Bottomonium at finite temperature from Lattice QCD

Sinead Ryan

Trinity College Dublin & Jefferson Laboratoryand

Jonivar Skullerud, Bugra Oktay, Seyong Kim, Maria-Paola Lombardo and Don Sinclair

Quarkonium Working Group, Hamburg, October 2007

Sinead Ryan (TCD & JLab) Bottomonium from LQCD QWG07 1 / 17

Outline

BackgroundI Follows from Charmonium at finite temperature on dynamical (Nf = 2)

lattices. [arXiv:0705.2198]I NRQCD and relativistic bottomonium on dynamical latticesI Zero temperature spectroscopy

F the value of extended operators for bb excitations

ResultsI preliminary results from NRQCD and relativistic simulations

Some conclusions and outlook

Sinead Ryan (TCD & JLab) Bottomonium from LQCD QWG07 2 / 17

Why bottomonium?

Many b quarks will be produced at ALICE

Melting of S and P waves?

TΥd ∼ 5Tc , difficult to do on a lattice

Use two approaches and compare results:NRQCD and relativistic.

Sinead Ryan (TCD & JLab) Bottomonium from LQCD QWG07 3 / 17

Dynamical anisotropic lattices

A large number of points in the time direction required

To reach T = 2Tc , O(10) points ⇒ at ∼ 0.025fm.

Far too expensive with an isotropic (as = at) lattice ⇒ anisotropic,at � as .

Gives an independent handle on temperature

Sinead Ryan (TCD & JLab) Bottomonium from LQCD QWG07 4 / 17

Dynamical anisotropic lattices

A large number of points in the time direction required

To reach T = 2Tc , O(10) points ⇒ at ∼ 0.025fm.

Far too expensive with an isotropic (as = at) lattice ⇒ anisotropic,at � as .

Gives an independent handle on temperature

Introduces 2 additional parameters to the action

Non-trivial but now understood tuning problem [PRD 74 014505(2006)]

Sinead Ryan (TCD & JLab) Bottomonium from LQCD QWG07 5 / 17

Simulation parameters

arXiv:07075.2198

Light quarks mπ/mρ 0.54Anisotropy ξ 6Lattice spacing at 0.025fm

as 0.17fmLattice volume N3

s 83 → 123

Critical temp. Tc 1/33.5at 210MeV1/Temperature Nt 16 T ∼ 2.1Tc

24 T ∼ 1.4Tc

32 T ∼ 1.05Tc

80 T ∼ 0Use all-to-all propagators and extended operators for better overlap withstates.

Sinead Ryan (TCD & JLab) Bottomonium from LQCD QWG07 6 / 17

b-quark methods on the lattice

Need amb < 1 which becomes increasingly difficult for heavy quarks

Fermilab: mass-dependent renormalisation of the action andoperators. Expensive to improve beyond O(a).

NRQCD: Good for b quarks, not c and no continuum limit.Use an action good to lowest order in v2.

Anisotropic relativistic: keeps atmb < 1. Continuum limit possible.Use an action improved to O(a3

s , a2t , αsa

2s ).

Compare NRQCD and Relativistic anisotropic results on the samedynamical (Nf = 2) background configurations.

Sinead Ryan (TCD & JLab) Bottomonium from LQCD QWG07 7 / 17

(Relativistic) zero-temperature spectroscopy: S waves

0 5 10 15 20 25 30 35tmin

1.2

1.25

1.3

1.35

1.4

1.45

1.5

1.55

1.6

Fitte

d M

ass

1S2S3S

Sliding window plots for the 1S

0η

b state

FIG. 1: Sliding window plots for the 0−+

ηb state.

2

Sinead Ryan (TCD & JLab) Bottomonium from LQCD QWG07 8 / 17

(Relativistic) zero-temperature spectroscopy: S waves

0 5 10 15 20 25 30 35tmin

1.2

1.25

1.3

1.35

1.4

1.45

1.5

1.55

1.6

1.65

1.7

1.75

Fitte

d M

ass

1S2S4S3S5S6S

Sliding window plots for the 3S

1 1

- - Υ state.

FIG. 1: Sliding window plots for the 1−−

Υ state.

2

Sinead Ryan (TCD & JLab) Bottomonium from LQCD QWG07 9 / 17

(Relativistic) zero-temperature spectroscopy: P waves→ P − S splitting ≈ 400MeV. Persists above Tc

Sinead Ryan (TCD & JLab) Bottomonium from LQCD QWG07 10 / 17

NRQCD: S and P waves at T = 0, T > Tc

Sinead Ryan (TCD & JLab) Bottomonium from LQCD QWG07 11 / 17

NRQCD: S and P waves at T = 0, T > Tc

→ P-S splitting survives at T > Tc .Sinead Ryan (TCD & JLab) Bottomonium from LQCD QWG07 12 / 17

Spectral functions from Maximum Entropy Method

Spectral functions give information about hadrons in the medium

Can be used to determine transport coefficients

ρΓ(ω,~p) related to the euclidean correlator GΓ(t, ~p) by

GΓ(t, ~p) =

∫ρΓ(ω,~p)

cosh[ω(t − 1/2T )]

sinh(ω/2T )

ill-posed problem - needs a large number of timeslices

use mem to determine the most likely ρ(ω).

Preliminary results: no mem systematics included.

Sinead Ryan (TCD & JLab) Bottomonium from LQCD QWG07 13 / 17

ηb (1S0) T dependence

Sinead Ryan (TCD & JLab) Bottomonium from LQCD QWG07 14 / 17

hb (1P1) T dependence

Sinead Ryan (TCD & JLab) Bottomonium from LQCD QWG07 15 / 17

χb1(3P1) T dependence

Sinead Ryan (TCD & JLab) Bottomonium from LQCD QWG07 16 / 17

Outlook

Early stages of this workI zero temperature spectroscopy and MEM in reasonable agreementI little dependence in the MEM of S or P waves on temperature. Up to

T ∼ 2Tc .I good signals in NRQCD correlators and observed P-S splitting.

Discretisation errorsI finer lattice spacings being generated

More reliable determination of statesI Use both extended and point operators (with all-to-all propagators)I Better analysis of excitations including particle identification

Reconstructed correlators

MEM systematicsI vary the default model, time ranges etc.

More in-depth comparison of NRQCD and relativistic results from thesame lattices

Sinead Ryan (TCD & JLab) Bottomonium from LQCD QWG07 17 / 17