G 2 QCD Neutron Star. Ouraman Hajizadeh in collaboration with Axel Maas. November 30, 2016

Transcription

1 G 2 QCD Neutron Star Ouraman Hajizadeh in collaboration with Axel Maas November 30, 2016

2 Motivation Why Neutron Stars? Neutron Stars: Laboratory of Strong Interaction Dense Objects: Study of strong interaction at high densities Different phases: Explanation of phase transition based on the fundamental theory Macroscopic objects: Show large scale effects of a non-abelian gauge theory. Ouraman Hajizadeh G 2 QCD Neutron Star November 30, / 23

3 Motivation Why G 2? SU(3)QCD Theory of Strong interaction Lattice gauge theory: A non-perturbative ab-initio method for SU(3) at finite density : sign problem no positive probability Alternative approach: Study of a gauge theory without sign problem sharing similarities with SU(3) G 2 : a QCD like theory without sign problem, with neutrons Ouraman Hajizadeh G 2 QCD Neutron Star November 30, / 23

4 Motivation Constructing a neutron star in G 2 QCD is possible Equation of state of G 2 QCD neutron star from Lattice simulation Mass-radius of G 2 neutron star from e.o.s. Qualitative insight to the case of a real neutron star, based on similarities Signatures of possible phase transitions inside the star on the Mass-radius curve Role of theory parameter in large scales: effect of the current mass of quark on the mass of neutron star Theoretical information about large scale effects of a non-abelian interaction, mainly driven by differences. Role of the properties of gauge group: How and to which extent the structure of neutron star is determined by the underlying gauge theory, if at all? Are there universal properties of the structure under the change of the gauge group?... Spectrum of the theory and chemical composition of the star Ouraman Hajizadeh G 2 QCD Neutron Star November 30, / 23

5 G 2 -QCD G 2 Group Structure Facts G 2 has 14 generators 14 Gluon Fundamental representation = Quark number = 7 All the representations are real : No sign problem Diquarks are color singlets: 7 7 = 1... qq: Diquark qqq: Neutron like = 1... qggg: Hybrid = 1... Rank 2 : like SU(3) Ouraman Hajizadeh G 2 QCD Neutron Star November 30, / 23

6 G 2 -QCD Why G 2? Shares many feauture with SU(3) QCD Chiral and deconfinement transition coincide. (J. Danzer, C. Gattringer, A. Maas JHEP 2009; G. Cossu, M. D Elia, A. Di Giacomo, B. Lucini, C. Pica JHEP 2007, E.M. Ilgenfritz, A. Maas 2012) Phase transition [Gev] P (a.u.), <ΨΨ> (a.u.), χ 1/ Polyakov loop Chiral condensate Topological susceptibility T/T c A decisive result for further study. Ouraman Hajizadeh G 2 QCD Neutron Star November 30, / 23

7 G 2 -QCD Running Coupling in 3 dimensions (A. Maas, S. Olejnik, JHEP 2008) Running coupling ] 1 )/p [GeV 2 α(p p [GeV] SU(3) (black) and G 2 (red) YM agree qualitatively for low and quantitatively for high momenta. Ouraman Hajizadeh G 2 QCD Neutron Star November 30, / 23

8 G 2 -QCD Spectrum of G 2 QCD Mass of proton is set equal to the QCD proton. Chiral symmetry breaking manifests itself in the spectrum. (B. H. Wellegehausen et. al., Phys. Rev. D 89) N N Δ Δ d m d d N d η N d d d η d Δ Δ 938 m in MeV Ouraman Hajizadeh G 2 QCD Neutron Star November 30, / 23

9 Structure of neutron star Matter and gravity Mass-radius relation Heavy, compact stars: general relativity is applied Neutron star nuclear matter ideal fluid Einstein euations quantify the relation between matter and space-time: G(g µν ) T µν Metric tensor: g µν represents gravity Energy-momentum tensor: T µν represents matter For a static star: T µ µ = p(r) pressure µ = 1, 2, 3 T 0 0 = ɛ(r) energy density Ouraman Hajizadeh G 2 QCD Neutron Star November 30, / 23

10 Structure of neutron star Oppenheimer-Volkoff Equation Solving Einstein equations for static, spherical symmetric metric, which approximate metric of the neutron star, gives Oppenheimer-Volkoff (O-V) equation: dp(r) dr = [p(r) + ɛ(r)] [M(r) + 4πr 3 p(r)] r [r 2M(r)] (M(r) is the mass-energy enclosed in radius r: M(r) = 4π r 0 ɛ(r ) r 2 dr ) O-V equation together with the equation of state ɛ(p) give an ordinary differential equation for ɛ(r) with initial conditions ɛ(0) = ɛ 0, M(0) = 0 Result: mass-radius relation of the star M(r) corresponding to each central energy. Ouraman Hajizadeh G 2 QCD Neutron Star November 30, / 23

11 Structure of neutron star Limit on the mass O-V equation leads to a limit on the mass, that a star can get for each equation of state. Repulsive nuclear interaction increases the mass limit The value of mass limit is determined having the equation of state The upper bound on the limit, is set by stability and causality arguments, around 3.14M We find the limit on the mass of a G 2 QCD neutron star by obtaining M(r) for different values of central chemical potential relevant for neutron star. Ouraman Hajizadeh G 2 QCD Neutron Star November 30, / 23

12 Mass-Radius relation of G 2 neutron star Mass-Radius relation: M(r) To find M(r) for G 2 QCD neutron star we need equation of state E.o.s given by n(µ) and p = µn(µ) ɛ And cold matter approximation for energy density: ɛ = mn(µ) dp At zero temperature: dµ = n We write Oppenheimer-Volkoff equation in terms of µ dµ(r) dr = [µ(r)] [M(r) + 4πr 3 p(r)] r [r 2M(r)] Next step is to solve Oppenheimer-Volkoff equation for this e.o.s after modifying the result of interpolation of lattice data for low density regime according to normal matter condition: n(µ) = α(µ 2 m 2 ) 3 2, α is set by the continuity condition of e.o.s Ouraman Hajizadeh G 2 QCD Neutron Star November 30, / 23

13 Mass-Radius relation of G 2 neutron star G 2 QCD versus free Fermi gas E.o.S: n fm µ fm baryon number density in terms of nucleon chemical potential: Orange curve: Free Fermi gas, Blue curve: G 2 QCD Ouraman Hajizadeh G 2 QCD Neutron Star November 30, / 23

14 Mass-Radius relation of G 2 neutron star Mass-radius curves M 1.2 M R km Blue: G 2 QCD, Orange: free Fermi gas (O. Hajizadeh, A. Maas, arxiv: ) Ouraman Hajizadeh G 2 QCD Neutron Star November 30, / 23

15 Mass-Radius relation of G 2 neutron star Observations: Comparing to free Fermi gas G 2 QCD neutron stars show Sudden, steeper rise in mass Sharper maximum Dense population of stars close to the maximum Smaller mass for lower region of chemical potential Negative slop in both cases, as a generic feauture. M M 0.2 R km Ouraman Hajizadeh G 2 QCD Neutron Star November 30, / 23

16 Mass-Radius relation of G 2 neutron star Explanation Sharper rise in G 2 case similar value for masses at low central chemical potential in both cases sudden rise in G(2) M-R curve after specific value of µ c M 1.2 M µ c fm Mass vs central chemical potential for neutron stars of type G 2 QCD: blue and free Fermi gas: orange. green line indicates the end of the region of dilute Fermi gas approximation. Ouraman Hajizadeh G 2 QCD Neutron Star November 30, / 23

17 Mass-Radius relation of G2 neutron star Interplay of O-V equation and e.o.s µ(r ) inside the stars is an informative quantity µ fm µfm r G2 QCD km r km Free Fermi gas (O. Hajizadeh, A. Maas, arxiv: ) Ouraman Hajizadeh G2 QCD Neutron Star November 30, / 23

18 Mass-Radius relation of G 2 neutron star µ(r) curves diverge further after the crossing point in free case than in the G 2 QCD diagram. The softer the equation of state, the more rapid drop in µ(r) for smaller radii(where accumulated mass is still negligible). dµ n(µ c )µ c dµ(r) dr = [µ(r)] [M(r) + 4πr 3 p(r)] r [r 2M(r)] nfm µfm Orange: Free neutron gas, blue: G 2 QCD nuclear matter Ouraman Hajizadeh G 2 QCD Neutron Star November 30, / 23

19 Mass-Radius relation of G 2 neutron star Systematic variation of the equation of state We can get slightly higher mass by reducing the region of the free Fermi gas approximation. M M R 16 km Ouraman Hajizadeh G 2 QCD Neutron Star November 30, / 23

20 Mass-Radius relation of G 2 neutron star The region of low chemical potential, determine the direction of the curves M M R km Mass-radius curves for different value of transition to dilute Fermi gas region, µ t = 5.24fm 1 : blue, µ t = 4.89fm 1 : orange n fm 3 n fm µ fm µ fm n(µ) for µ t = 4.89fm 1 orange left, µ t = 5.24fm 1 orange right, compared to the free case:blue Ouraman Hajizadeh G 2 QCD Neutron Star November 30, / 23

21 Mass-Radius relation of G 2 neutron star How does n(µ) affect the direction of M-R? generic direction is given by the low density behavior similar to the free case gravity is the dominant force in low density for the case of dilute fermi gas deviation from generic behavior ( dm dr < 0) occurs deviating from free gas, leading to a more important role from nuclear attracting force the origin of attraction is nonzero baryon density for µ < m n can be interpreted as the effect of Goldstones which are non-physical degrees of freedom here. Ouraman Hajizadeh G 2 QCD Neutron Star November 30, / 23

22 Mass-Radius relation of G 2 neutron star Systematic variation of the equation of state Variation of theory parameter: M-R curve for different quark s current mass gives qualitatively same result light ensemble: m π = 1.254fm, heavy ensemble: m π = 1.653fm. Ouraman Hajizadeh G 2 QCD Neutron Star November 30, / 23

23 Conclusion and Outlook Conclusion Equation of state derived from G 2 QCD simulation on the lattice gives the qualitative expected behavior for M-R curves of neutron stars, and maximum value within the allowed region. Different phases in the e.o.s are indicated by the mass-radius curve behavior for stars with different central chemical potential. The variation of the parameters of the theory at a preliminary level doesn t seem to affect the result significantly. Ouraman Hajizadeh G 2 QCD Neutron Star November 30, / 23

24 Conclusion and Outlook Outlook Inclusion of Goldstones: Stable composite star? Study of the bulk properties to estimate viability of ideal fluid approximation and to see if there is color superconductivity in the core of the neutron star Improving the lattice data: Precision of e.o.s Estimation of lattice artifacts Further spectroscopy to see if hybrids are heavier than G 2 nucleon, so that neutronic matter exists like neutron stars. Ouraman Hajizadeh G 2 QCD Neutron Star November 30, / 23