The equivalence theorem and effective Lagrangians

Abstract

We point out that the equivalence theorem, which relates the amplitude for a process with external longitudinally polarized vector bosons to the amplitude in which the longitudinal vector bosons are replaced by the corresponding pseudo-Goldstone bosons, is not valid for effective Lagrangians. However, a more general formulation of this theorem also holds for effective interactions. The generalized theorem can be utilized to determine the high-energy behaviour of scattering processes just by power counting and to simplify the calculation of the corresponding amplitudes. We apply this method to the phenomenologically most interesting terms describing effective interactions of the electroweak vector and Higgs bosons in order to examine their effects on vector-boson scattering and on vector-boson-pair production in ff annihilation. The use of the equivalence theorem in the literature is examined. *

One-loop γγ → W L + W L − and γγ → Z L Z L from the Electroweak Chiral Lagrangian with a light Higgs-like scalar

“…3. We use the Equivalence Theorem (ET) [49][50][51][52] that has been proven to work also within the context of a SIEWSBS [53][54][55][56]. For the present computation it means that, for energies well above the EW gauge boson masses, m W , m Z ≪ √ s, the following approximations can be done:…”

Effective field theory analysis of new physics in e + e −→W + W − at a linear collider

“…These unitarity violations are associated with the longitudinal modes of the W bosons as can be seen by inspection of our results or, more generally, by a straightforward application of the equivalence theorem [51,52]. A general discussion of the equivalence theorem in the context of chiral Lagrangians can be found in [53,54]. In this section we will rederive the large-s limit of the e + e − → W + W − cross-section in a more transparent way by working in the Landau gauge, where the Goldstone modes ϕ ± appear explicitly.…”

On non-standard couplings among the electroweak vector bosons

“…This is true for all terms in (3.16) 6 . For the scattering of two vector-bosons into two vector-bosons the O(s 0 ) behavior for all terms has been shown in [26]. Using the formalism of [26], one easily generalizes this result of a constant, O(s 0 ), behavior to all two-boson into two-boson processes, i.e.…”

“…For the scattering of two vector-bosons into two vector-bosons the O(s 0 ) behavior for all terms has been shown in [26]. Using the formalism of [26], one easily generalizes this result of a constant, O(s 0 ), behavior to all two-boson into two-boson processes, i.e. for any combination of external Higgs bosons and vector-bosons in an arbitrary polarization state.…”

“…if one uses the sum of the Lagrangians (2.1), (2.17) and (3.15), the cross sections rise as O(s) independently of whether only c 1 , c 2 and c 4 or also c 3 and c 5 are different from zero (if one neglects the terms quadratic in the non-standard couplings). The less decent high energy behavior as compared to the case with a Higgs boson is entirely due to the omission of the standard Higgs interactions[26,27].…”