in-medium qq potential from lattice qcd & the generalized
TRANSCRIPT
ALEXANDER ROTHKOPF - UIS
In-medium QQ potential from lattice
QCD & the generalized Gauss-law
THE 17TH INTERNATIONAL CONFERENCE ON QCD IN EXTREME CONDITIONS – JUNE 25TH 2019 – TOKYO, JAPAN
Alexander RothkopfFaculty of Science and Technology
Department of Mathematics and Physics
University of Stavanger
References:
P. Petreczky, A.R., J. Weber, NPA982 (2019) 735 & (in preparation)
D. Lafferty, A.R., arXiv:1906.00035
ALEXANDER ROTHKOPF - UIS
A challenge to theoryIN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
[CM
S c
olla
bo
ratio
n]
PR
L120 (2
018) 1
42301
[AL
ICE
co
llab
ora
tion
]JH
EP
1902 (2
019) 0
12
High statistics data available for both flavors, accumulated at run2
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
Bottomonium: a non-equilibrium
probe of the full QGP evolution
Charmonium: a partially equilibrated
probe, sensitive to the late stages
ALEXANDER ROTHKOPF - UIS
A challenge to theoryIN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
[CM
S c
olla
bo
ratio
n]
PR
L120 (2
018) 1
42301
[AL
ICE
co
llab
ora
tion
]JH
EP
1902 (2
019) 0
12
High statistics data available for both flavors, accumulated at run2
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
Goal: provide first principles interpretation to intricate phenomenology
Bottomonium: a non-equilibrium
probe of the full QGP evolution
Charmonium: a partially equilibrated
probe, sensitive to the late stages
ALEXANDER ROTHKOPF - UIS
Quarkonium in Heavy-Ion collisionsIN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Glasma,
pre-thermalization
t~1fm
hydroexpansion
QGPt~5-10 fm
freeze-out,
hadronization
TPC~155MeV
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
ALEXANDER ROTHKOPF - UIS
Quarkonium in Heavy-Ion collisionsIN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Glasma,
pre-thermalization
t~1fm
hydroexpansion
QGPt~5-10 fm
freeze-out,
hadronization
TPC~155MeV
production /
formationmedium interaction
partial
equilibration?freezeout
Q
Q
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
ALEXANDER ROTHKOPF - UIS
Selected theory goalsIN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Q
Q
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
Properties of equilibrium QQ
Extraction of the in-medium
potential on realistic lattices
with P. Petreczky, J. Weber: NPA982 (2019) 735
with D. Lafferty arXiv:1906.00035
Novel parametrization of the
potential for use in
phenomenology
ALEXANDER ROTHKOPF - UIS
Selected theory goalsIN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Beyond Schrödinger:
Open-quantum-systems
descr. of real-time evolution
Connecting OQS to
EFT language of potential
Real-time QQ evol. in local
thermal equilibrium
( see talk by Takahiro Miura )
Q
Q
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
Properties of equilibrium QQ
Extraction of the in-medium
potential on realistic lattices
with P. Petreczky, J. Weber: NPA982 (2019) 735
with D. Lafferty arXiv:1906.00035
Novel parametrization of the
potential for use in
phenomenology
ALEXANDER ROTHKOPF - UIS
( see talk by Alexander Lehmann)
QQ realtime evol.
in the initial stages
classical statistical
simulations for gluons
+
real-time NRQCD
First exploratory
steps in the glasma
Selected theory goalsIN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Beyond Schrödinger:
Open-quantum-systems
descr. of real-time evolution
Connecting OQS to
EFT language of potential
Real-time QQ evol. in local
thermal equilibrium
( see talk by Takahiro Miura )
Q
Q
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
Properties of equilibrium QQ
Extraction of the in-medium
potential on realistic lattices
with P. Petreczky, J. Weber: NPA982 (2019) 735
with D. Lafferty arXiv:1906.00035
Novel parametrization of the
potential for use in
phenomenology
ALEXANDER ROTHKOPF - UIS
Quarkonium in thermal equilibrium
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Intuition on in-medium modification from potential based studies
ρ(ω)
ω
ρ(ω)
J/ψ ψ‘
D/D thr.
ω
medium effects
ALEXANDER ROTHKOPF - UIS
Re[V](r) Im[V](r)
r r
Quarkonium in thermal equilibrium
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Intuition on in-medium modification from potential based studies
ρ(ω)
ω
ρ(ω)
J/ψ ψ‘
D/D thr.
ω
medium effects
ALEXANDER ROTHKOPF - UIS
Re[V](r) Im[V](r)
r r
Quarkonium in thermal equilibrium
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Intuition on in-medium modification from potential based studies
ρ(ω)
ω
ρ(ω)
J/ψ ψ‘
D/D thr.
ω
Generic prediction:
if potential picture valid,
in-medium quarkonium
becomes lighter as T
increases
medium effects
ALEXANDER ROTHKOPF - UIS
The real-time interquark potentialIN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Re
lativis
tic T
>0
fie
ld th
eo
ry
Qu
an
tum
me
ch
an
ics
QCD
Dirac fields
pNRQCD
Singlet/OctetNRQCD
Pauli fields
Exploit to treat heavy quarks non-relativistically
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
Brambilla et.al. Rev.Mod.Phys. 77 (2005) 1423
ALEXANDER ROTHKOPF - UIS
The real-time interquark potentialIN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Re
lativis
tic T
>0
fie
ld th
eo
ry
Qu
an
tum
me
ch
an
ics
QCD
Dirac fields
pNRQCD
Singlet/OctetNRQCD
Pauli fields
Exploit to treat heavy quarks non-relativistically
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
Brambilla et.al. Rev.Mod.Phys. 77 (2005) 1423
Matching to underlying QCD in the infinite mass limit: Wilson loop
t
x,y,zQ Q
R
ALEXANDER ROTHKOPF - UIS
The real-time interquark potentialIN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Re
lativis
tic T
>0
fie
ld th
eo
ry
Qu
an
tum
me
ch
an
ics
QCD
Dirac fields
pNRQCD
Singlet/OctetNRQCD
Pauli fields
Exploit to treat heavy quarks non-relativistically
Wilson loop: potential emerges at late times
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
Brambilla et.al. Rev.Mod.Phys. 77 (2005) 1423
Matching to underlying QCD in the infinite mass limit: Wilson loop
t
x,y,zQ Q
R
ALEXANDER ROTHKOPF - UIS
The real-time interquark potentialIN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Re
lativis
tic T
>0
fie
ld th
eo
ry
Qu
an
tum
me
ch
an
ics
QCD
Dirac fields
pNRQCD
Singlet/OctetNRQCD
Pauli fields
Exploit to treat heavy quarks non-relativistically
Wilson loop: potential emerges at late times
∊ℂIm[V]: Laine et al. JHEP03 (2007) 054;
Beraudo et. al. NPA 806:312,2008
Brambilla et.al. PRD 78 (2008) 014017
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
Brambilla et.al. Rev.Mod.Phys. 77 (2005) 1423
Matching to underlying QCD in the infinite mass limit: Wilson loop
t
x,y,zQ Q
R
ALEXANDER ROTHKOPF - UIS
The real-time interquark potentialIN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Re
lativis
tic T
>0
fie
ld th
eo
ry
Qu
an
tum
me
ch
an
ics
QCD
Dirac fields
pNRQCD
Singlet/OctetNRQCD
Pauli fields
Exploit to treat heavy quarks non-relativistically
Wilson loop: potential emerges at late times
∊ℂIm[V]: Laine et al. JHEP03 (2007) 054;
Beraudo et. al. NPA 806:312,2008
Brambilla et.al. PRD 78 (2008) 014017
In this form: Minkowski time quantities and not accessible on the lattice
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
Brambilla et.al. Rev.Mod.Phys. 77 (2005) 1423
Matching to underlying QCD in the infinite mass limit: Wilson loop
t
x,y,zQ Q
R
ALEXANDER ROTHKOPF - UIS
Non-perturbative evaluation of V(R)IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
How to connect to the Euclidean domain: spectral functionsA.R., T.Hatsuda & S.Sasaki
PRL 108 (2012) 162001
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
ALEXANDER ROTHKOPF - UIS
Non-perturbative evaluation of V(R)IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
How to connect to the Euclidean domain: spectral functionsA.R., T.Hatsuda & S.Sasaki
PRL 108 (2012) 162001
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
ALEXANDER ROTHKOPF - UIS
Spectral Decomposition
A.R., T.Hatsuda & S.Sasaki PoS LAT2009 (2009) 162
Non-perturbative evaluation of V(R)IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
How to connect to the Euclidean domain: spectral functionsA.R., T.Hatsuda & S.Sasaki
PRL 108 (2012) 162001
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
ALEXANDER ROTHKOPF - UIS
Spectral Decomposition
A.R., T.Hatsuda & S.Sasaki PoS LAT2009 (2009) 162
Non-perturbative evaluation of V(R)IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
How to connect to the Euclidean domain: spectral functionsA.R., T.Hatsuda & S.Sasaki
PRL 108 (2012) 162001
ω
ρ☐
(R,ω
)
Γ0
ω0 well defined V(R)
if low lying Breit-
Wigner present in
Wilson loop
spectral functionFor technical details see
Y.B., A.R. PRD86 (2012) 051503
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
ALEXANDER ROTHKOPF - UIS
Spectral Reconstruction
In case of usual ΔW/W=10-2 statistical un-
certatinty in W□: Bayesian inference
In case of small ΔW/W<10-3 statistical un-
certatinty in W□ also Pade approximation
incorporate prior information to regularize
the inversion task (BR method)
exploit the analyticity of the
Wilson correlator to extract spectra
Spectral Decomposition
A.R., T.Hatsuda & S.Sasaki PoS LAT2009 (2009) 162
Non-perturbative evaluation of V(R)IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
How to connect to the Euclidean domain: spectral functionsA.R., T.Hatsuda & S.Sasaki
PRL 108 (2012) 162001
ω
ρ☐
(R,ω
)
Γ0
ω0 well defined V(R)
if low lying Breit-
Wigner present in
Wilson loop
spectral functionFor technical details see
Y.B., A.R. PRD86 (2012) 051503
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
ALEXANDER ROTHKOPF - UIS
Pade spectral reconstruction
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
In case of high statistics data: Pade approximation stable alternative to Bayes
Project imaginary frequency correlator onto rational basis functions
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
ALEXANDER ROTHKOPF - UIS
Pade spectral reconstruction
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
In case of high statistics data: Pade approximation stable alternative to Bayes
Project imaginary frequency correlator onto rational basis functions
Generalized complex Schlessinger formula: stable P(n-1,n) approximation, decay at large ωfor purely real Schlessinger see R. Tripolt e.t al. arXiv:1801.10348
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
ALEXANDER ROTHKOPF - UIS
Pade spectral reconstruction
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
In case of high statistics data: Pade approximation stable alternative to Bayes
Project imaginary frequency correlator onto rational basis functions
Generalized complex Schlessinger formula: stable P(n-1,n) approximation, decay at large ωfor purely real Schlessinger see R. Tripolt e.t al. arXiv:1801.10348
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Appropriate continuation of the Euclidean correlator gives retarded correlator
ALEXANDER ROTHKOPF - UIS
Extracting the potential
Example: Pade based reconstructions at β=7.825 T=407MeV Nτ=12
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
ALEXANDER ROTHKOPF - UIS
Extracting the potential
Example: Pade based reconstructions at β=7.825 T=407MeV Nτ=12
DFT
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
ALEXANDER ROTHKOPF - UIS
Extracting the potential
Example: Pade based reconstructions at β=7.825 T=407MeV Nτ=12
DFT
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
ALEXANDER ROTHKOPF - UIS
Extracting the potential
Example: Pade based reconstructions at β=7.825 T=407MeV Nτ=12
DFT
Beware of Pade artifacts besides peak:
e.g. positivity violation, spikes
Always find well defined lowest peak:
potential picture appears viable
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
ALEXANDER ROTHKOPF - UIS
Latest results on the lattice potential
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Lattices with dynamical u,d,s quarks
(HISQ action, HotQCD & TUMQCD)
fixed box (Ns=48 - Nτ=12, Nτ=16) &
very high statistics 4000-9000 realizations
realistic mπ~161MeV (T=151-1451MeV)
A. Bazavov et.al. PRD97 (2018) 014510, HotQCD PRD90 (2014) 094503
P. P
etr
eczky, A
.R., J
. W
eb
er,
NP
A982 (
2019)
735
Pade based extraction for Re[V] possible
Re[V] close to color singlet free energy.
Smooth transition from Cornell @ T=0
to Debye screened @ T>TC
ALEXANDER ROTHKOPF - UIS
Latest results on the lattice potential
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Lattices with dynamical u,d,s quarks
(HISQ action, HotQCD & TUMQCD)
fixed box (Ns=48 - Nτ=12, Nτ=16) &
very high statistics 4000-9000 realizations
realistic mπ~161MeV (T=151-1451MeV)
A. Bazavov et.al. PRD97 (2018) 014510, HotQCD PRD90 (2014) 094503
Finite Im[V] above Tc present
P. P
etr
eczky, A
.R., J
. W
eb
er,
NP
A982 (
2019)
735
Pade based extraction for Re[V] possible
Re[V] close to color singlet free energy.
Smooth transition from Cornell @ T=0
to Debye screened @ T>TC
ALEXANDER ROTHKOPF - UIS
An improved Gauss law approach
Strategy:
αs,σ and c are vacuum prop.
and do not change with T
For use in phenomenology applications: analytic expression for Re[V] and Im[V]
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
ALEXANDER ROTHKOPF - UIS
An improved Gauss law approach
Strategy:
αs,σ and c are vacuum prop.
and do not change with T
For use in phenomenology applications: analytic expression for Re[V] and Im[V]
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
String-like: a=+1 q=σCoulombic: a=-1 q=αs V. V. Dixit,
Mod. Phys. Lett. A 5, 227 (1990)
ALEXANDER ROTHKOPF - UIS
An improved Gauss law approach
Strategy:
αs,σ and c are vacuum prop.
and do not change with T
For use in phenomenology applications: analytic expression for Re[V] and Im[V]
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
String-like: a=+1 q=σCoulombic: a=-1 q=αs V. V. Dixit,
Mod. Phys. Lett. A 5, 227 (1990)
Immerse non-perturbative charge in weak coupling HTL medium: permittivity ε original idea: Y.Burnier, A.R. Phys.Lett. B753 (2016) 232 improved derivation D.Lafferty and A.R. arXiv:1906.00035
ALEXANDER ROTHKOPF - UIS
An improved Gauss law approach
Strategy:
αs,σ and c are vacuum prop.
and do not change with T
For use in phenomenology applications: analytic expression for Re[V] and Im[V]
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
String-like: a=+1 q=σCoulombic: a=-1 q=αs V. V. Dixit,
Mod. Phys. Lett. A 5, 227 (1990)
Immerse non-perturbative charge in weak coupling HTL medium: permittivity ε original idea: Y.Burnier, A.R. Phys.Lett. B753 (2016) 232 improved derivation D.Lafferty and A.R. arXiv:1906.00035
``
ALEXANDER ROTHKOPF - UIS
An improved Gauss law approach
Strategy:
αs,σ and c are vacuum prop.
and do not change with T
For use in phenomenology applications: analytic expression for Re[V] and Im[V]
3 vacuum parameters and 1 temperature dependent mD fix both Re[V] and Im[V].
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
String-like: a=+1 q=σCoulombic: a=-1 q=αs V. V. Dixit,
Mod. Phys. Lett. A 5, 227 (1990)
Immerse non-perturbative charge in weak coupling HTL medium: permittivity ε original idea: Y.Burnier, A.R. Phys.Lett. B753 (2016) 232 improved derivation D.Lafferty and A.R. arXiv:1906.00035
``
ALEXANDER ROTHKOPF - UIS
Gauss-law solution to Re[V] & Im[V]
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
We find an interesting connection to the classic Karsch-Mehr-Satz result:
ALEXANDER ROTHKOPF - UIS
Gauss-law solution to Re[V] & Im[V]
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
We find an interesting connection to the classic Karsch-Mehr-Satz result:
+
Provides justification for presence of entropic term a la Satz in the string part c.f. e.g. H. Satz, EPJC75 (2015) 193 and Guo et.al. arXiv:1806.04376
ALEXANDER ROTHKOPF - UIS
Gauss-law solution to Re[V] & Im[V]
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
We find an interesting connection to the classic Karsch-Mehr-Satz result:
+
Provides justification for presence of entropic term a la Satz in the string part c.f. e.g. H. Satz, EPJC75 (2015) 193 and Guo et.al. arXiv:1806.04376
Gauss-Law result allows to fit the lattice data even in the non-perturbative regimeD.Lafferty and A.R. arXiv:1906.00035
ALEXANDER ROTHKOPF - UIS
Gauss-law solution to Re[V] & Im[V]
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
We find an interesting connection to the classic Karsch-Mehr-Satz result:
+
Provides justification for presence of entropic term a la Satz in the string part c.f. e.g. H. Satz, EPJC75 (2015) 193 and Guo et.al. arXiv:1806.04376
Gauss-Law result allows to fit the lattice data even in the non-perturbative regimeD.Lafferty and A.R. arXiv:1906.00035
ALEXANDER ROTHKOPF - UIS
Continuum corrected spectral functions
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Need to manually correct for lattice artefacts: TC and string tension not yet physical
Pheno fit to T=0 quarkonium Continuum corrected Debye mass
Y.Burnier, O.Kaczmarek, A.R. JHEP 1512 (2015) 101
ALEXANDER ROTHKOPF - UIS
Continuum corrected spectral functions
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Need to manually correct for lattice artefacts: TC and string tension not yet physical
Pheno fit to T=0 quarkonium Continuum corrected Debye mass
Charmonium
S-wave channel
Via Schrödinger equation for spectral functions with the Gauss-law parametrizationD.Lafferty and A.R. arXiv:1906.00035
Y.Burnier, O.Kaczmarek, A.R. JHEP 1512 (2015) 101
ALEXANDER ROTHKOPF - UIS
Continuum corrected spectral functions
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Need to manually correct for lattice artefacts: TC and string tension not yet physical
Pheno fit to T=0 quarkonium Continuum corrected Debye mass
Shifting to lower mass and broadening hierarchichally ordered with vacuum Ebind
Charmonium
S-wave channel
Via Schrödinger equation for spectral functions with the Gauss-law parametrizationD.Lafferty and A.R. arXiv:1906.00035
Y.Burnier, O.Kaczmarek, A.R. JHEP 1512 (2015) 101
ALEXANDER ROTHKOPF - UIS
Towards the ψ’ to J/ψ ratio
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Assume instantaneous freezeout: T>0 states
convert to real vacuum particles at around TC
Y.B
urn
ier,
O.K
aczm
are
k, A
.R.
JH
EP
1512 (
2015)
101
ALEXANDER ROTHKOPF - UIS
Towards the ψ’ to J/ψ ratio
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
In-medium dilepton emission from area under
spectral resonance peaks
( to leading order )
Assume instantaneous freezeout: T>0 states
convert to real vacuum particles at around TC
Y.B
urn
ier,
O.K
aczm
are
k, A
.R.
JH
EP
1512 (
2015)
101
ALEXANDER ROTHKOPF - UIS
Towards the ψ’ to J/ψ ratio
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
In-medium dilepton emission from area under
spectral resonance peaks
( to leading order )
Assume instantaneous freezeout: T>0 states
convert to real vacuum particles at around TC
”How many vacuum states do the
in-medium peaks correspond to?”
Y.B
urn
ier,
O.K
aczm
are
k, A
.R.
JH
EP
1512 (
2015)
101
ALEXANDER ROTHKOPF - UIS
Towards the ψ’ to J/ψ ratio
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
In-medium dilepton emission from area under
spectral resonance peaks
( to leading order )
Number density: divide in-medium
by T=0 dimuon emission rate:
Y.Burnier, O. Kaczmarek, A.R.
JHEP 1512 (2015) 101
Assume instantaneous freezeout: T>0 states
convert to real vacuum particles at around TC
”How many vacuum states do the
in-medium peaks correspond to?”
Y.B
urn
ier,
O.K
aczm
are
k, A
.R.
JH
EP
1512 (
2015)
101
ALEXANDER ROTHKOPF - UIS
Towards the ψ’ to J/ψ ratio
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
In-medium dilepton emission from area under
spectral resonance peaks
( to leading order )
Number density: divide in-medium
by T=0 dimuon emission rate:
Y.Burnier, O. Kaczmarek, A.R.
JHEP 1512 (2015) 101
Assume instantaneous freezeout: T>0 states
convert to real vacuum particles at around TC
”How many vacuum states do the
in-medium peaks correspond to?”
ALICE Collaboration JHEP05(2016)179
T>0spectra
Y.B
urn
ier,
O.K
aczm
are
k, A
.R.
JH
EP
1512 (
2015)
101
ALEXANDER ROTHKOPF - UIS
Modeling the ratio at lower beam energy
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Interpolate lattice extracted mD values with an ansatz
ALEXANDER ROTHKOPF - UIS
Modeling the ratio at lower beam energy
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Interpolate lattice extracted mD values with an ansatz
At small μB: perturbation theory - At large μB: dimensional arguments
ALEXANDER ROTHKOPF - UIS
Modeling the ratio at lower beam energy
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Interpolate lattice extracted mD values with an ansatz
HIC yields & statistical model
At small μB: perturbation theory - At large μB: dimensional arguments
ALEXANDER ROTHKOPF - UIS
Modeling the ratio at lower beam energy
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Interpolate lattice extracted mD values with an ansatz
HIC yields & statistical model
At small μB: perturbation theory - At large μB: dimensional arguments
D.L
affe
rtyan
d A
.R. a
rXiv
:1906.0
0035
ALEXANDER ROTHKOPF - UIS
Gauss-law model & bottomonium
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Current state-of-the-art setup to describe bottomonium has three ingredients:
Folding together over real-time evolution gives RAA
Anisotropic
Hydro (mD(τ,x))
Glauber initial pure
state QQ prod.
VQQ in Schrödinger Eq.
Ebind and Γ(τ,x)& &
Intent: remove modelling input (up to now: color singlet free energies + pert. ImV)
ALEXANDER ROTHKOPF - UIS
Gauss-law model & bottomonium
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Current state-of-the-art setup to describe bottomonium has three ingredients:
Folding together over real-time evolution gives RAA
Anisotropic
Hydro (mD(τ,x))
Glauber initial pure
state QQ prod.
VQQ in Schrödinger Eq.
Ebind and Γ(τ,x)& &
Intent: remove modelling input (up to now: color singlet free energies + pert. ImV)
Larger Im[V] in the lattice vetted potential: stronger suppression - good at STAR
ALEXANDER ROTHKOPF - UIS
Gauss-law model & bottomonium
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Current state-of-the-art setup to describe bottomonium has three ingredients:
Folding together over real-time evolution gives RAA
Anisotropic
Hydro (mD(τ,x))
Glauber initial pure
state QQ prod.
VQQ in Schrödinger Eq.
Ebind and Γ(τ,x)& &
Intent: remove modelling input (up to now: color singlet free energies + pert. ImV)
Larger Im[V] in the lattice vetted potential: stronger suppression - good at STAR
B.
Kro
up
pa
, A
.R., M
. S
tric
kla
nd
PR
D97 (
2018)
016017
Absence of e.g. dissipative effects leads to underestimation of yields at LHC
ALEXANDER ROTHKOPF - UIS
SummaryIN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
Progress in the extraction of the complex in-medium potential
Quantitative insight: transition from Cornell to Debye + non-pert. Im[V]
Realistic lattices with mπ=161MeV & temperature range T=140-1450MeV
Progress in applying the lattice results to phenomenology
Improved derivation of analytic parametrization via generalized Gauss law
Lattice vetted parametrization easily included in bottomonium simulations
ψ’ / J/ψ in instantaneous freezeout scenario: good agreement with data
Pade approximation for the T>0 potential in high statistics full QCD
ALEXANDER ROTHKOPF - UIS
SummaryIN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
ご清聴ありがとうございましたThank you for your attention
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
Progress in the extraction of the complex in-medium potential
Quantitative insight: transition from Cornell to Debye + non-pert. Im[V]
Realistic lattices with mπ=161MeV & temperature range T=140-1450MeV
Progress in applying the lattice results to phenomenology
Improved derivation of analytic parametrization via generalized Gauss law
Lattice vetted parametrization easily included in bottomonium simulations
ψ’ / J/ψ in instantaneous freezeout scenario: good agreement with data
Pade approximation for the T>0 potential in high statistics full QCD
ALEXANDER ROTHKOPF - UIS
The Bayesian reconstruction
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Inversion of Laplace transform required to obtain spectra from correlators
ALEXANDER ROTHKOPF - UIS
The Bayesian reconstruction
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Inversion of Laplace transform required to obtain spectra from correlators
1. Nω parameters ρl >> Nτ datapoints
2. data Di has finite precision
ALEXANDER ROTHKOPF - UIS
The Bayesian reconstruction
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Inversion of Laplace transform required to obtain spectra from correlators
1. Nω parameters ρl >> Nτ datapoints
2. data Di has finite precision
Give meaning to problem by incorporating prior knowledge: Bayesian approachM. Jarrell, J. Gubernatis, Physics Reports 269 (3) (1996)
Bayes theorem: Regularize the naïve χ2 functional P[D|ρ] through a prior P[ρ|I]
ALEXANDER ROTHKOPF - UIS
The Bayesian reconstruction
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Inversion of Laplace transform required to obtain spectra from correlators
1. Nω parameters ρl >> Nτ datapoints
2. data Di has finite precision
Our 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 approachM. Jarrell, J. Gubernatis, Physics Reports 269 (3) (1996)
Bayes theorem: Regularize the naïve χ2 functional P[D|ρ] through a prior P[ρ|I]
ALEXANDER ROTHKOPF - UIS
The Bayesian reconstruction
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Have to carry out a numerical optimization problem: the most probable spectrum
Inversion of Laplace transform required to obtain spectra from correlators
1. Nω parameters ρl >> Nτ datapoints
2. data Di has finite precision
Our 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 approachM. Jarrell, J. Gubernatis, Physics Reports 269 (3) (1996)
Bayes theorem: Regularize the naïve χ2 functional P[D|ρ] through a prior P[ρ|I]
ALEXANDER ROTHKOPF - UIS
The Bayesian reconstruction
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Have to carry out a numerical optimization problem: the most probable spectrum
Inversion of Laplace transform required to obtain spectra from correlators
1. Nω parameters ρl >> Nτ datapoints
2. data Di has finite precision
Our prior enforces: ρ positive definite, smoothness of ρ, result independent of units
Convergence to unique global extremum:
partially determined by data partially by prior info
Y.Burnier, A.R.
PRL 111 (2013) 18, 182003
Give meaning to problem by incorporating prior knowledge: Bayesian approachM. Jarrell, J. Gubernatis, Physics Reports 269 (3) (1996)
Bayes theorem: Regularize the naïve χ2 functional P[D|ρ] through a prior P[ρ|I]
ALEXANDER ROTHKOPF - UIS
Quenched QCD potential
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
Extraction on 323xNτ anisotropic lattices with β=6.1 and ξ=4: as=0.097fm L=3.1fm
No signs for modification of Re[V] for T<TC: glueballs too heavy to interfere binding
Deconfined gluons efficiently screen Re[V], lead to a finite value of Im[V] above TC
ALEXANDER ROTHKOPF - UIS
Mock data tests with HTL & Pade (II)
Perform mock data analysis with resummed perturbative Wilson correlators (HTL)
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
No plateau in effective potential
Veff=-log[Wi/Wi+1]: large spectral widths
HTL correlators: Y.Burnier, A.R. PRD87 (2013) 114019
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
ALEXANDER ROTHKOPF - UIS
Mock data tests with HTL & Pade (II)
Perform mock data analysis with resummed perturbative Wilson correlators (HTL)
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
No plateau in effective potential
Veff=-log[Wi/Wi+1]: large spectral widths
HTL correlators: Y.Burnier, A.R. PRD87 (2013) 114019
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan
ALEXANDER ROTHKOPF - UIS
Mock data tests with HTL & Pade (II)
Perform mock data analysis with resummed perturbative Wilson correlators (HTL)
At Nτ=12, errors of dD/D=10-2 detrimental to
Im[V] but Re[V] well reconstructed
IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW
No plateau in effective potential
Veff=-log[Wi/Wi+1]: large spectral widths
HTL correlators: Y.Burnier, A.R. PRD87 (2013) 114019
The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan