Transport coefficients of QCD at NLO Jacopo Ghiglieri, CERN in - PowerPoint PPT Presentation

Transport coefficients of QCD at NLO Jacopo Ghiglieri, CERN in collaboration with Guy Moore and Derek Teaney SEWM2018, Barcelona, June 27 2018

Outline • Transport coefficients: introduction and motivation • Transport from an effective kinetic theory • (almost) NLO kinetic theory and first-order coefficients 
 (full) NLO kinetic theory for jets: pedagogical review in JG Teaney QGP5 (2015), gritty details in JG Moore Teaney JHEP1603 (2015) 
 (almost) NLO 1 st -order JG Moore Teaney, JHEP1803 (2018) • Second-order relaxation: results and bounds 
 JG Moore Teaney, 1805.02663

Overview


 
 
 
 Hydrodynamics • Field theories admit a long-wavelength hydrodynamical limit. Hydrodynamics: Effective Theory based on a gradient expansion of the flow velocity • For hydro fluctuations with local flow velocity v around an equilibrium state (with temp. T ), at first order in the gradients and in v 
 T 00 = e, T 0 i = ( e + p ) v i ✓ ∂ i v j + ∂ j v i � 2 ◆ T ij = ( p � ζ r · v ) δ ij � η 3 δ ij r · v Navier-Stokes hydro, two transport coefficients : bulk and shear viscosity

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 Estimating η (or why is η /s natural) • Weak coupling: long • Strong coupling: short distances between distances between collisions, easy collisions, little diffusion. Large η /s 
 diffusion. Small η /s


 
 
 Estimating η (or why is η /s natural) • (Mean free path) -1 ~ cross section x density 
 s ∼ Tl mfp ∼ T 1 η n σ ∼ T 2 σ • Cross section in a perturbative gauge theory ( T only scale*) 
 s ∼ 1 σ ∼ g 4 η g 4 T 2 * Coulomb divergences and screening scales ( m D ~ gT ) in gauge theories 
 1 σ ∼ g 4 η T 2 ln(1 /g ) s ∼ g 4 ln(1 /g ) N = 4 • From holography one instead has η /s= 1/(4 ! ) (for 
 SYM) and a conjectured lower limit 
 Kovtun Son Starinets Policastro PRL87 (2001) PLR94 (2004)

Theory approaches to (QCD) transport coefficients 2 • pQCD: QCD action (and EFTs and kinetic theories thereof). Real world: extrapolate from g ≪ 1 to α s ~0.3 • lattice QCD: Euclidean QCD action. Real world: analytically continue to Minkowskian domain 
 (see H. Meyer’s talk for a related topic) • AdS/CFT: action, weak and strong N =4 coupling. Real world: extrapolate to QCD

Motivation ? • Holography: Kovtun Son Starinets Policastro PRL87 (2001) PLR94 (2004), λ -3/2 corrections: Buchel et al (2005-2008) • pQCD: Arnold Moore Yaffe (AMY) (2000-2003)

Motivation ? • Add NLO to the right, understand kinetic theory beyond LO

The effective kinetic theory

The weak-coupling picture ∼ Hard particles, P~T Soft field Soft α s = g 2 field 4 π modes P~gT Figure by D. Teaney • Hard (quasi)-particles carry most of the stress-energy tensor. (Parametrically) largest contribution to thermodynamics

The weak-coupling picture ∼ Hard particles, P~T Soft field Soft α s = g 2 field 4 π modes P~gT Figure by D. Teaney • The gluonic soft fields have large occupation numbers ⇒ they can be treated classically 1 ω ⇠ 1 T ω ∼ gT n B ( ω ) = ' e ω /T � 1 g

Weak-coupling thermodynamics 1.0 0.8 0.6 χ u 2 = ∂ 2 p ( T, µ ) χ u 2 ∂ µ 2 SB SB u HTLpt 3-loop truncated 0.4 BNL-B WB 0.2 HTLpt 1-loop exact DR 0.0 200 400 600 800 1000 T H MeV L Mogliacci Andersen Strickland Su Vuorinen JHEP1312 (2013) • Successful for static (thermodynamical) quantities. Possibility of solving the soft sector non-perturbatively (3D theory on the lattice). See talk by P. Schicho tomorrow

Weak-coupling thermodynamics 1.0 0.8 0.6 χ u 2 = ∂ 2 p ( T, µ ) χ u 2 ∂ µ 2 SB SB u HTLpt 3-loop truncated 0.4 BNL-B WB 0.2 HTLpt 1-loop exact DR 0.0 200 400 600 800 1000 T H MeV L Mogliacci Andersen Strickland Su Vuorinen JHEP1312 (2013) • Extra motivation: understand how to set up a similar resummation program for kinetics

The effective kinetic theory Baym Braaten Pisarski Arnold Moore Yaffe Baier Dokshitzer Mueller Schiff Son Peigné Wiedemann Gyulassy Wang Aurenche Gelis Zaraket Blaizot Iancu . . .

The effective kinetic theory • The effective theory is obtained by integrating out (off- shell) quantum fluctuations • Boltzmann equation for the single-particle phase space- distribution: its convective derivative equals a collision operator ( ∂ t + v p · r ) f ( p , x , t ) = C [ f ] • In other words at weak coupling the underlying QFT has well- defined quasi-particles. These are weakly interacting with a mean free time (1/ g 4 T ) larger than the actual duration of an individual collision (1/ T ) • Justified at weak coupling, can be extended to factor in non- perturbative contributions


 
 
 The AMY kinetic theory • Effective Kinetic Theory (EKT) for the phase space density of quarks and gluons 
 ✓ ∂ s ◆ f ( p ) = C 2 ↔ 2 + C 1 ↔ 2 ∂ t + v · r x • At leading order : elastic, number-preserving 2 ↔ 2 processes and collinear, number-changing effective 1 ↔ 2 processes AMY (2003) 
 ( ω , q ⊥ ) p 0 k 0 ( p, 0) Q ( p − ω , − q ⊥ ) p k Landau-Pomeranchuk-Migdal resummation (Wait for the next talk )

Transport coeffs from the EKT