http://cds.cern.ch/record/147992/files/198312192.pdf

Chiral perturbation theory to one loop

Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

The anatomy of electroweak symmetry breaking: Tome I: The Higgs boson in the Standard Model

We argue that certain apparently consistent low-energy effective field theories described by local, Lorentzinvariant Lagrangians, secretly exhibit macroscopic non-locality and cannot be embedded in any UV theory whose S-matrix satisfies canonical analyticity constraints. The obstruction involves the signs of a set of leading irrelevant operators, which must be strictly positive to ensure UV analyticity. An IR manifestation of this restriction is that the “wrong” signs lead to superluminal fluctuations around non-trivial backgrounds, making it impossible to define local, causal evolution, and implying a surprising IR breakdown of the effective theory. Such effective theories can not arise in quantum field theories or weakly coupled string theories, whose S-matrices satisfy the usual analyticity properties. This conclusion applies to the DGP brane-world model modifying gravity in the IR, giving a simple explanation for the difficulty of embedding this model into controlled stringy backgrounds, and to models of electroweak symmetry breaking that predict negative anomalous quartic couplings for the W and Z. Conversely, any experimental support for the DGP model, or measured negative signs for anomalous quartic gauge boson couplings at future accelerators, would constitute direct evidence for the existence of superluminality and macroscopic non-locality unlike anything previously seen in physics, and almost incidentally falsify both local quantum field theory and perturbative string theory.

/pdf/causality-analyticity-and-an-ir-obstruction-to-uv-completion-22cu1hivl9.pdf

Causality, analyticity and an IR obstruction to UV completion

We discuss some general aspects of renormalization group flows in four dimensions. Every such flow can be reinterpreted in terms of a spontaneously broken conformal symmetry. We analyze in detail the consequences of trace anomalies for the effective action of the Nambu-Goldstone boson of broken conformal symmetry. While the c-anomaly is algebraically trivial, the a-anomaly is “non-Abelian”, and leads to a positive-definite universal contribution to the S-matrix element of 2 → 2 dilaton scattering. Unitarity of the S-matrix results in a monotonically decreasing function that interpolates between the Euler anomalies in the ultraviolet and the infrared, thereby establishing the a-theorem.

On renormalization group flows in four dimensions

Timelike scalar and vector form factors are recalculated by use of chiral perturbation theory and dispersion theory. It is shown that chiral perturbation theory at the one-loop level violates the final-state theorem (i.e., unitarity). In order to satisfy this theorem, chiral perturbation theory should be applied to the inverse of the form factor whose result is shown to be equivalent to the Pade-approximant method.

Chiral perturbation theory and final-state theorem.

Using the forward dispersion relations for \ensuremath{\pi}\ensuremath{\pi} scattering, we show that the coefficients of the derivative quartic terms in the chiral Lagrangian are positive. The Skyrme term is mainly given by the \ensuremath{\rho}-meson contribution to the I=1 total cross section and gives a proton mass of 1.27 GeV. The non-Skyrme term is found of comparable strength from the I=0 S-wave \ensuremath{\pi}\ensuremath{\pi} data.

Evaluation of the derivative quartic terms of the meson chiral Lagrangian from forward dispersion relations.

Resolution of the η → 3π problem

We have carried out a coupled-channel ({pi}{pi},{ital K{bar K}}) analysis of the effects of final-state interactions on the branching ratios for the decay modes of a light Higgs boson. We find no large enhancement of {ital H}{r arrow}{pi}{pi} relative to {ital H}{r arrow}{mu}{bar {mu}} for {ital m}{sub {ital H}}{lt}950 MeV.

Tran N. Truong

Papers

Chiral perturbation theory and final-state theorem.

Evaluation of the derivative quartic terms of the meson chiral Lagrangian from forward dispersion relations.

Resolution of the η → 3π problem

Branching ratios for decays of light Higgs bosons.

K→π, K→2π and K→3π amplitudes with unitarity