Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1993-06-11
Phys.Rev. D48 (1993) 4375-4384
Physics
High Energy Physics
High Energy Physics - Phenomenology
25 pages including figures in pictex. text uses harvmac. BUHEP-93-14, HUTP-93/A016
Scientific paper
10.1103/PhysRevD.48.4375
Many years ago Weinberg formulated a definition of ``naturalness'' for effective theories: if an effective theory is to make sense, coefficients must not change too much when the cutoff scale is changed by a factor of order 1. As an example, we consider simple field theories in which an $O(N)$ symmetry spontaneously breaks to $O(N-1)$. We show that in these theories Weinberg's criterion for a natural effective theory may be applied directly to the $S$-matrix; it implies that the scale of new physics, beyond the Goldstone bosons, may not be too large: there is always a particle or a cut of mass below or about $4 \pi f / \sqrt{N}$. We discuss the range of convergence of the expansion of the chiral Lagrangian. It appears to be impossible to construct an underlying theory of the type considered here that fails to satisfy Weinberg's criterion.
Dugan Michael J.
Golden Mitchell
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