Introduction QCD at zero µ , zero B QCD at nonzero µ QCD at nonzero B Summary QCD phase diagram: overview of recent lattice results Gergely Endr˝ odi University of Regensburg Fairness 2013, 19th September, 2013 QCD phase diagram Gergely Endr˝ odi University of Regensburg
Introduction QCD at zero µ , zero B QCD at nonzero µ QCD at nonzero B Summary Outline • introduction ◮ QCD ◮ nonzero temperature / density / magnetic field ◮ lattice approach • lattice results about the phase diagram ◮ QCD at zero µ , zero B ◮ QCD at nonzero µ ◮ QCD at nonzero B • summary QCD phase diagram Gergely Endr˝ odi University of Regensburg
Introduction QCD at zero µ , zero B QCD at nonzero µ QCD at nonzero B Summary QCD and quark-gluon plasma • elementary particle interactions: gravitational, electromagnetic, weak, strong � �� � Standard Model • strong sector: Quantum Chromodynamics • elementary particles: quarks ( ∼ electrons) and gluons ( ∼ photons) but: they cannot be observed directly ⇒ confinement at low temperatures • asymptotic freedom [Gross, Politzer, Wilczek ’04] ⇒ heating or compressing the system leads to deconfinement : quark-gluon plasma is formed • transition between the two phases characteristics: order (1st/2nd/crossover) critical temperature T c QCD phase diagram Gergely Endr˝ odi University of Regensburg
Introduction QCD at zero µ , zero B QCD at nonzero µ QCD at nonzero B Summary QCD phase diagram • why is the physics of the quark-gluon plasma interesting? ◮ large T : early Universe, cosmological models ◮ large ρ : neutron stars ◮ large T and/or ρ : heavy-ion collisions, experiment design QCD phase diagram Gergely Endr˝ odi University of Regensburg
Introduction QCD at zero µ , zero B QCD at nonzero µ QCD at nonzero B Summary QCD phase diagram • why is the physics of the quark-gluon plasma interesting? ◮ large T : early Universe, cosmological models ◮ large ρ : neutron stars ◮ large T and/or ρ : heavy-ion collisions, experiment design QCD phase diagram Gergely Endr˝ odi University of Regensburg
Introduction QCD at zero µ , zero B QCD at nonzero µ QCD at nonzero B Summary QCD phase diagram • why is the physics of the quark-gluon plasma interesting? ◮ large T : early Universe, cosmological models ◮ large ρ : neutron stars ◮ large T and/or ρ : heavy-ion collisions, experiment design QCD phase diagram Gergely Endr˝ odi University of Regensburg
Introduction QCD at zero µ , zero B QCD at nonzero µ QCD at nonzero B Summary QCD phase diagram • why is the physics of the quark-gluon plasma interesting? ◮ large T : early Universe, cosmological models ◮ large ρ : neutron stars ◮ large T and/or ρ : heavy-ion collisions, experiment design QCD phase diagram Gergely Endr˝ odi University of Regensburg
Introduction QCD at zero µ , zero B QCD at nonzero µ QCD at nonzero B Summary QCD phase diagram • why is the physics of the quark-gluon plasma interesting? ◮ large T : early Universe, cosmological models ◮ large ρ : neutron stars ◮ large T and/or ρ : heavy-ion collisions, experiment design • additional, relevant parameter: ◮ external magnetic field B QCD phase diagram Gergely Endr˝ odi University of Regensburg
Introduction QCD at zero µ , zero B QCD at nonzero µ QCD at nonzero B Summary Example 1: neutron star [Rea et al. ’13] • possible quark core at center with high density, low temperature • magnetars: extreme strong magnetic fields QCD phase diagram Gergely Endr˝ odi University of Regensburg
Introduction QCD at zero µ , zero B QCD at nonzero µ QCD at nonzero B Summary Typical magnetic fields 10 − 5 T magnetic field of Earth • 10 − 3 T common magnet • 10 2 T • strongest man-made field in lab 10 10 T magnetar surface • QCD phase diagram Gergely Endr˝ odi University of Regensburg
Introduction QCD at zero µ , zero B QCD at nonzero µ QCD at nonzero B Summary Typical magnetic fields 10 − 5 T magnetic field of Earth • 10 − 3 T common magnet • 10 2 T • strongest man-made field in lab 10 10 T magnetar surface • Wikipedia: “At a distance halfway to the moon, a magnetar could strip information from the magnetic stripes of all credit cards on Earth.” QCD phase diagram Gergely Endr˝ odi University of Regensburg
Introduction QCD at zero µ , zero B QCD at nonzero µ QCD at nonzero B Summary Example 2: heavy-ion collision [STAR collaboration, ’10] • off-central collisions generate magnetic fields: strength controlled by √ s and impact parameter (centrality) QCD phase diagram Gergely Endr˝ odi University of Regensburg
Introduction QCD at zero µ , zero B QCD at nonzero µ QCD at nonzero B Summary Example 2: heavy-ion collision 30 25 r=(0,0,0) r=(3 fm, 0, 0) 20 r=(0, 3 fm, 0) 4 2 >/ m r=(3 fm, 3 fm, 0) 15 <(e B) 10 5 0 0 2 4 6 8 10 12 14 b (fm) [Bloczynski et al. ’12] • off-central collisions generate magnetic fields: strength controlled by √ s and impact parameter (centrality) QCD phase diagram Gergely Endr˝ odi University of Regensburg
Introduction QCD at zero µ , zero B QCD at nonzero µ QCD at nonzero B Summary Typical magnetic fields 10 − 5 T magnetic field of Earth • 10 − 3 T common magnet • 10 2 T • strongest man-made field in lab 10 10 T magnetar surface • 10 15 T • LHC Pb-Pb at 2.7 TeV, b = 10 fm [Skokov ’09] QCD phase diagram Gergely Endr˝ odi University of Regensburg
Introduction QCD at zero µ , zero B QCD at nonzero µ QCD at nonzero B Summary Typical magnetic fields 10 − 5 T magnetic field of Earth • 10 − 3 T common magnet • 10 2 T • strongest man-made field in lab 10 10 T magnetar surface • 10 15 T • LHC Pb-Pb at 2.7 TeV, b = 10 fm [Skokov ’09] 10 5 b = 4 fm b = 8 fm b = 12 fm 10 4 eB (MeV 2 ) 10 3 10 2 10 1 10 0 0 0.5 1 1.5 2 2.5 3 [Tuchin ’13] τ (fm) QCD phase diagram Gergely Endr˝ odi University of Regensburg
Introduction QCD at zero µ , zero B QCD at nonzero µ QCD at nonzero B Summary Approaches to study QCD • various methods in various regimes: ◮ high T /µ/ B : perturbation theory ◮ low T /µ/ B : hadronic models ◮ transition region: non-perturbative methods, lattice gauge theory [Wilson, ’74] L = 1 F µν = − i 4 F µν F µν + ¯ ψ ( / D + m ) ψ, D µ = ∂ µ + ig s A µ , [ D µ , D ν ] g s • discretize quark and gluon fields ψ and A µ on a 4D space-time lattice with spacing a • functional integral gives the partition function � � � � D A µ D ¯ d 4 x L Z = ψ D ψ exp − QCD phase diagram Gergely Endr˝ odi University of Regensburg
Introduction QCD at zero µ , zero B QCD at nonzero µ QCD at nonzero B Summary Approaches to study QCD • various methods in various regimes: ◮ high T /µ/ B : perturbation theory ◮ low T /µ/ B : hadronic models ◮ transition region: non-perturbative methods, lattice gauge theory [Wilson, ’74] L = 1 F µν = − i 4 F µν F µν + ¯ ψ ( / D + m ) ψ, D µ = ∂ µ + ig s A µ , [ D µ , D ν ] g s • discretize quark and gluon fields ψ and A µ on a 4D space-time lattice with spacing a • functional integral gives the partition function � � � � � / d 4 x 1 � Z = D A µ exp − 4 F µν F µν · det D + m solve 10 9 dimensional integrals ⇒ Monte-Carlo methods QCD phase diagram Gergely Endr˝ odi University of Regensburg
Introduction QCD at zero µ , zero B QCD at nonzero µ QCD at nonzero B Summary Lattice QCD • biggest challenges are to ◮ extrapolate a → 0 ‘continuum limit’ and keep physical size fixed: # of lattice points → ∞ ◮ fix bare parameters of L : quark masses tune m such that hadron masses at T = 0 are as in nature QCD phase diagram Gergely Endr˝ odi University of Regensburg
Introduction QCD at zero µ , zero B QCD at nonzero µ QCD at nonzero B Summary Lattice QCD • biggest challenges are to ◮ extrapolate a → 0 ‘continuum limit’ and keep physical size fixed: # of lattice points → ∞ ◮ fix bare parameters of L : quark masses tune m such that hadron masses at T = 0 are as in nature QCD phase diagram Gergely Endr˝ odi University of Regensburg
Introduction QCD at zero µ , zero B QCD at nonzero µ QCD at nonzero B Summary Lattice QCD • biggest challenges are to ◮ extrapolate a → 0 ‘continuum limit’ and keep physical size fixed: # of lattice points → ∞ ◮ fix bare parameters of L : quark masses tune m such that hadron masses at T = 0 are as in nature • check: different discretizations should give the same result QCD phase diagram Gergely Endr˝ odi University of Regensburg
Introduction QCD at zero µ , zero B QCD at nonzero µ QCD at nonzero B Summary QCD phase diagram • how to map out the transition line? QCD phase diagram Gergely Endr˝ odi University of Regensburg
Introduction QCD at zero µ , zero B QCD at nonzero µ QCD at nonzero B Summary Observables sensitive to transition • chiral condensate → chiral symmetry breaking ψ f ψ f = ∂ log Z ¯ ∂ m f • chiral susceptibility → chiral symmetry breaking χ f = ∂ 2 log Z ∂ m 2 f • Polyakov loop → deconfinement �� � P = Tr exp A 4 ( x , t ) d t QCD phase diagram Gergely Endr˝ odi University of Regensburg
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