Study on charmonium and bottomonium
correlation functions in lattice QCD
at finite temperature
H. Ohno1,2

in collaboration with H.-T. Ding3 and O. Kaczmarek4
1University of Tsukuba, 2Brookhaven National Laboratory,
3Central China Normal University, 4Bielefeld University

理研シンポジウム・iTHES研究会「熱場の量子論とその応用」
理化学研究所大河内記念ホール、2014年9月4日

Quarkonium in hot medium
At extremely high temperature and density
Deconfinement of quarks and gluons

Quark Gluon Plasma (QGP)
The Debye screening prevents heavy quark-antiquark bound state(quarkonium) formation above a certain dissociation temperature→ important probe of QGP created in heavy ion collisions@ RHIC, LHC
T. Matsui and H. Satz, PLB 178 (1986) 416
N. Brambilla et al., EPJ C71 (2011) 1534
Sequential Bottomonium suppression @ LHC →Investigating dissociation
temperatures of charmonia andbottomonia by first principle lattice
QCD calculation is important
S. Chatrchyan et al., PRL 109 (2012) 222301
H. Ohno
熱場の量子論とその応用2014

Study on charmonium and bottomonium correlation functions
in lattice QCD at finite temperature

1/16

Transport coefficient
The evolution of the system in hydro models← Transport coefficients are important.

Determination by the firstprinciple calculation in QCD isneeded.

Adare et al. [PHENIX Collaboration], PRL 98 (2007) 172301
H. Ohno
熱場の量子論とその応用2014

Study on charmonium and bottomonium correlation functions
in lattice QCD at finite temperature

2/16

Meson correlator & spectral function
Temporal Euclidian meson correlator
Spectral function
has all information about inmedium meson propertiesρ(ω,p=0)/ω2

ρ(ω,p=0)/ω2

T<Tc

Ground stateρ(ω,p=0)/ω2

T>Tc

Zero mode/trans port peak (V, S, AV)(Free case)Zero mode/transport peak(V, S, AV)

Exited stateω
H. Ohno
熱場の量子論とその応用2014

T→∞ω
Study on charmonium and bottomonium correlation functions
in lattice QCD at finite temperatureω
3/16

Heavy quark diffusion constant: spatial component of vector spectral function

ρ(ω,p=0)/ω2

T>Tc: Quark number susceptibility

Zero mode/trans port peak (V, S, AV)

ωH. Ohno
熱場の量子論とその応用2014

D is related to the vector spectral
function around zero frequency.

Study on charmonium and bottomonium correlation functions
in lattice QCD at finite temperature

4/16

Recent lattice studies : spectral functions• Charmonia– Quenched QCD– Both S- and P-wave states are
dissociated above ~1.5Tc.
H.-T. Ding et al., PRD 86 (2012) 014509• Bottomonia– 2-flavor, nonrelativistic QCD– Υ has no temperature dependence up to 2.09Tc.
– χb0 is sensitive to the presence of thermal
medium immediately above Tc.
– Momentum dependence is effectively
temperature independent.

G.Aarts et al., PRL 106 (2011) 061602
G.Aarts et al., JHEP 1303 (2012) 084

H. Ohno
熱場の量子論とその応用2014

Study on charmonium and bottomonium correlation functions
in lattice QCD at finite temperature

5/16

Recent lattice studies : diffusion constant

H.-T. Ding et al., PRD 86 (2012) 014509• Perturbative estimate
2πDT ≈ 71.2 in LO
2πDT ≈ 8.4 in NLO

Moore and Teaney, PRD 71 (2005) 064904,
Caron-Hout and Moore, PRL 100 (2008) 052301
H. Ohno
熱場の量子論とその応用2014• Strong coupling limit
2πDT ≈ 1
Kovtun, Son and Starinets, JHEP 0310 (2004) 064

Study on charmonium and bottomonium correlation functions
in lattice QCD at finite temperature

6/16

Screening mass
Screening mass↓Spatial meson correlator

If there is a lowest lying bound stateHigh T limit (free case)2+1 flavor, p4 staggered

Quark mass↓
F. Karsch et al., PRD 85 (2012) 114501

H. Ohno
熱場の量子論とその応用2014

Study on charmonium and bottomonium correlation functions
in lattice QCD at finite temperature

7/16

Simulation Setup
•••
•
••
•

Standard plauette gauge & O(a)-improved Wilson quark actions
In quenched QCD
On fine and large isotropic lattices
2 different cutoff
T = 0.7－1.4Tc
4Both charm & bottom
Computing meson correlation functionsExperimental values: mJ/Ψ = 3.096.916(11) GeV, mΥ = 9.46030(26) GeV
J. Beringer et al. [PDG], PRD 86 (2012) 010001
H. Ohno
熱場の量子論とその応用2014

Study on charmonium and bottomonium correlation functions
in lattice QCD at finite temperature

8/16

Results (1) : Screening mass
β = 7.192

S wave: Mscr increases monotonically as increasing temperature.
P wave: Mscr has non -monotonic behavior.
Only small temperature dependence for bottom.
H. Ohno
熱場の量子論とその応用2014

Study on charmonium and bottomonium correlation functions
in lattice QCD at finite temperature

9/16

Reconstructed correlator

requals to unity
at all τ

if the spectral function doesn’t vary with temperature
S. Datta et al., PRD 69 (2004) 094507

H.-T. Ding et al., PRD 86 (2012) 014509
H. Ohno
熱場の量子論とその応用2014

Study on charmonium and bottomonium correlation functions
in lattice QCD at finite temperature

10/16

Results (2) : reconstructed correlator

V, S and Av channels have strong modification at large τ, whichmight be related to the transport peak
H. Ohno
熱場の量子論とその応用2014

Study on charmonium and bottomonium correlation functions
in lattice QCD at finite temperature

11/16

Results (2) : reconstructed correlator
Midpoint subtraction

Most part of the strong enhancement at large τ/a for V channel comesfrom the zero mode contribution.
H. Ohno
熱場の量子論とその応用2014

Study on charmonium and bottomonium correlation functions
in lattice QCD at finite temperature

12/16

Results (3) : heavy quark diffusion constant: Quark number susceptibility

The contribution from thetransport peak should be dominant
in G – Grec at τT = ½.

χ00 increases as increasing temperature for charm.
χ00 has quite small temperature dependence for bottom.
H. Ohno
熱場の量子論とその応用2014

Study on charmonium and bottomonium correlation functions
in lattice QCD at finite temperature

13/16

Results (3) : heavy quark diffusion constant

H.-T. Ding et al., PRD 86 (2012) 014509
β = 7.192

β = 7.793

Charm: 2πTD ≈ 0.6－4 (β = 7.192), 2πTD ≈ 0.5－3 (β = 7.793) for mq = 1－2 GeV
Bottom: there is no intersection for mq = 4－5 GeV
H. Ohno
熱場の量子論とその応用2014

Study on charmonium and bottomonium correlation functions
in lattice QCD at finite temperature

14/16

Conclusions• We calculate meson correlation functions– On fine and large isotropic lattices– With 2 different cutoff & quark mass for both charm and bottom• Screening masses– different temperature dependence between S and P wave states– small temperature dependence for bottomonia• Meson spectral functions are investigated by using
reconstructed correlators– V, S and Av channel have strong modification at large τ, whichmight be related to the transport peak.
– From the difference between the ordinary and reconstructedcorrelators, the heavy quark diffusion constant is roughly
estimated in the charm case.

H. Ohno
熱場の量子論とその応用2014

Study on charmonium and bottomonium correlation functions
in lattice QCD at finite temperature

15/16

Outlook• Taking continuum limit• Investigating spectral functions directly– Bayesian analysis• Estimating transport coefficients more accurately.
• Investigating exited states– variational analysis

H. Ohno
熱場の量子論とその応用2014

Study on charmonium and bottomonium correlation functions
in lattice QCD at finite temperature

16/16

End