Abstract
The spectral properties of a set of local gauge-invariant composite operators are investigated in the U(1) Higgs model quantized in the ’t Hooft Rξ gauge. These operators enable us to give a gauge-invariant description of the spectrum of the theory, thereby surpassing certain incommodities when using the standard elementary fields. The corresponding two-point correlation functions are evaluated at one-loop order and their spectral functions are obtained explicitly. As expected, the above mentioned correlation functions are independent from the gauge parameter ξ, while exhibiting positive spectral densities as well as gauge-invariant pole masses corresponding to the massive photon and Higgs physical excitations.
Highlights
The success of making use of the non-gauge-invariant elementary fields can be traced back to the so called Nielsen identities [3,4,5,6,7] which follow from the Slavnov-Taylor identities encoding the BRST symmetry of quantized gauge theories
The above mentioned correlation functions are independent from the gauge parameter ξ, while exhibiting positive spectral densities as well as gauge-invariant pole masses corresponding to the massive photon and Higgs physical excitations
The Nielsen identities ensure that the pole masses of both transverse gauge bosons and Higgs field propagators do not depend on the gauge parameters entering the gauge fixing condition, a pivotal property shared by the S-matrix elements
Summary
We start from the U(1) Abelian Higgs classical action as given in eq (1.1). The parameter v, corresponding to the minimum of the classical potential present in the starting action, gives the vacuum expectation value (vev) of the scalar field to zeroth order in , φ 0 = v. We notice that both the gauge field and the Higgs field have acquired the following masses m2 = e2v2, m2h = λv. We notice that both the gauge field and the Higgs field have acquired the following masses m2 = e2v2, m2h = λv2 With this parametrization, the Higgs coupling λ and the parameter v can be fixed in terms of m, mh and e, whose values will be suitably chosen later on in the text
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