Possible Cooper instabilities in pair Green functions of the two-dimensional Hubbard model

In analogy with ordinary BCS superconductivity, we identify possible pairing instabilities with poles in a certain class of Green functions of the two-dimensional repulsive Hubbard model, which normally signify bound states. Relating the gap to the location of these poles, we find that these instabilities exist in the range of hole doping between 0.03 and 0.24. The magnitude of the gap can be calculated without introducing an explicit cut-off, and for reasonably large coupling U/t = 10, the maximum gap is on the order of 0.08 in units of the hopping parameter t.