QGP from the quantum ground-state of QCD? beautiful math or New - PowerPoint PPT Presentation


 QGP from the quantum ground-state of QCD? 
 beautiful math or “New Physics” of QCD? Roman Pasechnik � 1

Summary: stages of the “micro Big Bang” L eff / λ 4 ( ⨯ 10 3 ) L eff / λ 4 ( ⨯ 10 3 ) L eff / λ 4 ( ⨯ 10 3 ) 1.0 1.0 1.0 0.5 0.5 0.5 1.2 J / λ 4 1.2 J / λ 4 1.2 J / λ 4 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 - 0.5 - 0.5 - 0.5 - 1.0 - 1.0 - 1.0 - 1.5 - 1.5 - 1.5 - 2.0 - 2.0 - 2.0 Stage I Stage II Stage III • quantum ground state 
 • (almost) classical homogeneous 
 • energy “swap” from condensate 
 formation (CE mostly 
 CE gluon condensate evolution to the fluctuations (quasiclassical pic.) + initiation of CM) • small inhomogeneities • large inhomogeneities (plasma modes) • large distances/essentially 
 • perturbative regime 
 • parametric resonance effect 
 quantum dynamics (short distances) (particle production mechanism) • domain-wall formation 2 �

QCD vacuum: short vs long distances Running QCD coupling Confinement Asymptotic freedom Color charge anti-screening Short range strong interactions Color confinement! � 3

Stage I 4

Homogeneous gluon condensate: semi-classics Corrections are small 
 Classical YM Lagrangian: for gYM<<1 
 L cl = − 1 4 F a µ ν F µ ν F a µ ν = ∂ µ A a ν − ∂ ν A a µ + g YM f abc A b µ A c (short distances!) a ν Basis for canonical (Hamiltonian) quantisation of “condensate+waves” system: temporal (Hamilton) A a e a i A a e a i e a e a i e b k ≡ A ik k = δ ik i = δ ab 0 = 0 gauge x ) = δ ik U ( t ) + � A ik ( t, ⃗ A ik ( t, ⃗ x ) due to local SU(2) ~ SO(3) isomorphism � Ω d 3 xA ik ( t, ⃗ x ) U ( t ) ≡ 1 � 3 δ ik ⟨ A ik ( t, ⃗ x ) ⟩ ⃗ ⟨ A ik ( t, ⃗ x ) ⟩ ⃗ x = x , Ω d 3 x Zeroth-order in waves = “pre-quilibrium state”? 1.0 � ( ∂ 0 U ) 2 + g 2 U 4 � H YM ≃ H YMC = 3 ∂ 0 ∂ 0 U + 2 g 2 U 3 = 0 , 0.5 2 0.0 U � U 0 � U � 0.5 dU U ′ (0) = 0 t = − � 0 − g 2 U 4 , U (0) = U 0 , � 1.0 g 2 U 4 U � t � U 0 U 0 cos � kgU 0 t � � 1.5 0.0 0.5 1.0 1.5 2.0 5 t � T U

Stage II 6

Condensate+waves semi-classical system � “condensate+waves” system evolution: − δ lk ( ∂ 0 ∂ 0 U + 2 g 2 U 3 ) + ( − ∂ 0 ∂ 0 � A lk + ∂ i ∂ i � A lk − ∂ i ∂ k � A li − ge lmk ∂ i � A mi U − 2 ge lip ∂ i � A pk U A mi U + g 2 � A kl U 2 − g 2 � − ge lmi ∂ k � A lk U 2 − 2 g 2 δ lk � A ii U 2 ) + ( − ge lmp ∂ i � A mi � � � � � A pk A pi + g 2 � A ik U + g 2 � A ki U + g 2 � − 2 ge lmp � A mi ∂ i � A pk − ge lmp ∂ k � A mi � A li � A li � A ik � � � � � � � � � A il U − − − 2 g 2 � A ii � A lk U − g 2 δ lk � A pi � A pi U ) + g 2 ( � A li � A pk � A pi − � A pi � A pi � A lk ) = 0 . � tensor basis decomposition p , χ ⃗ p l = s σ l η ⃗ σ + n l λ ⃗ p p + n i n k Λ ⃗ � ψ ⃗ p ik = ψ ⃗ p λ Q λ ik + ϕ ⃗ σ ( n i s σ k + n k s σ i ) + ( δ ik − n i n k ) Φ ⃗ p p A ik = ψ ik + e ikl χ l = 1 σ + ∂ 0 Φ ∂ 0 Φ † + 1 � 2 ∂ 0 Λ ∂ 0 Λ † + ∂ 0 η σ ∂ 0 η † ∂ 0 ψ λ ∂ 0 ψ † H waves λ + ∂ 0 φ σ ∂ 0 φ † Full Hamiltonian YM σ 2 λ + p 2 σ + p 2 ΦΦ † + p 2 + ∂ 0 λ ∂ 0 λ † + p 2 ψ λ ψ † σ + p 2 λλ † 2 φ σ φ † 2 η σ η † − p 2 2 e γσ ( η σ φ † γ + φ γ η † σ ) + igp U e σγ η σ η † γ − igp U Q λγ ψ λ ψ † γ � H waves γ − igp U (2 Φ λ † − 2 λ Φ † + Λ λ † − λ Λ † ) H YM = H YMC + − igpUe σγ φ σ φ † YM ⃗ p + 2 g 2 U 2 η σ η † σ + 2 g 2 U 2 λλ † + g 2 U 2 (4 ΦΦ † + 2 ΦΛ † + 2 ΛΦ † + ΛΛ † ) � Longitudinally polarised (plasma) mode becomes physical due to interactions with the homogeneous condensate! 7

Decay of the homogeneous condensate � ∂ 0 U ∂ 0 U + g 2 U 4 � H U = 3 , 2 � � H particles = 1 σ + ∂ 0 Φ ∂ 0 Φ † + 1 2 ∂ 0 Λ ∂ 0 Λ † + ∂ 0 η σ ∂ 0 η † ∂ 0 ψ λ ∂ 0 ψ † λ + ∂ 0 φ σ ∂ 0 φ † σ 2 ⃗ p λ + p 2 σ + p 2 ΦΦ † + p 2 + ∂ 0 λ ∂ 0 λ † + p 2 ψ λ ψ † σ + p 2 λλ † 2 φ σ φ † 2 η σ η † � − p 2 2 e γσ ( η σ φ † γ + φ γ η † σ ) , � � H int = 1 igp U e σγ η σ η † γ − igp U Q λγ ψ λ ψ † γ 2 ⃗ p γ − igp U (2 Φ λ † − 2 λ Φ † + Λ λ † − λ Λ † ) − igpUe σγ φ σ φ † � H H + 2 g 2 U 2 η σ η † σ + 2 g 2 U 2 λλ † + g 2 U 2 (4 ΦΦ † + 2 ΦΛ † + 2 ΛΦ † + ΛΛ † ) . 1.0 0.5 U � U 0 0.0 � 0.5 � 1.0 0 1 2 3 4 5 t � T U Ultra-relativistic gluon plasma production! 8

Stage III 9

QCD confinement as a dual Meissner effect type-II superconductor usual Meissner effect Superconductor L solenoid solenoid N S Flux tube Energy of the magnetic “monopole-antimonopole” pair is proportional to L (string potential) Magnetic field cannot penetrate through a superconductor, except by burning out a narrow tube where the superconductivity is destroyed (the Abrikosov vortex) The dual Meissner effect in QCD (analogous to that in dual superconductors): • the QCD vacuum as a condensate of chromo-magnetic monopoles 
 (c.f. condensation of BCS pairs in usual superconductors) • quarks are sources of chromo-electric field • inside the quark-antiquark tube the chromo-magnetic condensate is destroyed • electric field is squeezed inside the tube (the Abrikosov-Nielsen-Olesen vortex) � 10

Long distances: chromo-magnetic condensate Quantum-topological (chromomagnetic) vacuum in QCD Ground-state CM condensate: at long distances: Λ cosm ∼ 10 − 47 GeV 4 ✏ vac ∼ 10 − 2 GeV 4 Vacuum in QCD has incredibly wrong energy scale… or We must be missing something very important!? 11

Effective YM action approach [37] H. Pagels and E. Tomboulis, Nucl. Phys. B 143 , 485 At least, for SU(2) gauge symmetry, (1978). the all-loop and one-loop effective Lagrangians e A a µ ≡ g YM A a L cl = − 1 are practically indistinguishable (by FRG approach) 4 F a µ ν F µ ν µ a d F a µ ν ≡ g YM F a µ ν . [15] P. Dona, A. Marciano, Y. Zhang and C. Antolini, Phys. possesses well-kn Inverse running coupling 
 Rev. D 93 (2016) no.4, 043012. g - 2 is a better expansion 0.02 parameter! [14] A. Eichhorn, H. Gies and J. M. Pawlowski, Phys. Rev. D 83 (2011) 045014 [Phys. Rev. D 83 (2011) 069903]. Effective YM Lagrangian: 1.2 J / λ 4 0.2 0.4 0.6 0.8 1.0 - 0.02 Effective Lagrangian: J - 0.04 L e ff = g 2 ( J ) , J = − F a a , µ ν F µ ν L eff / λ 4 ( ⨯ 10 3 ) 4¯ - 0.06 1.0 - 0.08 0.5 1.2 J / λ 4 The energy-momentum tensor: 0.2 0.4 0.6 0.8 1.0 - 0.5 g 2 ) g 2 ) µ = 1 h � (¯ a +1 � (¯ - 1.0 i⇣ ⌘ T ν F a µ λ F νλ 4 � ν � � ν � 1 µ J g 2 J . µ - 1.5 g 2 ¯ 2 8¯ - 2.0 Equations of motion: trace anomaly: hich we r  F µ ν at J ⇤ > 0, g 2 ) ✓ 1 − � (¯ ◆� chromoelectric (CE) condensate − → D ab b =0 , g 2 ) µ = − � (¯ ν g 2 (Savvidy vacuum) ¯ 2 T µ g 2 J he only p 2¯ → − � ab − → ⇣ ⌘ D ab @ ν − f abc A c , ν ≡ ν [111] G. K. Savvidy, Phys. Lett. 71B , 133 (1977). ⇣ � →− J , J ← g 2 | g 2 ) d ln | ¯ = β (¯ appears to be NOTE: the RG equation invariant under d ln |J | /µ 4 g 2 =¯ g 2 ( |J | ) 2 | , ¯ 0 12

CE condensate on non-stationary (FLRW) background Q ⌘ 32 11 ⇡ 2 e ( ⇠ Λ QCD ) � 4 T µ µ [ U ] h 4 U 4 i Savvidy (CE) vacuum Classical YM condensate ( U 0 ) 2 � 1 a � 4 ( ⇠ Λ QCD ) � 4 = 6 e e Q ( U ) = 1 Exact partial solution: − 1 on | Q | = 1, ”Time” CE instantons 
 are formed first! Quantum corrections � “Radiation” medium QCD vacuum: 
 Asymptotic tracker solution! � YM ∝ 1 /a 4 a ferromagnetic undergoing ✏ CE ! +const t !1 spontaneous magnetisation (Pagels&Tomboulis) Unstable solution! Stable solution! • In fact, both chromoelectric and chromomagnetic condensates 
 are stable on non-stationary (FLRW) background of expanding Universe 13

“ Mirror” symmetry of the ground state In a vicinity of the ground state, the effective Lagrangian L e ff = J e J ' J ⇤ g 2 4¯ is invariant under g 2 ( J ∗ ) ← g 2 ( J ∗ ) , g 2 g 2 Z 2 : J ∗ ← →− J ∗ , ¯ →− ¯ � (¯ ∗ ) ← →− � (¯ ∗ ) , � (1) = � bN g 2 48 ⇡ 2 ¯ where b = 11 For pure gluodynamics at one-loop: (1) α s ( µ 2 0 ) g 2 α s = ¯ µ 2 ⌘ α s ( µ 2 ) = p |J | , µ 1 + β 0 α s ( µ 2 0 ) ln( µ 2 /µ 2 0 ) 4 π µ 2 p , 0 ⌘ |J ⇤ | as the physical scale Choosing the ground state value of the condensate p ⌘ |J | ⌘ we observe that the mirror symmetry, indeed, holds provided ↵ s ( µ 2 ! � ↵ s ( µ 2 0 ) 0 ) e J ' J ⇤ i.e. in the ground state only! 14