Meson masses in large Nf QCD from the Bethe-Salpeter equation

Abstract

We solve the homogeneous Bethe-Salpeter (HBS) equation for the scalar, pseudoscalar, vector, and axial-vector bound states of quark and anti-quark in large Nf QCD with the improved ladder approximation in the Landau gauge. The quark mass function in the HBS equation is obtained from the Schwinger-Dyson (SD) equation in the same approximation for consistency with the chiral symmetry. Amazingly, due to the fact that the two-loop running coupling of large Nf QCD is explicitly written in terms of an analytic function, large Nf QCD turns out to be the first example in which the SD equation can be solved in the complex plane and hence the HBS equation directly in the time-like region. We find that approaching the chiral phase transition point from the broken phase, the scalar, vector, and axial-vector meson masses vanish to zero with the same scaling behavior, all degenerate with the massless pseudoscalar meson. This may suggest a new type of manifestation of the chiral symmetry restoration in large Nf QCD.

arXiv comment33 pages, 16 figures. Typos are corrected. Minor corrections and references are added. Version to appear in Phys. Rev. D

References in corpus (24)

• QCD Phenomenology based on a Chiral Effective Lagrangian
• Dyson-Schwinger Equations: Density, Temperature and Continuum Strong QCD
• Hidden Local Symmetry at Loop -- A New Perspective of Composite Gauge Boson and Chiral Phase Transition
• Pion mass and decay constant
• Chiral Restoration in Hot and/or Dense Matter
• Conformal Phase Transition in Gauge Theories
• The Zero Temperature Chiral Phase Transition in SU(N) Gauge Theories
• On the Manifestation of Chiral Symmetry in Nuclei and Dense Nuclear Matter
• Mesons in a Poincare Covariant Bethe-Salpeter Approach
• The Phase Structure of an SU(N) Gauge Theory with N_f Flavors
• Can the QCD running coupling have a causal analyticity structure?
• Vector Manifestation of the Chiral Symmetry
• Relations between Observables and the Infrared Fixed-Point in QCD
• Lattice QCD with 8 Light Quark Flavors
• QCD with Large Number of Quarks: Effects of the Instanton -- Anti-instanton Pairs
• Conformal Phase Transition and Fate of the Hidden Local Symmetry in Large N_f QCD
• A Comment on the Zero Temperature Chiral Phase Transition in $SU(N)$ Gauge Theories
• External Gauge Invariance and Anomaly in BS Vertices and Boundstates
• Wilson Renormalization Group Equations for the Critical Dynamics of Chiral Symmetry
• Quantum Chromodynamics with Many Flavors
• Phase structure of QCD for general number of flavors
• Dynamical Chiral Symmetry Breaking in Effective Models of QCD in the Bethe-Salpeter Approach
• Solving the Homogeneous Bethe-Salpeter Equation
• Approximation of the Schwinger--Dyson and the Bethe--Salpeter Equations and Chiral Symmetry of QCD

Cited by in corpus (40)

• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• Chiral phase structure of QCD with many flavors
• Supersymmetry Inspired QCD Beta Function
• Maximum Wavelength of Confined Quarks and Gluons and Properties of Quantum Chromodynamics
• Conformal Windows of SU(N) Gauge Theories, Higher Dimensional Representations and The Size of The Unparticle World
• The discontinuities of conformal transitions and mass spectra of V-QCD
• 125 GeV Higgs from a not so light Technicolor Scalar
• UV fixed-point structure of the three-dimensional Thirring model
• Critical behavior of the (2+1)-dimensional Thirring model
• Techni-dilaton at Conformal Edge
• Beyond Miransky Scaling
• Study of the Change from Walking to Non-Walking Behavior in a Vectorial Gauge Theory as a Function of Nf
• Holographic techni-dilaton at 125 GeV
• 2 TeV Walking Technirho at LHC?
• Behavior of the S Parameter in the Crossover Region Between Walking and QCD-Like Regimes of an SU(N) Gauge Theory
• An Analysis of Scheme Transformations in the Vicinity of an Infrared Fixed Point
• SUSY Unparticle and Conformal Sequestering
• Discovering 125 GeV techni-dilaton at LHC
• Scheme-Independent Series Expansions at an Infrared Zero of the Beta Function in Asymptotically Free Gauge Theories
• Holographic Techni-dilaton
• Dropping rho and A_1 Meson Masses at Chiral Phase Transition in the Generalized Hidden Local Symmetry
• Z Boson Propagator Correction in Technicolor Theories with ETC Effects Included
• New Scheme Transformations and Application to Study Scheme Dependence of an Infrared Zero of the Beta Function in Gauge Theories
• First-order restoration of SU(Nf) x SU(Nf) chiral symmetry with large Nf and Electroweak phase transition
• Phenomenology of flavorful composite vector bosons in light of $B$ anomalies
• Walking on the Ladder: 125 GeV Technidilaton, or Conformal Higgs -Dedicated to the late Professor Yoichiro Nambu-
• Dynamical chiral symmetry breaking with Minkowski space integral representations
• Study of the conformal hyperscaling relation through the Schwinger-Dyson equation
• On the $\pi$ and $K$ as $q\bar{q}$ Bound States and Approximate Nambu-Goldstone Bosons
• Conformal Barrier and Hidden Local Symmetry Constraints: Walking Technirhos in LHC Diboson Channels
• pi^+ - pi^0 mass difference from the Bethe-Salpeter equation
• Walking Technipions in a Holographic Model
• Determination of SU(4)${}_{TC}$ Technicolor Gauge Group from Embedding in Extended Technicolor
• Techni-dilaton as Dark Matter
• Soft Walls in Dynamic AdS/QCD and the Techni-dilaton
• Scalar Decay Constant and Yukawa Coupling in Walking Gauge Theories
• Gluonic Effects on g-2: Holographic View
• Quark-antiquark composite systems: the Bethe-Salpeter equation in the spectral-integration technique
• Quark-antiquark composite systems:the Bethe--Salpeter equation in the spectral-integration technique in the case of the different quark masses
• Phase transitions for SU(N) gauge theories with arbitrary number of flavors