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Title: Hopf Skyrmion in QCD with adjoint quarks

Abstract

We consider a modification of QCD in which conventional fundamental quarks are replaced by Weyl fermions in the adjoint representation of the color SU(N). In the case of two flavors the low-energy chiral Lagrangian is that of the Skyrme-Faddeev model. The latter supports topologically stable solitons with mass scaling as N{sup 2}. Topological stability is due to the existence of a nontrivial Hopf invariant in the Skyrme-Faddeev model. Our task is to identify, at the level of the fundamental theory, adjoint QCD, an underlying reason responsible for the stability of the corresponding hadrons. We argue that all 'normal' mesons and baryons, with mass O(N{sup 0}), are characterized by (-1){sup Q}(-1){sup F}=1, where Q is a conserved charge corresponding to the unbroken U(1) surviving in the process of the chiral symmetry breaking (SU(2){yields}U(1) for two adjoint flavors). Moreover, F is the fermion number (defined mod 2 in the case at hand). We argue that there exist exotic hadrons with mass O(N{sup 2}) and (-1){sup Q}(-1){sup F}=-1. They are in one-to-one correspondence with the Hopf Skyrmions. The transition from nonexotic to exotic hadrons is due to a shift in F, namely F{yields}F-H where H is the Hopf invariant. To detect this phenomenonmore » we have to extend the Skyrme-Faddeev model by introducing fermions.« less

Authors:
 [1];  [2]
  1. Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen O (Denmark)
  2. William I. Fine Theoretical Physics Institute, University of Minnesota, 116 Church St. S.E., Minneapolis, Minnesota 55455 (United States)
Publication Date:
OSTI Identifier:
21020199
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.75.065020; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BARYONS; CHIRAL SYMMETRY; CHIRALITY; COLOR MODEL; FLAVOR MODEL; LAGRANGIAN FUNCTION; MESONS; QUANTUM CHROMODYNAMICS; QUARKS; SKYRME POTENTIAL; SOLITONS; SU GROUPS; SYMMETRY BREAKING; TOPOLOGY

Citation Formats

Bolognesi, S., and Shifman, M. Hopf Skyrmion in QCD with adjoint quarks. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.065020.
Bolognesi, S., & Shifman, M. Hopf Skyrmion in QCD with adjoint quarks. United States. doi:10.1103/PHYSREVD.75.065020.
Bolognesi, S., and Shifman, M. Thu . "Hopf Skyrmion in QCD with adjoint quarks". United States. doi:10.1103/PHYSREVD.75.065020.
@article{osti_21020199,
title = {Hopf Skyrmion in QCD with adjoint quarks},
author = {Bolognesi, S. and Shifman, M.},
abstractNote = {We consider a modification of QCD in which conventional fundamental quarks are replaced by Weyl fermions in the adjoint representation of the color SU(N). In the case of two flavors the low-energy chiral Lagrangian is that of the Skyrme-Faddeev model. The latter supports topologically stable solitons with mass scaling as N{sup 2}. Topological stability is due to the existence of a nontrivial Hopf invariant in the Skyrme-Faddeev model. Our task is to identify, at the level of the fundamental theory, adjoint QCD, an underlying reason responsible for the stability of the corresponding hadrons. We argue that all 'normal' mesons and baryons, with mass O(N{sup 0}), are characterized by (-1){sup Q}(-1){sup F}=1, where Q is a conserved charge corresponding to the unbroken U(1) surviving in the process of the chiral symmetry breaking (SU(2){yields}U(1) for two adjoint flavors). Moreover, F is the fermion number (defined mod 2 in the case at hand). We argue that there exist exotic hadrons with mass O(N{sup 2}) and (-1){sup Q}(-1){sup F}=-1. They are in one-to-one correspondence with the Hopf Skyrmions. The transition from nonexotic to exotic hadrons is due to a shift in F, namely F{yields}F-H where H is the Hopf invariant. To detect this phenomenon we have to extend the Skyrme-Faddeev model by introducing fermions.},
doi = {10.1103/PHYSREVD.75.065020},
journal = {Physical Review. D, Particles Fields},
number = 6,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}
  • The self-effect of pseudoscalar mesons does not lead to the existence of locally stable solitons as nucleons. The mass of the chiral soliton which is stabilized when the interaction with vector ..omega.. and rho mesons is taken into account is roughly twice the mass of a nucleon.
  • We study baryonic matter in holographic QCD with D4/D8/D8 multi-D brane system in type IIA superstring theory. The baryon is described as the 'brane-induced Skyrmion', which is a topologically nontrivial chiral soliton in the four-dimensional meson effective action induced by holographic QCD. We employ the ''truncated-resonance model'' approach for the baryon analysis, including pion and {rho} meson fields below the ultraviolet cutoff scale M{sub KK}{approx}1 GeV, to keep the holographic duality with QCD. We describe the baryonic matter in large N{sub c} as single brane-induced Skyrmion on the three-dimensional closed manifold S{sup 3} with finite radius R. The interactions betweenmore » baryons are simulated by the curvature of the closed manifold S{sup 3}, and the decrease of the size of S{sup 3} represents the increase of the total baryon-number density in the medium in this modeling. We investigate the energy density, the field configuration, the mass and the root-mean-square radius of single baryon on S{sup 3} as the function of its radius R. We find a new picture of 'pion dominance' near the critical density in the baryonic matter, where all the (axial) vector meson fields disappear and only the pion fields survive. We also find the swelling phenomena of the baryons as the precursor of the deconfinement, and propose the mechanism of the swelling in the general context of QCD. The properties of the deconfinement and the chiral symmetry restoration in the baryonic matter are examined by taking the proper order parameters. We also compare our truncated-resonance model with another instanton description of the baryon in holographic QCD, considering the role of cutoff scale M{sub KK}.« less
  • Dynamics of SU(N{sub c}) Yang-Mills theories with N{sub f} adjoint Weyl fermions is quite different from that of SU(N{sub c}) gauge theories with fundamental quarks. The symmetry breaking pattern is SU(N{sub f}){yields}SO(N{sub f}). The corresponding sigma model supports Skyrmions whose microscopic identification is not immediately clear. We address this issue as well as the issue of the Skyrmion stability. The case of N{sub f}=2 had been considered previously. Here we discuss N{sub f}{>=}3. We discuss the coupling between the massless Goldstone bosons and massive composite fermions [with mass O(N{sub c}{sup 0})] from the standpoint of the low-energy chiral sigma model.more » We derive the Wess-Zumino-Novikov-Witten term and then determine Skyrmion statistics. We also determine their fermion number (mod 2) and observe an abnormal relation between the statistics and the fermion number. This explains the Skyrmion stability. In addition, we consider another microscopic theory--SO(N{sub c}) Yang-Mills with N{sub f} Weyl fermions in the vectorial representation--which has the same chiral symmetry breaking pattern and the same chiral Lagrangian. We discuss distinctive features of these two scenarios.« less
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