Chiral symmetry and the axial current in nuclear matter

Bentz, Wolfgang; Baier, H.

doi:10.1016/0003-4916(90)90244-i

Cited by 21 publications

(9 citation statements)

References 30 publications

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“…In principle, the hadronic vector current ψ + N ψ N δ µ 0 and the axial vector current ψ + N σ i ψ N δ µ i can be modified in a medium. The vector and axial coupling constants C V and C A undergo renormalization; however, their values can be changed in a medium within 10-15% [23,24]. Therefore we neglect this effect.…”

Section: General Formalismmentioning

confidence: 99%

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Neutrino-nucleus interactions at low energies within Fermi-liquid theory

Lykasov

Bednyakov

2007

Phys. Rev. C

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Cross sections are calculated for neutrino scattering off heavy nuclei at energies below 50 MeV. The theory of Fermi liquid is applied to estimate the rate of neutrino-nucleon elastic and inelastic scattering in a nuclear medium in terms of dynamic form factors. The cross sections, obtained here in a rather simple way, are in agreement with the results of the other much more sophisticated nuclear models. A background rate from the solar neutrino interactions within a large Ge detector is estimated in the above-mentioned approach. The knowledge of the rate is in particular rather important for new-generation large-scale neutrino experiments.

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Section: General Formalismmentioning

confidence: 99%

“…In a medium they are renormalized within 10-20% (see Ref. [23]). Therefore for simplicity we neglect this effect in our consideration.…”

Section: Dynamic Form Factors In Neutrino Processes a Neutral Currentsmentioning

confidence: 99%

Neutrino-nucleus interactions at low energies within Fermi-liquid theory

Lykasov

Bednyakov

2007

Phys. Rev. C

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“…No one has yet derived the analogue to (185) for the axial current. Attempts using axial Ward identities in analogy to the EM case have not met with success [106]. The difficulty has presumably to do with the role of the Goldstone bosons in nuclear matter which is not well understood.…”

Section: Axial Charge Transitionmentioning

confidence: 99%

Dense nuclear matter: Landau Fermi-liquid theory and chiral Lagrangian with scaling

Song

2001

Physics Reports

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The relation between the effective chiral Lagrangian whose parameters scale according to Brown and Rho scaling("BR scaling") and Landau Fermi-liquid theory for hadronic matter is discussed in order to make a basis to describe the fluctuations under the extreme condition relevant to neutron stars. It is suggested that BR scaling gives the background around which the fluctuations are weak. A simple model with BR-scaled parameters is constructed and reproduces the properties of the nuclear ground state at normal nuclear matter density successfully. It shows that the tree level in the model Lagrangian is enough to describe the fluctuations around BR-scaled background. The model Lagrangian is consistent thermodynamically and reproduces relativistic Landau Fermi-liquid properties. Such points are important for dealing with hadronic matter under extreme condition. On the other hand it is shown that the vector current obtained from the chiral Lagrangian is the same as that obtained from Landau-Migdal approach. We can determine the Landau parameter in terms of BR-scaled parameter. However these two approaches provide different results, when applied to the axial charge. The numerical difference is small. It shows that the axial response is not included properly in the LandauMigdal approach. 6The 3-body contributions to the energy per nucleon vs. Fermi momentum in the FTS models. The short-dashed line represents the contribution of the φ 3 term in the FTS2 with the Q1 parameters. The long-dashed and the solid lines represent the contributions of the cubic terms (φω 2 and φ 3 ) in the FTS1 with the T1 parameters for d = 2.7. 7The comparison of CERES dilepton experiments and the theoretical predictions with the free-mass mesons and with scaled mass mesons. The figure comes from [61]. 45 8 The in-medium ρ-meson mass and Z factor obtained in [66] for Γ t = 0. 47 9 E/A − M vs. ρ for FTS1 theory ("T1" parameter), the "S3", "B1" and "B3" models defined in Table 4.

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“…No one has yet derived the analogue to (17) for the axial current. Attempts using axial Ward identities in analogy to the electromagnetic case have not met with success [37].…”

Section: Axial Charge Transitionsmentioning

confidence: 99%

Scaling of chiral Lagrangians and Landau Fermi liquid theory for dense hadronic matter

1999

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We discuss the Fermi-liquid properties of hadronic matter derived from a chiral Lagrangian field theory in which Brown-Rho (BR) scaling is incorporated. We identify the BR scaling as a contribution to Landau's Fermi liquid fixed-point quasiparticle parameter from "heavy" isoscalar meson degrees of freedom that are integrated out from a low-energy effective Lagrangian. We show that for the vector (convection) current, the result obtained in the chiral Lagrangian approach agrees precisely with that obtained in the semi-phenomenological Landau-Migdal approach. This precise agreement allows one to determine the Landau parameter that enters in the effective nucleon mass in terms of the constant that characterizes BR scaling. When applied to the weak axial current, however, these two approaches differ in a subtle way. While the difference is small numerically, the chiral Lagrangian approach implements current algebra and low-energy theorems associated with the axial response that the Landau method misses and hence is expected to be more predictive.

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Chiral symmetry and the axial current in nuclear matter

Cited by 21 publications

References 30 publications

Neutrino-nucleus interactions at low energies within Fermi-liquid theory

Neutrino-nucleus interactions at low energies within Fermi-liquid theory

Dense nuclear matter: Landau Fermi-liquid theory and chiral Lagrangian with scaling

Scaling of chiral Lagrangians and Landau Fermi liquid theory for dense hadronic matter

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