In-medium QQ potential from lattice QCD & the generalized Gauss-law 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 T HE 17 TH I NTERNATIONAL C ONFERENCE ON QCD IN E XTREME C ONDITIONS – J UNE 25 TH 2019 – T OKYO , J APAN A LEXANDER R OTHKOPF - U I S
I N - MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED G AUSS - LAW A challenge to theory High statistics data available for both flavors, accumulated at run2 [CMS collaboration] PRL120 (2018) 142301 [ALICE collaboration] JHEP 1902 (2019) 012 Bottomonium : a non-equilibrium Charmonium : a partially equilibrated probe of the full QGP evolution probe, sensitive to the late stages The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan A LEXANDER R OTHKOPF - U I S
I N - MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED G AUSS - LAW A challenge to theory High statistics data available for both flavors, accumulated at run2 [CMS collaboration] PRL120 (2018) 142301 [ALICE collaboration] JHEP 1902 (2019) 012 Bottomonium : a non-equilibrium Charmonium : a partially equilibrated probe of the full QGP evolution probe, sensitive to the late stages Goal: provide first principles interpretation to intricate phenomenology The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan A LEXANDER R OTHKOPF - U I S
I N - MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED G AUSS - LAW Quarkonium in Heavy-Ion collisions hydro expansion QGP freeze-out, Glasma, hadronization pre-thermalization t ～ 1fm t ～ 5-10 fm T PC ~155MeV The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan A LEXANDER R OTHKOPF - U I S
I N - MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED G AUSS - LAW Quarkonium in Heavy-Ion collisions hydro expansion QGP freeze-out, Glasma, hadronization pre-thermalization t ～ 1fm t ～ 5-10 fm T PC ~155MeV Q Q partial freezeout production / medium interaction equilibration? formation The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan A LEXANDER R OTHKOPF - U I S
I N - MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED G AUSS - LAW Selected theory goals Q Q Properties of equilibrium QQ Extraction of the in-medium potential on realistic lattices Novel parametrization of the potential for use in phenomenology with P. Petreczky, J. Weber: NPA982 (2019) 735 with D. Lafferty arXiv:1906.00035 The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan A LEXANDER R OTHKOPF - U I S
I N - MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED G AUSS - LAW Selected theory goals Q Q Real-time QQ evol. in local Properties of equilibrium QQ thermal equilibrium Extraction of the in-medium Beyond Schrödinger: potential on realistic lattices Open-quantum-systems descr. of real-time evolution Novel parametrization of the potential for use in Connecting OQS to phenomenology EFT language of potential ( see talk by Takahiro Miura ) with P. Petreczky, J. Weber: NPA982 (2019) 735 with D. Lafferty arXiv:1906.00035 The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan A LEXANDER R OTHKOPF - U I S
I N - MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED G AUSS - LAW Selected theory goals Q Q QQ realtime evol. Real-time QQ evol. in local Properties of equilibrium QQ in the initial stages thermal equilibrium Extraction of the in-medium First exploratory Beyond Schrödinger: potential on realistic lattices steps in the glasma Open-quantum-systems descr. of real-time evolution classical statistical Novel parametrization of the simulations for gluons potential for use in Connecting OQS to + phenomenology EFT language of potential real-time NRQCD ( see talk by Alexander Lehmann) ( see talk by Takahiro Miura ) with P. Petreczky, J. Weber: NPA982 (2019) 735 with D. Lafferty arXiv:1906.00035 The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan A LEXANDER R OTHKOPF - U I S
I N - MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED G AUSS - LAW Quarkonium in thermal equilibrium Intuition on in-medium modification from potential based studies ρ ( ω ) ρ ( ω ) J/ ψ ψ‘ medium effects D/D thr. ω ω The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan A LEXANDER R OTHKOPF - U I S
I N - MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED G AUSS - LAW Quarkonium in thermal equilibrium Intuition on in-medium modification from potential based studies ρ ( ω ) ρ ( ω ) J/ ψ ψ‘ medium effects D/D thr. ω ω Re[V](r) Im[V](r) r r The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan A LEXANDER R OTHKOPF - U I S
I N - MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED G AUSS - LAW Quarkonium in thermal equilibrium Intuition on in-medium modification from potential based studies ρ ( ω ) ρ ( ω ) J/ ψ ψ‘ medium effects D/D thr. ω ω Re[V](r) Im[V](r) Generic prediction : if potential picture valid, in-medium quarkonium becomes lighter as T r r increases The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan A LEXANDER R OTHKOPF - U I S
I N - MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED G AUSS - LAW The real-time interquark potential Exploit to treat heavy quarks non-relativistically Relativistic T>0 Brambilla et.al. Rev.Mod.Phys. 77 (2005) 1423 mechanics Quantum field theory pNRQCD NRQCD QCD Singlet/Octet Dirac fields Pauli fields The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan A LEXANDER R OTHKOPF - U I S
I N - MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED G AUSS - LAW The real-time interquark potential Exploit to treat heavy quarks non-relativistically Relativistic T>0 Brambilla et.al. Rev.Mod.Phys. 77 (2005) 1423 mechanics Quantum field theory pNRQCD NRQCD QCD Singlet/Octet Dirac fields Pauli fields Matching to underlying QCD in the infinite mass limit: Wilson loop t R Q Q x,y,z The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan A LEXANDER R OTHKOPF - U I S
I N - MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED G AUSS - LAW The real-time interquark potential Exploit to treat heavy quarks non-relativistically Relativistic T>0 Brambilla et.al. Rev.Mod.Phys. 77 (2005) 1423 mechanics Quantum field theory pNRQCD NRQCD QCD Singlet/Octet Dirac fields Pauli fields Matching to underlying QCD in the infinite mass limit: Wilson loop t Wilson loop: potential emerges at late times R Q Q x,y,z The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan A LEXANDER R OTHKOPF - U I S
I N - MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED G AUSS - LAW The real-time interquark potential Exploit to treat heavy quarks non-relativistically Relativistic T>0 Brambilla et.al. Rev.Mod.Phys. 77 (2005) 1423 mechanics Quantum field theory pNRQCD NRQCD QCD Singlet/Octet Dirac fields Pauli fields Matching to underlying QCD in the infinite mass limit: Wilson loop t Wilson loop: potential emerges at late times R Im[V]: Laine et al. JHEP03 (2007) 054; ∊ℂ Beraudo et. al. NPA 806:312,2008 Q Q Brambilla et.al. PRD 78 (2008) 014017 x,y,z The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan A LEXANDER R OTHKOPF - U I S
I N - MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED G AUSS - LAW The real-time interquark potential Exploit to treat heavy quarks non-relativistically Relativistic T>0 Brambilla et.al. Rev.Mod.Phys. 77 (2005) 1423 mechanics Quantum field theory pNRQCD NRQCD QCD Singlet/Octet Dirac fields Pauli fields Matching to underlying QCD in the infinite mass limit: Wilson loop t Wilson loop: potential emerges at late times R Im[V]: Laine et al. JHEP03 (2007) 054; ∊ℂ Beraudo et. al. NPA 806:312,2008 Q Q Brambilla et.al. PRD 78 (2008) 014017 x,y,z 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 A LEXANDER R OTHKOPF - U I S
I N - MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED G AUSS - LAW Non-perturbative evaluation of V(R) A.R., T.Hatsuda & S.Sasaki How to connect to the Euclidean domain: spectral functions PRL 108 (2012) 162001 The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan A LEXANDER R OTHKOPF - U I S
I N - MEDIUM QQ POTENTIAL FROM LATTICE QCD & THE GENERALIZED G AUSS - LAW Non-perturbative evaluation of V(R) A.R., T.Hatsuda & S.Sasaki How to connect to the Euclidean domain: spectral functions PRL 108 (2012) 162001 The 17th Int. Conf. on QCD in Extreme Conditions – June 25th 2019 – Tokyo, Japan A LEXANDER R OTHKOPF - U I S
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