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A power counting rule is provided that allows us to obtain upper bounds forthe absolute values of Feynman parametric integrands. The rule reflects boththe ultraviolet and infrared behavior taking into account that the externalmomenta are on the mass shell. It gives us the ability to rigorously prove theabsolute convergence of the corresponding integrals. The consideration islimited to the case of the quantum electrodynamics Feynman graphs contributingto the lepton magnetic moments and not containing either lepton loops orultraviolet divergent subgraphs. However, a rigorous mathematical proof isgiven for all Feynman graphs satisfying these restrictions. The power countingrule is formulated in terms of Hepp's sectors, ultraviolet degrees ofdivergence and so-called I-closures. The obtained upper bound can not besubstantially improved: the illustrative example is provided. The paperprovides the first mathematically rigorous treatment of the ultravioletbehavior together with the on-shell infrared behavior with some kind ofgenerality. Practical applications of this rule are explained.

Infrared and Ultraviolet Power Counting on the Mass Shell in Quantum Electrodynamics