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Gaussian functional approximation to ’t Hooft’s extension of the linear Σ model

Nakamura, Issei and Dmitrašinović, V. (2012) Gaussian functional approximation to ’t Hooft’s extension of the linear Σ model. Physical Review D, 85 (5). Art. No. 056004. ISSN 2470-0010. doi:10.1103/PhysRevD.85.056004.

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We apply a self-consistent relativistic mean-field variational “Gaussian functional” (or optimized one-loop perturbation theory, or Hartree+RPA) approximation to the extended N_f=2 linear σ model with spontaneously and explicitly broken chiral SU_R(2)×SU_L(2)×U_A(1)≡O(4)×O(2) symmetry. We set up the self-consistency, or gap equations that dress up the bare fields with “cactus tree” loop diagrams, and the Bethe-Salpeter equations that provide further dressing with one-loop irreducible diagrams. In a previous publication [ V. Dmitrašinović and I. Nakamura J. Math. Phys. (N.Y.) 44 2839 (2003)] we have already shown the ability of this approximation to create composite (i.e., bound and/or resonance) states. With explicit SU_R(2)×SU_L(2)×U_A(1) chiral symmetry breaking first we consider how the U_A(1) symmetry induced scalar-pseudoscalar meson mass relation that is known to hold in fermionic chiral models is modified by the bosonic gap equations. Then we solve the gap and Bethe-Salpeter equations numerically and discuss the solutions’ properties and the particle content of the theory. We show that in the strong-coupling regime two, sometimes even three solutions to the η meson channel Bethe-Salpeter equation may coexist.

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Nakamura, Issei0000-0002-2701-6913
Additional Information:© 2012 American Physical Society. Received 22 July 2011; published 15 March 2012. This work was done while the first author (I. N.) was an M.Sc. student at RCNP, Osaka University, but the present material was not included in this author’s M.Sc. thesis. The other author (V. D.) would like to acknowledge a center-of-excellence (COE) professorship and the hospitality of RCNP during the school year 2000/1 when this work was started. We wish to acknowledge kind help in all matters concerning computers and software that we received from Ms. Miho Takayama-Koma. The authors also wish to acknowledge Professor H. Toki for enabling this collaboration.
Issue or Number:5
Classification Code:PACS: 11.30.-j, 11.30.Qc, 11.30.Rd
Record Number:CaltechAUTHORS:20120412-132812194
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:30068
Deposited By: Tony Diaz
Deposited On:17 Apr 2012 18:36
Last Modified:09 Nov 2021 19:35

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