Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball

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1 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball Joan Soto Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos Universitat de Barcelona

2 Plan Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.1/38

3 Plan Heavy Quarkonium Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.1/38

4 Plan Heavy Quarkonium Vacuum Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.1/38

5 Plan Heavy Quarkonium Vacuum Quark Gluon Plasma Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.1/38

6 Plan Heavy Quarkonium Vacuum Quark Gluon Plasma Fireball Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.1/38

7 Plan Heavy Quarkonium Vacuum Quark Gluon Plasma Fireball Conclusions Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.1/38

8 Heavy Quarkonium Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.2/38

9 Heavy Quarkonium Heavy quark-antiquark system: Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.2/38

10 Heavy Quarkonium Heavy quark-antiquark system: Charmonium (c c, J/ψ family) Bottomonium (b b, Υ family) Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.2/38

11 Heavy Quarkonium Heavy quark-antiquark system: Charmonium (c c, J/ψ family) Bottomonium (b b, Υ family) Also: B c (b c) t- t q q, g g, Double-heavy baryons (ccq, q = u,d,s) Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.2/38

12 Heavy Quarkonium Heavy quark-antiquark system: Charmonium (c c, J/ψ family) Bottomonium (b b, Υ family) Also: B c (b c) t- t q q, g g, Double-heavy baryons (ccq, q = u,d,s) Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.2/38

13 Heavy Quarkonium Q Q bound state, m Q >> Λ QCD, α s (m Q ) << 1 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.3/38

14 Heavy Quarkonium Q Q bound state, m Q >> Λ QCD, α s (m Q ) << 1 Heavy quarks move slowly v << 1 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.3/38

15 Heavy Quarkonium Q Q bound state, m Q >> Λ QCD, α s (m Q ) << 1 Heavy quarks move slowly v << 1 Non-relativistic system multiscale problem Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.3/38

16 Heavy Quarkonium Q Q bound state, m Q >> Λ QCD, α s (m Q ) << 1 Heavy quarks move slowly v << 1 Non-relativistic system multiscale problem m Q >> m Q v >> m Q v 2 m Q >> Λ QCD Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.3/38

17 Heavy Quarkonium Q Q bound state, m Q >> Λ QCD, α s (m Q ) << 1 Heavy quarks move slowly v << 1 Non-relativistic system multiscale problem m Q >> m Q v >> m Q v 2 m Q >> Λ QCD EFTs are useful (N. Brambilla, A. Pineda, JS and A. Vairo, Rev. Mod. Phys. 77, 1423 (2005)) Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.3/38

18 NRQCD W.E. Caswell and G.P. Lepage, Phys. Lett. 167B, 437 (1986) G. T. Bodwin, E. Braaten and G. P. Lepage, Phys. Rev. D 51 (1995) 1125 L ψ = ψ { + c D 8m 2 Q m Q >> m Q v, m Q v 2, Λ QCD id D m Q 8m 3 D 4 + c F σ.gb + Q 2m Q (D.gE ge.d) + i c S 8m 2 Q σ.(d ge ge D) +... c F, c D and c S are short distance matching coefficients which depend on m Q and µ (factorization scale) } ψ Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.4/38

19 NRQCD (Cont.) Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.5/38

20 NRQCD (Cont.) The hierarchy m Q v m Q v 2 is not taken advantage of Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.5/38

21 NRQCD (Cont.) The hierarchy m Q v m Q v 2 is not taken advantage of Proposals: Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.5/38

22 NRQCD (Cont.) The hierarchy m Q v m Q v 2 is not taken advantage of Proposals: Integrate out energy scales m Q v Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.5/38

23 NRQCD (Cont.) The hierarchy m Q v m Q v 2 is not taken advantage of Proposals: Integrate out energy scales m Q v pnrqcd, A. Pineda and JS, Nucl. Phys. Proc. Suppl. 64, 428 (1998) L pnrqcd depends on the relative size between Λ QCD and m Q v 2 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.5/38

24 NRQCD (Cont.) The hierarchy m Q v m Q v 2 is not taken advantage of Proposals: Integrate out energy scales m Q v pnrqcd, A. Pineda and JS, Nucl. Phys. Proc. Suppl. 64, 428 (1998) L pnrqcd depends on the relative size between Λ QCD and m Q v 2 Mode decomposition Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.5/38

25 NRQCD (Cont.) The hierarchy m Q v m Q v 2 is not taken advantage of Proposals: Integrate out energy scales m Q v pnrqcd, A. Pineda and JS, Nucl. Phys. Proc. Suppl. 64, 428 (1998) L pnrqcd depends on the relative size between Λ QCD and m Q v 2 Mode decomposition vnrqcd, M. E. Luke, A. V. Manohar and I. Z. Rothstein, Phys. Rev. D 61, (2000) Λ QCD is neglected Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.5/38

26 pnrqcd Λ QCD m Q v 2 L pnrqcd = : weak coupling regime { d 3 r Tr S (i 0 h s (r,p,p R,S 1,S 2,µ)) S + } +O (id 0 h o (r,p,p R,S 1,S 2,µ)) O +V A (r,µ)tr + V B(r,µ) 2 { } O r ges + S r geo { } Tr O r geo + O Or ge h s, h o = quantum mechanical Hamiltonians with scale dependent potentials calculable in perturbation theory in α s (m Q v) +... Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.6/38

27 Heavy Quarkonium in a QGP Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.7/38

28 Heavy Quarkonium in a QGP Quark-Gluon Plasma (QGP) If T Λ QCD then α s (T) 1 weakly coupled quarks and gluons It is expected to be produced in Heavy Ion Collision (HIC) experiments (RHIC, LHC) Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.7/38

29 Heavy Quarkonium in a QGP Quark-Gluon Plasma (QGP) If T Λ QCD then α s (T) 1 weakly coupled quarks and gluons It is expected to be produced in Heavy Ion Collision (HIC) experiments (RHIC, LHC) Properties of the QGP are extracted indirectly by comparing AA X + anything pp X + anything X = Hard Probe (jets, heavy quarks, heavy quarkonia,...) is particularly useful Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.7/38

30 Heavy Quarkonium in a QGP Heavy Quarkonium Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.8/38

31 Heavy Quarkonium in a QGP Heavy Quarkonium If m Q T it does not thermalise Hard Probe Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.8/38

32 Heavy Quarkonium in a QGP Heavy Quarkonium If m Q T it does not thermalise Hard Probe How does the medium modify the heavy quarkonium properties? Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.8/38

33 Heavy Quarkonium in a QGP Heavy Quarkonium If m Q T it does not thermalise Hard Probe How does the medium modify the heavy quarkonium properties? Early proposal (Matsui, Satz, 86): V (r) V (r,t) = C fα s r e m Dr, m D gt Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.8/38

34 Heavy Quarkonium in a QGP Heavy Quarkonium If m Q T it does not thermalise Hard Probe How does the medium modify the heavy quarkonium properties? Early proposal (Matsui, Satz, 86): V (r) V (r,t) = C fα s r e m Dr, m D gt Implies sequential melting of heavy quarkonium states as T increases Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.8/38

35 Heavy Quarkonium in a QGP Heavy Quarkonium If m Q T it does not thermalise Hard Probe How does the medium modify the heavy quarkonium properties? Early proposal (Matsui, Satz, 86): V (r) V (r,t) = C fα s r e m Dr, m D gt Implies sequential melting of heavy quarkonium states as T increases Can we quantify these arguments from QCD? Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.8/38

36 QED as a toy model for QCD Muonic Hydrogen Heavy Quarkonium (Eiras, JS, 00) Muon, Proton Heavy Quarks Photon Gluons Electron, Positron Light Quarks Electron-positron plasma (EPP) Quark-gluon plasma Photon Gluons Electron, Positron Light Quarks M.A. Escobedo, JS, Phys. Rev. A 78, (2008); A 82, (2010) Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.9/38

37 Relevant scales Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.10/38

38 Relevant scales m 0, T = 0 case: m (hard), muon mass mα/n (soft), inverse Bohr radius, α = e 2 /4π; e, muon charge mα 2 /n 2 (ultrasoft), binding energy Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.10/38

39 Relevant scales m 0, T = 0 case: m (hard), muon mass mα/n (soft), inverse Bohr radius, α = e 2 /4π; e, muon charge mα 2 /n 2 (ultrasoft), binding energy m = 0, T 0 case: T (hard), temperature et (soft), Debye mass Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.10/38

40 Relevant scales m 0, T = 0 case: m (hard), muon mass mα/n (soft), inverse Bohr radius, α = e 2 /4π; e, muon charge mα 2 /n 2 (ultrasoft), binding energy m = 0, T 0 case: T (hard), temperature et (soft), Debye mass m 0, T 0 case: what is the interplay among the scales above? Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.10/38

41 EFTs e 0.3 (α 1/137), the scales are well separated, EFTs are useful: Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.11/38

42 EFTs e 0.3 (α 1/137), the scales are well separated, EFTs are useful: m 0, T = 0 case: m (hard), QED mα/n (soft), NRQED mα 2 /n 2 (ultrasoft), pnrqed Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.11/38

43 EFTs e 0.3 (α 1/137), the scales are well separated, EFTs are useful: m 0, T = 0 case: m (hard), QED mα/n (soft), NRQED mα 2 /n 2 (ultrasoft), pnrqed m = 0, T 0 case: T (hard), QED et (soft), HTL (Hard Thermal Loops) Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.11/38

44 EFTs e 0.3 (α 1/137), the scales are well separated, EFTs are useful: m 0, T = 0 case: m (hard), QED mα/n (soft), NRQED mα 2 /n 2 (ultrasoft), pnrqed m = 0, T 0 case: T (hard), QED et (soft), HTL (Hard Thermal Loops) m 0, T 0 case: contributions of energies above T are exponentially suppressed by Boltzmann factors Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.11/38

45 Hard Thermal Loops EFT (m=0) δl HTL = 1 2 m2 D F µα dω 4π k α k β (k. ) 2Fµβ + m 2 f ψγ µ dω 4π k µ k.d ψ k = (1,ˆk), m 2 D = e2 T 2 /3, m 2 f = e2 T 2 /8 (Braaten, Pisarsky, 1992) Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.12/38

46 The m e = 0, T m µ α/n case pnrqed can be used as a starting point Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.13/38

47 The m e = 0, T m µ α/n case pnrqed can be used as a starting point The potentials remain the same as in the T = 0 case Thermal effects are encoded in the ultrasoft gluons Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.13/38

48 The m e = 0, T m µ α/n case pnrqed can be used as a starting point The potentials remain the same as in the T = 0 case Thermal effects are encoded in the ultrasoft gluons For T = β 1 m µ α 2 /n 2, same contribution as in the hydrogen atom Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.13/38

49 The m e = 0, T m µ α/n case pnrqed can be used as a starting point The potentials remain the same as in the T = 0 case Thermal effects are encoded in the ultrasoft gluons For T = β 1 m µ α 2 /n 2, same contribution as in the hydrogen atom For T = β 1 m µ α 2 /n 2, HTL resummations necessary Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.13/38

50 The m e = 0, T m µ α/n case pnrqed can be used as a starting point The potentials remain the same as in the T = 0 case Thermal effects are encoded in the ultrasoft gluons For T = β 1 m µ α 2 /n 2, same contribution as in the hydrogen atom For T = β 1 m µ α 2 /n 2, HTL resummations necessary. Analytic results possible for: T m µ α 2 /n 2 et T et m µ α 2 /n 2 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.13/38

51 The m e = 0, T m µ α/n case pnrqed can be used as a starting point The potentials remain the same as in the T = 0 case Thermal effects are encoded in the ultrasoft gluons For T = β 1 m µ α 2 /n 2, same contribution as in the hydrogen atom For T = β 1 m µ α 2 /n 2, HTL resummations necessary. Analytic results possible for: T m µ α 2 /n 2 et. Results available for QCD O(m Q αs) 5 (Brambilla, Escobedo, Ghiglieri, JS, Vairo (10)) T et m µ α 2 /n 2. Results available for QCD O(m Q αs) 5 (Brambilla, Escobedo, JS, Vairo, in preparation) Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.13/38

52 The T mα/n case For T = β 1 mα 2 /n 2 : δe n = 4π3 α 45β 4 n x Pn (H 0 E n ) x n δγ n = 0 For T = β 1 mα 2 /n 2 : δe n = δγ n = 4Z2 α 3 3βn 2 n 2 )2 ( )) 1 + O (( n2 βmα )2 απ 3mβ 2 + 2α n v r 2 2π (E n E r )(ln( 3π β E r n E r ) γ) ( (1 + O ( βmα ) ) ( 1 + O ( )) βmα n 2 Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.14/38

53 The m e = 0, T m µ case NRQED can be used as a starting point Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.15/38

54 The m e = 0, T m µ case NRQED can be used as a starting point The potentials depend on T Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.15/38

55 The m e = 0, T m µ case NRQED can be used as a starting point The potentials depend on T For T m µ α/n et m µ α 2 /n 2 further contributions to the potential from the scale et (HTLs necessary) Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.15/38

56 The m e = 0, T m µ case NRQED can be used as a starting point The potentials depend on T For T m µ α/n et m µ α 2 /n 2 further contributions to the potential from the scale et (HTLs necessary) For T m µ α/n, and et m µ α/n all contributions to the potential from HTLs Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.15/38

57 The m e = 0, m µ α/n T m µ case The results also hold for heavy quarkonium [ α C f α s, m µ m Q /2, m 2 D = e2 T 2 /3 m 2 D = g2 T 2 (N c + N f /2) ] Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.16/38

58 The m e = 0, m µ α/n T m µ case The results also hold for heavy quarkonium [ α C f α s, m µ m Q /2, m 2 D = e2 T 2 /3 m 2 D = g2 T 2 (N c + N f /2) ] One can start from NRQED, and integrate out the largest scale, T Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.16/38

59 The m e = 0, m µ α/n T m µ case The results also hold for heavy quarkonium [ α C f α s, m µ m Q /2, m 2 D = e2 T 2 /3 m 2 D = g2 T 2 (N c + N f /2) ] One can start from NRQED, and integrate out the largest scale, T One obtains a HTL Lagrangian in the photon sector and temperature corrections to the NRQCD matching coefficients Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.16/38

60 The m e = 0, m µ α/n T m µ case The results also hold for heavy quarkonium [ α C f α s, m µ m Q /2, m 2 D = e2 T 2 /3 m 2 D = g2 T 2 (N c + N f /2) ] One can start from NRQED, and integrate out the largest scale, T One obtains a HTL Lagrangian in the photon sector and temperature corrections to the NRQCD matching coefficients One next matches to pnrqed, obtaining a et dependent potential Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.16/38

61 The m e = 0, m µ α/n T m µ case The results also hold for heavy quarkonium [ α C f α s, m µ m Q /2, m 2 D = e2 T 2 /3 m 2 D = g2 T 2 (N c + N f /2) ] One can start from NRQED, and integrate out the largest scale, T One obtains a HTL Lagrangian in the photon sector and temperature corrections to the NRQCD matching coefficients One next matches to pnrqed, obtaining a et dependent potential Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.16/38

62 The m e = 0, m µ α/n T m µ case V (r,t) = αe m Dr r φ(x) = 2 0 ( ) αt 2 αm D + iαtφ(m D r) + O dzz (z 2 + 1) 2 [ sin(zx) zx ] 1 m µ It has an imaginary part! (Laine, Philipsen, Romatschke, Tassler, 06; Escobedo, JS, 08; Brambilla, Ghiglieri, Vairo, Petreczky, 08) The dissociation temperature becomes T d m µ α 2/3 /ln 1/3 α < m µ α 1/2 where m µ α 1/2 ( m D et ) is the scale of the disociation temperature for the screening mechanism (Matsui, Satz, 86) Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.17/38

63 The m q = 0, m Q α s T m Q case The melting temperature T d can be parametrically estimated to be T d m Q αs 2/3 /ln 1/3 α s Υ(1S) T d 500MeV J/ψ T d 200MeV The Υ(1S) spectral function -ρ/m Q T=250 MeV T=300 MeV T=350 MeV T=400 MeV T=450 MeV T=500 MeV ω/m Q Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.18/38

64 Moving through the QGP Bound state at rest, the medium moves at velocity v (Weldom, 82) f(βk 0 ) f(β µ k µ ) = 1 e βµ k µ ± 1, βµ = γ T (1,v) v = v, γ = 1/ 1 v 2 O(3) rotational symmetry is reduced to O(2) In light cone coordinates k + = k 0 + k 3, k = k 0 k 3 β µ k µ = 1 ( k+ + k ) 1 + v 1 v, T + = T 2 T + T 1 v, T = T 1 + v For v 1 (moderate velocities), T + T T For v 1 (relativistic velocities), T + T T Collinear region, k + T +, k T Soft (ultrasoft) region, k + k T Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.19/38

65 Moving through the QGP -ρ/m Q 2 Results (Escobedo, Mannarelli, JS, 11; + Giannuzzi, 13): For T mα/n the thermal decay width (Γ) decreases with v For et mα/n T : At moderate velocities Γ increases with v At ultrarelativistic velocities Γ decreases with v The Υ(1S) spectral function at v 0 T = 250 MeV v=0. v=0.4 v=0.8 v=0.9 v=0.99 -ρ/m Q T = 400 MeV v=0. v=0.4 v=0.8 v=0.9 v= ω/m Q Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, ω/m Q Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.20/38

66 Embeding it in Heavy Ion Collisions M.A. Escobedo, AIP Conf. Proc (2016) N. Brambilla, M.A. Escobedo, JS, A. Vairo, in preparation Not really an equilibirium QGP, more like an expanding fireball. t 0, formation time Expansion ( T decreases) t F, hadronization time (T T c ) Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.21/38

67 Embeding it in Heavy Ion Collisions Open quantum system approach (Akamatsu, Rothkopt, 11; Akamatsu 12; 14): At t = 0, ρ = ρ HQ ρ ldf From 0 < t < t 0, ρ HQ and ρ ldf evolve independently, ρ HQ as in the vacuum, and ρ ldf to ρ QGP From t 0 < t < t F, ρ QGP evolves according to the Bjorken model, and ρ HQ according to pnrqcd (rt 1) Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.22/38

68 Embeding it in Heavy Ion Collisions Open quantum system approach (Akamatsu, Rothkopt, 11; Akamatsu 12; 14): At t = 0, ρ = ρ HQ ρ ldf From 0 < t < t 0, ρ HQ and ρ ldf evolve, ρ HQ as in your favorite QGP formation model and ρ ldf to ρ QGP From t 0 < t < t F, ρ QGP evolves according to your favorite hydro model, and ρ HQ according to pnrqcd (rt 1) Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.23/38

69 Dilepton emission dr = e2 L µν (k 1, k 2 ) k 1 k 2 (k 1 + k 2 ) 4 McLerran, Toimela (85) d 4 λ 1 d 4 λ 2 e i(k 1+k 2 )(λ 1 λ 2 ) Tr(ρJ µ (λ 1 )J ν (λ 2 )) k 1, k 2, lepton momenta J µ (λ 1 ) QCD electromagnetic current The formula is adapted to include: Heavy quarks in J µ (λ 1 ) Non thermalized heavy quarks in ρ = ρ HQ ρ ldf Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.24/38

70 Evolution of ρ HQ For ρ s we have: ρ HQ = ρ s 0 0 ρ o 2 1 = dρ s (t) dt = ih s,eff (t)ρ s (t) + iρ s (t)h s,eff (t) + F(ρ o(t),t) Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.25/38

71 Evolution of ρ HQ The interaction with the medium depends on E i (t)e j (t ) only H = h s,eff + h s,eff 2, Γ = i(h s,eff h s,eff ) t ρ s = i[h,f s ] 1 2 {Γ,f s} + F(f o ) Screening. Decay. Creation. Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.26/38

72 Evolution of ρ HQ For ρ o we have: dρ o (t) dt = ih o,eff (t)ρ o (t)+iρ o (t)h o,eff (t)+f 1(ρ s (t),t)+f 2 (ρ o (t),t) For quasistatic evolution of ρ QGP (dt/dt TE), h s,eff (t), h o,eff (t), F(ρ o (t),t), F 1 (ρ s (t),t), F 2 (ρ o (t),t), can be obtained from equilibrium distributions. If in addition t is large (t 1/E), h s,eff (t), h o,eff (t) become slowly varying in time and can be obtained directly from previous calculations. We have further assumed that ρ o is diagonal in color space and taken the A 0 = 0 gauge. Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.27/38

73 Solution of ρ HQ (t) Initial conditions: Scaling of NRQCD LO production: ρ o = bρ s /α s (m), b = O(1) Tr(ρ s ) + Tr(ρ o ) = 1 Rewrite the evolution equation in the Lindblad form dρ HQ dt = i[h,ρ HQ ] + i (C i ρ HQ C i 1 2 {C i C i,ρ HQ }) Decompose in partial waves and truncate beyond a given angular momentum ( t t 0 dt r 2 T(t ) 3 1) Use standard libraries to numerically solve the Lindblad equation (Johansson, Nation, Nori, 12) Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.28/38

74 Solution of ρ HQ (t) The case 1/r T E m D C 0 i = C 1 i = H = 1 2 h s,eff + h s,eff 0 0 h o,eff + h o,eff 4TF α s (µ E )T 3 4CF α s (µ E )T 3. ( 2ipi + N ) cα s (1/a o )r i 0 1 M b 2r 0 0 ( 2ip i + N ) cα s (1/a o )r i 0 0 M b 2r 1 0 C 2 i = 2 M b (N 2 c 4)α s (µ E )T N c p i Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.29/38

75 R AA for bottomonium 1.0 1S 2S R AA time(fm) LO NRQCD production scaling (b = 1), µ E = 2πT Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.30/38

76 R AA for bottomonium 1.0 1S 2S R AA time(fm) More singlet than LO NRQCD production scaling (b = 0.1), µ E = 2πT Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.31/38

77 R AA for bottomonium 1.0 1S 2S R AA time(fm) More octet than LO NRQCD production scaling (b = 10), µ E = 2πT Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.32/38

78 Solution of ρ HQ (t) The case 1/r T m D E For T relevant for LHC, it leads to negative decay widths The case 1/r T m D E g(t) large, more realistic case, but non-perturbative inputs needed: dλ 0 T E A,i (t + λ 0 2,0)EA,i (t λ 0 2,0) Two real functions, one of them related to the heavy quark energy loss, available on the lattice (Kaczmarek, 14; Francis, Kaczmarek, Laine, Neuhaus, Ohno, 15) Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.33/38

79 Solution of ρ HQ (t) The case 1/r T m D E C 0 i = 2 2T F κ(t) N c (N 2 c 1) ri 0 1 N 2 c 1 0 C 1 i = 2(Nc 2 4)κ(t) N c (Nc 2 1) ri ( δh = γ(t)t 3 r 2 8T F 3 2N c 9 ) C F 0 0 T F N c + N2 c 4 4N c κ(t), real part of the correlator (from lattice QCD) γ(t), imaginary part of the correlator (estimated in perturbative QCD) Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.34/38

80 Solution of ρ HQ (t) The case 1/r T m D E κ T 3 γ d R AA (1S) 30 50% centrality % centrality R AA (2S) R AA (1S) R AA (1S) R AA (2S) R AA (1S) Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.35/38

81 2012 CMS data R AA s NN 1.4 CMS PbPb = 2.76 TeV ϒ(1S), stat. unc. ϒ(1S), syst. unc. ϒ(2S), stat. unc. ϒ(2S), syst. unc. L int -1 = 150 µb y < 2.4 p µ T > 4 GeV/c % 30-40% 20-30% % 10-20% 5-10% 0-5% N part Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.36/38

82 Solution of ρ HQ (t) The case 1/r T m D E κ T 3 γ d R AA (1S) 30 50% centrality % centrality R AA (2S) R AA (1S) R AA (1S) R AA (2S) R AA (1S) Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.37/38

83 Conclusions Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.38/38

84 Conclusions Non-Relativistic EFTs had been combined to Thermal EFTs in order to elucidate the behavior of Non-relativistic bound states in a thermal bath under well controlled approximations Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.38/38

85 Conclusions Non-Relativistic EFTs had been combined to Thermal EFTs in order to elucidate the behavior of Non-relativistic bound states in a thermal bath under well controlled approximations The above results have been incorporated to the theory of Open Quantum Systems in order to obtain a framework suitable for Heavy Ion Collisions Symposium on Effective Field Theory and Lattice Field Theory, TUM-IAS, Garching, May 20th, 2016 Effective Field Theory in Open Quantum Systems: Heavy Quarkonium in a Fireball p.38/38

Heavy Quarkonium in a Quark-Gluon Plasma

Heavy Quarkonium in a Quark-Gluon Plasma Joan Soto Departament d Estructura i Constituents de la Matèria and Institut de Ciències del Cosmos Universitat de Barcelona Charmonium Eichten, Godfrey, Mahlke,