Hadrons in hot and dense matter I

Size: px
Start display at page:

Download "Hadrons in hot and dense matter I"

Transcription

1 Hadrons in hot and dense matter I Hendrik van Hees Goethe University Frankfurt and FIAS July 17-21, 2017 Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

2 Outline 1 Plan of the lectures and motivation 2 The phase diagram of strongly interacting matter 3 QCD and chiral symmetry Particles and forces in the Standard Model Quantum Electrodynamics (QED) Quantum Chromodynamics (QCD) and chiral symmetry Chiral effective models for hadrons 4 Strongly interacting matter: QCD/hadronic models at finite T,µ 5 References 6 Quiz Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

3 Plan of the lectures Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

4 Plan of the Lectures Lecture I: Fundamentals symmetries and conservation laws in (quantum) field theory the Standard Model in a nutshell QCD, chiral symmetry, and effective models for hadrons Lecure II: electrodynamic probes in heavy-ion collisions (fundamentals) transport and hydrodynamics collective flow radiation of electromagnetic probes from a thermal transparent medium (McLerran-Toimela formula) effective hadronic models for vector mesons Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

5 Plan of the Lectures Lecture III: Dileptons in heavy-ion collisions hadronic models for transport models: baryon resonances Gießen Boltzmann-Uehling-Uhlenbeck (GiBUU) Ultrarelativistic Quantum Molecular Dynamics (UrQMD) medium modifications: transport-hydro hybrid and coarse-graining approach Lecture IV: Electromagnetic probes in heavy-ion collisions hard-thermal-loop approved dilepton rates (emission from QGP) hadronic many-body theories (emission from hadron gas) dileptons at SPS and RHIC access to the phase diagram? Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

6 Phase diagram, HICs, dileptons Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

7 The phase diagram of strongly interacting matter hot and dense matter: quarks and gluons inside hadrons compressed highly energetic scatterings deconfinement/chiral phase transition quarks and gluons relevant d.o.f. Quark-Gluon Plasma still strongly couples: fast thermalization! in the vacuum quark condensate q q 0 at high T,µ B : chiral phase transition q q = 0 T [GeV] 0.25 Quark-Gluon Plasma 0.20 RHIC qq = qq = 0 SPS 0.15 crit. point AGS hadron gas qq 0 SIS muclei 0.0 µ N 1st order qq 0 Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

8 Ultra-relativistic heavy-ion collisions highly energetic collisions of (heavy) nuclei many collisions of partons inside the nucleons creation of many particles hot and dense fireball generation of the Quark-Gluon Plasma (QGP)? properties of QGP and/or compressed baryonic matter? signatures of 1st-order phase transition (critical end point)? Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

9 Hydrodynamical behavior particle spectra compatible with collective motion of an ideal fluid small viscosity Medium in local thermal equilibrium (after short formation time 1 fm/c ) y Au Au x v 2 = p 2 x p 2 y p 2 x +p2 y p t (GeV) Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

10 Why Electromagnetic Probes? γ,l ± : only e. m. interactions reflect whole history of collision chance to see chiral symm. rest. directly? dn ee / dydm π o,η Dalitz-decays ρ,ω Φ DD J/Ψ π,... ρ/ω γ e Ψ l e + Drell-Yan a 1 Low- Intermediate- High-Mass Region > 10 fm > 1 fm < 0.1 fm Fig. by A. Drees (from [RW00]) mass [GeV/c 2 ] Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

11 Vacuum Baseline: e + e hadrons u, d, s 3 loop pqcd Naive quark model R Sum of exclusive Inclusive measurements measurements s(gev) R := σ e + e hadrons σ e +e µ + µ probes all hadrons with quantum numbers of γ R QM = N c f =u,d,s Q 2 f = 3 [(2/3) 2 + ( 1/3) 2 + ( 1/3) 2 ] = 2 Our aim pp l + l, pa l + l, AA l + l (l = e,µ) Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

12 The CERES findings: Dilepton enhancement pp (pbe): elementary reactions ; baseline (mandatory to understand first!) pa: cold nuclear matter effects ; next step (important as baseline for other observables like J /ψ suppression ) AA: medium effects ; hope to learn something about in-medium properties of vector mesons, fundamental QCD properties Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

13 The CERES findings: Dilepton enhancement Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

14 QCD and chiral symmetry Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

15 The standard model in a nutshell: particles and forces [graphics from Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

16 Quantum Electrodynamics (QED) Literature: [Nac90, DGH92, B + 12], conventions as in [Nac90] electrons+positrons: massive spin-1/2 Dirac field ψ 4 describes electron (charge q e = 1) and antielectron (=positron) photon: massless vector field A µ antisymmmetric field-strength tensor ( E, B ) 0 E 1 E 2 E 3 E F µν = µ A ν ν A µ = 1 0 B 3 B 2 E 2 B 3 0 B 1 E 3 B 2 B 1 0 Lagrangian (e > 0: em. coupling constant e 2 /(4π) = α em 1/137 = 1 4 F µνf µν + ψ[i( / + iq e e /A) m]ψ, q e = 1 Dirac matrices: γ µ 4 4, µ {0, 1, 2, 3}, γ µ,γ ν = 2η µν = diag(1, 1, 1, 1), ψ = ψ γ 0 Feynman slash /A = A µ γ µ, / = γ µ µ = γ µ Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38 x µ

17 Symmetries of QED as a classical field theory: Least-action principle equations of motion action (Lorentz invariant!) S[A,ψ] = d 4 x symmetries lead to conservation laws (Noether s Theorem) space-time symmetries time translations: energy conservation space translations: momentum conservation rotations: angular-momentum conservation intrinsic symmetry: invariant under change of phase factor ψ exp( iq e e α)ψ, α electric-charge conservation here even local gauge symmetry: j (e)µ em = q ee ψγ µ ψ, µ j (e)µ em = 0 ψ exp[ iq e e χ(x )]ψ, A µ A µ + q e µ χ local symmetry gauge boson Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

18 Quantization fields operators physical quantities S-matrix elements: T f i 2 transition probabilities for scattering from asymptotic free initial to asymptotic free final state local, microcausal quantum field theory with stable ground state spin-statistics relation: half-integer spin fermions, integer spin bosons can only evaluate in perturbation theory Feynman rules Internal lines: Propagators External lines: Initial and final states µ µ p ν = ig γ µν ε µ (p) p (ε µ ) = ieγ µ = ig e (p) G µν γ = η µν /(p 2 + i0 + ), G e = (/p m)/(p 2 m 2 + i0 + ) e + in final state or e in initial state e + in initial state or e in final state Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

19 Quantum Chromodynamics: QCD Theory for strong interactions: QCD QCD = 1 4 F µν a F a µν + ψ(i /D ˆM )ψ non-abelian gauge group SU(3) color each quark: color triplet covariant derivative: D µ = µ + ig Tˆ a A a (a {1,..., 8}) field-strength tensor F a = µν µa a ν νa a g f a b c A b µ µ Ac ν group structure constants: [ Tˆ a, Tˆ b ] = if a b c Tˆ c, Tˆ a = ( Tˆ a ) 3 3 Particle content: ψ: Quarks with flavor (u,d ; c, s ; t, b ) (mass eigenstates!) ˆM = diag(m u,m d,m s,...) = current quark masses A a µ : gluons, gauge bosons of SU(3) color Symmetries fundamental building block: local SU(3) color symmetry in light-quark sector: approximate chiral symmetry ( ˆM 0) dilation symmetry (scale invariance for ˆM 0) Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

20 Features of QCD asymptotically free: at large momentum transfers α s = 4πg 2 s 0 running from renormalization group (due to self-interactions of gluons!): Nobel prize 2004 for Gross, Wilczek, Politzer 0.3 α s µ(gev) quarks and gluons confined in hadrons theoretically not fully understood (nonperturbative phenomenon!) need of effective hadronic models at low energies: (Chiral) symmetry! Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

21 Chiral Symmetry of (massless) QCD Consider only light u, d quarks u iso-spin 1/2 doublet: ψ = = d ψ1 ψ 2 NB: ψ has three indices : Dirac spinor, color, flavor iso-spin! γ matrices: γ µ,γ ν = 2ηµν 1, γ 5 := iγ 0 γ 1 γ 2 γ 3, γ 5 γ µ = γ µ γ 5, γ 5 = γ 5, γ 2 5 = 1 Diracology of left and right-handed components ψ L = 1 γ 5 ψ = P L ψ, ψ R = 1 + γ 5 ψ = P R ψ, 2 2 P 2 L/R = P L/R, P R P L = P L P R = 0, P L/R γ 5 = γ 5 P L/R = P L/R P L/R γ µ = γ µ P R /L, P L ψ = ψp R, P R ψ = ψp L ψγ µ ψ = ψ L γ µ ψ L + ψ R γ µ ψ R, ψψ = ψ L ψ R + ψ R ψ L ψ := ψ γ 0, γ 5 ψ = ψ γ 5 γ 0 = ψγ 5 in the massless limit (m u = m d = 0) u,d = ψi /D ψ = ψ L i /D ψ L + ψ R i /D ψ R Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

22 Chiral Symmetry of (massless) QCD in the massless limit (m u = m d = 0) a lot of global chiral symmetries: change of independent phases for left and right components: ψ L (x ) exp( iφ L )ψ L (x ), ψ R (x ) exp( iφ R )ψ R (x ) symmetry group U(1) L U(1) R independent iso-spin rotations ψ L (x ) exp( i α L T )ψ L (x ), ψ R (x ) exp( i α R T )ψ R (x ) T = τ/2, τ: Pauli matrices; symmetry group SU(2) L SU(2) R alternative notation scalar-pseudoscalar phases/iso-spin rotations ψ exp( iφ s )ψ, ψ exp( iγ 5 φ a )ψ ψ exp( i α V T )ψ, ψ exp( iγ 5 α A T )ψ U(1) s and SU(2) V are subgroups that are symmetries even if m u = m d 0 Heisenberg s iso-spin symmetry! Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

23 Currents: relation to mesons based on [Koc97, Sch03, Din11] Noether: each global symmetry leads to a conserved quantity from chiral symmetries j µ s = ψγµ ψ, j µ a = ψγµ γ 5 ψ j µ V = ψγµ T ψ, j µ A = ψγµ γ 5 T ψ Link to mesons: Build Lorentz-invariant objects with corresponding quantum numbers σ: ψψ (scalar and iso-scalar) π s: iψ T γ 5 ψ (pseudoscalar and iso-vector) ρ s: ψγ µ T ψ (vector and iso-vector) a 1 s: ψγ µ γ 5 T ψ (axialvector and iso-axialvector) in nature: σ and π s; ρ s and a 1 s do not have same mass! reason: QCD ground state not symmetric under pseudoscalar and pseudovector trafos since vac ψψ vac 0 Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

24 Spontaneous symmetry breaking spontaneously broken symmetry: ground state not symmetric vacuum necessarily degenerate vacuum invariant under scalar and vector transformations: U(1) L U(1) R broken to U(1) s ; SU(2) L SU(2) R broken to SU(2) V for each broken symmetry massless scalar Goldstone boson there are three pions which are very light compared to other hadrons (finite masses due to explicit breaking through m u, m d!) but no pseudoscalar isoscalar light particle! (m η 548 MeV) reason: U(1) a anomaly axialscalar symmetry does not survive quantization! good for explanation of correct decay rate for π 0 γγ axialscalar current not conserved µ j µ a = 3/8α s ε µνρσ G a µν G a ρσ explicit breaking due to quark masses can be treated perturbatively chiral perturbation theory axial-vector current only approximately conserved PCAC a lot of low-energy properties of hadrons derivable Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

25 Chiral transformations σ meson and pions (chiral partners) meson = q -q bound state infinitesimal chiral transformations for quarks ( T = τ/2) in SU(2) L SU(2) R model ψ (1 iδ α V τ/2)ψ ψ (1 iγ 5 δ α A τ/2)ψ (iso-vector transformation) (axial-vector transformation) transformation properties under χ transformations as σ ψψ, π iψ τγ 5 ψ σ σ δ α A π, π π + δ α V π + δ α A σ σ 2 + π 2 invariant χ symmetry realized as SO(4) rotations Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

26 The minimal linear σ model chiral symmetry realized by SO(4): meson fields φ 4 describes σ and pions (π ±, π 0 ) χlimit = 1 2 ( µφ)( µ φ) V (φ) = 1 2 ( µφ)( µ φ) λ 4 (φ2 f 2 π )2 spontaneous symmetry breaking: mexican-hat potential V φ0 φ2 φ1 doesn t cost energy to excite field in direction of the rim massless Nambu-Goldstone bosons (pions) vacuum expectation value φ 0 = f π 0 symmetry spontaneously broken from SO(4) to SO(3) V particle spectrum: 4 field-degrees of freedom vacuum inv. 3-dim SO(3) 3 massless pions 4 3 = 1 massive σ Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

27 Pion decay and PCAC weak decay π + µ + + ν µ weak interaction J µ V J µ A pion pseudoscalar decay must be due to axial current 0 J a µ A (x ) π b (p ) = ip µ δ a b f π exp( ip x ) decay rate from Fermi model f π 93 MeV 0 µ J a µ A (x ) π b (p ) = f π p 2 δ a b exp( ip x ) = f π m 2 π δa b exp( ip x ) exact chiral symmetry m π = 0 (Goldstone theorem!) µ J a µ A = 0 Noether m π 0 but small partial conservation of axial current (PCAC) in effective model J a µ A,π = f π µ φ a, a {1, 2, 3} Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

28 Explicit symmetry breaking explicit breaking due to finite quark masses symmetry-breaking term in QCD: χsb = m ψψ m = (m u + m d )/2; from ψψ σ now write for σ-pion potential χsb = εσ V (σ, π) = λ (σ 2 + π 2 ) v εσ 4 tilted in σ-direction selects direction of vacuum expectation value minimum at f π v 0 = f π ε, m 2 2λfπ 2 σ = 2λf 2 π + ε, m 2 π f = ε π f π Noether with symmetry breaking + PCAC (consistency!): µ J a µ A = επ a PCAC = f π m 2 π πa ε = f π m 2 π χsb in QCD as in effective model Gell-Mann-Oaks-Renner Relation 0 εσ 0 = f π ε = m 2 π f 2 π = m 0 ψψ 0 Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

29 Adding nucleons axial current of nucleon J µ A,nucl = g a Ψγ µ γ 5 τ 2 Ψ from neutron-β decay g a = 1.25 total axial current J µ A = J µ A,π + J µ A,nucl should fulfill PCAC µ J µ A = f πm 2 π π Goldberger-Treiman relation extension of linear σ model ( + m 2 π )πa = g a i M f π Ψγ 5 τψ g πn N = g a M f π 12.6 vs. g exp πn N = 13.4 nucl = Ψi / Ψ g πn N iψγ5 τψ π + ΨΨσ + µψψ GT relation: 0 σ 0 = f π M = g A M µ µ = (g A 1)M M 4 Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

30 T,µ Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

31 Finite Temperature/Density: Idealized theory picture partition sum: Z (V,T,µ q,φ) = Tr{exp[ (H[Φ] µ q N)/T ]} Real Time Z[V,T, µ,φ] Imag. Time Dynamical quantities off equilibrium: derivation of BUU,... T, µ 0 vacuum analytic continuation Thermodyn. potentials bulk properties lattice QCD [CSHY85, Lv87, LeB96, KG06] Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

32 Finite Temperature Asymptotic freedom quark condensate melts at high enough temperatures/densities all bulk properties from partition sum: Free energy: Ω = T V lnz = P Quark condensate: ψ q ψ q T,µ q = V T Z (V,T,µ q ) = Tr{exp[ (H µ q N)/T ]} P m q Lattice QCD (at µ q = 0) chiral symmetry ψψ deconfinement transition Polyakov Loop tr P exp(i β 0 dτa0 ) Chiral symmetry restoration and deconfinement transition at same T c Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

33 What can we learn from em. probes in heavy-ion collisions? only penetrating probe leptons and photons leave hot and dense fireball unaffected they are produced during the entire fireball evolution dileptons provide information on in-medium spectral properties of hadrons theoretical challenge need an understanding of QCD medium at all stages of its evolution transport models, hydrodynamics need to identify all sources of dileptons and photons perturbative QCD not applicable non-perturbative QCD, effective hadronic models evaluate dilepton and photon rates QFT at finite T and µ B Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

34 Bibliography I [B + 12] J. Beringer, et al., Review of Particle Physics (RPP), Phys. Rev. D 86 (2012) [CSHY85] K. Chou, Z. Su, B. Hao, L. Yu, Equilibrium and Nonequilibrium Formalisms made unified, Phys. Rept. 118 (1985) 1. [DGH92] [Din11] [KG06] J. F. Donoghue, E. Golowich, B. R. Holstein, Dynamics of the Standard Model, Cambridge University press (1992). M. Dine, Goldstone Bosons and Chiral Symmetry Breaking in QCD (2011), lecture notes. http: //scipp.ucsc.edu/~dine/ph222/goldstone_lecture.pdf J. I. Kapusta, C. Gale, Finite-Temperature Field Theory; Principles and Applications, Cambridge University Press, 2 ed. (2006). Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

35 Bibliography II [Koc97] V. Koch, Aspects of chiral symmetry, Int. J. Mod. Phys. E 6 (1997) [LeB96] [Lv87] [Nac90] [RW00] M. LeBellac, Thermal Field Theory, Cambridge University Press, Cambridge, New York, Melbourne (1996). N. P. Landsmann, C. G. van Weert, Real- and Imaginary-time Field Theory at Finite Temperature and Density, Physics Reports 145 (1987) O. Nachtmann, Elementary Particle Physics - Concepts and Phenomenology, Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo (1990). R. Rapp, J. Wambach, Chiral symmetry restoration and dileptons in relativistic heavy-ion collisions, Adv. Nucl. Phys. 25 (2000) 1. Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

36 Bibliography III [Sch03] S. Scherer, Introduction to chiral perturbation theory, Adv. Nucl. Phys. 27 (2003) Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

37 Quiz 1 What are the peaks in the following figure of R e +e hadrons? 2 Can you explain the horizontal lines (values: 2, 3.333, 3.667)? Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

38 Quiz 4 Why is chiral symmetry (intuitively) only true for massless quarks? 5 What s the main consequence of spontaneous symmetry breaking? 6 Why can one measure the vector and axial-vector current-current correlators from τ even/odd number of pions + ν? Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter I July 17-21, / 38

Phenomenology of Heavy-Ion Collisions

Phenomenology of Heavy-Ion Collisions Phenomenology of Heavy-Ion Collisions Hendrik van Hees Goethe University Frankfurt and FIAS October 2, 2013 Hendrik van Hees (GU Frankfurt/FIAS) HIC Phenomenology October 2, 2013 1 / 20 Outline 1 Plan

More information

Medium Modifications of Hadrons and Electromagnetic Probe

Medium Modifications of Hadrons and Electromagnetic Probe Medium Modifications of Hadrons and Texas A&M University March 17, 26 Outline QCD and Chiral Symmetry QCD and ( accidental ) Symmetries Theory for strong interactions: QCD L QCD = 1 4 F a µν Fµν a + ψ(i

More information

The Dilepton Probe from SIS to RHIC

The Dilepton Probe from SIS to RHIC The Dilepton Probe from SIS to RHIC Hendrik van Hees Justus-Liebig Universität Gießen May 13, 2011 Institut für Theoretische Physik JUSTUS-LIEBIG- UNIVERSITÄT GIESSEN Hendrik van Hees (JLU Gießen) The

More information

Dileptons with a coarse-grained transport approach

Dileptons with a coarse-grained transport approach Dileptons with a coarse-grained transport approach Hendrik van Hees Goethe University Frankfurt and FIAS July 19, 017 in collaboration with S. Endres, J. Weil, M. Bleicher Hendrik van Hees (GU Frankfurt/FIAS)

More information

Dileptons in NN and AA collisions

Dileptons in NN and AA collisions Dileptons in NN and AA collisions Hendrik van Hees Goethe-Universität Frankfurt November 28, 2011 Hendrik van Hees (GU Frankfurt) The Dilepton Probe November 28, 2011 1 / 24 Outline 1 Electromagnetic probes

More information

Probing the QCD phase diagram with dileptons a study using coarse-grained transport dynamics

Probing the QCD phase diagram with dileptons a study using coarse-grained transport dynamics Probing the QCD phase diagram with dileptons a study using coarse-grained transport dynamics Stephan Endres, Hendrik van Hees, and Marcus Bleicher Frankfurt Institute for Advanced Studies, Ruth-Moufang-Straße

More information

The Phases of QCD. Thomas Schaefer. North Carolina State University

The Phases of QCD. Thomas Schaefer. North Carolina State University The Phases of QCD Thomas Schaefer North Carolina State University 1 Motivation Different phases of QCD occur in the universe Neutron Stars, Big Bang Exploring the phase diagram is important to understanding

More information

The Dilepton Probe from SIS to RHIC

The Dilepton Probe from SIS to RHIC The Dilepton Probe from SIS to RHIC Hendrik van Hees Justus-Liebig Universität Gießen April 14, 2010 Institut für Theoretische Physik JUSTUS-LIEBIG- UNIVERSITÄT GIESSEN Hendrik van Hees (JLU Gießen) The

More information

Cold and dense QCD matter

Cold and dense QCD matter Cold and dense QCD matter GCOE sympodium Feb. 15, 2010 Yoshimasa Hidaka Quantum ChromoDynamics Atom Electron 10-10 m Quantum ChromoDynamics Atom Nucleon Electron 10-10 m 10-15 m Quantum ElectroDynamics

More information

The Phases of QCD. Thomas Schaefer. North Carolina State University

The Phases of QCD. Thomas Schaefer. North Carolina State University The Phases of QCD Thomas Schaefer North Carolina State University 1 Plan of the lectures 1. QCD and States of Matter 2. The High Temperature Phase: Theory 3. Exploring QCD at High Temperature: Experiment

More information

The Secret of Mass. Can we Evaporate the Vacuum at RHIC?

The Secret of Mass. Can we Evaporate the Vacuum at RHIC? : Can we Evaporate the Vacuum at RHIC? Texas A&M University February 24, 2007 Outline The Beauty of Nature: Symmetries The Beauty of Nature: Symmetries What is a symmetry? Geometry: Certain operations

More information

Dileptons in heavy-ion-collisions

Dileptons in heavy-ion-collisions Dileptons in heavy-ion-collisions Hendrik van Hees Goethe University Frankfurt and FIAS January 11, 018 Hendrik van Hees (GU Frankfurt/FIAS) Dileptons in HICs January 11, 018 1 / 46 Outline 1 Heavy-ion

More information

Low mass dileptons from Pb + Au collisions at 158 A GeV

Low mass dileptons from Pb + Au collisions at 158 A GeV PRAMANA cfl Indian Academy of Sciences Vol. 60, No. 5 journal of May 2003 physics pp. 1073 1077 Low mass dileptons from Pb + Au collisions at 158 A GeV SOURAV SARKAR 1, JAN-E ALAM 2;Λ and T HATSUDA 2 1

More information

Pions are Special Contents Chiral Symmetry and Its Breaking Symmetries and Conservation Laws Goldstone Theorem The Potential Linear Sigma Model Wigner

Pions are Special Contents Chiral Symmetry and Its Breaking Symmetries and Conservation Laws Goldstone Theorem The Potential Linear Sigma Model Wigner Lecture 3 Pions as Goldstone Bosons of Chiral Symmetry Breaking Adnan Bashir, IFM, UMSNH, Mexico August 2013 Hermosillo Sonora Pions are Special Contents Chiral Symmetry and Its Breaking Symmetries and

More information

Speculations on extensions of symmetry and interctions to GUT energies Lecture 16

Speculations on extensions of symmetry and interctions to GUT energies Lecture 16 Speculations on extensions of symmetry and interctions to GUT energies Lecture 16 1 Introduction The use of symmetry, as has previously shown, provides insight to extensions of present physics into physics

More information

Introduction to Quantum Chromodynamics (QCD)

Introduction to Quantum Chromodynamics (QCD) Introduction to Quantum Chromodynamics (QCD) Jianwei Qiu Theory Center, Jefferson Lab May 29 June 15, 2018 Lecture One The plan for my four lectures q The Goal: To understand the strong interaction dynamics

More information

The symmetries of QCD (and consequences)

The symmetries of QCD (and consequences) The symmetries of QCD (and consequences) Sinéad M. Ryan Trinity College Dublin Quantum Universe Symposium, Groningen, March 2018 Understand nature in terms of fundamental building blocks The Rumsfeld

More information

Nonequilibrium quark-pair and photon production

Nonequilibrium quark-pair and photon production Nonequilibrium quark-pair and photon production Hendrik van Hees Frank Michler, Dennis Dietrich, Carsten Greiner, and Stefan Leupold Goethe Universität Frankfurt June 29, 2012 H. van Hees (GU Frankfurt)

More information

A Theoretical View on Dilepton Production

A Theoretical View on Dilepton Production A Theoretical View on Dilepton Production Transport Calculations vs. Coarse-grained Dynamics Stephan Endres (in collab. with M. Bleicher, H. van Hees, J. Weil) Frankfurt Institute for Advanced Studies

More information

Dilepton Production from Coarse-grained Transport Dynamics

Dilepton Production from Coarse-grained Transport Dynamics Dilepton Production from Coarse-grained Transport Dynamics Stephan Endres (in collab. with M. Bleicher, H. van Hees, J. Weil) Frankfurt Institute for Advanced Studies ITP Uni Frankfurt ECT* Trento Workshop

More information

Theory toolbox. Chapter Chiral effective field theories

Theory toolbox. Chapter Chiral effective field theories Chapter 3 Theory toolbox 3.1 Chiral effective field theories The near chiral symmetry of the QCD Lagrangian and its spontaneous breaking can be exploited to construct low-energy effective theories of QCD

More information

The Gauge Principle Contents Quantum Electrodynamics SU(N) Gauge Theory Global Gauge Transformations Local Gauge Transformations Dynamics of Field Ten

The Gauge Principle Contents Quantum Electrodynamics SU(N) Gauge Theory Global Gauge Transformations Local Gauge Transformations Dynamics of Field Ten Lecture 4 QCD as a Gauge Theory Adnan Bashir, IFM, UMSNH, Mexico August 2013 Hermosillo Sonora The Gauge Principle Contents Quantum Electrodynamics SU(N) Gauge Theory Global Gauge Transformations Local

More information

Critical lines and points. in the. QCD phase diagram

Critical lines and points. in the. QCD phase diagram Critical lines and points in the QCD phase diagram Understanding the phase diagram Phase diagram for m s > m u,d quark-gluon plasma deconfinement quark matter : superfluid B spontaneously broken nuclear

More information

Spontaneous symmetry breaking in particle physics: a case of cross fertilization. Giovanni Jona-Lasinio

Spontaneous symmetry breaking in particle physics: a case of cross fertilization. Giovanni Jona-Lasinio Spontaneous symmetry breaking in particle physics: a case of cross fertilization Giovanni Jona-Lasinio QUARK MATTER ITALIA, 22-24 aprile 2009 1 / 38 Spontaneous (dynamical) symmetry breaking Figure: Elastic

More information

Lectures on Chiral Perturbation Theory

Lectures on Chiral Perturbation Theory Lectures on Chiral Perturbation Theory I. Foundations II. Lattice Applications III. Baryons IV. Convergence Brian Tiburzi RIKEN BNL Research Center Chiral Perturbation Theory I. Foundations Low-energy

More information

Heavy Quarks in Heavy-Ion Collisions

Heavy Quarks in Heavy-Ion Collisions Heavy Quarks in Heavy-Ion Collisions Hendrik van Hees with T. Lang, J. Steinheimer, M. Bleicher Goethe University Frankfurt and FIAS July 18, 213 Hendrik van Hees (GU Frankfurt/FIAS) Heavy Quarks in HICs

More information

Lecture 03. The Standard Model of Particle Physics. Part II The Higgs Boson Properties of the SM

Lecture 03. The Standard Model of Particle Physics. Part II The Higgs Boson Properties of the SM Lecture 03 The Standard Model of Particle Physics Part II The Higgs Boson Properties of the SM The Standard Model So far we talked about all the particles except the Higgs If we know what the particles

More information

Hadrons in hot and dense matter IV

Hadrons in hot and dense matter IV Hadrons in hot and dense matter IV Hendrik van Hees Goethe University Frankfurt and FIAS July 17-1, 17 Hendrik van Hees (GU Frankfurt/FIAS) Hadrons in hot and dense matter IV July 17-1, 17 1 / 58 Outline

More information

The Strong Interaction and LHC phenomenology

The Strong Interaction and LHC phenomenology The Strong Interaction and LHC phenomenology Juan Rojo STFC Rutherford Fellow University of Oxford Theoretical Physics Graduate School course Lecture 2: The QCD Lagrangian, Symmetries and Feynman Rules

More information

Quantum ChromoDynamics (Nobel Prize 2004) Chris McLauchlin

Quantum ChromoDynamics (Nobel Prize 2004) Chris McLauchlin Quantum ChromoDynamics (Nobel Prize 2004) Chris McLauchlin Outline The Four Fundamental Forces The Strong Force History of the Strong Force What These People Did Experimental Support 1 Fundamental Forces

More information

Hot and Magnetized Pions

Hot and Magnetized Pions .. Hot and Magnetized Pions Neda Sadooghi Department of Physics, Sharif University of Technology Tehran - Iran 3rd IPM School and Workshop on Applied AdS/CFT February 2014 Neda Sadooghi (Dept. of Physics,

More information

Heavy flavor with

Heavy flavor with Heavy flavor with CBM@FAIR Hendrik van Hees Goethe University Frankfurt and FIAS April 21, 2015 Hendrik van Hees (GU Frankfurt/FIAS) Heavy flavor with CBM@FAIR April 21, 2015 1 / 22 Outline 1 Motivation:

More information

Quantum Field Theory. and the Standard Model. !H Cambridge UNIVERSITY PRESS MATTHEW D. SCHWARTZ. Harvard University

Quantum Field Theory. and the Standard Model. !H Cambridge UNIVERSITY PRESS MATTHEW D. SCHWARTZ. Harvard University Quantum Field Theory and the Standard Model MATTHEW D. Harvard University SCHWARTZ!H Cambridge UNIVERSITY PRESS t Contents v Preface page xv Part I Field theory 1 1 Microscopic theory of radiation 3 1.1

More information

The chiral anomaly and the eta-prime in vacuum and at low temperatures

The chiral anomaly and the eta-prime in vacuum and at low temperatures The chiral anomaly and the eta-prime in vacuum and at low temperatures Stefan Leupold, Carl Niblaeus, Bruno Strandberg Department of Physics and Astronomy Uppsala University St. Goar, March 2013 1 Table

More information

LQCD at non-zero temperature : strongly interacting matter at high temperatures and densities Péter Petreczky

LQCD at non-zero temperature : strongly interacting matter at high temperatures and densities Péter Petreczky LQCD at non-zero temperature : strongly interacting matter at high temperatures and densities Péter Petreczky QCD and hot and dense matter Lattice formulation of QCD Deconfinement transition in QCD : EoS

More information

Lecture 8. September 21, General plan for construction of Standard Model theory. Choice of gauge symmetries for the Standard Model

Lecture 8. September 21, General plan for construction of Standard Model theory. Choice of gauge symmetries for the Standard Model Lecture 8 September 21, 2017 Today General plan for construction of Standard Model theory Properties of SU(n) transformations (review) Choice of gauge symmetries for the Standard Model Use of Lagrangian

More information

Thermal dileptons from coarse-grained transport as probes of hot and dense QCD matter

Thermal dileptons from coarse-grained transport as probes of hot and dense QCD matter Thermal dileptons from coarse-grained transport as probes of hot and dense QCD matter Lunch Club Seminar, Universität Gießen Florian Seck TU Darmstadt in collaboration with T. Galatyuk, R. Rapp & J. Stroth

More information

QCD in the light quark (up & down) sector (QCD-light) has two mass scales M(GeV)

QCD in the light quark (up & down) sector (QCD-light) has two mass scales M(GeV) QCD in the light quark (up & down) sector (QCD-light) has two mass scales M(GeV) 1 m N m ρ Λ QCD 0 m π m u,d In a generic physical system, there are often many scales involved. However, for a specific

More information

Electromagnetic Probes in Ultrarelativistic Heavy-Ion Collisions

Electromagnetic Probes in Ultrarelativistic Heavy-Ion Collisions Electromagnetic Probes in Ultrarelativistic Heavy-Ion Collisions Hendrik van Hees Justus-Liebig Universität Gießen September 1, 2009 Institut für Theoretische Physik JUSTUS-LIEBIG- UNIVERSITÄT GIESSEN

More information

QGP Thermodynamics and Phase Transitions. Mahnaz Q. Haseeb Department of Physics CIIT, Islamabad

QGP Thermodynamics and Phase Transitions. Mahnaz Q. Haseeb Department of Physics CIIT, Islamabad QGP Thermodynamics and Phase Transitions Mahnaz Q. Haseeb Department of Physics CIIT, Islamabad Outline Thermodynamics in QGP What are the phase transitions? Order of the phase transition Where to study

More information

Thermal Electromagnetic Radiation in Heavy-Ion Collisions

Thermal Electromagnetic Radiation in Heavy-Ion Collisions EPJ manuscript No. (will be inserted by the editor) Thermal Electromagnetic Radiation in Heavy-Ion Collisions R. Rapp 1, H. van Hees,3 1 Cyclotron Institute and Department of Physics & Astronomy, Texas

More information

η π 0 γγ decay in the three-flavor Nambu Jona-Lasinio model

η π 0 γγ decay in the three-flavor Nambu Jona-Lasinio model TIT/HEP-38/NP INS-Rep.-3 η π 0 γγ decay in the three-flavor Nambu Jona-Lasinio model arxiv:hep-ph/96053v 8 Feb 996 Y.Nemoto, M.Oka Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 5,

More information

QCD Phases with Functional Methods

QCD Phases with Functional Methods QCD Phases with Mario PhD-Advisors: Bernd-Jochen Schaefer Reinhard Alkofer Karl-Franzens-Universität Graz Institut für Physik Fachbereich Theoretische Physik Rab, September 2010 QCD Phases with Table of

More information

3.3 Lagrangian and symmetries for a spin- 1 2 field

3.3 Lagrangian and symmetries for a spin- 1 2 field 3.3 Lagrangian and symmetries for a spin- 1 2 field The Lagrangian for the free spin- 1 2 field is The corresponding Hamiltonian density is L = ψ(i/ µ m)ψ. (3.31) H = ψ( γ p + m)ψ. (3.32) The Lagrangian

More information

Confined chirally symmetric dense matter

Confined chirally symmetric dense matter Confined chirally symmetric dense matter L. Ya. Glozman, V. Sazonov, R. Wagenbrunn Institut für Physik, FB Theoretische Physik, Universität Graz 28 June 2013 L. Ya. Glozman, V. Sazonov, R. Wagenbrunn (Institut

More information

SUNY Stony Brook August 16, Wolfram Weise. with. Thomas Hell Simon Rössner Claudia Ratti

SUNY Stony Brook August 16, Wolfram Weise. with. Thomas Hell Simon Rössner Claudia Ratti SUNY Stony Brook August 16, 27 PHASES of QCD POLYAKOV LOOP and QUASIPARTICLES Wolfram Weise with Thomas Hell Simon Rössner Claudia Ratti C. Ratti, M. Thaler, W. Weise: Phys. Rev. D 73 (26) 1419 C. Ratti,

More information

Introduction to particle physics Lecture 6

Introduction to particle physics Lecture 6 Introduction to particle physics Lecture 6 Frank Krauss IPPP Durham U Durham, Epiphany term 2009 Outline 1 Fermi s theory, once more 2 From effective to full theory: Weak gauge bosons 3 Massive gauge bosons:

More information

The Big Picture. Thomas Schaefer. North Carolina State University

The Big Picture. Thomas Schaefer. North Carolina State University The Big Picture Thomas Schaefer North Carolina State University 1 Big Questions What is QCD? What is a Phase of QCD? What is a Plasma? What is a (perfect) Liquid? What is a wqgp/sqgp? 2 What is QCD (Quantum

More information

Thermal dileptons as fireball probes at SIS energies

Thermal dileptons as fireball probes at SIS energies Thermal dileptons as fireball probes at SIS energies Critical Point and Onset of Deconfinement 2016, Wrocław. Florian Seck TU Darmstadt in collaboration with T. Galatyuk, P. M. Hohler, R. Rapp & J. Stroth

More information

Introduction to Quantum Chromodynamics (QCD)

Introduction to Quantum Chromodynamics (QCD) Introduction to Quantum Chromodynamics (QCD) Jianwei Qiu August 16 19, 018 Four Lectures The 3 rd WHEPS, August 16-4, 018, Weihai, Shandong q The Goal: The plan for my four lectures To understand the strong

More information

Goldstone Bosons and Chiral Symmetry Breaking in QCD

Goldstone Bosons and Chiral Symmetry Breaking in QCD Goldstone Bosons and Chiral Symmetry Breaking in QCD Michael Dine Department of Physics University of California, Santa Cruz May 2011 Before reading this handout, carefully read Peskin and Schroeder s

More information

Electric Dipole Moments and the strong CP problem

Electric Dipole Moments and the strong CP problem Electric Dipole Moments and the strong CP problem We finally understand CP viola3on.. QCD theta term Jordy de Vries, Nikhef, Amsterdam Topical Lectures on electric dipole moments, Dec. 14-16 Introductory

More information

Bethe Salpeter studies of mesons beyond rainbow-ladder

Bethe Salpeter studies of mesons beyond rainbow-ladder Bethe Salpeter studies of mesons beyond rainbow-ladder Richard Williams 1 st June 2010 12th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon College of William and Mary,

More information

An Introduction to the Standard Model of Particle Physics

An Introduction to the Standard Model of Particle Physics An Introduction to the Standard Model of Particle Physics W. N. COTTINGHAM and D. A. GREENWOOD Ж CAMBRIDGE UNIVERSITY PRESS Contents Preface. page xiii Notation xv 1 The particle physicist's view of Nature

More information

Mesons beyond the quark-antiquark picture: glueballs, hybrids, tetraquarks - part 1 - Francesco Giacosa

Mesons beyond the quark-antiquark picture: glueballs, hybrids, tetraquarks - part 1 - Francesco Giacosa Mesons beyond the quark-antiquark picture: glueballs, hybrids, tetraquarks - part 1-55 Cracow School of Theoretical Physics 20 28/6/2015, Zakopane, Poland Outline The Lagrangian of QCD and its symmetries

More information

Electroweak Physics. Krishna S. Kumar. University of Massachusetts, Amherst

Electroweak Physics. Krishna S. Kumar. University of Massachusetts, Amherst Electroweak Physics Krishna S. Kumar University of Massachusetts, Amherst Acknowledgements: M. Grunewald, C. Horowitz, W. Marciano, C. Quigg, M. Ramsey-Musolf, www.particleadventure.org Electroweak Physics

More information

QCD and the Nambu Jona-Lasinio Model

QCD and the Nambu Jona-Lasinio Model Lecture 1 QCD and the Nambu Jona-Lasinio Model Ian Cloët The University of Adelaide & Argonne National Laboratory CSSM Summer School Non-perturbative Methods in Quantum Field Theory 11 th 15 th February

More information

The Origin of the Visible Mass in the Universe

The Origin of the Visible Mass in the Universe The Origin of the Visible Mass in the Universe Or: Why the Vacuum is not Empty Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA Cyclotron REU Program 2007 Texas

More information

Outline: Introduction

Outline: Introduction Electromagnetic radiation in hadronic interactions: from pp to AA collisions Outline: Introduction Lijuan Ruan (Brookhaven National Laboratory) Recent results on dileptons (dielectrons) Recent results

More information

How nucleon gets its mass

How nucleon gets its mass Fiz-Tech, Dec 05, 2006 How nucleon gets its mass Dmitri Diakonov Petersburg Nuclear Physics Institute 1. Quantum Chromodynamics: the theory of strong interactions 2. Chiral symmetry of strong interactions

More information

Quantum Field Theory 2 nd Edition

Quantum Field Theory 2 nd Edition Quantum Field Theory 2 nd Edition FRANZ MANDL and GRAHAM SHAW School of Physics & Astromony, The University of Manchester, Manchester, UK WILEY A John Wiley and Sons, Ltd., Publication Contents Preface

More information

Introduction to the Standard Model New Horizons in Lattice Field Theory IIP Natal, March 2013

Introduction to the Standard Model New Horizons in Lattice Field Theory IIP Natal, March 2013 Introduction to the Standard Model New Horizons in Lattice Field Theory IIP Natal, March 2013 Rogerio Rosenfeld IFT-UNESP Lecture 1: Motivation/QFT/Gauge Symmetries/QED/QCD Lecture 2: QCD tests/electroweak

More information

High Energy Frontier Recent Results from the LHC: Heavy Ions I

High Energy Frontier Recent Results from the LHC: Heavy Ions I High Energy Frontier Recent Results from the LHC: Heavy Ions I Ralf Averbeck ExtreMe Matter Institute EMMI and Research Division GSI Helmholtzzentrum für Schwerionenforschung Darmstadt, Germany Winter

More information

The hadronization into the octet of pseudoscalar mesons in terms of SU(N) gauge invariant Lagrangian

The hadronization into the octet of pseudoscalar mesons in terms of SU(N) gauge invariant Lagrangian The hadronization into the octet of pseudoscalar mesons in terms of SU(N gauge invariant Lagrangian National Research Nuclear University Moscow 115409, Moscow, Russia E-mail: a kosh@internets.ru By breaking

More information

Overview. The quest of Particle Physics research is to understand the fundamental particles of nature and their interactions.

Overview. The quest of Particle Physics research is to understand the fundamental particles of nature and their interactions. Overview The quest of Particle Physics research is to understand the fundamental particles of nature and their interactions. Our understanding is about to take a giant leap.. the Large Hadron Collider

More information

A fresh look at the radiation from the QGP

A fresh look at the radiation from the QGP A fresh look at the radiation from the QGP Wolfgang Cassing (Uni. Giessen) In collaboration with Taesoo Song, Elena Bratkovskaya, Pierre Moreau The Erice School on Nuclear Physics 2018 The Strong Interaction:

More information

The Hadronic Decay Ratios of η 5π at NLO in χpt

The Hadronic Decay Ratios of η 5π at NLO in χpt EJTP 11, No. 1 (2014) 11 140 Electronic Journal of Theoretical Physics The Hadronic Decay Ratios of η 5π at NLO in χpt M. Goodarzi and H. Sadeghi Department of Physics, Faculty of Science, Arak University,

More information

The Quark-Gluon plasma in the LHC era

The Quark-Gluon plasma in the LHC era The Quark-Gluon plasma in the LHC era Journées de prospective IN2P3-IRFU, Giens, Avril 2012 t z IPhT, Saclay 1 Quarks and gluons Strong interactions : Quantum Chromo-Dynamics Matter : quarks ; Interaction

More information

Contents. 3 Protons and Other Hadrons in Quark Model Probing the Parton Structure in the Proton 37. iii

Contents. 3 Protons and Other Hadrons in Quark Model Probing the Parton Structure in the Proton 37. iii Contents 1 Introduction to QCD and the Standard Model 1 1.1 Quarks............................................ 1 1.2 Gluons and Quantum Chromodynamics......................... 3 1.3 Force Between Quarks,

More information

Introduction to gauge theory

Introduction to gauge theory Introduction to gauge theory 2008 High energy lecture 1 장상현 연세대학교 September 24, 2008 장상현 ( 연세대학교 ) Introduction to gauge theory September 24, 2008 1 / 72 Table of Contents 1 Introduction 2 Dirac equation

More information

Pions in the quark matter phase diagram

Pions in the quark matter phase diagram Pions in the quark matter phase diagram Daniel Zabłocki Instytut Fizyki Teoretycznej, Uniwersytet Wrocławski, Poland Institut für Physik, Universität Rostock, Germany Bogoliubov Laboratory of Theoretical

More information

Quark Model. Ling-Fong Li. (Institute) Note 8 1 / 26

Quark Model. Ling-Fong Li. (Institute) Note 8 1 / 26 Quark Model Ling-Fong Li (Institute) Note 8 1 / 6 QCD Quark Model Isospin symmetry To a good approximation, nuclear force is independent of the electric charge carried by the nucleons charge independence.

More information

Photoabsorption and Photoproduction on Nuclei in the Resonance Region

Photoabsorption and Photoproduction on Nuclei in the Resonance Region Photoabsorption and Photoproduction on Nuclei in the Resonance Region Susan Schadmand Institut für Kernphysik First Workshop on Quark-Hadron Duality Frascati, June 6-8, 2005 electromagnetic probes Hadron

More information

Electromagnetic probes: Messengers from the hot and dense fireball

Electromagnetic probes: Messengers from the hot and dense fireball Electromagnetic probes: Messengers from the hot and dense fireball Hendrik van Hees Goethe University Frankfurt November 5, 2014 Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, 2014

More information

Nonequilibrium dynamics and transport near the chiral phase transition of a quark-meson model

Nonequilibrium dynamics and transport near the chiral phase transition of a quark-meson model FAIRNESS 2013, 15-21 September 1 Nonequilibrium dynamics and transport near the chiral phase transition of a quark-meson model A Meistrenko 1, C Wesp 1, H van Hees 1,2 and C Greiner 1 1 Institut für Theoretische

More information

The direct photon puzzle

The direct photon puzzle The direct photon puzzle Jean-François Paquet January 16, 2017 ALICE Journal Club Jean-François Paquet (Stony Brook) 2 What is the direct photon puzzle? > Background

More information

Gian Gopal Particle Attributes Quantum Numbers 1

Gian Gopal Particle Attributes Quantum Numbers 1 Particle Attributes Quantum Numbers Intro Lecture Quantum numbers (Quantised Attributes subject to conservation laws and hence related to Symmetries) listed NOT explained. Now we cover Electric Charge

More information

Kern- und Teilchenphysik II Lecture 1: QCD

Kern- und Teilchenphysik II Lecture 1: QCD Kern- und Teilchenphysik II Lecture 1: QCD (adapted from the Handout of Prof. Mark Thomson) Prof. Nico Serra Dr. Marcin Chrzaszcz Dr. Annapaola De Cosa (guest lecturer) www.physik.uzh.ch/de/lehre/phy213/fs2017.html

More information

EDMs from the QCD θ term

EDMs from the QCD θ term ACFI EDM School November 2016 EDMs from the QCD θ term Vincenzo Cirigliano Los Alamos National Laboratory 1 Lecture II outline The QCD θ term Toolbox: chiral symmetries and their breaking Estimate of the

More information

A.A. Godizov. Institute for High Energy Physics, Protvino, Russia

A.A. Godizov. Institute for High Energy Physics, Protvino, Russia arxiv:1410.886v1 [hep-ph] 0 Oct 2014 QCD and nuclear physics. How to explain the coincidence between the radius of the strong interaction of nucleons and the characteristic scale of neutron-neutron electrostatic

More information

The Quest for Light Scalar Quarkonia from elsm

The Quest for Light Scalar Quarkonia from elsm Institut für Theoretische Physik Goethe-Universität Frankfurt am Main The Quest for Light calar Quarkonia from elm Denis Parganlija [Based on arxiv: 5.3647] In collaboration with Francesco Giacosa and

More information

National Nuclear Physics Summer School Lectures on Effective Field Theory. Brian Tiburzi. RIKEN BNL Research Center

National Nuclear Physics Summer School Lectures on Effective Field Theory. Brian Tiburzi. RIKEN BNL Research Center 2014 National Nuclear Physics Summer School Lectures on Effective Field Theory I. Removing heavy particles II. Removing large scales III. Describing Goldstone bosons IV. Interacting with Goldstone bosons

More information

Theoretical Review of Dileptons from Heavy Ion Collisions

Theoretical Review of Dileptons from Heavy Ion Collisions Theoretical Review of Dileptons from Heavy Ion Collisions Hendrik van Hees Texas A&M University February 8, 28 Hendrik van Hees (Texas A&M University) Theoretical Dilepton Review February 8, 28 1 / 22

More information

A short overview on strong interaction and quantum chromodynamics

A short overview on strong interaction and quantum chromodynamics A short overview on strong interaction and quantum chromodynamics Christoph Klein Universität Siegen Doktorandenseminar 08.10.2008 Christoph Klein (Universität Siegen) QCD and strong interaction Doktorandenseminar

More information

Anomaly. Kenichi KONISHI University of Pisa. College de France, 14 February 2006

Anomaly. Kenichi KONISHI University of Pisa. College de France, 14 February 2006 Anomaly Kenichi KONISHI University of Pisa College de France, 14 February 2006 Abstract Symmetry and quantization U A (1) anomaly and π 0 decay Origin of anomalies Chiral and nonabelian anomaly Anomally

More information

This means that n or p form a doublet under isospin transformation. Isospin invariance simply means that. [T i, H s ] = 0

This means that n or p form a doublet under isospin transformation. Isospin invariance simply means that. [T i, H s ] = 0 1 QCD 1.1 Quark Model 1. Isospin symmetry In early studies of nuclear reactions, it was found that, to a good approximation, nuclear force is independent of the electromagnetic charge carried by the nucleons

More information

The SU(3) Group SU(3) and Mesons Contents Quarks and Anti-quarks SU(3) and Baryons Masses and Symmetry Breaking Gell-Mann Okubo Mass Formulae Quark-Mo

The SU(3) Group SU(3) and Mesons Contents Quarks and Anti-quarks SU(3) and Baryons Masses and Symmetry Breaking Gell-Mann Okubo Mass Formulae Quark-Mo Lecture 2 Quark Model The Eight Fold Way Adnan Bashir, IFM, UMSNH, Mexico August 2014 Culiacán Sinaloa The SU(3) Group SU(3) and Mesons Contents Quarks and Anti-quarks SU(3) and Baryons Masses and Symmetry

More information

Q a u r a k k m a m t a t t e t r e p r p ob o e b d e d b y b y di d l i e l p e t p o t n o s

Q a u r a k k m a m t a t t e t r e p r p ob o e b d e d b y b y di d l i e l p e t p o t n o s Quark matter probed by dileptons Olena Linnyk July 02, 2010 Information from photons and dileptons 14 12 10 ε/t 4 8 6 4 2 Lattice QCD: µ B =0 µ B =530 MeV 0 0.5 1.0 1.5 2.0 2.5 3.0 T/T c But what are the

More information

Most of Modern Physics today is concerned with the extremes of matter:

Most of Modern Physics today is concerned with the extremes of matter: Most of Modern Physics today is concerned with the extremes of matter: Very low temperatures, very large numbers of particles, complex systems Æ Condensed Matter Physics Very high temperatures, very large

More information

Week 3: Renormalizable lagrangians and the Standard model lagrangian 1 Reading material from the books

Week 3: Renormalizable lagrangians and the Standard model lagrangian 1 Reading material from the books Week 3: Renormalizable lagrangians and the Standard model lagrangian 1 Reading material from the books Burgess-Moore, Chapter Weiberg, Chapter 5 Donoghue, Golowich, Holstein Chapter 1, 1 Free field Lagrangians

More information

Most of Modern Physics today is concerned with the extremes of matter:

Most of Modern Physics today is concerned with the extremes of matter: Most of Modern Physics today is concerned with the extremes of matter: Very low temperatures, very large numbers of particles, complex systems Æ Condensed Matter Physics Very high temperatures, very large

More information

Kern- und Teilchenphysik I Lecture 13:Quarks and QCD

Kern- und Teilchenphysik I Lecture 13:Quarks and QCD Kern- und Teilchenphysik I Lecture 13:Quarks and QCD (adapted from the Handout of Prof. Mark Thomson) Prof. Nico Serra Dr. Patrick Owen, Dr. Silva Coutinho http://www.physik.uzh.ch/de/lehre/phy211/hs2016.html

More information

PHYSICS PARTICLE. An Introductory Course of. Palash B. Pal. CRC Press. Saha Institute of Nuclear Physics. Kolkata, India. Taylor &.

PHYSICS PARTICLE. An Introductory Course of. Palash B. Pal. CRC Press. Saha Institute of Nuclear Physics. Kolkata, India. Taylor &. An Introductory Course of PARTICLE PHYSICS Palash B. Pal Saha Institute of Nuclear Physics Kolkata, India W CRC Press Taylor &. Francis Croup Boca Raton London New York CRC Press is an imprint of the &

More information

Symmetries in Effective Field Theory

Symmetries in Effective Field Theory Symmetries in Effective Field Theory Sourendu Gupta SERC Main School 2014, BITS Pilani Goa, India Effective Field Theories December, 2014 Outline Outline Symmetries in EFTs Softly broken symmetries in

More information

Can we locate the QCD critical endpoint with a Taylor expansion?

Can we locate the QCD critical endpoint with a Taylor expansion? Can we locate the QCD critical endpoint with a Taylor expansion? Bernd-Jochen Schaefer Karl-Franzens-Universität Graz, Austria 7 th February - 6 th March, 1 48. Internationale Universitätswochen für Theoretische

More information

Particle Physics I Lecture Exam Question Sheet

Particle Physics I Lecture Exam Question Sheet Particle Physics I Lecture Exam Question Sheet Five out of these 16 questions will be given to you at the beginning of the exam. (1) (a) Which are the different fundamental interactions that exist in Nature?

More information

Physics 4213/5213 Lecture 1

Physics 4213/5213 Lecture 1 August 28, 2002 1 INTRODUCTION 1 Introduction Physics 4213/5213 Lecture 1 There are four known forces: gravity, electricity and magnetism (E&M), the weak force, and the strong force. Each is responsible

More information

4. The Standard Model

4. The Standard Model 4. The Standard Model Particle and Nuclear Physics Dr. Tina Potter Dr. Tina Potter 4. The Standard Model 1 In this section... Standard Model particle content Klein-Gordon equation Antimatter Interaction

More information

The Standard Model of Electroweak Physics. Christopher T. Hill Head of Theoretical Physics Fermilab

The Standard Model of Electroweak Physics. Christopher T. Hill Head of Theoretical Physics Fermilab The Standard Model of Electroweak Physics Christopher T. Hill Head of Theoretical Physics Fermilab Lecture I: Incarnations of Symmetry Noether s Theorem is as important to us now as the Pythagorean Theorem

More information

The Electro-Strong Interaction

The Electro-Strong Interaction The Electro-Strong Interaction Taking into account the Planck Distribution Law of the electromagnetic oscillators, we can explain the electron/proton mass rate and the Weak and Strong Interactions. Lattice

More information