Abstract
Gauge invariance requires even in the weak interactions that physical, observable particles are described by gauge-invariant composite operators. Such operators have the same structure as those describing bound states, and consequently the physical versions of the $W^\pm$, the $Z$, and the Higgs should have some kind of substructure. To test this consequence, we use lattice gauge theory to study the physical weak vector bosons off-shell, especially their form-factor and weak radius, and compare the results to the ones for the elementary particles. We find that the physical particles show substantial deviations from the structure of a point-like particle. At the same time the gauge-dependent elementary particles exhibit unphysical behavior.
Highlights
Physical states have to be gauge invariant
Concluding, we have studied for the first time off-shell and interaction properties of the physical vector particles in the weak sector
The gaugedependent correlation functions for the WÆ and Z gauge bosons, which we evaluated on the lattice and automatically include all orders in perturbation theory, show distinctively unphysical features off shell
Summary
Physical states have to be gauge invariant. This, almost trivial, statement applies to the weak interaction [1,2,3,4,5,6,7,8]. As we observe qualitative differences, our results suggest that momentumresolved form factors of the weak vector bosons are candidates for an experimental investigation and tests of both the underlying field theory as well as of GIPT as a tool. For those who wish to skip the technical details of the lattice computation, we refer to the theoretical background in Sec. II as well as the results in Secs.
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