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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 present an effective field theory of the $Delta$-resonance as an interacting Weinbergs $(3/2,0)oplus (0,3/2)$ field in the multi-spinor formalism. We derive its interactions with nucleons $N$, pions $pi$ and photons $gamma$, and compute the $Delta
A regularization for effective field theory with two propagating heavy particles is constructed. This regularization preserves the low-energy analytic structure, implements a low-energy power counting for the one-loop diagrams, and preserves symmetries respected by dimensional regularization.
We study the unitarized meson-baryon scattering amplitude at leading order in the strangeness $S=-1$ sector using time-ordered perturbation theory for a manifestly Lorentz-invariant formulation of chiral effective field theory. By solving the coupled
Lattice calculations using the framework of effective field theory have been applied to a wide range few-body and many-body systems. One of the challenges of these calculations is to remove systematic errors arising from the nonzero lattice spacing.
Thanks to the unnaturally small value of the QCD vacuum angle $bartheta < 10^{-10}$, time-reversal ($T$) violation offers a window into physics beyond the Standard Model (SM) of particle physics. We review the effective-field-theory framework that es