Quarkonium dissociation by anisotropy in a strongly coupled plasma Mariano ¡Chernicoff ¡ DAMTP, ¡University ¡of ¡Cambridge ¡ Based on 1208.2672 (and 1202.3696) in collaboration with D. Fernandez, D. Mateos and D. Trancanelli
Plan for the talk • Motivation • The AdS/CFT toolkit • Quarkonium physics • Conclusions
Motivation For the creation of the quark gluon plasma 400 nucleons go in 8000 hadrons are produced 1-10 GeV per hadron Energy of CM 200 GeV
Motivation The time evolution of the quark gluon plasma τ iso . 1fm [Romantschke ¡et ¡al; ¡Mrowczynski ¡et ¡al.] ¡ longitudinal ¡direc>on ¡ z ≡ transverse ¡direc>on ¡ x, y ≡ Collision τ out τ iso Anisotropic Isotropic Far from hydrodynamics hydrodynamics equilibrium P ? 6 = P k P ? = P k
Motivation Things we know about the quark gluon plasma After a very short period of time the system is in thermal equilibrium ∼ 200 − 400MeV
Motivation Things we know about the quark gluon plasma After a very short period of time the system is in thermal equilibrium ∼ 200 − 400MeV It is a strongly coupled system ( ideal fluid + small ) η /s Perturbative methods are inapplicable and lattice QCD is not well suited to study real-time dynamics.
Motivation Things we know about the quark gluon plasma After a very short period of time the system is in thermal equilibrium ∼ 200 − 400MeV It is a strongly coupled system ( ideal fluid + small ) η /s Perturbative methods are inapplicable and lattice QCD is not well suited to study real-time dynamics. Some observables are sensitive to the presence of an anisotropy • Quarkonium physics ( ) [Dumitru ¡et ¡al.; ¡Philipsen ¡et ¡al.] ¡ ¡ J/ Ψ [Dumitru ¡et ¡al.; ¡Mehtar-‑Tani; ¡Romantschke ¡et ¡al.] ¡ • Momentum broadening
Motivation About quarkonium in heavy ion collisions: Quarkonium refers to charm-anticharm mesons ( , , , ... ) J/ Ψ Ψ 0 χ c and bottom-antibottom mesons ( , , ... ) Υ Υ 0 1s ¡state ¡
Motivation About quarkonium in heavy ion collisions: Quarkonium refers to charm-anticharm mesons ( , , , ... ) J/ Ψ Ψ 0 χ c and bottom-antibottom mesons ( , , ... ) Υ Υ 0 mesons survive as bound states in a hot medium up to some J/ Ψ dissociation temperature that is higher than the deconfinement T d temperature ( lattice predicts: ). T d ( J/ Ψ ) ' 2 T c T c
Motivation About quarkonium in heavy ion collisions: Quarkonium refers to charm-anticharm mesons ( , , , ... ) J/ Ψ Ψ 0 χ c and bottom-antibottom mesons ( , , ... ) Υ Υ 0 mesons survive as bound states in a hot medium up to some J/ Ψ dissociation temperature that is higher than the deconfinement T d temperature ( lattice predicts: ). T d ( J/ Ψ ) ' 2 T c T c RHIC data: - suppression in nucleus-nucleus collisions when J/ Ψ compared to proton-proton collisions. mesons are screened in the quark gluon plasma J/ Ψ
Motivation It is important to understand how they are screened by the QGP What is the effect of the anisotropy? They might be moving with significant transverse momentum through the hot medium, what is the effect of such “wind”? We will use the AdS/CFT correspondence to address this questions
AdS/CFT toolkit AdS 5 × S 5 Type IIB on N = 4 SYM = on Minkowski 3+1 xy u = 0 z T = 0 = u = ∞ λ ≡ L 4 ds 2 = L 2 = g 2 − dt 2 + d ~ x 2 + du 2 ⇤ YM N c ⇥ l 4 u 2 s
AdS/CFT toolkit at finite temperature Schwarzschild AdS black hole N = 4 SYM = xy u = 0 z T 6 = 0 = u = u h ds 2 = L 2 x 2 + du 2 − f ( u ) dt 2 + d ~ ⇥ ⇤ u 2 f ( u ) f ( u ) = 1 − u 4 with u 4 h Note: we will refer to this metric as the isotropic metric
AdS/CFT toolkit External quark Fundamental string = Quark ¡ u = 0 = T 6 = 0 u = u h • A fundamental string extending from the boundary at to the u = 0 horizon corresponds to an infinitely massive quark. • The string endpoint represents the quark, while the rest of the string codifies the profile of the gluonic field
AdS/CFT toolkit meson (bound state) = U-shaped string ` u = 0 ` = T 6 = 0 u = u h
AdS/CFT toolkit meson (bound state) moving U-shaped string moving at = at constant velocity constant velocity u = 0 = T 6 = 0 u = u h
AdS/CFT toolkit meson (bound state) moving U-shaped string moving at = at constant velocity constant velocity u = 0 = T 6 = 0 u = u h But we are interested in studying an anisotropic strongly coupled plasma How can we do that using the AdS/CFT correspondence?
AdS/CFT toolkit The gauge theory that we will consider is a deformation of N = 4 SYM T 6 = 0 Z S = S N =4 + ✓ ( ~ x )Tr F ∧ F with ✓ ( ~ x ) = 2 ⇡ n D 7 z dimensions ¡of ¡energy ¡
AdS/CFT toolkit The gauge theory that we will consider is a deformation of . N = 4 SYM The field dual to the -term is the axion θ xy u = 0 z T 6 = 0 = χ = az Z S = S N =4 + ✓ ( ~ x )Tr F ∧ F u = u h with ✓ ( ~ x ) = 2 ⇡ n D 7 z τ = θ 2 π + 4 π i = χ + ie − φ g 2 YM The axion is magnetically sourced by D7-branes
AdS/CFT toolkit The gauge theory that we will consider is a deformation of N = 4 SYM The field dual to the -term is the axion θ xy u = 0 z T 6 = 0 = χ = az Z S = S N =4 + ✓ ( ~ x )Tr F ∧ F u = u h with ✓ ( ~ x ) = 2 ⇡ n D 7 z S 5 t x y z u N c D 3 x x x x n D 7 D 7 x x x x
AdS/CFT toolkit The gauge theory that we will consider is a deformation of N = 4 SYM The field dual to the -term is the axion θ xy u = 0 z T 6 = 0 = χ = az Z S = S N =4 + ✓ ( ~ x )Tr F ∧ F u = u h with ✓ ( ~ x ) = 2 ⇡ n D 7 z and Density ¡of ¡D7-‑branes ¡ a = λ n D 7 distributed ¡along ¡z ¡ 4 π N c is ¡a ¡measure ¡of ¡the ¡anisotropy ¡
AdS/CFT toolkit The gauge theory that we will consider is a deformation of N = 4 SYM The field dual to the -term is the axion θ xy u = 0 z T 6 = 0 = χ = az Z S = S N =4 + ✓ ( ~ x )Tr F ∧ F u = u h with ✓ ( ~ x ) = 2 ⇡ n D 7 z Finally, putting all these ingredients together, and solving the eom...
AdS/CFT toolkit The anisotropic metric is ds 2 = L 2 − F ( u ) B ( u ) dt 2 + dx 2 + dy 2 + H ( u ) dz 2 + du 2 h i u 2 F ( u ) and χ ( z ) = az φ ≡ φ ( u ) [Mateos ¡and ¡Trancanelli] ¡ H 6 H 6 1.2 1.2 5 5 1. B 1. 4 4 0.8 0.8 3 3 F F 0.6 0.6 2 2 0.4 0.4 B 1 1 0.2 0.2 0 0 0 0 φ φ - 1 - 1 - 0.2 - 0.2 - 2 - 2 0. 0.2 0.4 0.6 0.8 1. 0. 0.2 0.4 0.6 0.8 1. u/u h u/u h
AdS/CFT toolkit The anisotropic metric is ds 2 = L 2 − F ( u ) B ( u ) dt 2 + dx 2 + dy 2 + H ( u ) dz 2 + du 2 h i u 2 F ( u ) [Mateos ¡and ¡Trancanelli] ¡ Regular on and outside the horizon RG flow between AdS (UV) and Lifshitz type (IR) The entropy density interpolates between s ⇠ a 1 / 3 T 8 / 3 s ⇠ T 3 and T � a T ⌧ a There is an analytical expression for the near-boundary behavior of metric functions O ( u 6 )
Quarkonium physics Preliminaries The screening length is define as the separation between a L s q ¯ q ` < L s ( ` > L s ) such that for it is energetically favorable for the pair to be bound (unbound).
Quarkonium physics Preliminaries The screening length is define as the separation between a L s q ¯ q ` < L s ( ` > L s ) such that for it is energetically favorable for the pair to be bound (unbound). We will determine by comparing the action of the pair to L s S ( ` ) q ¯ q the action of the unbound system; i.e. S unb ∆ S ( ` ) = S ( ` ) − S unb (In the Euclidean version, this criterion corresponds to determining which configuration has the lowest free energy) The screening length is the maximum value of for which is positive ∆ S `
Quarkonium physics 1. Static case (to warm up) Given the rotational symmetry in the xy-plane, the most general case is to consider the dipole in the xz-plane. u = 0 x θ z u = u h Choosing the static gauge , , and the string embedding: τ = t σ = u and Z ( u ) = z ( u ) cos θ X ( u ) = x ( u ) sin θ
Quarkonium physics 1. Static case The action for the U-shaped string takes the form Z u max S = − L 2 Z du 1 q B (1 + FH cos 2 θ z 0 2 + F sin 2 θ x 0 2 ) 2 πα 0 2 dt u 2 0
Quarkonium physics 1. Static case The action for the U-shaped string takes the form Z u max S = − L 2 Z du 1 q B (1 + FH cos 2 θ z 0 2 + F sin 2 θ x 0 2 ) 2 πα 0 2 dt u 2 0 Two conserved momenta and associated to translation Π z Π x invariance in the x, z direction. Then, the on-shell action can be written as √ Z u max S = − L 2 Z du 1 B FH 2 πα 0 2 dt u 2 p FBH − u 4 ( Π 2 z + H Π 2 x ) 0 where the turning point is determined from the condition u max x 0 ( u max ) = z 0 ( u max ) → ∞
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