Quark matter: the high-density frontier Mark Alford Washington - PowerPoint PPT Presentation

Quark matter: the high-density frontier Mark Alford Washington University in St. Louis

Outline I Quarks at high density Confined, quark-gluon plasma, color superconducting II Color superconducting phases Color-flavor locking (CFL), and beyond III Quark matter in the real world Battle between color superconductivity and the strange quark mass IV Quark matter in neutron stars Mass-radius: signatures of a first-order transition Mergers: the role of transport and dissipation V Looking to the future

I. Quarks at high density Conjectured QCD phase diagram T heavy ion collider QGP non−CFL hadronic = color− superconducting CFL gas liq quark matter nuclear compact star µ superfluid /supercond heavy ion collisions: crossover and chiral critical point [ Stephanov (Mon) ] compact stars: color superconducting quark matter core?

Color superconductivity BCS pairing mechanism applies to degenerate fermions with µ an attractive interaction: E • electrons in a cold metal p • 3 He atoms • neutrons in nuclear matter • quarks in quark matter �� � � � � � � � Fermi p a † cos( θ p )+sin( θ p ) a † | BCS � = cos( θ p )+sin( θ p ) a p a − p � − p sea � p > pF p < pF particles holes | BCS � , not | Fermi sea � , is the ground state.

Physical consequences of Cooper pairing Changes low energy excitations, affecting transport properties . ◮ Goldstone bosons: massless degrees of freedom arising from spontaneous breaking of global symmetries. Dominate low energy behavior, e.g.: Superfluidity ◮ Meissner effect: exclusion of magnetic fields arising from spontaneous breaking of local (gauged) symmetries. Massive gauge bosons, e.g.: Superconductivity ◮ Gap in fermion spectrum. Adding a fermion near the Fermi surface E particle hole icle qua now costs energy because it disrupts the t si r a p condensate. ∆ p a † p a † p (cos θ + sin θ a † − p ) = cos θ a † p i s h o qua l e Fermions frozen out of transport

Handling QCD at high density Lattice : “Sign problem”—negative probabilities [ Bedaque (Mon) ] Holography : gravity dual of QCD-like theory [ Mateos (Mon) ] large N : Quarkyonic phase? pert : Applicable far beyond nuclear density. Neglects confinement and instantons. NJL : Model, applicable at low density. Follows from instanton liquid model. EFT : Effective field theory for lightest degrees of freedom. “Parameterization of our ignorance”: assume a phase, guess coefficients of interaction terms (or match to pert theory), obtain phenomenology.

II. Color superconducting phases Attractive QCD interaction ⇒ Cooper pairing of quarks. We expect pairing between different flavors . color α, β = r , g , b ia q β Quark Cooper pair: � q α jb � flavor i , j = u , d , s spin a , b = ↑ , ↓ Each possible BCS pairing pattern P is an 18 × 18 color-flavor-spin matrix ia q β jb � 1 PI = ∆ P P αβ � q α ij ab color antisymmetric [most attractive] space symmetric [ s -wave pairing] The attractive channel is: spin antisymmetric [isotropic] ⇒ flavor antisymmetric Start with the most symmetric case, where all three flavors are massless.

Three massless quark flavors Valid at very high density ( µ ≫ m s ) Color-flavor locked pairing pattern i q β i δ β j δ β � q α j � ∼ δ α j − δ α i = ǫ αβ n ǫ ijn This is invariant under equal and opposite color α, β flavor i , j rotations of color and (vector) flavor SU (3) color × SU (3) L × SU (3) R × U (1) B → SU (3) C + L + R × Z 2 � �� � � �� � ⊃ U (1) Q ⊃ U (1) ˜ Q ◮ Breaks chiral symmetry, but not by a � ¯ qq � condensate ◮ Unbroken “rotated” electromagnetism: photon-gluon mixture ◮ Continuity between hadronic (hyperonic) and CFL phases ◮ Transparent insulator (but see [ Windisch (Mon) ])

Conjectured QCD phase diagram T heavy ion collider QGP non−CFL hadronic CFL gas liq nuclear µ compact star superfluid /supercond

III. Quark matter in the real world In the real world there are three factors that combine to oppose pairing between different flavors. 1. Strange quark mass is not infinite nor zero, but intermediate. It depends on density, and ranges between about 500 MeV in the vacuum and about 100 MeV at high density. 2. Neutrality requirement. Bulk quark matter must be neutral with respect to all gauge charges: color and electromagnetism. 3. Weak interaction equilibration. In a compact star there is time for weak interactions to proceed: neutrinos escape and flavor is not conserved. These factors favor different Fermi momenta for different flavors which obstructs pairing between different flavors.

Mismatched Fermi surfaces vs. Cooper pairing E µ p s p F p d s and d quarks near their Fermi F surfaces cannot have equal and opposite momenta. The strange quark mass is the cause of the mismatch. p Fd − p Fs ≈ p Fd − p Fu ≈ M 2 s 4 µ

Phases of quark matter, again T NJL model, uniform phases only heavy ion collider 60 t NQ 50 QGP uSC guSC → 40 T (MeV) 2SC CFL non−CFL t 30 t ← gCFL hadronic p2SC − → t χ SB g2SC 20 CFL-K 0 CFL 10 gas liq NQ 0 350 400 450 500 550 µ B / 3 (MeV) nuclear compact star µ Warringa, hep-ph/0606063 superfluid /supercond But there are also non-uniform phases, such as the crystalline (“LOFF”/”FFLO”) phase. [ Incera (Mon) ]

IV. Quark matter in neutron stars? Conventional scenario Strange Matter Hypothesis [ Mannarelli (Mon) ] Neutron/hybrid star Strange star nuclear nuclear crust crust neutron NM SQM SQM star strangelet crust NM hybrid SQM SQM star

Signatures of quark matter in compact stars ← Microphysical properties Observable (and neutron star structure) ← Phases of dense matter Property Nuclear phase Quark phase known unknown; mass, radius eqn of state ε ( p ) up to ∼ n sat many models

Signatures of quark matter in compact stars ← Microphysical properties Observable (and neutron star structure) ← Phases of dense matter Property Nuclear phase Quark phase known unknown; mass, radius eqn of state ε ( p ) up to ∼ n sat many models bulk viscosity spindown Depends on Depends on shear viscosity (spin freq, age) phase: phase: heat capacity cooling unpaired n p e neutrino emissivity (temp, age) CFL n p e , µ thermal cond. CFL- K 0 n p e , Λ, Σ − shear modulus glitches n superfluid 2SC vortex pinning (superfluid, CSL p supercond energy crystal) LOFF π condensate 1SC K condensate mergers eqn of state . . . (grav waves) bulk viscosity

Probing the Equation of State Assuming that General Relativity is correct [ Llanes-Estrada (Tues) ] , Equation of State can be indirectly measured via its effect on mass-radius relation, and on gravitational and electromagnetic signals emitted in neutron star mergers [ Rezzolla (Tues) ][ Gorda (Tues) ] ◮ EoS may be very similar in different phases (e.g. superfluid vs. “normal”). ◮ Transport properties are a better discriminator [ Stetina (Tues) ] ◮ Strongly first order phase transition is reflected in EoS, (e.g. nuclear to quark matter?) How would a strong first-order transition in the EoS be manifest in mass-radius measurements?

CSS: EoS with generic first-order transition Model-independent parameterization with • Sharp 1st-order transition ε ( p ) = ε trans +∆ ε + c − 2 QM ( p − p trans ) • Constant [density-indp] Speed of Sound (CSS) Quark Matter Energy Density QM EoS params: -2 c QM ε 0,QM Slope = Δε p trans /ε trans ε trans ∆ ε/ε trans c 2 Nuclear QM Matter p trans Pressure Zdunik, Haensel, arXiv:1211.1231 ; Alford, Han, Prakash, arXiv:1302.4732

Hybrid star M ( R ) Hybrid star branch in M ( R ) relation has 4 typical forms “Connected” “Both” M M ∆ ε < ∆ ε crit small energy density jump at phase transition R R “Absent” “Disconnected” M M ∆ ε > ∆ ε crit large energy density jump at phase transition R R

“Phase diagram” of hybrid star M ( R ) Soft NM + CSS( c 2 QM =1) Schematic n trans /n 0 2.0 3.0 4.0 5.0 n causal 6.0 1.2 A 1 D Δε/ε trans = λ-1 trans 0.8 ∆ε ε B 0.6 C 0.4 0.2 0 p ε trans 0 0.1 0.2 0.3 0.4 0.5 trans p trans /ε trans ∆ ε crit = 1 2 + 3 p trans Above the red line (∆ ε > ∆ ε crit ), ε trans 2 ε trans connected branch disappears Disconnected branch exists in regions D and B.

Constraints on QM EoS from M max 2 M ⊙ observation allows two scenarios: • high p trans : very small connected branch • low p trans : modest ∆ ε , no disconnected branch. Alford, Han arXiv:1508.01261 QM � 1 With c 2 3 it is difficult for any EoS to achieve a 2 M ⊙ star.

Neutron star mergers Mergers probe the properties of nuclear/quark matter at high density (up to ∼ 4 n sat ) and temperature (up to ∼ 60 MeV) t = 2 . 42 ms 15 15 10 log 10 ( ρ [g / cm 3 ]) 5 In developing signatures 14 y [km] 0 for quark matter, we must include all the − 5 13 relevant physics for − 10 nuclear matter. − 15 12 − 15 − 10 − 5 0 5 10 15 x [km] Rezzolla group, Frankfurt Video

Nuclear material in a neutron star merger M. Hanauske, Rezzolla group, Frankfurt Significant spatial/temporal variation in: so we need to allow for temperature thermal conductivity fluid flow velocity shear viscosity density bulk viscosity