Naturalness Bounds on Dipole Moments from New Physics

Abstract

Assuming naturalness that the quantum corrections to the mass should not exceed the order of the observed mass, we derive and apply model-independent bounds on the anomalous magnetic moments and electric dipole moments of leptons and quarks due to new physics. PACS number(s): 12.60. Cn, 11.10.Gh, In spite of its splendor of the phenomenological successes, the standard model of the elementary particles still leaves unanswered many fundamental questions, such as the origin of the quark-lepton generations, the curious pattern of their mass spectrum, and the unnatural fine tuning in the Higgs mass renormalization [11]. The quantum corrections to the masses due to these effects, diverge badly with an effective momentum cut-off at the new physics scale. On the other hand, masses of the quarks, leptons, gauge bosons, and Higgs scalar are observed to be small or very small in comparison with the expected new-physics scale. It is unnatural that the large quantum corrections accidentally cancel its large bare mass to give the small or very small observed masses, unless it is protected by some dynamical mechanism which does not work at the tree level. This last exception is very unlikely. Thus we can assume that the quantum contribution δm new from the new physics should not exceed the order of the observed mass m obs .The δm new in the left hand side of (1) is written in terms of the new-physics parameters (the effective coupling constants, the cutoff scales, the heavy state masses, etc.) and other known quantities, and consequently it imposes a bound on the new-physics parameters. In fact, a relation of the type (1) We suppose that the new-physics induces the anomalous magnetic moment µ and/or electric dipole moments d of quark or lepton ψ at low energies in comparison with new-physics scale Λ. The latter violates CP invariance. The effective Lagrangian for the interaction is given bywhere F µν is the field strength of photon A µ . Though (2) is a low-energy approximation for the real physics, we need to take into account its quantum effects up to its characteristic scale. If (2) were a fundamental interaction, the diagram in Fig. 1 would give rise to a quadratically divergent contribution to the fermion mass, which severely violates renormalizability. Now we argue that the internal line momenta of the diagram are, in many cases, effectively cut off at the characteristic scale of the new physics. For example, in the composite models, or the brane world models, the interaction for the momenta much higher than the inverse size of the composite particle extension or the brane world width can no longer be expressed in the form (2). Even though the effects of the high momenta should be taken into account by some other way, it is not through (2). Thus we cutoff the momenta as far as (2) is concerned. In the supersymmetric models, no real quadratic divergece in the diagram in Fig. 1 exists because they are canceled by those from the diagrams with the super partner internal lines. The symmetry, however, is broken, and the cont...

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