Limits of chiral perturbation theory

Abstract

We consider the relation between the breakdown scale of chiral perturbation theory, Λ χ , for large values of N (flavor), and the scale associated with "new" physical thresholds. This question is addressed using both the linear σ model and an asymptotically-free gauge theory to describe the high energy dynamics. It is suggested that the massive physical threshold could be well above Λ χ .

On the consistency of the =1 SYM spectra from wrapped five-branes

“…The full theory remains in a single phase. It is known from effective field theory that in the intermediate energy range Λ < E < Λ N =1 there is no new threshold for massless states [35] whilst massive modes have been integrated in our case. is the only allowed configuration (fine tuned) that leads to finite results after renormalisation, for both the potential and the quarks distance.…”

Electroweak Effective Lagrangians

“…47 These statements have been criticized in Ref. 48 on the basis that the breakdown of the expansion in a derivative series only implies that one must sum terms of all orders before deriving any conclusions, and that there are functions (which may represent Green's functions) for which the derivative expansion has large coefficients but still may be summed into an analytic result.…”

Implications of naturalness in effective field theory on the masses of resonances

“…Note that this argument would apply to the SU (N ) L × SU (N ) R → SU (N ) V linear σmodel as well, in contradiction to the claims of [5]. Any model with a well-defined N → ∞ limit in which there is a low-energy amplitude enhanced by a factor of N -no matter what the symmetry group or the pattern of symmetry breaking -will have resonances whose masses go like f / √ N 4 .…”

“…Similarly, all other intermediate 2n pion states are suppressed for n ≥ 2. From this we see that a 00 satisfies elastic unitarity in the N → ∞ limit, and so it lies on the Argand 5 It is easy to see that there are theories that have a well-defined N → ∞ limit that are not of this form. For example, consider a scalar field theory with the pions contained in an O(N ) vector, and include an additional symmetric tensor.…”