Effective theory calculation of resonant high-energy scattering

Abstract

Tests of the standard model and its hypothetical extensions require precise theoretical predictions for processes involving massive, unstable particles. It is well-known that ordinary weak-coupling perturbation theory breaks down due to intermediate singular propagators. Various pragmatic approaches have been developed to deal with this difficulty. In this paper we construct an effective field theory for resonant processes utilizing the hierarchy of scales between the mass of the unstable particle, M, and its width, Gamma. The effective theory allows calculations to be systematically arranged into a series in g^2 and Gamma/M, and preserves gauge invariance in every step. We demonstrate the applicability of this method by calculating explicitly the inclusive line shape of a scalar resonance in an abelian gauge-Yukawa model at next-to-leading order in Gamma/M and the weak couplings. We also discuss the extension to next-to-next-to-leading order and compute an interesting subset of these corrections.Comment: 45 page

Effective Theory Approach to Unstable Particle Production

“…Applying our method to the Standard Model might require more tedious calculations, but the main result remains valid. In particular, as discussed in [4], NNLO line-shape calculations now appear feasible.…”

“…It has to include operators that allow the production and decay of the unstable particle. Without introducing additional modes it is not possible to include such vertices as ordinary interaction terms in the effective Lagrangian [4]. The reason is that the momenta associated with generic collinear fields ψ c1 andχ c2 do not add up to a momentum of the form P = M v +k.…”

“…The reason is that the momenta associated with generic collinear fields ψ c1 andχ c2 do not add up to a momentum of the form P = M v +k. Either we have to implement this kinematic constraint on our external states by hand [4] or we have to introduce a new "external-collinear" mode. Adopting the second option, we define an external-collinear mode with large momentum in the n − direction by assigning it a momentumM n − /2 + k, where k ∼ δ.…”

“…In particular, this involves the computation of (the hard part) of the vertex diagram, and the additional wave-function normalization factor ̟ −1/2 mentioned above has to be taken into account. For the precise matching equation as well as the explicit result for C (1) we refer to [4]. Here it suffices to say that these are standard loop calculations.…”

Next-to-Next-to-Next-to-Leading Order QCD Prediction for the Top AntitopS-Wave Pair Production Cross Section Near Threshold ine+e−Annihilation

“…For the same reason, it will be mandatory to consider the process e + e − → W + W − bb including the non-resonant contributions. Non-resonant effects have been computed to NLO and partially to NNLO accuracy [33][34][35][36], and can be naturally separated in the framework of unstable particle EFT [37,38]. d) Electromagnetic initial-state radiation generates large logarithms ln(4m 2 t /m 2 e ), where m e is the electron mass, which must be summed.…”