Condensation of nucleons and quarks: from nuclei to neutron stars and color superconductors

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1 Condensation of nucleons and quarks: from nuclei to neutron stars and color superconductors Gordon Baym University of Illinois, Urbana Workshop on Universal Themes of Bose-Einstein Condensation Leiden 12 March 2013

2 Condensation in nuclei: BCS pairing of nucleons

3 BCS applied to nuclear systems Pairing of even numbers of neutrons or protons outside closed shells *David Pines brings BCS to Niels Bohr s Institute in Copenhagen, Summer 1957, as BCS was being finished in Urbana. * BCS paper submitted July 8, 1957; published Dec. 1, *Aage Bohr, Ben Mottelson and Pines (57) suggest BCS pairing in nuclei to explain energy gap in single particle spectrum odd-even mass differences *Pairing gaps deduced from odd-even mass differences: Δ ~ 12 A -1/2 MeV for both protons and neutrons

4 Energies of first excited states: even-even (BCS paired) vs. odd A (unpaired) nuclei Energy gap

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6 Rotational spectra of nuclei: E = J 2 / 2I, indicate that moment of inertia, I, reduced from rigid body value, I cl.. Reduction of moment of inertia due to BCS pairing = analog of Meissner effect. Non-zero superfluid mass density!! Detailed calculations by Migdal (1959).

7 Condensation in neutron stars: BCS pairing of neutrons, and protons Niels Bohr commenting on the BCS theory in Fall idea but nature isn t that simple. 1957, It s an interesting

8 BCS pairing of nucleons in neutron stars Mass ~ 1.4 M sun Radius ~ km Temperature ~ K Surface gravity ~10 14 that of Earth Surface binding ~ 1/10 mc 2 Mountains < 1 mm 1 S 0 neutrons 1 S 0 protons 3 P 2 neutrons Density ~ 2x10 14 g/cm 3

9 Neutron drip Beyond density ρ drip ~ 4.3 X g/cm 3 neutron bound states in nuclei become filled through capture of high Fermi momentum electrons by protons: e - +p n +ν. Further neutrons must go into continuum states. Form degenerate neutron Fermi sea. Neutrons in neutron sea are in equilibrium with those inside nucleus Protons never drip, but remain in bound states until nuclei merge into interior liquid.

10 Superfluidity of nuclear matter in neutrons stars Migdal 1959, Ginzburg & Kirshnits 1964; Ruderman 1967; GB, Pines & Pethick, 1969 First estimates of pairing gaps based on scattering phase shifts CRUST LIQUID CORE Neutron fluid in crust BCS-paired in relative 1 S 0 states Neutron fluid in core 3 P 2 paired Proton fluid 1 S 0 paired n =Hoffberg et al. 1970, p =Chao et al. 1972

11 Quantum Monte Carlo 1 S 0 nn gap in crust: A. Gezerlis & J. Carlson, PR C77, (2008) include polarization effects Comparison with older calculations

12 3 P 2 nn gap in interior: M. Baldo and G.F. Burgio, Rep Prog Phys. 2012

13 Pulsar glitches Sudden speedups in rotation period, relaxing back in days to years, with no significant change in pulsed electromagnetic emission ~ 90 glitches detected in ~ 30 pulsars Vela (PSR ) Period=1/Ω=0.089sec 15 glitches since discovery in 1969 ΔΩ/Ω ~ 10-6 Largest = X 10-6 on Jan. 16, 2000 Moment of inertia ~ 1045 gcm => ΔErot ~ 1043 erg Feb. 28, 1969 Reichley and Downs, Nature 1969 Radhakrishnan and Manchester, Nature 1969 Crab (PSR ) P = 0.033sec 14 glitches since 1969 ΔΩ/Ω ~ 10-9

14 Rotating superfluid neutrons Rotating superfluid threaded by triangular lattice of vortices parallel to stellar rotation axis Quantized circulation of superfluid velocity: Vortex core ~ 10 fm Vortex separation ~ 0.01P(s) 1/2 cm; Vela contains ~ vortices Angular momentum of vortex =N~(1-r 2 /R 2 ) decreases as vortex moves outwards => to spin down must move vortices outwards Superfluid spindown controlled by rate at which vortices can move against barriers, under dissipation. Vortices pinned to nuclei in crust Catastrophic unpinning => pulsar glitch A. Passamonti & N. Andersson, MNRAS., 413, 47 (2011)

15 Superconducting protons in magnetic field Even though superconductors expel magnetic flux, for magnetic field below critical value, flux diffusion times in neutron stars are >> age of universe. Proton superconductivity forms with field present. Proton fluid threaded by triangular (Abrikosov) lattice of vortices parallel to magnetic field (for Type II superconductor) Quantized magnetic flux per vortex: = φ 0 = 2 X 10-7 G. Vortex core ~ 10 fm, n vort = B/φ 0 => spacing ~ 5 x cm (B /10 12 G) -1/2

16 Condensation in quark matter: BCS pairing and color superconductivity

17 Compress matter to form new states Atoms Plasma Nuclei Nuclear matter ρ~2.5x10 14 gm/cm 3 = ρ nm = 0.17 baryons/fm 3 (1 fm = cm) Hadrons (n,p,...) Quark matter

18 Quark degrees of freedom Quarks = fractionally charged spin-1/2 fermions, baryon no. = 1/3, with internal SU(3) color degree of freedom. Flavor ( Mass(MeV Charge/ e u 2/3 ( ) 5 d -1/3 ( ) 10 s -1/3 (54-92) 150 c b t 2/3-1/3 2/ Hadrons are composed of quarks: proton = u + u + d neutron = _ u + d + d π + = u + d, etc. Form of baryons in the early universe at t < 1µ sec (T > 100 MeV). Basic degrees of freedom in deep interiors of neutron stars.

19 Quark-gluon plasma state Degrees of freedom are deconfined quarks and gluons Many more degrees of freedom than hadronic matter (color, spin, particle-antiparticle, & flavor); much larger entropy at given temperature. <= Large latent heat (or sharp rise at least) At low temperatures form Fermi seas of degenerate u,d, and s quarks: (e.g., in neutron stars?)

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21 2SC Neutron stars? CFL

22 Color pairing in quark matter Review: Alford, Rajagopal, Schaefer & Schmitt, RMP 80, 1455 (2008) 0Temperature 150 MeV Ultrarelativistic heavy-ion collisions Hadronic matter Nuclear liquid-gas Quark-gluon plasma 1 GeV Neutron stars Baryon chemical potential? 2SC CFL Superfluidity condensate of paired quarks => superfluid baryon density (n s ) Color Meissner effects transverse color fields screened on spatial scale ~ London penetration depth ~ (m/g 2 n s ) 1/2 Two interesting phases: 2SC (u,d) Color-flavor locked (CFL) (m u =m d =m s )

23 BCS Pairing of Quarks Flavor singlet 1 p 2 udi dui isoscalar Spin singlet 1 p 2 "#i #"i _ Color 3 1 p 2 RGi GRi Two flavor (u,d) order parameter Pair Red and Green quarks. Breaks SU(3) color hu R" d G# i = hd G" u R# i = hu R# d G" i

24 Gluon exchange attractive in color singlet states: fundamental difference from Coulomb 1 p 2 ( RGi GRi) α = 1,, 8 RG! RG 3 RR 3 GG + 8 RR 8 GG = 2/3 RG! GR ( 1 RG) 2 +( 2 RG) 2 =2 RGi GRi! RGi GRi 2 2/3 = 8/3 attraction!

25 Color-flavor locked state (CFL) m u = m d = m s Alford, Rajagopal, & Wilczek, PL B422 (1998) 247 hq ai q bj i = ijk abk d hu R d G i = => hd G s B i = hs B u R i = d hu G d R i = hd R s B i = hs B u R i = d hu B d G i =... d All 9 (3 flavor x 3 color) quarks are paired. Compare with 2SC (isoscalar) with only 4 quarks paired (u R, u G, d R, d G ), with 5 quarks unpaired. => E CFL < E 2SC (T = 0 )

26 Chiral symmetry breaking Pair to unbroken parity:: hu Rr d Gr i = hu R`d G`i, etc. => both right helicity and left helicity locked to color => right and left locked! Broken chiral symmetry, as in nuclear matter CFL symmetry group G qcd = SU(3) c SU(3) right SU(3) left U(1) baryon G hadrons = SU(3) chiral U(1) b BCS pairing: U(1) b! Z 2 chiral symmetry breaking: SU(3) r SU(3)`! SU(3) chiral G CFL = SU(3) c+r+` Z 2 Continuity from hadronic (u,d,s) matter with hadronic pairing to CFL state of (u,d,s)

27 Fukushima & Hatsuda, Rep. Prog. Phys. 74 (2011)

28 Interplay between BCS pairing and chiral condensate Hadronic phase breaks chiral symmetry, producing chiral (particleantiparticle) bosonic condensate: qq Analogous to polarization in two component Fermi gases Color superconducting phase has particle-particle pairings d qq Spontaneous breaking of the axial U(1) A symmetry of QCD (axial anomaly) leads to attractive ( t Hooft 6-quark interaction) between the chiral condensate and pairing fields. Each encourages the other! Φ Φ d R Φ Φ ~ - Φ 3 d * ~ - d * L L d R Φ

29 New critical point in phase diagram: induced by chiral condensate diquark pairing coupling via axial anomaly Hatsuda, Tachibana, Yamamoto & GB, PRL 97, (2006) Yamamoto, Hatsuda, Tachibana & GB, PRD76, (2007) GB, Hatsuda, Tachibana, & Yamamoto. J. Phys. G: Nucl. Part. 35 (2008) Abuki, GB, Hatsuda, & Yamamoto,Phys. Rev. D81, (2010) Normal QGP Hadronic q q 0 (as m s increases) Color SC q q 0 qq 0

30 BEC-BCS crossover in QCD phase diagram J. Phys.G: Nucl. Part. Phys. 35 (2008) Normal Hadronic (as m s increases) Color SC Hadrons BCS-BEC crossover BCS paired quark matter Small quark pairs are diquarks

31 Phase diagram of cold fermions vs. interaction strength Unitary regime (Feshbach resonance) -- crossover. No phase transition through crossover

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33 Phase diagram in Nambu Jona-Lasinio model H. Abuki, GB, T. Hatsuda, & N. Yamamoto, PR D81, (2010) P. Powell & GB, PR D 85, (2012) P. Powell & GB, arxiv:

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35 Learning about dense matter from neutron star observations

36 Mass vs. radius determination of neutron stars in burst sources Ozel et al., ApJ U in globular cluster NGC 6624, D = kpc 4U in NGC 6624 EXO in globular cluster Terzan 5, D = 6.3±0.6 kpc (HST) KS Galactic bulge source

37 Comparison of PNJL theoretical equations of state (pts) with phenomenological equation of state to fit observed M and R of neutron stars Single hatching: Özel, GB, Guver, PRD82 (2010) Cross hatching: Steiner, Lattimer & Brown 2010, 2011 Varying level of stiffness: vector repulsion among quarks g_v = 0 (diamonds), G (squares), 1.5 G (triangles) [G = basic Nambu Jona-Lasinio quark coupling].

38 Cold atom simulations of QCD? 1) Analog models, e.g., three hyperfine states ó quarks of 3 colors 2) Can simulate external magnetic fields. Major challenge is to induce electromagnetic-like interactions between atoms! (Dipolar atoms) 3) Cold atoms as analog computer. ex. Hubbard model. Can one eventually do simulations of lattice gauge theory? Will one be able eventually to address fields on each link of lattice, or at least more locally? Eventual goal: SU(3) quantum chromodynamics with quarks.

39 THE END