In-medium QQ potential from lattice QCD & the generalized - - PowerPoint PPT Presentation

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 Rothkopf

Faculty 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 theory

IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW

[CMS collaboration] PRL120 (2018) 142301 [ALICE collaboration] JHEP 1902 (2019) 012

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 theory

IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW

[CMS collaboration] PRL120 (2018) 142301 [ALICE collaboration] JHEP 1902 (2019) 012

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 collisions

IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW

Glasma, pre-thermalization t～1fm

hydro expansion

QGP

t～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 collisions

IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW

Glasma, pre-thermalization t～1fm

hydro expansion

QGP

t～5-10 fm freeze-out, hadronization

TPC~155MeV

production / formation medium 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 goals

IN-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 goals

IN-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 goals

IN-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 potential

IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW Relativistic T>0 field theory Quantum mechanics QCD Dirac fields pNRQCD Singlet/Octet NRQCD 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 potential

IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW Relativistic T>0 field theory Quantum mechanics QCD Dirac fields pNRQCD Singlet/Octet NRQCD 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,z

Q Q R

ALEXANDER ROTHKOPF - UIS

The real-time interquark potential

IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW Relativistic T>0 field theory Quantum mechanics QCD Dirac fields pNRQCD Singlet/Octet NRQCD 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,z

Q Q R

ALEXANDER ROTHKOPF - UIS

The real-time interquark potential

IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW Relativistic T>0 field theory Quantum mechanics QCD Dirac fields pNRQCD Singlet/Octet NRQCD Pauli fields

Exploit to treat heavy quarks non-relativistically Wilson loop: potential emerges at late times

∊ℂ

Im[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,z

Q Q R

ALEXANDER ROTHKOPF - UIS

The real-time interquark potential

IN-MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED GAUSS-LAW Relativistic T>0 field theory Quantum mechanics QCD Dirac fields pNRQCD Singlet/Octet NRQCD Pauli fields

Exploit to treat heavy quarks non-relativistically Wilson loop: potential emerges at late times

∊ℂ

Im[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,z

Q 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 functions

A.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 functions

A.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 functions

A.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 functions

A.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 function

For 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 functions

A.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 function

For 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 ω

for 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 ω

for 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. Petreczky, A.R., J. Weber, NPA982 (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 T

c present

• P. Petreczky, A.R., J. Weber, NPA982 (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=σ Coulombic: 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=σ Coulombic: 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

• riginal 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=σ Coulombic: 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

• riginal 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=σ Coulombic: 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

• riginal 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 regime

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: +

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 regime

D.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 parametrization

D.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 parametrization

D.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.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

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.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

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.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

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.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

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>0 spectra

Y.Burnier, O.Kaczmarek, A.R. JHEP 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.Lafferty and A.R. arXiv:1906.00035

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. Krouppa, A.R., M. Strickland

PRD97 (2018) 016017

Absence of e.g. dissipative effects leads to underestimation of yields at LHC

ALEXANDER ROTHKOPF - UIS

Summary

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

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

Summary

IN-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 approach

• M. 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 approach

• M. 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 approach

• M. 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 approach

• M. 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