The Equivalence Theorem and Effective Lagrangians

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 $f\bar{f}$ annihilation. The use of the equivalence theorem in the literature is examined.Comment: 20 pages LaTeX, BI-TP 94/1

Integrating out the Standard Higgs Field in the Path Integral

We integrate out the Higgs boson in the electroweak standard model at one loop and construct a low-energy effective Lagrangian assuming that the Higgs mass is much larger than the gauge-boson masses. Instead of applying diagrammatical techniques, we integrate out the Higgs boson directly in the path integral, which turns out to be much simpler. By using the background-field method and the Stueckelberg formalism, we directly find a manifestly gauge-invariant result. The heavy-Higgs effects on fermionic couplings are derived, too. At one loop the \log\MH-terms of the heavy-Higgs limit of the electroweak standard model coincide with the UV-divergent terms in the gauged non-linear $\sigma$-model, but vertex functions differ in addition by finite constant terms. Finally, the leading Higgs effects to some physical processes are calculated from the effective Lagrangian.Comment: 39 pages, latex, 7 figures uuencoded postscript, revised version, to appear in Nucl. Phys.

Effective Lagrangians with Higher Order Derivatives

The problems that are connected with Lagrangians which depend on higher order derivatives (namely additional degrees of freedom, unbound energy from below, etc.) are absent if effective Lagrangians are considered because the equations of motion may be used to eliminate all higher order time derivatives from the effective interaction term. The application of the equations of motion can be realized by performing field transformations that involve derivatives of the fields. Using the Hamiltonian formalism for higher order Lagrangians (Ostrogradsky formalism), Lagrangians that are related by such transformations are shown to be physically equivalent (at the classical and at the quantum level). The equivalence of Hamiltonian and Lagrangian path integral quantization (Matthews's theorem) is proven for effective higher order Lagrangians. Effective interactions of massive vector fields involving higher order derivatives are examined within gauge noninvariant models as well as within (linearly or nonlinearly realized) spontaneously broken gauge theories. The Stueckelberg formalism, which relates gauge noninvariant to gauge invariant Lagrangians, becomes reformulated within the Ostrogradsky formalism.Comment: 17 pages LaTeX, BI-TP 93/2

Equivalence of Hamiltonian and Lagrangian Path Integral Quantization: Effective Gauge Theories

The equivalence of correct Hamiltonian and naive Lagrangian (Faddeev--Popov) path integral quantization (Matthews's theorem) is proven for gauge theories with arbitrary effective interaction terms. Effective gauge-boson self-interactions and effective interactions with scalar and fermion fields are considered. This result becomes extended to effective gauge theories with higher derivatives of the fields.Comment: 14 pages LaTeX, BI-TP 93/40, August 199

Deriving Non-decoupling Effects of Heavy Fields from the Path Integral: a Heavy Higgs Field in an SU(2) Gauge Theory

We describe a method to remove non-decoupling heavy fields from a quantized field theory and to construct a low-energy one-loop effective Lagrangian by integrating out the heavy degrees of freedom in the path integral. We apply this method to the Higgs boson in a spontaneously broken SU(2) gauge theory (gauged linear sigma-model). In this context, the background-field method is generalized to the non-linear representation of the Higgs sector by applying (a generalization of) the Stueckelberg formalism. The (background) gauge-invariant renormalization is discussed. At one loop the log M_H-terms of the heavy-Higgs limit of this model coincide with the UV-divergent terms of the corresponding gauged non-linear sigma-model, but vertex functions differ in addition by finite (constant) terms in both models. These terms are also derived by our method. Diagrammatic calculations of some vertex functions are presented as consistency check.Comment: 33 Pages LaTeX, 6 figures uuencoded postscrip

Compton Scattering by a Pion and off--Shell Effects

We consider Compton scattering by a pion in the framework of chiral perturbation theory. We investigate off--shell effects in the s-- and u--channel pole diagrams. For that purpose we perform a field transformation which, in comparison with the standard Gasser and Leutwyler Lagrangian, generates additional terms at order $p^4$ proportional to the lowest--order equation of motion. As a result of the equivalence theorem the two Lagrangians predict the same Compton scattering S--matrix even though they generate different off--shell form factors. We conclude that off--shell effects are not only model--dependent but also representation--dependent.Comment: 13 pages in LaTeX, using RevTex macro, TRIUMF preprint TRI-PP-94-6

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements