Effective field theory of boson-fermion mixtures and bound fermion   states on a vortex of boson superfluid
  We construct a Galilean invariant low-energy effective field theory of boson-fermion mixtures and study bound fermion states on a vortex of boson superfluid. We derive a simple criterion to determine for which values of the fermion angular momentum l there exist an infinite number of bound energy levels. We apply our formalism to two boson-fermion mixed systems: the dilute solution of He3 in He4 superfluid and the cold polarized Fermi gas on the BEC side of the "splitting point". For the He3-He4 mixture, we determine parameters of the effective theory from experimental data as functions of pressure. We predict that infinitely many bound He3 states on a superfluid vortex with l=-2,-1,0 are realized in a whole range of pressure, 0\sim20 atm, where experimental data are available. As for the cold polarized Fermi gas, while only S-wave (l=0) and P-wave (l=\pm1) bound fermion states are possible in the BEC limit, those with higher negative angular momentum become available as one moves away from the BEC limit. 
Yusuke Nishida and Dam Thanh Son