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
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
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
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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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
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
OUR SETUP: Kinetically equilibrated heavy quarks
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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
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
OUR SETUP: Kinetically equilibrated heavy quarks
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
Heavy quarks on!the lattice !
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
Heavy Quarks on the Lattice !
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT 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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT 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
QCD Dirac fields
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT 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
NRQCD Pauli fields LNRQCD = †�iDt +
D2i
2MQ+ . . .
� + ⇠†
�. . .)⇠-
1
4Fµ⌫Fµ⌫ + q̄
�. . .
�q
�
†(x),�(x)
⇠
†(x), ⇠(x)�†�iDt +
D2i
2MQ+ . . .
��+ ⇠†
�. . .
�⇠
QCD Dirac fields
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
Heavy Quarks on the Lattice !
LNRQCD = †�iDt +D2
i
2MQ+ . . .
� + ⇠†
�. . .)⇠-
1
4Fµ⌫Fµ⌫ + q̄
�. . .
�q
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
NRQCD Pauli fields LNRQCD = †�iDt +
D2i
2MQ+ . . .
� + ⇠†
�. . .)⇠-
1
4Fµ⌫Fµ⌫ + q̄
�. . .
�q
�
†(x),�(x)
⇠
†(x), ⇠(x)�†�iDt +
D2i
2MQ+ . . .
��+ ⇠†
�. . .
�⇠
QCD Dirac fields
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
Heavy Quarks on the Lattice !
LNRQCD = †�iDt +D2
i
2MQ+ . . .
� + ⇠†
�. . .)⇠-
1
4Fµ⌫Fµ⌫ + q̄
�. . .
�q
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
NRQCD Pauli fields LNRQCD = †�iDt +
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, ⌧)
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
Heavy Quarks on the Lattice !
LNRQCD = †�iDt +D2
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)
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
NRQCD Pauli fields LNRQCD = †�iDt +
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, ⌧)
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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
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
483x12 with rela&vely light pions Mπ~ 161MeV and a TC=159±3MeV
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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
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
483x12 with rela&vely light pions Mπ~ 161MeV and a TC=159±3MeV
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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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
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
483x12 with rela&vely light pions Mπ~ 161MeV and a TC=159±3MeV
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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
A Novel Bayesian Approach!
Inversion of Laplace transform required to obtain spectra from correlators
D(⌧) =
Z1
-2MQ
d!e-⌧!⇢(!)
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
A Novel Bayesian Approach!
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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
A Novel Bayesian Approach!
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
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]
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
A Novel Bayesian Approach!
P[⇢|I] / eS S = ↵
N!X
l=1
�!l
⇣1-
⇢l
ml+ log
h⇢l
ml
i⌘
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
New prior enforces: ρ positive definite, smoothness of ρ, result independent of units
Y.Burnier, A.R. PRL 111 (2013) 18, 182003
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]
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
A Novel Bayesian Approach!
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
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
New prior enforces: ρ positive definite, smoothness of ρ, result independent of units
Y.Burnier, A.R. PRL 111 (2013) 18, 182003
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]
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
A Novel Bayesian Approach!
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
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
New prior enforces: ρ positive definite, smoothness of ρ, result independent of units
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
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]
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
Bottomonium in lattice NRQCD !
!S.Kim, P. Petreczky, A.R.: Phys.Rev. D 91 (2015) 054511���
!
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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
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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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
“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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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
“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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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 ground state peak very well resolved, next peak mostly from Y(2S)
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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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 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-‐wave T≈0 P-‐wave T≈0
S.K
im, P
.Pet
recz
ky, A
.R.
Phys.Rev. D
91 (201
5) 054
511
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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
∆Γ=6 MeV∆m=4 MeV
Nτ32
Nτ12
1 1.5 2
∆ω [GeV]
β=6.950
∆Γ=8 MeV∆m=7 MeV
Nτ32
Nτ12
1 1.5 2
∆ω [GeV]
β=7.280
Nτ64 (44)
Nτ12
∆Γ=21 MeV∆m=31 MeV
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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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
∆Γ=6 MeV∆m=4 MeV
Nτ32
Nτ12
1 1.5 2
∆ω [GeV]
β=6.950
∆Γ=8 MeV∆m=7 MeV
Nτ32
Nτ12
1 1.5 2
∆ω [GeV]
β=7.280
Nτ64 (44)
Nτ12
∆Γ=21 MeV∆m=31 MeV
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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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!
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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!
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
S- & P-wave Survival At T=249MeV!
Our strategy: systematic comparison to non-interacting spectra!
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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)
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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)
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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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)
Expectation: Presence of wiggly features due to numerical Gibbs ringing
Numerically: Reconstruct from free NRQCD (Uμ=1)
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
Towards Charmonium !in lattice NRQCD!
!S.Kim, P. Petreczky, A.R.: in preparation!
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
T=0 Charmonium Correlators!
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 [��]
����
����
����
����
����
����
����
��������
� /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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
T=0 Charmonium Correlators!
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 [��]
����
����
����
����
����
����
����
��������
� /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
“Integra&ng out Mc” induces energy shik of ~2Mc
Cshift(�)���� ���� ���� ���� ���� ����β
����
����
����
����
����
������[���]
Mexp
J/ = MNRQCD
J/ + 2(ZMcMc - E0)
Mexp
J/ = 3.096916(11)GeV
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
T=0 Charmonium Correlators!
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 [��]
����
����
����
����
����
����
����
��������
� /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
“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� (�=�)
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
Charmonium At T=140MeV!
Comparison between interacting and free spectral functions !
PRELIMINARY PRELIMINARY
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
Conclusions !
Quarkonium is a precision probe of the QGP produced in heavy-‐ion collisions
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
Conclusions !
Combined EFT and ladce QCD approach (ladceNRQCD): efficient and accurate Quarkonium is a precision probe of the QGP produced in heavy-‐ion collisions
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
Conclusions !
Combined EFT and ladce QCD approach (ladceNRQCD): efficient and accurate Quarkonium is a precision probe of the QGP produced in heavy-‐ion collisions
New Bayesian spectral reconstruc&on offers improved resolu&on to MEM
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
Conclusions !
Combined EFT and ladce QCD approach (ladceNRQCD): efficient and accurate Quarkonium is a precision probe of the QGP produced in heavy-‐ion collisions
New Bayesian spectral reconstruc&on offers improved resolu&on to MEM
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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
Conclusions !
Combined EFT and ladce QCD approach (ladceNRQCD): efficient and accurate Quarkonium is a precision probe of the QGP produced in heavy-‐ion collisions
New Bayesian spectral reconstruc&on offers improved resolu&on to MEM
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
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
2015 RHIC & AGS Annual Users' Meeting – BNL Upton, NY USA – June 9th
IN-MEDIUM HEAVY QUARKONIUM FROM EFT ON THE LATTICE
Conclusions !
Combined EFT and ladce QCD approach (ladceNRQCD): efficient and accurate Quarkonium is a precision probe of the QGP produced in heavy-‐ion collisions
Thank you for your attention
New Bayesian spectral reconstruc&on offers improved resolu&on to MEM
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
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