Nuclear Physics from the sky

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Nuclear Physics from the sky

• Vikram Soni
• CTP

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Strongly Interacting matter _at_high density (gt 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)
• 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, 158ii) However, we have purely nuclear
  stars made up of entirely from n, p, e
• which can have M_max gt 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 /fm3), 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 fm3 ( n_B 0,57/fm3) in the
nuclear (APR A18 dv UIX) phase and ends
up at1/n_B 1.25 fm3 (n_B 0.8/ fm3) in the
quark matter phase (tree level sigma mass 850
Mev) If the central density of the star
(0.62/fm3) lt density at which the phase
transition begins ( n_B 0,57/fm3 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
gluonsIt 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 . gtgt 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 fp
• 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 R3) 0.77 fm-3
• \
• Thus the quark bound states in nucleon persist
  until a much higher density
• 0.8/fm3 than the density at which the nuclear
  quark matter
• transition begins (0.57/fm3) or the maximum
  central density of the APR
• star,(0.62/fm3) .
• 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/g2
• Minimizing this with respect to , X
• E_min/(g f_\pi) \sqrt3.12 N .24 /g2
  - 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

• 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