Journal
PHYSICAL REVIEW D
Volume 99, Issue 7, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.99.074001
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Funding
- JSPS KAKENHI [15K05042]
- Grants-in-Aid for Scientific Research [15K05042] Funding Source: KAKEN
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We derive general relationships between the number of complex poles of a propagator and the sign of the spectral function originating from the branch cut in the Minkowski region under some assumptions on the asymptotic behaviors of the propagator. We apply this relation to the mass-deformed Yang-Mills model with one-loop quantum corrections, which is identified with a low-energy effective theory of the Yang-Mills theory, to show that the gluon propagator in this model has a pair of complex conjugate poles or tachyonic poles of multiplicity two, in accordance with the fact that the gluon field has a negative spectral function, while the ghost propagator has at most one unphysical pole. Finally, we discuss implications of these results for gluon confinement and other nonperturbative aspects of the Yang-Mills theory.
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