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E. N. Argyres

Publications and source records attributed to E. N. Argyres.

13 recordsLinked to original sources

Quantum Extremism: Effective Potential and Extremal Paths

The reality and convexity of the effective potential in quantum field theories has been studied extensively in the context of Euclidean space-time. It has been shown that canonical and path-integral approaches may yield different results, thus resolving the `convexity problem'. We discuss the transferral of these treatments to Minkowskian space-time, which also necessitates a careful discussion of precisely which field configurations give the dominant contributions to the path integral. In particular, we study the effective potential for the N=1 linear sigma model.

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The Path-Integral Approach to the N=2 Linear Sigma Model

In QFT the effective potential is an important tool to study symmetry breaking phenomena. It is known that, in some theories, the canonical approach and the path-integral approach yield different effective potentials. In this paper we investigate this for the Euclidean N=2 linear sigma model. Both the Green's functions and the effective potential will be computed in three different ways. The relative merits of the various approaches are discussed.

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Path Integrals in Polar Field Variables in QFT

We show how to transform a $d$-dimensional Euclidean path integral in terms of two (Cartesian) fields to a path integral in terms of polar field variables. First we present a conjecture that states how this transformation should be done. Then we show that this conjecture is correct in the case of two toy models. Finally the conjecture will be proven for a general QFT model with two fields.

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Non-Concave Bare Actions with Concave Effective Actions I: Zero Dimensions

We perform an explicit computation of the effective action for a few zero-dimensional Euclidean field theories in which the bare action exhibits several (or infinitely many) minima. In all cases the effective action is well-defined for all field values, as well as purely concave, in contrast to the bare action. We give arguments against the validity of the naive perturbative approach, which would lead to spontaneous symmetry breaking.

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Recursive actions for scalar theories

We introduce a class of self-interacting scalar theories in which the various coupling contants obey a recursive relation. These imply a particularly simple form for the generating function of the Feynman amplitudes with vanishing external momenta, as well as for the effective potential. In addition we discuss an interesting duality inherent in these models. Specializing to the case of zero spacetime dimensions we find intriguing nullification properties for the amplitudes.

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Zero-dimensional field theory

A study of zero-dimensional theories, based on exact results, is presented. First, relying on a simple diagrammatic representation of the theory, equations involving the generating function of all connected Green's functions are constructed. Second, exact solutions of these equations are obtained for several theories. Finally, renormalization is carried out. Based on the anticipated knowledge of the exact solutionsthe full dependence on the renormalized coupling constant is studied.

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Nullification in scalar theories with derivative couplings

We discuss the structure of scalar field theories having the property that all on-shell S-matrix elements vanish in tree approximation. It is shown that there exists a large class of such theories, with derivative couplings, which are all locally related to a free theory by a nonlinear transformation. It is also shown that a field-dependent wave-function renormalization provides all necessary counterterms so that all on-shell S-matrix elements vanish also at the one-loop level.

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Trilinear Gauge Boson Couplings in the MSSM

We study the C and P even WWγand WWZ trilinear gauge boson vertices (TGV's), in the context of the MSSM assuming that the external W's are on their mass shell. We find that for energies less than 200 GeV squark and slepton contributions to the aforementioned couplings are two orders of magnitude smaller than those of the Standard Model (SM). In the same energy range the bulk of the supersymmetric Higgs corrections to the TGV's is due to the lightest neutral Higgs, h_0, whose contribution is like that of a Standard Model Higgs of the same mass. The contributions of the Neutralinos and Charginos are sensitive to the input value for the soft gaugino mass M_{1/2}, being more pronounced for values M_{1/2} < 100 GeV. In this case and in the unphysical region, 0 < \sqrt{s} < 2 M_W , their contributions are substantially enhanced resulting in large corrections to the static quantities of the W boson. However, such an enhancement is not observed in the physical region. In general for 2 M_W < \sqrt{s} < 200 GeV the MSSM predictions differ from those of the SM but they are of the same order of magnitude. To be detectable deviations from the SM require sensitivities reaching the per mille level and hence unlikely to be observed at LEP200. For higher energies SM and MSSM predictions exhibit a fast fall off behaviour, in accord with unitarity requirements, getting smaller,in most cases, by almost an order of magnitude already at energies \sqrt{s} 0.5 TeV.

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WW Cross-sections and Distributions

We present the results obtained by the "WW Cross-sections and Distributions" working group during the CERN Workshop "Physics at LEP2" (1994/1995)

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Nullification of multi-Higgs threshold amplitudes in the Standard Model

We show that nullification of all tree-order threshold amplitudes involving Higgs particles in the Standard Model occurs, provided that certain equations relating the masses of all existing elementary particles to the mass of the Higgs scalar are satisfied. The possible role of these relations in restoring the high-multiplicity unitarity and their phenomenological relevance are briefly discussed.

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Multiscalar amplitudes to all orders in perturbation theory

A method for calculating loop amplitudes at the multiboson threshold is presented, based on Feynman-diagram techniques. We explicitly calculate the one-loop amplitudes in both $ϕ^4$-symmetric and broken symmetry cases, using dimensional regularization. We argue that, to all orders in the perturbation expansion, the unitarity-violating behaviour of the tree-order amplitudes persists.

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On amplitude zeros at threshold

The occurrence of zeros of 2 to n amplitudes at threshold in scalar theories is studied. We find a differential equation for the scalar potential, which incorporates all known cases where the 2 to n amplitudes at threshold vanish for all sufficiently large $n$, in all space-time dimensions, $d\ge 1$. This equation is related to the reflectionless potentials of Quantum Mechanics and to integrable theories in 1+1 dimensions. As an application, we find that the sine-Gordon potential and its hyperbolic version, the sinh-Gordon potential, also have amplitude zeros at threshold, ${\cal A}(2\to n)=0$, for $n\ge 4$ and $d\ge 2$, independently of the mass and the coupling constant.

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Multiscalar production amplitudes beyond threshold

We present exact tree-order amplitudes for $H^* \to n~H$, for final states containing one or two particles with non-zero three-momentum, for various interaction potentials. We show that there are potentials leading to tree amplitudes that satisfy unitarity, not only at threshold but also in the above kinematical configurations and probably beyond. As a by-product, we also calculate $2\to n$ tree amplitudes at threshold and show that for the unbroken $ϕ^4$ theory they vanish for $n>4~$, for the Standard Model Higgs they vanish for $n\ge 3~$ and for a model potential, respecting tree-order unitarity, for $n$ even and $n>4~$. Finally, we calculate the imaginary part of the one-loop $1\to n$ amplitude in both symmetric and spontaneously broken $ϕ^4$ theory.

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