  We find the threshold structure of the two- and three-nucleon systems, with
the deuteron and 3H/3He as the only bound nuclei, sufficient to predict a pair
of four-nucleon states: a deeply bound state which is identified with the
helium-4 ground state, and a shallow, unstable state at an energy 0.38(25) MeV
above the triton-proton threshold which is consistent with data on the first
excited state of helium-4. The analysis employs the framework of Pionless EFT
at leading order with a generalized regulator prescription which probes
renormalization-group invariance of the two states with respect to higher-order
perturbations including asymmetrical disturbances of the short-distance
structure of the interaction. In addition to this invariance of the bound-state
spectrum and the diagonal triton-proton 1S0 phase shifts in the helium-4
channel with respect to the short-distance structure of the nuclear
interaction, our multi-channel calculations with a resonating-group method
demonstrate the increasing sensitivity of nuclei to the neutron-proton P-wave
interaction. We show that two-nucleon phase shifts, the triton channel, and
three-nucleon negative-parity channels are less sensitive with respect to
enhanced two-nucleon P-wave attraction than the four-nucleon triton-proton 1S0
phase shifts.
