Baryon density of quarks coupled to a chiral field

Kahana, S.; Ripka, G.

doi:10.1016/0375-9474(84)90692-4

Cited by 272 publications

(174 citation statements)

References 11 publications

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“…In recent years numerous hedgehog models, such as the Skyrme model [18][19][20][21], chiral quark models [22][23][24][25][26][27], hybrid bag models [28], chiral models with confinement [26,[29][30][31], or the Nambu-Jona-Lasinio model [32] in the solitonic treatment [33][34][35][36][37][38][39], were quite successful in describing the phenomenology of nucleon structure. The basis for these hedgehogs models is the large-N c limit [40,41] of QCD.…”

Section: Introductionmentioning

confidence: 99%

Response of nucleons to external probes in hedgehog models. I. Electromagnetic polarizabilities

Broniowski

Cohen

1993

Phys. Rev. D

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Electromagnetic polarizabilities of the nucleon are analyzed in a hedgehog model with quark and meson degrees of freedom. Semiclassical methods are used (linear response theory, quantization via cranking). It is found that in hedgehog models (Skyrmion, chiral quark models, Nambu-Jona-Lasinio model), the average electric polarizability of the nucleon, α N , is of the order N c , and the splitting of the neutron and proton electric(proper) polarizabilities, δα = α n − α p , is of the order 1/N c . We present a general argument why one expects δα > 0 in models with a pionic cloud. Our model prediction for the sign and magnitude of δα is in agreement with recent measurements. The obtained value for α N , however, is roughly a factor of three too large. This is because of two problems with our particular model: a too strong pion tail, and the degeneracy of N and ∆ states in the large-N c limit. This degeneracy also results in a very strong N c -dependence of the paramagnetic part of the magnetic polarizability, β, which is of the order N 3 c . We compare the large-N c results to the one-loop chiral perturbation theory predictions, and show the importance of ∆-effects in pionic loops. We also investigate the role of non-minimal substitution terms in the effective lagrangian on the polarizabilities of the nucleon.

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Section: Introductionmentioning

confidence: 99%

Response of nucleons to external probes in hedgehog models. I. Electromagnetic polarizabilities

Broniowski

Cohen

1993

Phys. Rev. D

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“…These results indicate the possibility of the existence of the lowest energy shell filled up with four quarks and also, these may be the reason why 4 He is stable compared with other nuclei. X.…”

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confidence: 63%

Search For the Quark Shell Structure Using the Non-Topological Soliton Model

Sawado

Shiiki

Oryu

2003

Nuclear Dynamics: From Quarks to Nuclei

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We investigate higher baryon-number states in the Chiral Quark Soliton Model using the rational map ansatz for the background chiral fields. The soliton solutions are obtained self-consistently.We show that the baryon number density has point-like symmetries and the corresponding valence quark spectrum of the lowest energy exhibits approximate four-fold degenerate. Our results indicate the possibility of existence of the shell-like structure in the multi-baryonic system. The CQSM is derived from the instanton liquid model of the QCD vacuum and incorporates the non-perturbative feature of the low-energy QCD, spontaneous chiral symmetry breaking. The vacuum functional is defined by;where the SU(2) matrixdescribes chiral fields, ψ is quark fields and m is the dynamical quark mass. f π is the pion decay constant and experimentally f π ∼ 93MeV. Since our concern is the tree-level pions and one-loop quarks according to the Hartree mean field approach, the kinetic term of the pion fields which gives a contribution to higher loops can be neglected. Due to the interac- where Λ is cut-off parameter in the proper-time reguralization [9] and ǫ ν , ǫν are the eigenvalues of Dirac equation for a single quark with the vacuum sector defined by2In the Hartree picture, the baryon states are the quarks occupying all negative Dirac sea and valence levels. Hence, if we define the total soliton energy E total , the valence quark energy should be added;where E i val is the valence quark contribution to the i th baryon. For higher winding number solitons, it is expected the solution to have point-like symmetries from the study of the Skyrme model [10]. Therefore, we shall impose the same symmetries on the chiral fields using the rational map ansatz. According to the ansatz, the chiral field can be expressed as [11]whereand R(z) is a rational map.Rational maps are maps from CP (1) to CP (1) (equivalently, from S 2 to S 2 ) classified by winding number. It was shown in [11] that B = N skyrmions can be well-approximated by rational maps with winding number N. The rational map with winding number N possesses (2N + 1) complex parameters whose values can be determined by imposing the symmetry of the skyrmion. Thus, the rational maps for B = 2 ∼ 7 and B = 17 take the form;3 where the complex coordinate z on CP (1) is identified with the polar coordinates on S 2 by z = tan(θ/2)e iϕ via stereographic projection. Substituting (6) into (5), one obtains the complete form of the chiral fields with appropriate symmetry and winding number. Since the chiral fields in (5) are parameterized by the polar coordinates, one can apply the numerical technique developed for B = 1 to find higher soliton solutions [6].Demanding that the total energy in (4) be stationary with respect to variation of the profile function f (r), δ δf (r) E total = 0 , yeilds the field equationwhereThe procedure to obtain the self-consistent solution of Eq. (7) is that 1) solve the eigenequation in (3) under an assumed initial profile function f 0 (r), 2) use the resultant e...

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“…The total derivative terms go to zero after doing the spatial integrals. The remaining terms in (25) are clearly nontopological and cannot be expressed in terms of the algebraic structure of the winding number density in (9). These terms give a nonzero contribution to the spatial integral and depend sensitively on the profile of the field U , not just on the asymptotic behavior of U .…”

Section: B the Derivative Expansion Calculationmentioning

confidence: 99%

“…These terms give a nonzero contribution to the spatial integral and depend sensitively on the profile of the field U , not just on the asymptotic behavior of U . Substituting the fifth-order resolvent expression (25) into the general expression (12) for the finite temperature fermion number, it is a simple matter to evaluate the z integral. This gives the fifth order contribution to the finite T induced fermion number:…”

Section: B the Derivative Expansion Calculationmentioning

confidence: 99%

Finite temperature induced fermion number for quarks in a chiral field

Dunne

Rao

2003

Phys. Rev. D

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We compute the finite temperature correction to the induced fermion number for fermions coupled to a static SU(2) chiral background, using the derivative expansion technique. At zero temperature the induced fermion number is topological, being the winding number of the chiral background. At finite temperature however, higher order terms in the derivative expansion give nontopological corrections to the winding number. We use this result to show that the standard cancellation of the fractional parts of the fermion number inside and outside the bag in an SU(2) x SU(2) hybrid chiral bag model of the nucleon does not occur at nonzero temperature.

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Baryon density of quarks coupled to a chiral field

Cited by 272 publications

References 11 publications

Response of nucleons to external probes in hedgehog models. I. Electromagnetic polarizabilities

Response of nucleons to external probes in hedgehog models. I. Electromagnetic polarizabilities

Search For the Quark Shell Structure Using the Non-Topological Soliton Model

Finite temperature induced fermion number for quarks in a chiral field

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