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Register a new userUnstable-particle effective field theory
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M. Beneke
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Unstable particles are notorious in perturbative quantum field theory for producing singular propagators in scattering amplitudes that require regularization by the finite width. In this review I discuss the construction of an effective field theory for unstable particles, based on the hierarchy of scales between the mass, M, and the width,Gamma, of the unstable particle that allows resonant processes to be systematically expanded in powers of the coupling alpha and Gamma/M, thereby providing gauge-invariant approximations at every order. I illustrate the method with the next-to-leading order line-shape of a scalar resonance in an abelian gauge-Yukawa model, and results on NLO and dominant NNLO corrections to (resonant and non-resonant) pair production of W-bosons and top quarks.
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We illustrate the use of effective theory techniques to describe processes involving unstable particles close to resonance. First, we present the main ideas in the context of a scalar resonance in an Abelian gauge-Yukawa model. We then outline the necessary modifications to describe W-pair production close to threshold in electron-positron collisions.
We revisit the chiral kinetic equation from high density effective theory approach, finding a chiral kinetic equation differs from counterpart derived from field theory in high order terms in the $O(1/mu)$ expansion, but in agreement with the equation derived in on-shell effective field theory upon identification of cutoff. By using reparametrization transformation properties of the effective theory, we show that the difference in kinetic equations from two approaches are in fact expected. It is simply due to different choices of degree of freedom by effective theory and field theory. We also show that they give equivalent description of the dynamics of chiral fermions.
We discuss shallow resonances in the nonrelativistic scattering of two particles using an effective field theory (EFT) that includes an auxiliary field with the quantum numbers of the resonance. We construct the manifestly renormalized scattering amplitude up to next-to-leading order in a systematic expansion. For a narrow resonance, the amplitude is perturbative except in the immediate vicinity of the resonance poles. It naturally has a zero in the low-energy region, analogous to the Ramsauer-Townsend effect. For a broad resonance, the leading-order amplitude is nonperturbative almost everywhere in the regime of validity of the EFT. We regain the results of an EFT without the auxiliary field, which is equivalent to the effective-range expansion with large scattering length and effective range. We also consider an additional fine tuning leading to a low-energy amplitude zero even for a broad resonance. We show that in all cases the requirement of renormalizability when the auxiliary field is not a ghost ensures the resonance poles are in the lower half of the complex momentum plane, as expected by other arguments. The systematic character of the EFT expansion is exemplified with a toy model serving as underlying theory.
We develop the geometric formulation of the Standard Model Effective Field Theory (SMEFT). Using this approach we derive all-orders results in the $sqrt{2 langle H^dagger H rangle}/Lambda$ expansion relevant for studies of electroweak precision and Higgs data.
We revisit thermal Majorana dark matter from the viewpoint of minimal effective field theory. In this framework, analytic results for dark matter annihilation into standard model particles are derived. The dark matter parameter space subject to the latest LUX, PandaX-II and Xenon-1T limits is presented in a model-independent way. Applications to singlet-doublet and MSSM are presented.
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