We provide a new efficient diagrammatic tool, in the context of the scattering equations, for computation of covariant D-dimensional tree-level n-point amplitudes with pairs of spinning massive particles using compact exponential numerators. We discuss how this framework allows non-integer spin extensions of recurrence relations for amplitudes developed for integer spin. Our results facilitate the on-going program for generating observables in classical general relativity from on-shell tree amplitudes through the Kawai-Lewellen-Tye relations and generalized unitarity.
The ǫ-regime of dilaton chiral perturbation theory is introduced. We compute the dilaton mass, the chiral condensate and the topological susceptibility in the ǫ-regime, as a function of the fermion mass. The microscopic spectral density of the Dirac operator is obtained from dilaton chiral perturbation theory. Our main result is that the chiral condensate and the spectral density are related to their counterparts from ordinary chiral perturbation theory via a simple scaling relation. This relation originates from the mass dependence of the dilaton potential, and is valid in both the ǫ-regime and the p-regime. In the ǫ-regime, moreover, all results agree with the universal predictions to leading order in ǫ.
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