Renormalization group analysis of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ρ</mml:mi></mml:math>-meson properties at finite density

Kim, Youngman; Lee, Hyun Kyu

doi:10.1103/physrevc.62.037901

Phys. Rev. C

2000

DOI: 10.1103/physrevc.62.037901

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Renormalization group analysis ofρ-meson properties at finite density

Youngman Kim

Hyun Kyu Lee

Abstract: We calculate the density dependence of the ρ-meson mass and coupling constant(g ρN N ) for ρ-nucleon-nucleon vertex at one loop using the lagrangian where the ρ-meson is included as a dynamical gauge boson of a hidden local symmetry. From the condition that thermodynamic potential should not depend on the arbitrary energy scale, renormalization scale, one can construct a renormalization group equation for the thermodynamic potential and argue that the various renormalization group coefficients are functions of… Show more

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Cited by 7 publications

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“…A similar discussion can be found in Ref. [17] where we simply point out a pole at the continuum threshold, not clarifying its spurious nature. It is currently under-debate whether or not keep the terms in question in QCD sum rules with external fields [18].…”

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Use of the Double Dispersion Relation in QCD Sum Rules with External Fields

Kim¹

2000

Progress of Theoretical Physics

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In QCD sum rules with external fields, the double dispersion relation is often used to represent the correlation function. In this work, we point out that the double spectral density, when it is determined by successive applications of the Borel transformation, contains spurious terms which should be kept in the subtraction terms in the double dispersion relation. They are zero under the Borel transformation, but, if the dispersion integral is restricted with QCD duality, they contribute to the continuum. For the simple case with zero external momentum, it is shown that subtracting out the spurious terms is equivalent to the QCD sum rules represented by the single dispersion relation.The QCD sum rule 1) is widely used in studying hadronic properties based on QCD. 2) In this framework, a correlation function is introduced as a bridge between the hadronic and QCD representations. On the QCD side, the perturbative part and the power corrections are calculated in the deep space-like region (q 2 = −∞) using the operator product expansion (OPE), which is then used to extract the hadronic parameter of concern by matching with the corresponding hadronic representation.In matching the two representations, it is crucial to represent the correlator using a dispersion relation. Usually in the nucleon mass sum rule, as an example, the singlevariable dispersion relation is used. With this, the QCD correlator calculated in the deep space-like region can be related to its imaginary part defined in the time-like region, which is then compared with the corresponding hadronic spectral density to extract the hadronic parameter of concern. The hadronic spectral density contains contributions from higher resonances as well as the pole from the low-lying resonance of concern. To subtract out the continuum, QCD duality is invoked above a certain threshold, where the continuum contribution is equated to the perturbative part of QCD. This duality restricts the dispersion integral below the continuum threshold in the matching. Therefore, the predictive power of the QCD sum rules relies heavily on the duality assumption. Indeed, in quantum mechanical examples, the partonhadron duality works well for two-point correlation functions. 3) Often, within the QCD sum rule framework, a correlation function with an external field is considered to calculate, for examples, pion-nucleon couplings 4) -6) and nucleon magnetic moments. 7) In such a case, as the two baryonic lines propagate through the correlator at the tree level, the double-variable dispersion relation 8) can * ) JSPS fellow.

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confidence: 77%

Use of the Double Dispersion Relation in QCD Sum Rules with External Fields

Kim¹

2000

Progress of Theoretical Physics

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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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On the manifestation of chiral symmetry in nuclei and dense nuclear matter

2002

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Renormalization group analysis ofρ-meson properties at finite density

Cited by 7 publications

References 25 publications

Use of the Double Dispersion Relation in QCD Sum Rules with External Fields

Use of the Double Dispersion Relation in QCD Sum Rules with External Fields

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

On the manifestation of chiral symmetry in nuclei and dense nuclear matter

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