a model-independent view

Transcription

1 The state of cold quark matter: a model-independent view Renxin Xu ( 徐仁新 ) School of Physics, Peking University Compact stars in the QCD phase diagram II (CSQCD II), PKU May 24th, 2009.

2 What s the nature of pulsars? The physics of (cold) matter at supra-nuclear density: A big challenge Core-collapse supernovae?

3 Xu 2009, JPG

4 Summary Introduction: the H 2 O phases Cold QM: CS vs. clustering? To understand obs. by QSs Conclusions

5 A comparison between The QCD Phase Diagram The H2O Phase Diagram

6 Let s begin with an exercise You are given a large number of particles of e, p, 16 O (attraction & repulsion) at temperature of T ~ 300 K and density of ρ ~ 1 g/cm 3, with a proportion of n e :n p :n O = 10:2:1. Question: Can you predict the state of matter by calculation from first principles?

7 The number densities are: 23 3 n e = / cm, n n /5, p e = n = n /10, O e and the distance between each kind of particles are: l n 1/3 8 e = e = 1 10 cm, 8 l p = 2 10 cm, 8 l O = 3 10 cm. The de Broglie wavelengths are then: h λe = 2mkT e 7 8 =8 10 cm, λ p 2 10 cm, 9 = λ O = 4 10 cm. Therefore, quantum Fermi-Dirac statistics applies to electron and proton, while classical Maxwell-Boltzmann statistics to oxygen-16.

8 First, for simplicity, let s turn off the electromagnetic interaction there, and the degenerate electron and proton chemical potential at zero temperature are 2 h 2 2/3 2/3 5 μe = (3 π ) ne = 18eV=2 10 K >> T, 2me 2 h 2 2/3 2/3 μp = (3 π ) np = 0.003eV=38K < T. 2m p Conclusions if turning off interaction: Electron: strong degenerate Fermi gas, T ~ 0. Proton: weakly degenerated, classical gas Oxygen-16: classical gas (M-B statistics)

9 However, electro-magnetic interaction plays an important role there e+p system with length scale l ep : 2 2 p h kinematic energy ~ ~ 2 is bound by interaction 2 ~ e 2m 2mlep l ep lep ~ h = hc, E 2 2 ep ~ e = α hc em ~ αemmc. me α em mc lep lep For EM interaction, α em = 1/137 (hc = 200 MeV fm) l o ~ 0.55A~ a o = 0.52A, E ~ 27eV ~ R = 13.6eV. ep B ep H Conclusions if interaction exists: H-atom O-atom Particles are clustered! But, what about the next experience!

10 The water phase diagram by experiments! H 2 O radius: r ~ 2Å 18u/r 3 ~ 3.7 g/cm 3!

11 Center for Advanced Study in THU

12 What about the QCD (quark) Phase Diagram?

13 Summary Introduction: the H 2 O phases Cold QM: CS vs. clustering? To understand obs. by QSs Conclusions

14 Quark matter is predicted in QCD Expected in QCD To be a direct consequence of asympt. freedom T (Hadron gas) (QGP) Fermi liquid/gas? n B A very simple QCD phase diagram

15 What s ρ of realistic QM? PSR = NS Quark Star Weber (2005) 1.4M sun ρ = 3 4 π (10km) / g / cm 2.4 ρ0.

16 ρ is too low to de-confine? F. Wilczek Nature 445 (2007) Critical density n c to break nucleon? 3 3 nc = 1.5r 3 1 4π rn Note: r 1 = r n /(1fm) n c = 2ρ 0 if r 1 = 0.9 Would nucleon decrease radius at supra-nuclear density?

17 Quark matter at realistic ρ ~ 3ρ 0 Quark number density is n q ~ 1.4 fm -3, but n n n u = d ~ s 0.48fm = /cm. and the distances between quarks are then l 1/3 q = n q = 0.9fm, l = l ~ l n = 1.3fm. 1/3 u d s u The de Broglie wavelength is: h λ = =5 10 m T fm >> l! 3 1/2 1/2 q q 2mkT q where m 300 = m q /(300MeV), T 6 = T/(10 6 K). Quantum F-D statistics applies!

18 Turning off the interaction there, we have the degenerate quark chemical potential at zero temperature: μ μ ~ μ h = (3 π ) = 380MeV>> T! 2 NR NR NR 2 2/3 2/3 u d s nu 2mq ER 2 1/3 1/3 μu = h π u = ( c(3 ) n 480MeV>> T) Conclusions if turning off interaction: Quarks: Strongly degenerate Fermi gas! However, interactions between quarks near the Fermi surface may play an important role

19 A conjectured diagram with Colorsuperc. BCS-like superconductor Alford et al. RMP 80 (2008)1455

20 What if strong color-interaction exists? Strong interaction quark cluster? Diquark: color SU(3), Coulomb-like 3 3 = 6(repulsion) + 3 * (attraction) Let s estimate the length scale of and interaction strength in a quark cluster: 1 hc l ~ ~ 1fm / α, E ~300α MeV, 2 q 2 s q s αs mc if quarks are dressed, with mass ~ 300MeV. What about α s?

21 Color coupling in perturbation theory Xu 2009 at realistic ρ : α s ~ 1? α s > 1? α s >> 1? What if cold QM at realistic ρ ~ 3ρ 0? E ~ 300α MeV> μ ~400MeV if α s >~ 1 2 q s q

22 What if non-perturbative QCD? Non-perturbative QCD is related to one of the seven Millennium Prize Problems P versus NP The Hodge conjecture The Poincaré conjecture (solved) The Riemann hypothesis Yang-Mills existence and mass gap Navier-Stokes existence and smoothness Approaches to the non-perturbative effects of QCD: Lattice QCD QCD sum rules Dyson Schwinger equations (DSE) The Birch and Swinnerton-Dyer conjecture

23 The QCD running coupling from DSE Quark clustering is very likely in the approach of Dyson Schwinger equations at least! Fischer, JPG 32 (2006) R253 Fischer & Alkofer PLB 536 (2002) 177 where a 1 = 5.292GeV -2a2, a 2 = 2.324; b 1 = 0.034GeV -2b2, b 2 = 3.169; x = p 2, and α freezes at α (0) =

24 What kind of quark cluster? Q α, 2Q α, 18 quarks could be in a ground state of cluster 18 = 2( spin) 3( flavor) 3( coo l r) The distance between quark-alpha at 3ρ 0 : l cluster = 18 1/3 ( ) 2.3fm, while the cluster length l q ~ 1fm/α s < l cluster! The clusters could form quantum gas if the interaction between them is negligible, since de Broglie λ of free clusters may be > l cluster! To localize clusters, we need interaction of 2 h Ecluster ~ ~1MeV. 2 Very reliable! 2 m (2fm) cluster

25 Experiment-determined QCD phase diagram But where can we do experiments of cold QM? Observations of pulsar-like stars! We need solid quark stars to understand various observations!

26 Summary Introduction: the H 2 O phases Cold QM: CS vs. clustering? To understand obs. by QSs Conclusions

27 What can q-clustering do for us? A stiffer EoS higher maximum mass M(4U ) ~ 2M sun? To render the quark matter solidified pulsar glitch, precession, Planckian spectrum Extra energy released during star-quake SGR-giant flare ~ erg, AXP burst/glitch Ferro-magnetism phase transition? What s the origin of pulsar strong B-field?

28 Solid: classical or quantum? cluster lattice V potential quark cluster strong interaction ~2 fm weak interaction Classical solid: barrier penetration negligible Quantum solid: penetration significant x

29 Cold QM: CS vs. clustering? Speculate phenomenologically: : a solid state of QM? A likely reason If Xu (2003) Solid quark stars Based on possible astrophysical features detected. then Q α? Quarks may tend to go together sqgp? Quark-clusters in lattice (low T)

30 A solid state of quark matter? Xu 2005, updated? Clustering BEC BCS

31 Neutron stars vs. Quark stars

32 Summary Introduction: the H 2 O phases Cold QM: CS vs. clustering? To understand obs. by QSs Conclusions

33 Conclusions Realistic cold quark matter is suggested in a solid state where quark clustering occurs. Solid QS is necessary to understand obs. A A combined study should be very essential to know the real QCD phases: Lattice QCD QCD-based effective models (e.g. DSE, NJL) Phenomenological models (e.g. in astrophysics) Solid state QM: physical QCD-implications?