006 8
(g cm -3 ) 1 ~10-8 cm ~10-1 cm 10 14 (n) 10 15 ~10-13 cm (p) (q) RGB uds...
(contd.) 0 ~ fm np nn,pp
(contd.) 1 GeV 100 GeV 1 TeV RI FAIR GSI RHIC BNL LHC CERN
(contd.) T < 9 ~ 10 K
(contd.) (k B T «E F ) (E «U F int ) (mc» E F ) vs. (mc «E F ) 3 He ~10 11-15 g cm -3 > ~ 10 15 g cm -3 < ~ 10 4 cm -3 ~0.1 g cm -3 < ~10 MeV < ~100 MeV < ~ 100 K < ~1 K relativity mild extreme none none K
(condt.) ( ) 150 MeV 0 RHIC SPS 1 GeV GSI??? SC CFL K?
Ref. 57 (00) 883. n s ~ (µ / g n s ) 1/ SC
/µ BEC ~ s m µ BCS (CFL,SC,...) m s /µ (µ e /µ )
(contd.) : 4π g = (33 Nf)ln( µ / Λ Ref. Barrois, NPB 19 (1977) 390. Bailin & Love, Phys. Rep. 107 (1984) 35. µ =10 15 GeV (GUT scale) g~1/ ~g µ «~µ QCD ) «1 Quark Color a Color b (a) Gluon (color α) RG GR, GB BG, BR RB ee Color b Color a (b) BCS
(condt.) Ref. Son, PRD 59 (1999) 094019. ultrarelativistic plasma v F /c RPA For p 0 «p «µ, D αβ µν ( p) p δ αβ P iπ m T µν D p 0 4p δ p αβ P L µν + m D, m D N f g 18π µ quarks (T=0) BCS 1 1 ln = 3π ln = Λ UN g µ g UV F 5ln g +L D
(condt.) Ref. Pisarski & Rischke, PRL 83 (1999) 37. U A (1) J P =0 - (<q T Cq>) J P =0 + (<q Τ Cγ 5 q>)
(contd.) µ ~1-3 GeV T c ~ 10-100 MeV (» T Neutron Star ) u,d SC S=L=I=0, Rapp et al., PRL 83(1998)53. Quark Color a Left-handed Gluon cloud Color b (a) Right-handed Color b Left-handed Color a (b) Right-handed BCS Alford et al., PLB 4(1998)47. UV!
(contd.) Two optimal states determined from energy minimization 1. -flavor color superconducting (SC) state Gapped quarks: two colors and two flavors ( anisotropic ) Gluo-electromagnetic properties: Long wavelength gluons SC condensate at T=0 3 types: propagating 5 types: screened. Color-flavor locked (CFL) state. Gapped quarks: three colors and three flavors ( isotropic ) Gluo-electromagnetic properties: Long wavelength gluons CFL condensate at T=0 8 types: screened Cf. The CFL state is more favorable in the weak coupling limit.
(condt.) Ref. Iwasaki & Iwado, PLB 350 (1995) 163. Iida & Baym, PRD 63 (001) 074018. where N ab N N = RR ab = N GG = N BB = 0 for a b i= u, d, s V d 3 x ψ, ai ( x) γ 0 ψ bi ( x) SC Τ=0 1 0 k F k
(contd.) m uds =0 Small s quark mass sets in. m s 0 u,d,s k F u = k F d = k F s δµ = q µ i with i e δk 3ms µ e =, q 4µ u s 3 = m s F =, 3 µ q d, s = 1 3 d u s k F d > k F u > k F s Electric neutrality and weak equilibrium µ d µ s µ e µ u
(contd.) k F i k F j k Ref. Iida & Baym, PRD 63 (001) 074018; Iida et al. PRL 93 (004) 13001 m uds =0 T Normal: ud ds us CFL: ud ds us m s 0 T Normal: ud ds us SC: ud ds us dsc: ud ds us mcfl: ud ds us k F u = k F d = k F s k F d > k F u > k F s
(contd.) m s =150 MeV ud us ds Ref. Fukushima, hep-ph/051099.
(contd.) T=0 k k k vs. k F i j k j F vs. k F i k j k j F F vs. k F i k j k F j F m s»µ BCS Ref. Sarma, Phys. Chem. Solid 4 (1963) 109. µ δµ = BCS Ref. Müther & Sedrakian, PRD 67 (003) 08504. d µ u µ e δµ = E p) = µ d + µ p u ( + δµ Sarma 0. (µ/3) SC 0.3(µ/3)
(contd.) U(1), SU(3) Chromomagnetic instability LOFF Sarma instability Density-wave instability? BCS-normal
(contd.) m s =150 MeV us J α = ( m α M ) A α, ( m α M ) < 0 Ref. Fukushima, hep-ph/051099.
(contd.) m s»µ us Ref. Kiriyama, hep-ph/0608109. J α α M α M = ( m ) A, ( m ) < 0, α = α 4,5,6,7
(contd.) m s»µ, T=0 Debye screening length d quarks u quarks SC Normal electrons _ N + + SC + + Electrons nearly uniform throughout the system k k F d -ga α=4 k F u Ref. Iida & Fukushima,
(contd.) energy landscape BCS LOFF BCS-normal... Sarma Forbes et al., Kitazawa et al. LOFF : gluonic phases Gorbar et al. meson supercurrent Schäfer et al. baryon supercurrent Hong, Huang, Kryjevski LOFF Rajagopal et al., Giannakis et al., Casalbuoni et al. BEC Abuki et al., Nawa et al.
(e, ions) (n,p,e,µ,...) (u,d,s,e,µ) γ,ν
( ) (R) (M) UV ~1- R, ~0.4-1M e GM/Rc ~ 0.0001 <~10 8 g cm -3 UV ~10 km, ~1.4M n, (p, e, µ, Σ, Λ,...) GM/Rc ~ 0.4 ~10 15 g cm -3 ν <~10 km, <~M q, (e) GM/Rc <~ 0.6 ~10 15 g cm -3 ν R 70 km, M 10 33 g GM/Rc ~ 0.000004 ~100 g cm -3 B P radiative, ions convective <~10 4 K <~10 8 G > 1 hour ~0.1-8 M conductive, (ν) ~ 1 s e, µ, n radiative <~10 6 K ~10 8-10 15 G ~10-3 -10 3 s ~8-40 M ν, conductive ~subms e, q ( radiative) <~10 6 K??? ν, conductive pp chain e, ions convective ~6000 K <~000 G ~ 30 days radiative, (ν)
(contd.) CFL SU(3) c+f U(1) B SC U(1) em Cf. 10 19 G Ref. Iida & Baym, PRD 66 (00) 014015. Iida, PRD 71 (005) 054011.
(contd.) I NM SC NM SC NM SC NM B=HC B<HC (partial Meissner screening) II Lattice of magnetic vortices SC SC SC SC B~HC1 B<HC (partial Meissner screening)
(contd.) LOFF CFL LOFF Alford et al. LOFF Ruggieri et al.
energy landscape BCS LOFF BCS-normal...