In-medium Heavy Quarkonium properties from effective field ... · In-medium Heavy Quarkonium properties from effective field theory on the lattice! Alexander Rothkopf! Institute for

In-medium Heavy Quarkonium properties from effective field theory on the lattice

Alexander Rothkopf!Institute for Theoretical Physics

Heidelberg University

in collaboration with S. Kim and P. Petreczky !

References: !Y. Burnier, A.R.: Phys.Rev.Lett. 111 (2013) 182003

S.Kim, P. Petreczky, A.R.: Phys.Rev. D91 (2015) 054511S.Kim, P. Petreczky, A.R. in preparation

2015 RHIC & AGS ANNUAL USERS' MEETING – BNL UPTON, NY USA – JUNE 9TH

2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th

IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE

Motivation: Heavy-Ion Collisions !

Star&ng with RHIC: golden age of rela&vis&c heavy-‐ion collision experiments





Our interest: probes suscep&ble to medium but dis&nguishable Qprobe>> Tmed

Bound states of cc or bb: Heavy quarkonium MQ>>Tmed

Binding energy [GeV]0 0.2 0.4 0.6 0.8 1 1.2

AAR

0

0.2

0.4

0.6

0.8

1

1.2

1.4

< 30 GeV/c, |y| < 1.6)T

(2S) (6.5 < pψInclusive

(3S) (|y| < 2.4), 95% upper limitϒ

(2S) (|y| < 2.4)ϒ

< 30 GeV/c, |y| < 2.4)T

(6.5 < pψprompt J/

(1S) (|y| < 2.4)ϒ

(1S)Υ

ψJ/

(2S)Υ(3S)Υ

(2S)ψ

CMS Preliminary = 2.76 TeVNNsPbPb

0-100%

]2) [GeV/c-µ+µMass(7 8 9 10 11 12 13 14

)2Ev

ents

/ ( 0

.1 G

eV/c

0

200

400

600

800

1000

1200 = 2.76 TeVNNsCMS PbPb Cent. 0-100%, |y| < 2.4

-1bµ = 150 intL > 4 GeV/cµ

Tp

datatotal PbPb fitbackgroundpp shape

scaled)AA

(R

PR

L 10

9 22

2301

(20

12)

D.H

. Moo

n Q

uark

Mat

ter

2014





Goal: 1st principles understanding of qq modifica&on in the perfect liquid

Our interest: probes suscep&ble to medium but dis&nguishable Qprobe>> Tmed

Bound states of cc or bb: Heavy quarkonium MQ>>Tmed

Binding energy [GeV]0 0.2 0.4 0.6 0.8 1 1.2

AAR

0

0.2

0.4

0.6

0.8

1

1.2

1.4

< 30 GeV/c, |y| < 1.6)T

(2S) (6.5 < pψInclusive

(3S) (|y| < 2.4), 95% upper limitϒ

(2S) (|y| < 2.4)ϒ

< 30 GeV/c, |y| < 2.4)T

(6.5 < pψprompt J/

(1S) (|y| < 2.4)ϒ

(1S)Υ

ψJ/

(2S)Υ(3S)Υ

(2S)ψ

CMS Preliminary = 2.76 TeVNNsPbPb

0-100%

]2) [GeV/c-µ+µMass(7 8 9 10 11 12 13 14

)2Ev

ents

/ ( 0

.1 G

eV/c

0

200

400

600

800

1000

1200 = 2.76 TeVNNsCMS PbPb Cent. 0-100%, |y| < 2.4

-1bµ = 150 intL > 4 GeV/cµ

Tp

datatotal PbPb fitbackgroundpp shape

scaled)AA

(R

PR

L 10

9 22

2301

(20

12)

D.H

. Moo

n Q

uark

Mat

ter

2014



Quarkonium from first principles !

T. Matsui and H. Satz: Phys.Lett. B178 (1986) 416

presence of in-medium bound eigenstates?

modern approach: Lattice QCD meson spectra

OUR SETUP: Kinetically equilibrated heavy quarks














PRACTICAL CHALLENGE: High cost if light and heavy d.o.f share the same space&me grid

1

T= N⌧a ⇠ 1fma ⌧ 1

2mb⇡ 0.02fm








PRACTICAL CHALLENGE: High cost if light and heavy d.o.f share the same space&me grid

1

T= N⌧a ⇠ 1fma ⌧ 1

2mb⇡ 0.02fm

Turn the separa&on of scales into an advantage: effec&ve field theory NRQCD Thacker, Lepage Phys.Rev. D43 (1991) 196-208




Heavy quarks on!the lattice !



Heavy Quarks on the Lattice !




Effec&ve field theory from scale separa&on:

Rela&vis&c thermal field theory

Bra

mbi

lla e

t. al

. R

ev.M

od.P

hys.

77 (

2005

) 14

23

⇤QCD

mQ⌧ 1,

T

mQ⌧ 1,

pmQ

⌧ 1






Bra

mbi

lla e

t. al

. R

ev.M

od.P

hys.

77 (

2005

) 14

23

⇤QCD

mQ⌧ 1,

T

mQ⌧ 1,

pmQ

⌧ 1

QCD Dirac fields






Bra

mbi

lla e

t. al

. R

ev.M

od.P

hys.

77 (

2005

) 14

23

⇤QCD

mQ⌧ 1,

T

mQ⌧ 1,

pmQ

⌧ 1

NRQCD Pauli fields LNRQCD = †�iDt +

D2i

2MQ+ . . .

� + ⇠†

�. . .)⇠-

1

4Fµ⌫Fµ⌫ + q̄

�. . .

�q

�

†(x),�(x)

⇠

†(x), ⇠(x)�†�iDt +

D2i

2MQ+ . . .

��+ ⇠†

�. . .

�⇠

QCD Dirac fields




LNRQCD = †�iDt +D2

i

2MQ+ . . .

� + ⇠†

�. . .)⇠-

1

4Fµ⌫Fµ⌫ + q̄

�. . .

�q



Bra

mbi

lla e

t. al

. R

ev.M

od.P

hys.

77 (

2005

) 14

23

⇤QCD

mQ⌧ 1,

T

mQ⌧ 1,

pmQ

⌧ 1


D2i

2MQ+ . . .

� + ⇠†

�. . .)⇠-

1

4Fµ⌫Fµ⌫ + q̄

�. . .

�q

�

†(x),�(x)

⇠

†(x), ⇠(x)�†�iDt +

D2i

2MQ+ . . .

��+ ⇠†

�. . .

�⇠

QCD Dirac fields





i

2MQ+ . . .

� + ⇠†

�. . .)⇠-

1

4Fµ⌫Fµ⌫ + q̄

�. . .

�q



Bra

mbi

lla e

t. al

. R

ev.M

od.P

hys.

77 (

2005

) 14

23

⇤QCD

mQ⌧ 1,

T

mQ⌧ 1,

pmQ

⌧ 1


D2i

2MQ+ . . .

� + ⇠†

�. . .)⇠-

1

4Fµ⌫Fµ⌫ + q̄

�. . .

�q

�

†(x),�(x)

⇠

†(x), ⇠(x)�†�iDt +

D2i

2MQ+ . . .

��+ ⇠†

�. . .

�⇠

QCD Dirac fields

Individual Q or an&-‐Q in a medium background: Ini&al value problem G(τ)=<χ(τ)χ†(0)>

well behaved for nMQa ≥ 3!Davies, Thacker Phys.Rev. D45 (1992)

G(x, ⌧+ a) = U†4(x, ⌧)

�1-

p

2lat

2nMQa+ . . .

�G(x, ⌧)





i

2MQ+ . . .

� + ⇠†

�. . .)⇠-

1

4Fµ⌫Fµ⌫ + q̄

�. . .

�q

3S1 (J/ψ,Y) and 3P1 (χc1, χb1) channel correlators D(τ) from heavy quark propagators G(τ)

O(3S1; x, ⌧) = �i, O(3P1; x, ⌧) =$�i�j -

$�j�iD(⌧) =

X

x

hO(x, ⌧)Gx⌧O

†(x0, ⌧0)G†x⌧imed

Thacker, Lepage Phys.Rev. D43 (1991)



Bra

mbi

lla e

t. al

. R

ev.M

od.P

hys.

77 (

2005

) 14

23

⇤QCD

mQ⌧ 1,

T

mQ⌧ 1,

pmQ

⌧ 1


D2i

2MQ+ . . .

� + ⇠†

�. . .)⇠-

1

4Fµ⌫Fµ⌫ + q̄

�. . .

�q

�

†(x),�(x)

⇠

†(x), ⇠(x)�†�iDt +

D2i

2MQ+ . . .

��+ ⇠†

�. . .

�⇠

QCD Dirac fields

Individual Q or an&-‐Q in a medium background: Ini&al value problem G(τ)=<χ(τ)χ†(0)>

well behaved for nMQa ≥ 3!Davies, Thacker Phys.Rev. D45 (1992)

G(x, ⌧+ a) = U†4(x, ⌧)

�1-

p

2lat

2nMQa+ . . .

�G(x, ⌧)



T>0 QCD with Nf=2+1 HISQ flavors!

Light d.o.f. (gluons, u d s quarks) represented by HotQCD configura&ons A. Bazavov et. al., Phys. Rev. D 85 (2012) 054503





483x12 with rela&vely light pions Mπ～ 161MeV and a TC=159±3MeV





Important for the use with ladce NRQCD: 2.759 > Mba > 1.559 (ok if n=2) 0.757 > Mca > 0.427 (ok if n>=6)

HotQCD HISQ/tree action 483 ⇥N⌧ mu,d/ms = 0.05 TC = 154(9)MeV� 6.664 6.700 6.740 6.770 6.800 6.840 6.880

a[fm] 0.1169 0.1130 0.1087 0.1057 0.1027 0.09893 0.09528Mba 2.759 2.667 2.566 2.495 2.424 2.335 2.249

T/TC(N⌧ = 12) 0.911 0.944 0.980 1.008 1.038 1.078 1.119� 6.910 6.950 6.990 7.030 7.100 7.150 7.280

a[fm] 0.09264 0.08925 0.086 0.08288 0.07772 0.07426 0.06603Mba 2.187 2.107 2.030 1.956 1.835 1.753 1.559

T/TC(N⌧ = 12) 1.151 1.194 1.240 1.286 1.371 1.436 1.614








a[fm] 0.1169 0.1130 0.1087 0.1057 0.1027 0.09893 0.09528Mba 2.759 2.667 2.566 2.495 2.424 2.335 2.249

T/TC(N⌧ = 12) 0.911 0.944 0.980 1.008 1.038 1.078 1.119� 6.910 6.950 6.990 7.030 7.100 7.150 7.280

a[fm] 0.09264 0.08925 0.086 0.08288 0.07772 0.07426 0.06603Mba 2.187 2.107 2.030 1.956 1.835 1.753 1.559

T/TC(N⌧ = 12) 1.151 1.194 1.240 1.286 1.371 1.436 1.614


Temperature changed by varia&on of the ladce spacing 140MeV < T < 249MeV For a study based on the fixed scale approach see: FASTSUM G. Aarts et. al. JHEP 1407 (2014) 097, JHEP 1111 (2011) 103







a[fm] 0.1169 0.1130 0.1087 0.1057 0.1027 0.09893 0.09528Mba 2.759 2.667 2.566 2.495 2.424 2.335 2.249

T/TC(N⌧ = 12) 0.911 0.944 0.980 1.008 1.038 1.078 1.119� 6.910 6.950 6.990 7.030 7.100 7.150 7.280

a[fm] 0.09264 0.08925 0.086 0.08288 0.07772 0.07426 0.06603Mba 2.187 2.107 2.030 1.956 1.835 1.753 1.559

T/TC(N⌧ = 12) 1.151 1.194 1.240 1.286 1.371 1.436 1.614


Temperature changed by varia&on of the ladce spacing 140MeV < T < 249MeV

Low temperature configura&ons available at b=6.664, 6.8, 6.95, 7.28 (483x32,64)

For a study based on the fixed scale approach see: FASTSUM G. Aarts et. al. JHEP 1407 (2014) 097, JHEP 1111 (2011) 103



A Novel Bayesian Approach!

Inversion of Laplace transform required to obtain spectra from correlators

D(⌧) =

Z1

-2MQ

d!e-⌧!⇢(!)




Inversion of Laplace transform required to obtain spectra from correlators 1. Nω parameters ρl >> Nτ datapoints

2. data Di has finite precision Di =

N!X

l=1

exp[-!l⌧i] ⇢l �!l






N!X

l=1


Give meaning to problem by incorporating prior knowledge: Bayesian approach M. Jarrell, J. GubernaQs, Physics Reports 269 (3) (1996)

Bayes theorem: Regularize the naïve χ2 functional P[D|ρ] through a prior P[ρ|I]

P[⇢|D, I] / P[D|⇢] P[⇢|I]




P[⇢|I] / eS S = ↵

N!X

l=1

�!l

⇣1-

⇢l

ml+ log

h⇢l

ml

i⌘



N!X

l=1


New prior enforces: ρ positive definite, smoothness of ρ, result independent of units

Y.Burnier, A.R. PRL 111 (2013) 18, 182003



P[⇢|D, I] / P[D|⇢] P[⇢|I]




P[⇢|I] / eS S = ↵

N!X

l=1

�!l

⇣1-

⇢l

ml+ log

h⇢l

ml

i⌘

Different from Maximum Entropy Method: S not entropy, no more flat directions



N!X

l=1



Y.Burnier, A.R. PRL 111 (2013) 18, 182003



P[⇢|D, I] / P[D|⇢] P[⇢|I]




P[⇢|I] / eS S = ↵

N!X

l=1

�!l

⇣1-

⇢l

ml+ log

h⇢l

ml

i⌘

Different from Maximum Entropy Method: S not entropy, no more flat directions



N!X

l=1



No apriori restriction on the search space �

�⇢P[⇢|D, I]

��⇢=⇢BR

= 0Convergence to unique global extremum

Y.Burnier, A.R. PRL 111 (2013) 18, 182003



P[⇢|D, I] / P[D|⇢] P[⇢|I]



Bottomonium in lattice NRQCD !

!S.Kim, P. Petreczky, A.R.: Phys.Rev. D 91 (2015) 054511��

!



T=0 Bottomonium Correlators!

1e-18

1e-16

1e-14

1e-12

1e-10

1e-08

1e-06

0.0001

0.01

1

100

0 0.5 1 1.5 2 2.5 3 3.5 4

DΥ(τ

)

τ [fm]

S-wave T≈0

β=6.664 324

β=6.800 324β=6.950 324

β=7.280 483x64

1e-18

1e-16

1e-14

1e-12

1e-10

1e-08

1e-06

0.0001

0.01

1

100

0 0.5 1 1.5 2 2.5 3 3.5 4

Dχ

b1(τ

)

τ [fm]

P-wave T≈0

β=6.664 324

β=6.800 324β=6.950 324

β=7.280 483x64

S-‐wave Nmeas=100

P-‐wave Nmeas=100 S.

Kim

, P.P

etre

czky

, A.R

. Ph

ys.Rev. D

91 (201

5) 054

511




1e-18

1e-16

1e-14

1e-12

1e-10

1e-08

1e-06

0.0001

0.01

1

100

0 0.5 1 1.5 2 2.5 3 3.5 4

DΥ(τ

)

τ [fm]

S-wave T≈0

β=6.664 324

β=6.800 324β=6.950 324

β=7.280 483x64

1e-18

1e-16

1e-14

1e-12

1e-10

1e-08

1e-06

0.0001

0.01

1

100

0 0.5 1 1.5 2 2.5 3 3.5 4

Dχ

b1(τ

)

τ [fm]

P-wave T≈0

β=6.664 324

β=6.800 324β=6.950 324

β=7.280 483x64

S-‐wave Nmeas=100

P-‐wave Nmeas=100

0.8

1

1.2

1.4

1.6

1.8

2

0 0.5 1 1.5 2 2.5 3 3.5 4

mΥ e

ff =

-lo

g(D

Υ(τ

)/D

Υ(τ

+1

))/a

τ [G

eV

]

τ [fm]

β=6.664 324

β=6.800 324β=6.950 324

β=7.280 483x64

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2

mχ

b1

eff =

-lo

g(D

χb1(τ

)/D

χb1(τ

+1

))/a

τ [G

eV

]

τ [fm]

P-wave T≈0

β=6.664 324

β=6.800 324β=6.950 324

β=7.280 483x64

S-‐wave Nmeas=100

P-‐wave Nmeas=100

S.K

im, P

.Pet

recz

ky, A

.R.

Phys.Rev. D

91 (201

5) 054

511




1e-18

1e-16

1e-14

1e-12

1e-10

1e-08

1e-06

0.0001

0.01

1

100

0 0.5 1 1.5 2 2.5 3 3.5 4

DΥ(τ

)

τ [fm]

S-wave T≈0

β=6.664 324

β=6.800 324β=6.950 324

β=7.280 483x64

1e-18

1e-16

1e-14

1e-12

1e-10

1e-08

1e-06

0.0001

0.01

1

100

0 0.5 1 1.5 2 2.5 3 3.5 4

Dχ

b1(τ

)

τ [fm]

P-wave T≈0

β=6.664 324

β=6.800 324β=6.950 324

β=7.280 483x64

“Integra&ng out Mb” induces energy shik of ～2Mb

S-‐wave Nmeas=100

P-‐wave Nmeas=100

0.8

1

1.2

1.4

1.6

1.8

2

0 0.5 1 1.5 2 2.5 3 3.5 4

mΥ e

ff =

-lo

g(D

Υ(τ

)/D

Υ(τ

+1

))/a

τ [G

eV

]

τ [fm]

β=6.664 324

β=6.800 324β=6.950 324

β=7.280 483x64

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2

mχ

b1

eff =

-lo

g(D

χb1(τ

)/D

χb1(τ

+1

))/a

τ [G

eV

]

τ [fm]

P-wave T≈0

β=6.664 324

β=6.800 324β=6.950 324

β=7.280 483x64

S-‐wave Nmeas=100

P-‐wave Nmeas=100

Mexp

⌥(1S) = MNRQCD

⌥(1S) + 2(ZMbMb - E0)

Cshift(�)Mexp

⌥(1S) = 9.46030(26)GeV 8.05

8.1

8.15

8.2

8.25

8.3

8.35

8.4

8.45

8.5

8.55

8.6

6.6 6.7 6.8 6.9 7 7.1 7.2 7.3

Csh

ift [

Ge

V]

β

Cshift= (-0.779±0.006) x β + (13.765±0.041)

S.K

im, P

.Pet

recz

ky, A

.R.

Phys.Rev. D

91 (201

5) 054

511




1e-18

1e-16

1e-14

1e-12

1e-10

1e-08

1e-06

0.0001

0.01

1

100

0 0.5 1 1.5 2 2.5 3 3.5 4

DΥ(τ

)

τ [fm]

S-wave T≈0

β=6.664 324

β=6.800 324β=6.950 324

β=7.280 483x64

1e-18

1e-16

1e-14

1e-12

1e-10

1e-08

1e-06

0.0001

0.01

1

100

0 0.5 1 1.5 2 2.5 3 3.5 4

Dχ

b1(τ

)

τ [fm]

P-wave T≈0

β=6.664 324

β=6.800 324β=6.950 324

β=7.280 483x64

“Integra&ng out Mb” induces energy shik of ～2Mb

S-‐wave Nmeas=100

P-‐wave Nmeas=100

0.8

1

1.2

1.4

1.6

1.8

2

0 0.5 1 1.5 2 2.5 3 3.5 4

mΥ e

ff =

-lo

g(D

Υ(τ

)/D

Υ(τ

+1

))/a

τ [G

eV

]

τ [fm]

β=6.664 324

β=6.800 324β=6.950 324

β=7.280 483x64

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2

mχ

b1

eff =

-lo

g(D

χb1(τ

)/D

χb1(τ

+1

))/a

τ [G

eV

]

τ [fm]

P-wave T≈0

β=6.664 324

β=6.800 324β=6.950 324

β=7.280 483x64

S-‐wave Nmeas=100

P-‐wave Nmeas=100

Mexp

⌥(1S) = MNRQCD

⌥(1S) + 2(ZMbMb - E0)

Cshift(�)Mexp

⌥(1S) = 9.46030(26)GeV 8.05

8.1

8.15

8.2

8.25

8.3

8.35

8.4

8.45

8.5

8.55

8.6

6.6 6.7 6.8 6.9 7 7.1 7.2 7.3

Csh

ift [

Ge

V]

β

Cshift= (-0.779±0.006) x β + (13.765±0.041)

S.K

im, P

.Pet

recz

ky, A

.R.

Phys.Rev. D

91 (201

5) 054

511

M�b1(1P) = MNRQCD�b1

+ C(�) = 9.917(3)GeV > Mexp

�b1(1P)= 9.89278(26)(31)GeV



T=0 Bayesian Bottomonium Spectra!

Bayesian reconstruc&on:

0.001

0.01

0.1

1

10

100

1000

10000

1 1.5 2 2.5 3 3.5 4

ρΥ

-BR

(ω)

∆ω [GeV]

S-wave T≈0

β=6.664 324

β=6.800 324β=6.950 324

β=7.280 483x64

0.01

0.1

1

10

1 1.5 2 2.5 3 3.5 4

ρχ

b1-B

R(ω

)

∆ω [GeV]

P-wave T≈0

β=6.664 324

β=6.800 324β=6.950 324

β=7.280 483x64(44)

Nω=1200 Iω=[-‐0.5,30] βnum=20 Njack=10

ml=const, 512 bit precision, Δtol= 10-‐60

S-‐wave T≈0 P-‐wave T≈0

S.K

im, P

.Pet

recz

ky, A

.R.

Phys.Rev. D

91 (201

5) 054

511





0.001

0.01

0.1

1

10

100

1000

10000

1 1.5 2 2.5 3 3.5 4

ρΥ

-BR

(ω)

∆ω [GeV]

S-wave T≈0

β=6.664 324

β=6.800 324β=6.950 324

β=7.280 483x64

0.01

0.1

1

10

1 1.5 2 2.5 3 3.5 4

ρχ

b1-B

R(ω

)

∆ω [GeV]

P-wave T≈0

β=6.664 324

β=6.800 324β=6.950 324

β=7.280 483x64(44)

Nω=1200 Iω=[-‐0.5,30] βnum=20 Njack=10


S-‐wave ground state peak very well resolved, next peak mostly from Y(2S)


S.K

im, P

.Pet

recz

ky, A

.R.

Phys.Rev. D

91 (201

5) 054

511





0.001

0.01

0.1

1

10

100

1000

10000

1 1.5 2 2.5 3 3.5 4

ρΥ

-BR

(ω)

∆ω [GeV]

S-wave T≈0

β=6.664 324

β=6.800 324β=6.950 324

β=7.280 483x64

0.01

0.1

1

10

1 1.5 2 2.5 3 3.5 4

ρχ

b1-B

R(ω

)

∆ω [GeV]

P-wave T≈0

β=6.664 324

β=6.800 324β=6.950 324

β=7.280 483x64(44)

Nω=1200 Iω=[-‐0.5,30] βnum=20 Njack=10


S-‐wave ground state peak very well resolved, next peak mostly from Y(2S)

P-‐wave ground state broader: worse s/n ra&o and smaller physical peak size


S.K

im, P

.Pet

recz

ky, A

.R.

Phys.Rev. D

91 (201

5) 054

511



Reconstruction Accuracy: S-wave !

10-4

10-3

10-2

10-1

100

101

102

103

104

1 1.5 2

ρΥ

-BR

(ω)

∆ω [GeV]

β=6.664

S-wave

∆Γ=2 MeV∆m=2 MeV

Nτ32

Nτ12

1 1.5 2

∆ω [GeV]

β=6.800


Nτ32

Nτ12

1 1.5 2

∆ω [GeV]

β=6.950


Nτ32

Nτ12

1 1.5 2

∆ω [GeV]

β=7.280

Nτ64 (44)

Nτ12


High precision of the improved Bayesian reconstruc&on (narrow width resolved)

How does accuracy suffer from limited available informa&on at T>0 (Nτ=12) ?

One of the tests we ran: truncate T=0 dataset (Nτ=32/64) to Nτ=12

S.Kim, P

.Petreczky, A

.R.

Phys.Rev. D

91 (201

5) 054

511



Reconstruction Accuracy: S-wave !

10-4

10-3

10-2

10-1

100

101

102

103

104

1 1.5 2

ρΥ

-BR

(ω)

∆ω [GeV]

β=6.664

S-wave


Nτ32

Nτ12

1 1.5 2

∆ω [GeV]

β=6.800


Nτ32

Nτ12

1 1.5 2

∆ω [GeV]

β=6.950


Nτ32

Nτ12

1 1.5 2

∆ω [GeV]

β=7.280

Nτ64 (44)

Nτ12


High precision of the improved Bayesian reconstruc&on (narrow width resolved)

How does accuracy suffer from limited available informa&on at T>0 (Nτ=12) ?

One of the tests we ran: truncate T=0 dataset (Nτ=32/64) to Nτ=12

S.Kim, P

.Petreczky, A

.R.

Phys.Rev. D

91 (201

5) 054

511

Overall Limits: � = 6.664 : �mT < 2MeV, ��T < 5MeV� = 7.280 : �mT < 40MeV, ��T < 21MeV



Reconstruction Accuracy: P-wave !

10-2

10-1

100

101

1.5 2 2.5 3

ρχ

b1-B

R(ω

)

∆ω [GeV]

β=6.664

P-wave

∆Γ=-16 MeV

∆m=14 MeV

Nτ32

Nτ12

1.5 2 2.5 3

∆ω [GeV]

β=6.800

∆Γ=11 MeV

∆m=52 MeV

Nτ32

Nτ12

1.5 2 2.5 3

∆ω [GeV]

β=6.950

∆Γ=13 MeV

∆m=72 MeV

Nτ32

Nτ12

1.5 2 2.5 3

∆ω [GeV]

β=7.280

∆Γ=39 MeV

∆m=171 MeV

Nτ64(44)

Nτ12

Due to a worse signal-‐to noise ra&o, effect in P-‐wave is larger than for S-‐wave

Es&mate systema&cs: truncate T=0 dataset (Nτ=32/64) to Nτ=12

S.Kim, P

.Petreczky, A

.R.

Phys.Rev. D

91 (201

5) 054

511

Overall Limits: � = 6.664 : �mT < 60MeV, ��T < 20MeV� = 7.280 : �mT < 200MeV, ��T < 40MeV



Bottomonium T>0 Correlators!

0.995

1

1.005

1.01

1.015

0 0.2 0.4 0.6 0.8 1 1.2 1.4

DΥ

T>

0(τ

)/D

ΥT

=0(τ

)

τ [fm]

T=140MeV

T=160MeV

T=184MeV

T=249MeV

0.99

1

1.01

1.02

1.03

1.04

1.05

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Dχ

b1T

>0(τ

)/D

χb

1T

=0(τ

)τ [fm]

T=140MeV

T=160MeV

T=184MeV

T=249MeV

Sta&s&cally significant in-‐medium modifica&on above T=160MeV

S-wave at most 1% change P-wave at most 5% change !

Larger spa&al extend makes P-‐wave more suscep&ble to medium

S-wave !Nmeas=400!

P-wave !Nmeas=400!

S.Kim, P

.Petreczky, A

.R. P

hys.Re

v. D 91 (201

5) 054

511



Spectral Functions At T>0!

0.01

0.1

1

10

100

1000

10 11 12 13 14

ρΥ

-BR

(ω)

ω [GeV]

S-wave

T≈00.91TC0.94TC

0.98TC1.01TC1.04TC

1.08TC1.12TC1.15TC

1.19TC1.24TC1.29TC

1.37TC1.44TC1.61TC

Bayesian reconstruc&on: Nω=1200 Iω=[-‐1,25] βnum=20 Njack=10

ml=const 512 bit precision, Δtol=10-‐60

S-wave !New Bayes!

S.Kim, P

.Petreczky, A

.R. P

hys.Re

v. D 91 (201

5) 054

511

0.1

1

10

10 11 12 13 14

ρχ

b1-B

R(ω

)ω [GeV]

P-wave

T≈00.91TC0.94TC

0.98TC1.01TC1.04TC

1.08TC1.12TC1.15TC

1.19TC1.24TC1.29TC

1.37TC1.44TC1.61TC

Worse signal to noise ra&o leads to larger Jackknife errors in P-‐wave

P-wave New Bayes!



Spectral Functions At T>0!

0.01

0.1

1

10

100

1000

10 11 12 13 14

ρΥ

-BR

(ω)

ω [GeV]

S-wave

T≈00.91TC0.94TC

0.98TC1.01TC1.04TC

1.08TC1.12TC1.15TC

1.19TC1.24TC1.29TC

1.37TC1.44TC1.61TC

Naïve inspec&on by eye inconclusive: ground state peak present up to 1.61TC ?

Bayesian reconstruc&on: Nω=1200 Iω=[-‐1,25] βnum=20 Njack=10

ml=const 512 bit precision, Δtol=10-‐60

S-wave !New Bayes!

S.Kim, P

.Petreczky, A

.R. P

hys.Re

v. D 91 (201

5) 054

511

0.1

1

10

10 11 12 13 14

ρχ

b1-B

R(ω

)ω [GeV]

P-wave

T≈00.91TC0.94TC

0.98TC1.01TC1.04TC

1.08TC1.12TC1.15TC

1.19TC1.24TC1.29TC

1.37TC1.44TC1.61TC

Worse signal to noise ra&o leads to larger Jackknife errors in P-‐wave

P-wave New Bayes!



S- & P-wave Survival At T=249MeV!

Our strategy: systematic comparison to non-interacting spectra!





AnalyQcally known, no peaked features

G.Aarts et. al., JHEP 1111 (2011) 103

a⌧Ep = -log

⇣1-

p2lat

8Mbas

⌘

⇢S(!) =4⇡Nc

N2s

X

p

�(!- 2Ep)






G.Aarts et. al., JHEP 1111 (2011) 103

a⌧Ep = -log

⇣1-

p2lat

8Mbas

⌘

⇢S(!) =4⇡Nc

N2s

X

p

�(!- 2Ep)

Expectation: Presence of wiggly features due to numerical Gibbs ringing

Numerically: Reconstruct from free NRQCD (Uμ=1)

S.Kim, P

.Petreczky, A

.R.

Phys.Rev. D

91 (201

5) 054

511

At T=249 MeV: Ground state peak still stronger than numerical ringing

0.01

0.1

1

10

100

9 10 11 12 13 14

ρΥ-B

R(ω

)

ω [GeV]

M=1.56 T≈0 (τmax=12) Nc100T=249MeV Nc400

shifted free

0.01

0.1

1

10

100

9 10 11 12 13 14

ρχb1

-BR

(ω)

ω [GeV]

M=1.56 T≈0 (τmax=12) Nc100T=249MeV Nc400

rescaled free

S-wave P-wave

0.01

0.1

1

10

100

9 10 11 12 13 14

ρΥ

-BR

(ω)

S-wave

M=2.76T=140MeV Nc400

shifted free

0.01

0.1

1

10

100

9 10 11 12 13 14

ρΥ

-BR

(ω)

ω [GeV]

M=1.56T=249MeV Nc400

shifted free






G.Aarts et. al., JHEP 1111 (2011) 103

a⌧Ep = -log

⇣1-

p2lat

8Mbas

⌘

⇢S(!) =4⇡Nc

N2s

X

p

�(!- 2Ep)

Expectation: Presence of wiggly features due to numerical Gibbs ringing

Numerically: Reconstruct from free NRQCD (Uμ=1)



Towards Charmonium !in lattice NRQCD!

!S.Kim, P. Petreczky, A.R.: in preparation!



T=0 Charmonium Correlators!

β=6.664 (n=6)

β=6.800 (n=6)

β=6.950 (n=6)

� � � � τ [��]

��-��

��-��

��-�

��-�

��-�

�� /ψ[��]

S-‐wave Nmeas=100

β=6.664 (n=6)

β=6.800 (n=6)

β=6.950 (n=6)

� � � � τ [��]

��-��

��-��

��-�

��-�

��-�

�� χ� [��]

P-‐wave Nmeas=100 S.

Kim

, P.P

etre

czky

, A.R

. In prepa

raQo

n




S.K

im, P

.Pet

recz

ky, A

.R.

In prepa

raQo

n

β=6.664 (n=6)

β=6.800 (n=6)

β=6.950 (n=6)

�� τ [��]

��

��

��

��

��

��

��

��Δ��

� /ψ[��] S-‐wave Nmeas=100

β=6.664 (n=6)

β=6.800 (n=6)

β=6.950 (n=6)

�� τ [��]��

��

��

��Δ��

χ� [��]

P-‐wave Nmeas=100




S.K

im, P

.Pet

recz

ky, A

.R.

In prepa

raQo

n

β=6.664 (n=6)

β=6.800 (n=6)

β=6.950 (n=6)

�� τ [��]

��

��

��

��

��

��

��

��Δ��


β=6.664 (n=6)

β=6.800 (n=6)

β=6.950 (n=6)

�� τ [��]��

��

��

��Δ��

χ� [��]

P-‐wave Nmeas=100

“Integra&ng out Mc” induces energy shik of ～2Mc

Cshift(�)�� β

��

��

��

��

��

��[��]

Mexp

J/ = MNRQCD

J/ + 2(ZMcMc - E0)

Mexp

J/ = 3.096916(11)GeV




S.K

im, P

.Pet

recz

ky, A

.R.

In prepa

raQo

n

β=6.664 (n=6)

β=6.800 (n=6)

β=6.950 (n=6)

�� τ [��]

��

��

��

��

��

��

��

��Δ��


β=6.664 (n=6)

β=6.800 (n=6)

β=6.950 (n=6)

�� τ [��]��

��

��

��Δ��

χ� [��]

P-‐wave Nmeas=100

“Integra&ng out Mc” induces energy shik of ～2Mc

Cshift(�)�� β

��

��

��

��

��

��[��]

Mexp

J/ = MNRQCD

J/ + 2(ZMcMc - E0)

Mexp

J/ = 3.096916(11)GeV

Mexp

�c1= 3.51066(7)GeVM�c1

= MNRQCD�c1

+ C(�) = 3.546(4)GeV

T=140MeV (n=6)

T=160MeV

T=184MeV

T=249MeV (n=8)

�� τ [��]��

��

��

��

��

��

�� χ� (�)/� χ� (�=�)



Charmonium T>0 Correlators!

T=140MeV (n=6)

T=160MeV

T=184MeV

T=249MeV (n=8)

�� τ [��]��

��

��

��

��

�� /ψ(�)/�� /ψ(�=�)

At T=TC J/ψ shows as much change as Y at 249MeV

S-wave at most ~5% change P-wave at most ~12% change !

While signal/noise worse for P-‐wave, in-‐medium modifica&on at T=TC

S-wave !Nmeas=400!

P-wave !Nmeas=400!

S.Kim, P

.Petreczky, A

.R. in prep

araQ

on

S.Kim, P

.Petreczky, A

.R.

In prepa

raQo

n

J/ψ peak clearly visible, χc signal marginal but present: survival of S- and P-wave

1e-05

0.0001

0.001

0.01

0.1

1

10

100

0 1 2 3 4 5 6 7 8

ρ(ω

)

Δω [GeV]

J/ψ β=6.664

T=0 trunc τmax/a=12

T=140MeV Nt=12

free shifted

1e-05

0.0001

0.001

0.01

0.1

1

10

100

0 1 2 3 4 5 6 7 8

ρ(ω

)

Δω [GeV]

χc1 β=6.664

T=0 trunc τmax/a=12

T=140MeV Nt=12

free shifted



Charmonium At T=140MeV!

Comparison between interacting and free spectral functions !

PRELIMINARY PRELIMINARY



Conclusions !

Quarkonium is a precision probe of the QGP produced in heavy-‐ion collisions



Conclusions !

Combined EFT and ladce QCD approach (ladceNRQCD): efficient and accurate Quarkonium is a precision probe of the QGP produced in heavy-‐ion collisions



Conclusions !


New Bayesian spectral reconstruc&on offers improved resolu&on to MEM



Conclusions !



Bo{omonium from NRQCD in a realis&c thermal medium (HISQ -‐ HotQCD)

In-‐medium modifica&on of correlators above T=160MeV [up to 1% (ϒ) and 5% (χb1) ]

S-‐wave & P-‐wave ground state survive up to at least T=249MeV

Nτ=12 datapoints allow us to set upper bounds on in-‐medium modifica&on



Conclusions !







A first (preliminary) look at charmonium from NRQCD in a realis&c QCD medium

Correlator in-‐medium modifica&on present at all T [up to 5% (J/ψ) and 12% (χc1) ] S-‐wave & P-‐wave ground state however clearly survive at T=140MeV



Conclusions !


Thank you for your attention






A first (preliminary) look at charmonium from NRQCD in a realis&c QCD medium

Correlator in-‐medium modifica&on present at all T [up to 5% (J/ψ) and 12% (χc1) ] S-‐wave & P-‐wave ground state however clearly survive at T=140MeV

In-medium Heavy Quarkonium properties from effective field ... · In-medium Heavy Quarkonium properties from effective field theory on the lattice! Alexander Rothkopf! Institute for

Documents