ESTRELAS DE QUARKS E SUA FENOMENOLOGIA NO MODELO DIELTRICO DE COR'

1
Medium modified properties of the nucleon in a
combined Walecka-linear sigma model
Mirian Bracco and Marcello Chiapparini, UERJ,
BrazilPedro Alberto and Manuel Fiolhais, Coimbra
University, Portugal

• Study medium effects on nucleon properties
• Predict equations of state in the low density
  region

Objectives
Main ideas

• Use Walecka model-like model for the low density
  regime (nucleons)
• Use a chiral model - the linear sigma model to
  describe the nucleon
• Combine both models, bringing the chiral touch
  of the sigma model to Waleckas

Related precursor works
Guichon (QCM models)
Banerjee, Birse, and others (sigma-omega model
cdm or bag models)
2
I - LSM model
Gell-Mann, Levy Ripka, Kahana, Soni Banerjee,
Birse Rosina, Golli .

• Lagrangian density

Dirac field (quarks u, d, s) scalar-isoscalar
field (sigma meson) pseudoscalar-isovector field
(pi meson)
(no strangeness, either in the nucleon or in the
homogeneous quark matter)
Properties chiral symmetry, SBChS, PCAC,
3-quark solitons
3
Potential in the LSM
U

• Mexican hat

p
s

• Spontaneous chiral symmetry breaking

• The nucleon a projected chiral soliton with 3
  quarks interacting with chiral mesons

4
Modified linear Walecka (scalar - vector) model
Energy density
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In usual Walecka model, the nucleon mass in the
medium is determined self-consistently within the
model, by means of a variational procedure.
In our modified Walecka model, the nucleon mass
in the medium is determined also
self-consistently but using an effective model
describing the nucleon as a quark-meson soliton
(the linear sigma model)
For a given nuclear density, we minimize the
energy density with respect to S and w. Since M
depends on these fields in an unknown way the
procedure cannot be carried on analytically as in
the usual Walecka model. We consider additional
background fields S and w in the LSM. These
communal fields enter the interior of the
nucleon,affecting its mass and other properties.
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Soliton sector in the LSM the nucleon in the
vacuum and in the medium
Hedgehog
Energy of the nucleon (projection)
( with inclusion of scalar and vector communal
fields)
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Equations for the radial fields
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Mass of the nucleon is also insensitive to w
Only the S field communicates the medium
effects. Since M is independent of w, the
value of w for a given density is obtained
variationally from Walecka
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Parameter fixing
For a given (nucleon private) sigma field, adjust
ms in order to have MN 938 MeV
In baryon sector other two parameters yet to be
fixed the comunal scalar mass and the
omega-nucleon coupling constant.
Medium effects on the nucleon
quarks
mesons
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Nucleon static properties
gA
Mass
Mag. moments
Charge radii
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Back to Walecka
or
Energy per baryon
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e/r is expected to have a minimum at r0 0.15
fm3 at the right saturation energy
Little sensitivity to the parameter sets
scalar
Nucleon mass
omega
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EoS
Sigma and omega strengths
Quark mass
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Pressure
Compressibility
k287 MeV
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Summary, conclusions and perspectives

• Combine nuclear model (Walecka) with quark model
  (LSM) to
• Study medium effects on nucleon properties.
• Obtain an EoS for the nuclear density region
  using a microscopic description of the nucleon
  degrees of freedom.
• Obtain an EoS to describe quark matter at high
  densities by means of the same model used to
  describe the nucleon, aiming at a unified
  description of strongly interacting matter.