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