Some remarks on the spectral functions of the Abelian Higgs model

Abstract

We consider the unitary Abelian Higgs model and investigate its spectral functions at one-loop order. This analysis allows to disentangle what is physical and what is not at the level of the elementary particle propagators, in conjunction with the Nielsen identities. We highlight the role of the tadpole graphs and the gauge choices to get sensible results. We also introduce an Abelian Curci-Ferrari action coupled to a scalar field to model a massive photon which, like the non-Abelian Curci-Ferarri model, is left invariant by a modified non-nilpotent BRST symmetry. We clearly illustrate its non-unitary nature directly from the spectral function viewpoint. This provides a functional analogue of the Ojima observation in the canonical formalism: there are ghost states with nonzero norm in the BRST-invariant states of the Curci-Ferrari model. * david.dudal@kuleuven.be †

Gauge-invariant spectral description of the U (1) Higgs model from local composite operators

“…This negative contribution eventually overcomes the other ones, leading to a negative regime in the spectral function, independently of the value of ξ. This feature is consistent with the large-momentum behaviour of the Higgs propagator (23), for a detailed discussion see [21]. As one lowers the value of the gauge parameter ξ, this unphysical threshold is shifted towards lower t's and may occur for momentum values lower than the physical two-particle states of two Higgs particles or two photons.…”

“…In addition, the correlation functions V µ (x)V ν (y) T and O(x)O(y) exhibit a spectral KL representation with positive spectral densities, allowing for a physical interpretation in terms of observable particles. This property is in sharp contrast with the one-loop spectral density of the elementary non-gauge-invariant Higgs propagator h(x)h(y) , which displays an explicit dependence on the gauge parameter ξ [21]. Moreover, the longitudinal part of the correlator V µ (x)V ν (y) -which is independently gauge-invariant-is shown to exhibit the pole mass of the Higgs excitation.…”

“…In [21], we studied the spectral properties of the one-loop propagators for the photon field A µ (x) and the Higgs field h(x) and evaluated them for d = 4 through dimensional regularization in the MS-scheme.…”

“…The aim of this work, which generalizes a previous one [21] devoted to the study of the analytic properties of the propagators of the non gauge-invariant elementary fields, is that of discussing the features of two local gauge-invariant * david.dudal@kuleuven.be † This important feature makes apparent that the operators V µ (x) and O(x) give a gauge-invariant picture for the photon and Higgs modes. In addition, the correlation functions V µ (x)V ν (y) T and O(x)O(y) exhibit a spectral KL representation with positive spectral densities, allowing for a physical interpretation in terms of observable particles.…”

“…the pole mass or effective potential governing the Higgs vacuum expectation value in such gauges.A formulation of the properties of the observable excitations in terms of gauge-invariant variables is thus very welcome. Such an endeavour has been addressed by several authors 1 [17-20], who have been able to construct, out of the elementary fields, a set of local gauge-invariant composite operators which can effectively implement a gaugeinvariant framework by using the tools of quantum gauge field theories: renormalizability, locality, Lorentz covariance and BRST exact symmetry.The aim of this work, which generalizes a previous one [21] devoted to the study of the analytic properties of the propagators of the non gauge-invariant elementary fields, is that of discussing the features of two local gauge-invariant * david.dudal@kuleuven.be † This important feature makes apparent that the operators V µ (x) and O(x) give a gauge-invariant picture for the photon and Higgs modes. In addition, the correlation functions V µ (x)V ν (y) T and O(x)O(y) exhibit a spectral KL representation with positive spectral densities, allowing for a physical interpretation in terms of observable particles.…”