Hopf Skyrmion in QCD with adjoint quarks

Journal Article · Thu Mar 15 04:00:00 EDT 2007 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.75.065020· OSTI ID:21020199

Bolognesi, S ^[1]; Shifman, M ^[2]

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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)

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.

• OSTI ID: 21020199
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 6 Vol. 75; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

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