Coulomb problem for vector bosons

TL;DR

This paper resolves a longstanding paradox in the Coulomb problem for vector bosons by demonstrating that QED vacuum polarization prevents infinite charge accumulation, ensuring consistency with the Standard Model.

Contribution

It shows that vacuum polarization effects eliminate the infinite charge issue for vector bosons in Coulomb fields, aligning the problem with Standard Model principles.

Findings

Vacuum polarization introduces a strong repulsion near the Coulomb center.

The infinite charge paradox for vector bosons is resolved.

The Coulomb problem for vector bosons is now consistent with the Standard Model.

Abstract

The Coulomb problem for vector bosons W incorporates a well known difficulty; the charge of the boson localized in a close vicinity of the attractive Coulomb center proves be infinite. This fact contradicts the renormalizability of the Standard Model, which presumes that at small distances all physical quantities are well defined. The paradox is shown to be resolved by the QED vacuum polarization, which brings in a strong effective repulsion that eradicates the infinite charge of the boson on the Coulomb center. This property allows to define the Coulomb problem for vector bosons properly, making it consistent with the Standard Model.