Victor Flambaum

Argonne, Physics Division & University of New South Wales, Australia

Coulomb problem for vector particles

The Coulomb problem for W-bosons (spin S=1) incorporates a well known difficulty; the charge of the boson localized in a close vicinity of the attractive Coulomb center proves to be infinite. The vector boson falls on the Coulomb center. The phenomenon was discovered in the works of Tamm, Schwinger, Oppenheimer and others 66 years ago, and since then was a nuisance for the theory. The paradox is shown to be resolved by the QED vacuum polarization, which brings in a strong effective repulsion at very small distances that eradicates the infinite charge of the boson on the Coulomb center. This property allows one to define the Coulomb problem for vector bosons properly. It is interesting that the vacuum polarization for scalar and spinor particles produces only a weak effect while for vector bosons the situation is completely different, it produces the impenetrable potential barrier ~1/r4. Physical origin of this unexpected effect and its relation to the renormalizability of the QED and the Standard Model will be discussed. The renormalizability may be not enough for consistent solution of the non-perturbative problem.

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