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

s

(GeV) ξ mπ/mρ mπL Ns Nτ 1.5 3.5 0.446 3.9 16 128

• But mb ∼ 5 GeV...

Anisotropic Symanzik gauge/2+1 Wilson clover a−1

s

(GeV) ξ mπ/mρ mπL Ns Nτ 1.5 3.5 0.446 3.9 16 128

• But mb ∼ 5 GeV...

Effective field theory for heavy quarks

• Omit modes mb ∼ 5 GeV.
• Power counting in (p/mb)2 ∼ v2 ≈ 0.1.
• Heavy quark phase symmetry.

Anisotropic Symanzik gauge/2+1 Wilson clover a−1

s

(GeV) ξ mπ/mρ mπL Ns Nτ 1.5 3.5 0.446 3.9 16 128

• But mb ∼ 5 GeV...

Effective field theory for heavy quarks

• Omit modes mb ∼ 5 GeV.
• Power counting in (p/mb)2 ∼ v2 ≈ 0.1.
• Heavy quark phase symmetry.
• Eucl. Cont. NRQCD Lagrangian

L0 = ψ†(x)

• +Dτ − D2

2mb

• ψ(x),

Anisotropic Symanzik gauge/2+1 Wilson clover a−1

s

(GeV) ξ mπ/mρ mπL Ns Nτ 1.5 3.5 0.446 3.9 16 128

• But mb ∼ 5 GeV...

Effective field theory for heavy quarks

• Omit modes mb ∼ 5 GeV.
• Power counting in (p/mb)2 ∼ v2 ≈ 0.1.
• Heavy quark phase symmetry.
• Eucl. Cont. NRQCD Lagrangian

L0 = ψ†(x)

• +Dτ − D2

2mb

• ψ(x),

δLv2 = ψ†(x)

• −(D2)2

8m3

b

+ ig0 8m2

b

(D · E − E · D)

• ψ(x),

δLσ,v4 = ψ†(x)

• − g0

8m2

b

σ · (D × E − E × D) − g0 2mb σ · B

• ψ(x).

G(n + aτeτ) =

• 1 − aτH0|nτ +aτ

2

• U †

τ (n)

• 1 − aτH0|nτ

2

• (1 − aτδH) G(n)

Lattice NRQCD

• Heavy quark propagators solve initial value problem =

⇒ cheap. ☛ ‘Energy shift’ undefined.

• No continuum limit! Must keep a−1 mb.

G(n + aτeτ) =

• 1 − aτH0|nτ +aτ

2

• U †

τ (n)

• 1 − aτH0|nτ

2

• (1 − aτδH) G(n)

Lattice NRQCD

• Heavy quark propagators solve initial value problem =

⇒ cheap. ☛ ‘Energy shift’ undefined.

• No continuum limit! Must keep a−1 mb.

Tuning bare parameters

• Heavy quark rest mass plays no role.
• Tune ˆ

mb via meson dispersion relation.

• Use 1S spin-averaged ‘kinetic mass’.

• 0.02

0.02 0.04 0.06 0.08 0.1 0−+ 1+− 0++ 1++ 2++ aτM − aτMΥ JP C ηb(1S) hb(1P) χb0(1P) χb1(1P) χb2(1P) Lattice Experimental

T

Tc T

QGP HG

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 Lτ = Nτaτ = β and appropriate b.c.s.
• Fixed-scale approach: vary temperature by changing Nτ.

Ns Nτ T/Tc Ncfg 24 {16,. . .,40} {1.75,. . .,0.70} ≥500

0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 10 20 30 40 50 60 aτE(τ) τ/aτ Υ T/Tc = 0.22 T/Tc = 1.75 T/Tc = 1.40 T/Tc = 1.17 T/Tc = 1.00 T/Tc = 0.88 T/Tc = 0.78 T/Tc = 0.70 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 10 20 30 40 50 60 aτE(τ) τ/aτ χb1 T/Tc = 0.22 T/Tc = 1.75 T/Tc = 1.40 T/Tc = 1.17 T/Tc = 1.00 T/Tc = 0.88 T/Tc = 0.78 T/Tc = 0.70

Figure: Temperature dependence of the effective energies

Finite temperature

• Simulate with Lτ = Nτaτ = β and appropriate b.c.s.
• Fixed-scale approach: vary temperature by changing Nτ.

Ns Nτ T/Tc Ncfg 24 {16,. . .,40} {1.75,. . .,0.70} ≥500

0.98 1 1.02 1.04 1.06 1.08 1.1 1.12 2 4 6 8 10 12 14 16 G(τ, T/Tc = 1.75)/G(τ, T/Tc = 0) τ/aτ Υ ˆ mb = 1.20 ˆ mb = 2.00 ˆ mb = 2.92 ˆ mb = 4.01 ˆ mb = 12.32 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 2 4 6 8 10 12 14 16 G(τ, T/Tc = 1.75)/G(τ, T/Tc = 0) τ/aτ χb1 ˆ mb = 1.20 ˆ mb = 2.00 ˆ mb = 2.92 ˆ mb = 4.01 ˆ mb = 12.32

Figure: ˆ mb-dependence of the correlators

• Cont. nearly-free dynamics in NRQCD

G(τ) ∼ ∞

−ω0

dω π e−(ω+ω0)τρ(ω)

• Cont. nearly-free dynamics in NRQCD

G(τ) ∼ ∞

−ω0

dω π e−(ω+ω0)τρ(ω) ρfree(ω) ∼ ωαΘ(ω) = ⇒ Gfree(τ) ∼ e−ω0τ τ α+1

• Cont. nearly-free dynamics in NRQCD

G(τ) ∼ ∞

−ω0

dω π e−(ω+ω0)τρ(ω) ρfree(ω) ∼ ωαΘ(ω) = ⇒ Gfree(τ) ∼ e−ω0τ τ α+1 γeff(τ) = −τ G′(τ) G(τ) − → ω0τ + α + 1

• Cont. nearly-free dynamics in NRQCD

G(τ) ∼ ∞

−ω0

dω π e−(ω+ω0)τρ(ω) ρfree(ω) ∼ ωαΘ(ω) = ⇒ Gfree(τ) ∼ e−ω0τ τ α+1 γeff(τ) = −τ G′(τ) G(τ) − → ω0τ + α + 1

☛ Temperature dependence enters through interaction with the hot medium and not kinematically via the boundary conditions.

8 16 24 32 1 2 3 4 5

γeff

3S1 (vector) 8 16 24 32

τ/aτ

1 2 3 4 5 6 7

γeff

3P1 (axial-vector) T=0.42Tc T=1.05Tc T=1.40Tc T=2.09Tc free field

Figure: Previous study suggested melting P-wave at T/Tc ∼ 2 arXiv:1010.3725

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 2 4 6 8 10 12 14 γeff τ/aτ ˆ mb = 2.92, T/Tc = 1.75 Free lat. Υ Free lat. χb1 Υ χb1 Free cont. S-wave Free cont. P-wave

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 2 4 6 8 10 12 14 γeff τ/aτ ˆ mb = 2.92, T/Tc = 1.75 Free lat. Υ Free lat. χb1 Υ χb1 Free cont. S-wave Free cont. P-wave

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 2 4 6 8 10 12 14 γeff τ/aτ ˆ mb = 2.92, T/Tc = 1.75 Free lat. Υ Free lat. χb1 Υ χb1 Free cont. S-wave Free cont. P-wave

• 1
• 0.5

0.5 1 1.5 2 2 4 6 8 10 12 14 2.92 α ˆ mb T/Tc = 1.75 S-wave P-wave Free cont. S-wave Free cont. P-wave

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.

• 0.6
• 0.5
• 0.4
• 0.3
• 0.2
• 0.1

0.1 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 α Tc/T ˆ mb = 2.92 Υ

• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 α Tc/T ˆ mb = 2.92 Υ χb1

Sψ = a3

s

• n∈Λ

ψ†(n) [ψ(n) − K(nτ)ψ(n − aτeτ)] H0 = −∆(2) 2mb δHv2 = −(∆(2))2 8m3

b

+ ig0 8m2

b

(∇± · E − E · ∇±) δHσ = − g0 8m2

b

σ · (∇± × E − E × ∇±) − g0 2mb σ · B δHimp = a2

s∆(4)

24mb − aτ(∆(2))2 16km2

b

where ∆(2) =

• i

∇+

i ∇− i ,

and ∆(4) =

• i

(∇+

i ∇− i )2

[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.

0.2 0.205 0.21 0.215 0.22 0.225 0.23 0.235 0.24 0.245 0.2 0.4 0.6 0.8 1 1.2 aτE( ˜ P) ˜ P 2/a2

s

ˆ mb = 2.92 aτE(ηb) = 0.2059(2) + 0.0239(3) ˜ P 2/a2

s

aτE(Υ) = 0.2150(3) + 0.0241(3) ˜ P 2/a2

s

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 2 2.2 2.4 2.6 2.8 3 2.92 aτM kin = aτ

4 (Mkin(ηb) + 3Mkin(Υ))

ˆ mb aτM kin( ˆ mb) aτM expt aτM kin = 0.5092(49) ˆ mb + 0.181(12)

reality crossover mu,d,s = 0 ms 2nd O(4) ∞ Nf = 2 Nf = 1 ∞ mu,d 2nd Z2 ms,tric 2nd Z2 pure gauge 1st 1st