When renormalizability is not sufficient: Coulomb problem for vector bosons

Details When renormalizability is not sufficient: Coulomb problem for vector bosons When renormalizability is not sufficient: Coulomb problem for vector bosons

2006-09-19

arxiv.org/abs/hep-ph/0609194v1

Mod.Phys.Lett.A22:2971-2977,2007

Physics

High Energy Physics

High Energy Physics - Phenomenology

Four pages

Scientific paper

10.1142/S0217732307025984

The Coulomb problem for vector bosons W incorporates a known difficulty; the boson falls on the center. In QED the fermion vacuum polarization produces a barrier at small distances which solves the problem. In a renormalizable SU(2) theory containing vector triplet (W^+,W^-,gamma) and a heavy fermion doublet F with mass M the W^- falls on F^+, to distances r ~ 1/M, where M can be made arbitrary large. To prevent the collapse the theory needs additional light fermions, which switch the ultraviolet behavior of the theory from the asymptotic freedom to the Landau pole. Similar situation can take place in the Standard Model. Thus, the renormalizability of a theory is not sufficient to guarantee a reasonable behavior at small distances for non-perturbative problems, such as a bound state problem.

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