QGP

Is suppression of hard probes an effect of QGP?

Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Centrality: Participants vs. SpectatorsSlide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43Distribuzioni di pTSlide 45Freeze-out chimico e freeze-out termicoSlide 47Slide 48Slide 49Slide 50Slide 51Slide 52Slide 53Slide 54Slide 55Slide 56Slide 57

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