Effective field theory for two-body systems with shallow S-wave resonances

Effective Field Theory for Shallow P-Wave States

“…The authors of Ref. [40] therefore conclude that renormalization at leading order forces the effective range to be negative. Since a negative effective range admits only at most one solution of the equation −1/a +rk 2 /2 − ik = 0 in the upper half of the complex momentum plane, no unphysical poles in the amplitude corresponding to Re k = 0, Im k > 0 can appear.…”

“…Since a negative effective range admits only at most one solution of the equation −1/a +rk 2 /2 − ik = 0 in the upper half of the complex momentum plane, no unphysical poles in the amplitude corresponding to Re k = 0, Im k > 0 can appear. The authors thus come to the conclusion that renormalization automatically incorporates the causality constraint that a resonance represents decaying, not growing, states [40].…”

“…[30,39] for details. Recently, also highly fine tuned S-wave systems with shallow resonances have been analyzed in the EFTs without [40] and with [41] an auxiliary dimer field assuming the scaling behavior…”

“…For the formulation without auxiliary fields, the authors of Ref. [40] considered energy-independent contact interactions using the lcRG-invariant approach. That is, the expression for the on-shell amplitude resulting from the iteration of the potential C 0 + C 2 ( p 2 + p 2 ) in the cutoff-regularized LS equation is matched to the first two terms in the ERE for arbitrarily large values of the UV cutoff .…”

“…Secondly, we revisit the formalism and some of the conclusions of Refs. [30,[39][40][41], where halo EFT is applied to fine-tuned S-and P-wave systems.…”