Bottomonium at finite temperature A signal for the quark-gluon - PowerPoint PPT Presentation

Bottomonium at finite temperature A signal for the quark-gluon plasma from lattice NRQCD Tim Harris + FASTSUM

Anisotropic Symanzik gauge/2+1 Wilson clover a − 1 (GeV) ξ m π /m ρ m π L N s N τ s 1.5 3.5 0.446 3.9 16 128 • But m b ∼ 5 GeV...

Anisotropic Symanzik gauge/2+1 Wilson clover a − 1 (GeV) ξ m π /m ρ m π L N s N τ s 1.5 3.5 0.446 3.9 16 128 • But m b ∼ 5 GeV... Effective field theory for heavy quarks • Omit modes � m b ∼ 5 GeV. • Power counting in ( p/m b ) 2 ∼ v 2 ≈ 0 . 1 . • Heavy quark phase symmetry.

Anisotropic Symanzik gauge/2+1 Wilson clover a − 1 (GeV) ξ m π /m ρ m π L N s N τ s 1.5 3.5 0.446 3.9 16 128 • But m b ∼ 5 GeV... Effective field theory for heavy quarks • Omit modes � m b ∼ 5 GeV. • Power counting in ( p/m b ) 2 ∼ v 2 ≈ 0 . 1 . • Heavy quark phase symmetry. Eucl. Cont. NRQCD Lagrangian + D τ − D 2 � � L 0 = ψ † ( x ) ψ ( x ) , 2 m b

Anisotropic Symanzik gauge/2+1 Wilson clover a − 1 (GeV) ξ m π /m ρ m π L N s N τ s 1.5 3.5 0.446 3.9 16 128 • But m b ∼ 5 GeV... Effective field theory for heavy quarks • Omit modes � m b ∼ 5 GeV. • Power counting in ( p/m b ) 2 ∼ v 2 ≈ 0 . 1 . • Heavy quark phase symmetry. Eucl. Cont. NRQCD Lagrangian + D τ − D 2 � � L 0 = ψ † ( x ) ψ ( x ) , 2 m b − ( D 2 ) 2 � + ig 0 � δ L v 2 = ψ † ( x ) ( D · E − E · D ) ψ ( x ) , 8 m 3 8 m 2 b b � − g 0 σ · ( D × E − E × D ) − g 0 � δ L σ ,v 4 = ψ † ( x ) σ · B ψ ( x ) . 8 m 2 2 m b b

� � � � 1 − a τ H 0 | n τ + a τ 1 − a τ H 0 | n τ U † G ( n + a τ e τ ) = τ ( n ) (1 − a τ δH ) G ( n ) 2 2 Lattice NRQCD • Heavy quark propagators solve initial value problem = ⇒ cheap. ☛ ‘Energy shift’ undefined. • No continuum limit! Must keep a − 1 � m b .

� � � � 1 − a τ H 0 | n τ + a τ 1 − a τ H 0 | n τ U † G ( n + a τ e τ ) = τ ( n ) (1 − a τ δH ) G ( n ) 2 2 Lattice NRQCD • Heavy quark propagators solve initial value problem = ⇒ cheap. ☛ ‘Energy shift’ undefined. • No continuum limit! Must keep a − 1 � m b . Tuning bare parameters • Heavy quark rest mass plays no role. • Tune ˆ m b via meson dispersion relation. • Use 1 S spin-averaged ‘kinetic mass’.

Lattice Experimental 0.1 0.08 χ b 2 (1 P ) 0.06 h b (1 P ) χ b 1 (1 P ) χ b 0 (1 P ) a τ M − a τ M Υ 0.04 0.02 0 η b (1 S ) -0.02 0 − + 1 + − 0 ++ 1 ++ 2 ++ J P C

T 0

T QGP T c HG 0

Credit: Jeffery Mitchell. VNI model by Klaus Kinder-Geiger and Ron Longacre, Brookhaven National Laboratory

Credit: Jeffery Mitchell. VNI model by Klaus Kinder-Geiger and Ron Longacre, Brookhaven National Laboratory A signal for the QGP • Suppression of J/ψ yield in RHICs [Matsui & Satz]. • b -quark ‘cleaner’ probe. • Sequential Υ suppression observed at LHC arxiv:1208.2826 .

Finite temperature • Simulate with L τ = N τ a τ = β and appropriate b.c.s. • Fixed-scale approach: vary temperature by changing N τ . N s N τ T/T c N cfg 24 { 16, . . . ,40 } { 1.75, . . . ,0.70 } ≥ 500

Υ χ b 1 0.6 0.7 T/T c = 0 . 22 T/T c = 0 . 22 0.55 0.65 T/T c = 1 . 75 T/T c = 1 . 75 0.5 0.6 T/T c = 1 . 40 T/T c = 1 . 40 0.45 0.55 T/T c = 1 . 17 T/T c = 1 . 17 a τ E ( τ ) a τ E ( τ ) 0.4 0.5 T/T c = 1 . 00 T/T c = 1 . 00 T/T c = 0 . 88 T/T c = 0 . 88 0.35 0.45 T/T c = 0 . 78 T/T c = 0 . 78 0.3 0.4 T/T c = 0 . 70 T/T c = 0 . 70 0.25 0.35 0.2 0.3 0.15 0.25 0 10 20 30 40 50 60 0 10 20 30 40 50 60 τ/a τ τ/a τ Figure: Temperature dependence of the effective energies Finite temperature • Simulate with L τ = N τ a τ = β and appropriate b.c.s. • Fixed-scale approach: vary temperature by changing N τ . N s N τ T/T c N cfg 24 { 16, . . . ,40 } { 1.75, . . . ,0.70 } ≥ 500

1.12 1.4 Υ χ b 1 m b = 1 . 20 ˆ m b = 1 . 20 ˆ 1.35 1.1 ˆ m b = 2 . 00 m b = 2 . 00 ˆ G ( τ, T/T c = 1 . 75) /G ( τ, T/T c = 0) G ( τ, T/T c = 1 . 75) /G ( τ, T/T c = 0) m b = 2 . 92 ˆ m b = 2 . 92 ˆ 1.3 m b = 4 . 01 ˆ m b = 4 . 01 ˆ 1.08 m b = 12 . 32 ˆ m b = 12 . 32 ˆ 1.25 1.06 1.2 1.04 1.15 1.02 1.1 1 1.05 0.98 1 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16 τ/a τ τ/a τ Figure: ˆ m b -dependence of the correlators

Cont. nearly-free dynamics in NRQCD � ∞ d ω π e − ( ω + ω 0 ) τ ρ ( ω ) G ( τ ) ∼ − ω 0

Cont. nearly-free dynamics in NRQCD � ∞ d ω π e − ( ω + ω 0 ) τ ρ ( ω ) G ( τ ) ∼ − ω 0 G free ( τ ) ∼ e − ω 0 τ ρ free ( ω ) ∼ ω α Θ( ω ) = ⇒ τ α +1

Cont. nearly-free dynamics in NRQCD � ∞ d ω π e − ( ω + ω 0 ) τ ρ ( ω ) G ( τ ) ∼ − ω 0 G free ( τ ) ∼ e − ω 0 τ ρ free ( ω ) ∼ ω α Θ( ω ) = ⇒ τ α +1 γ eff ( τ ) = − τ G ′ ( τ ) − → ω 0 τ + α + 1 G ( τ )

Cont. nearly-free dynamics in NRQCD � ∞ d ω π e − ( ω + ω 0 ) τ ρ ( ω ) G ( τ ) ∼ − ω 0 G free ( τ ) ∼ e − ω 0 τ ρ free ( ω ) ∼ ω α Θ( ω ) = ⇒ τ α +1 γ eff ( τ ) = − τ G ′ ( τ ) − → ω 0 τ + α + 1 G ( τ ) ☛ Temperature dependence enters through interaction with the hot medium and not kinematically via the boundary conditions.

5 3 S 1 (vector) 4 3 γ eff 2 1 T=0.42T c T=1.05T c 0 0 8 16 24 32 T=1.40T c 7 T=2.09T c 6 free field 3 P 1 (axial-vector) 5 4 γ eff 3 2 1 0 0 8 16 24 32 τ /a τ Figure: Previous study suggested melting P -wave at T/T c ∼ 2 arXiv:1010.3725

5 m b = 2 . 92 , T/T c = 1 . 75 ˆ 4 . 5 Free lat. Υ Free lat. χ b 1 4 Υ χ b 1 3 . 5 Free cont. S -wave Free cont. P -wave 3 γ eff 2 . 5 2 1 . 5 1 0 . 5 0 0 2 4 6 8 10 12 14 τ/a τ

5 m b = 2 . 92 , T/T c = 1 . 75 ˆ 4 . 5 Free lat. Υ Free lat. χ b 1 4 Υ χ b 1 3 . 5 Free cont. S -wave Free cont. P -wave 3 γ eff 2 . 5 2 1 . 5 1 0 . 5 0 0 2 4 6 8 10 12 14 τ/a τ

5 m b = 2 . 92 , T/T c = 1 . 75 ˆ 4 . 5 Free lat. Υ Free lat. χ b 1 4 Υ χ b 1 3 . 5 Free cont. S -wave Free cont. P -wave 3 γ eff 2 . 5 2 1 . 5 1 0 . 5 0 0 2 4 6 8 10 12 14 τ/a τ

2.92 2 T/T c = 1 . 75 S -wave P -wave 1.5 Free cont. S -wave Free cont. P -wave 1 0.5 α 0 -0.5 -1 0 2 4 6 8 10 12 14 m b ˆ

NRQCD • Radiatively improve NRQCD action with automated LPT. Finite temperature • Compare analysis of correlators with spectral functions from MaxEnt. New ensembles with ξ = 7 • Anisotropy tuning with Wilson flow.

0.1 m b = 2 . 92 ˆ Υ 0 -0.1 -0.2 α -0.3 -0.4 -0.5 -0.6 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 T c /T

1 m b = 2 . 92 ˆ Υ 0.8 χ b 1 0.6 0.4 0.2 α 0 -0.2 -0.4 -0.6 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 T c /T

S ψ = a 3 � ψ † ( n ) [ ψ ( n ) − K ( n τ ) ψ ( n − a τ e τ )] s n ∈ Λ H 0 = − ∆ (2) 2 m b δH v 2 = − (∆ (2) ) 2 + ig 0 ( ∇ ± · E − E · ∇ ± ) 8 m 3 8 m 2 b b δH σ = − g 0 g 0 σ · ( ∇ ± × E − E × ∇ ± ) − 2 m b σ · B 8 m 2 b δH imp = a 2 24 m b − a τ (∆ (2) ) 2 s ∆ (4) 16 km 2 b ∆ (2) = ∆ (4) = � � ∇ + i ∇ − ( ∇ + i ∇ − i ) 2 where i , and i i

[1] CMS Collaboration. Observation of sequential Υ suppression in PbPb collisions. Physical Review Letters , 109:222301, 2012, arXiv:1208.2826 . [2] R. Rapp, D. Blaschke, and P. Crochet. Charmonium and bottomonium in heavy-ion collisions. Progress in Particle and Nuclear Physics , 65:209, 2010, arXiv:0807.2470 . [3] Y. Burnier, M. Laine, and M. Veps¨ al¨ ainen. Heavy quarkonium in any channel in resummed hot QCD. Journal of High Energy Physics , 0801:043, 2008, arXiv:0711.1743 . [4] G. Aarts, S. Kim, M. P. Lombardo, M. B. Oktay, S. M. Ryan, D. K. Sinclair, and J.-I. Skullerud. Bottomonium above deconfinement in lattice nonrelativistic QCD. Physical Review Letters , 106:061602, 2011, arXiv:1010.3725 .

m b = 2 . 92 ˆ 0.245 a τ E ( η b ) = 0 . 2059(2) + 0 . 0239(3) ˜ P 2 /a 2 s a τ E (Υ) = 0 . 2150(3) + 0 . 0241(3) ˜ P 2 /a 2 0.24 s 0.235 0.23 P ) 0.225 a τ E ( ˜ 0.22 0.215 0.21 0.205 0.2 0 0.2 0.4 0.6 0.8 1 1.2 ˜ P 2 /a 2 s

2.92 1.8 4 ( M kin ( η b ) + 3 M kin (Υ)) 1.7 1.6 1.5 1.4 a τ M kin = a τ 1.3 a τ M kin ( ˆ m b ) a τ M expt 1.2 a τ M kin = 0 . 5092(49) ˆ m b + 0 . 181(12) 1.1 2 2.2 2.4 2.6 2.8 3 m b ˆ

N f = 2 pure gauge ∞ 2nd O (4) 1st 2nd Z 2 m s N f = 1 m s, tric reality crossover 2nd Z 2 1st m u,d ∞ m u,d,s = 0