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Nuclear Physics from the sky Vikram Soni CTP

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Strongly Interacting matter @high density (> than saturation density) Extra Terrestrial From the Sky No experiments No Lattice Gauge Theory From the Sky - Stars The great Neutron Star(2010) ~ 2 Solar masses The Binary star :PSR J 1614-2230

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* The strong interaction Ground State : New Physics Neutron Star is the only laboratory at a High Density ( No lattice either) i) The discovery (2010) of a new 2 solar mass binary neutron star PSR J 1614-2230 : Mass 1.97 M_solar ii) Neutron stars with a non relativistic n, p, e exterior and ( soft ) quark matter interior: M_max ~1.6 solar mass Lattimer, J. M. and Prakash,M., 2001, ApJ, 550, 426 Soni, and Bhattacharya,, 2006, Phys. Lett. B, 643, 158 ii) However, we have purely nuclear stars made up of entirely from n, p, e which can have : M_max > 2 solar mass ( eg Pandharipande et al) New Implications for high density strong interactions

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Nuclear EOS APR Akmal, Pandharipande, Ravehall ( PhyRevC,58, 1804 (1998) Quark Matter EOS Soni, and Bhattacharya,, 2006, Phys. Lett. B, 643, 158

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THE NUCLEAR EQUATION OF STATE Going Back to the Akmal, Pandharipande, Ravenhall nuclear phase in in fig 11 of APR ( PRC,58, 1804 (1998)) we find that for the APR [A18 + dv +UIX] the central density of a star of 1.8 solar mass is ( n_B ~0.62 /fm^3), very close to the initial density at which the phase transition begins. The reason we are taking a static star mass of 1.8 solar mass from APR ( PRC,58, 1804 (1998)) is that for PSR -1614,the star is rotating fast at a period of 3 millisec and we expect a ~ 15% diminution of the central density from the rotation( Haensel et al….). the central density of a fast rotating 1.97 solar mass star ~ the central density of a static 1.8 solar mass star.

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. Frpm the figure below,, MAXWELL CONSTRUCTION the common tangent in the two phases starts at, 1/n_B ~ 1.75 fm^3 ( n_B ~0,57/fm^3 ) in the nuclear (APR [A18 + dv +UIX]) phase and ends up at1/n_B ~ 1.25 fm^3 (n_B ~ 0.8/ fm^3) in the quark matter phase (tree level sigma mass ~850 Mev) If the central density of the star (0.62/fm^3) ~ < density at which the phase transition begins ( n_B ~0,57/fm^3 we can conclude the star is NUCLEAR - Borderline

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Effective ( Intermediate) Theory Chiral sigma model with quarks and pions and sigma and gluons It plausibly describes quark matter and the nucleon as a soliton with quark bound states in Mean Field Theory One place to find the quark matter phase is in figure 2 of (Soni, V. and Bhattacharya, D., 2006, Phys. Lett. B, 643, 158)). This is based on an effective chiral symmetric theory that is QCD coupled to a chiral sigma model. The theory thus preserves the symmetries of QCD. In this effective theory chiral symmetry is spontaneously broken and the degrees of freedom are constituent quarks which couple to colour singlet, sigma and pion fields as well as gluons.

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Quark matter and the nucleon

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Quark Matter ( already Shown ) Such an effective theory has a range of validity up to centre of mass energies ( or quark chemical potentials) of ~ 800 Mev. For details we refer the reader to (Soni, V. and Bhattacharya, D., 2006, Phys. Lett. B, 643, 158)) This is the simplest effective chiral symmetric theory for the strong interactions at intermediate scale and we use this consistently to describe, both, the composite nucleon of quark boundstates and quark matter. >> Nuclear Equation of State?

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Chiral Quark matter Equation of state

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Beyond the Maxwell construction The Maxwell construction assumes point particle quark degrees of freedom and also point particle nucleon degtees of freedom (APR) It does not take the structure of the nucleon into account -needed at nucleon overlap/higher than nuclear density We need to move to higher resolution The ‘nucleon’ The ‘ nucleon ’ in such a theory is a colour singlet quark soliton with three valence quark bound states ( Ripka, Kahana, Soni)Nucl. Physics A 415, 351 (1984). The quark meson couplings are set by matching mass of the nucleon to its experimental value and the meson self coupling which sets the tree level sigma particle mass is set from pi-pi scattering to be of order 800 Mev.

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Bound Quarks in A Nucleon Figure uses Dimensionless Units : X = R. g f π The effective radius of the squeezed nucleon at which the bound state quarks are liberated to the continuum. this translates to nucleon density of n_B = 1/(6 R^3) ~ 0.77 fm^{-3} \ Thus the quark bound states in nucleon persist until a much higher density ~ 0.8/fm^3$ than the density at which the nuclear – quark matter transition begins (0.57/fm^3) or the maximum central density of the APR star,(0.62/fm^3). In other words, nucleons can survive well above the density at which the Maxwell phase transition begins and appreciably above the central density of the APR 2-solar-mass star.

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The binding energy of the quark in the nucleon,. E/(g f_pi) = ({3.12/X} N - 0.94. N) + 24 {X/g^2} Minimizing this with respect to, X E_{min}/(g f_{\pi}) = \sqrt[3.12 N.24 /g^2 ] - 0.94N For the nucleon we must set, $N = 3$.We can now evaluate the coupling, g, by setting the nucleon mass to $ ~960 MeV $. This yields a value for, $ g \sim 6.9$. E_{min/}(N g f_{\pi}) = ~ 0.5 for N = 3\\ ~ 0.83 for N =2\\ ~ 1.27 for N =1

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Binding energy of a quark in the Nucleon regardless of the value of $f_\pi $ we have bound states for N =2 and 3. $ g ~\sim 6.9$, the energy required to liberate a quark from such a nucleon. The energy of a two quark bound state and a free quark is $1707 $MeV in comparision to the energy of a 3 quark bound state nucleon which is, $~962 $ MeV. The difference gives the binding energy of the quark in the nucleon, $ ~ 745 $ MeV.

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.T 3)Another feature of the skyrme/ soliton model is the the N-N repulsion This is an indication that nucleon - nucleon potential becomes strongly repulsive. It thus follows that the phase transition from nuclear to quark matter will encounter a potential barrier before the quarks can go free. This effect cannot be seen by the coarse Maxwell construction which does not track their transition. This will modify the simple minded Maxwell construction which assumes only the energy and pressure that exist independently of nucleon structure and binding in the 2 phases. Here is where the internal structure of the nucleon will delay the transition.

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Nuclear Stars All in all this produces a very plausible scenario of how the ~ 2 solar mass star can be achieved in a purely nuclear phase. Since this high mass is close to the maximum allowed mass of neutron stars it means that stars with quark interiors may not exist at all.

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A new idea from this - Phase Diagram of QCD At chiral restoration, T_\Xi ~ 150 MeV thermal energy in a nucleon of size ~ 1 fermi which is approximately ~ 250 Mev the cost in gradient energy of decreasing the meson VEV 's from $ f _\pi $ at the boundary of a single soliton nucleon to 0 in chiral symmetry restored value outside of the nucleon over a size of 1 fermi is about 150 Mev. The sum of these energies is around 350 -400 Mev, whereas the binding energy of the quark in such a nucleon is $ \sim 750 Mev, indicating that at chiral restoration, T_\Xi ~ 150 Mev, the nucleon may yet be intact. ~

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Changes the T, µ phase diagram At finite but small baryon density and T_\Xi ~ 150 Mev, there may emerge a new intermediate mixed phase in which nucleons will exist as bound states of locally spontaneously broken chiral symmetry (SBCS) in a sea of chirally restored quark matter. This is quite the opposite to the popular bag notions of the nucleon as being islands of restored chiral symmetry in a SBCS sea. CHEERS for Prof Usmani and Lunch

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