Chiral extrapolations in effective field theory with bound states and resonances

Jaume Tarrús Castellà (Barcelona)

In the construction of an effective field theory it is crucial the determination of all of the relevant degrees of freedom.  An interesting problem arises when the low-energy degrees of freedom can form a bound state, a virtual state or a resonance close to threshold.  These states can be obtained resuming certain classes of diagrams or assuming an enhancement in certain couplings.  The proposal of this work is to introduce them explicitly and keep the low-energy constants of a natural size.  We have studied two systems in which such states are present.  The first is the nucleon-nucleon system, which in the 1S0 and 3S1 channels presents a virtual and a bound state respectively.  The second is the the pion-pion system, where a resonance appears in the scalar isospin zero channel.  We will show the effective field theories for these systems with the explicit inclusion of such states as explicit degrees of freedom.  Using these effective field theories we will present the chiral extrapolations of the scattering lengths in the 1S0 and 3S1 channels in the nucleon-nucleon system, and in the pion-pion system the quark mass dependence of the pion mass and decay constant as well as the pion-pion scattering lengths scalar isospin zero channel.

(Seminarraum II)