  The formation of Cooper pairs, a bound state of two electrons of opposite
spin and momenta by exchange of a phonon [1], is a defining feature of
conventional superconductivity. In the cuprate high temperature
superconductors, even though it has been established that the superconducting
state also consists of Cooper pairs, the pairing mechanism remains intensely
debated. Here we investigate superconducting pairing in the
Bi2Sr2CaCu2O8+\delta (Bi2212) cuprate by employing spectral functions obtained
directly from angle-resolved photoemission (ARPES) experiments as input to the
Bethe-Salpeter gap equation. Assuming that Cooper pairing is driven solely by
spin fluctuations, we construct the single-loop spin-fluctuation-mediated
pairing interaction, and use it to compute the eigenfunctions and eigenvalues
of the Bethe-Salpeter equation in the particle-particle channel for multiple
Bi2212 samples. The key point of our results is that, as the temperature is
reduced, the leading eigenvalue increases upon approaching Tc, reaching a value
of approximately 1 at the Tc corresponding to each doping value, indicating a
superconducting transition with d-wave eigenfunctions. This suggests that spin
fluctuations can approximately account for Tc and, consequently, mediate
pairing in the cuprate high temperature superconductors.
