For the past few days I've been studying supersymmetric quantum mechanics. My main sources that I use are David Tong's lecture notes on supersymmetric quantum mechanics, as well as Edward Witten's paper titled "Supersymmetry and Morse theory". As of now, I am trying to understand spontaneous supersymmetry breaking. I have two question regarding this aspect.
The first one involves how spontaneous supersymmetry breaking actually leads to the superpartners (so the boson and its fermion) having a difference in mass. I understand that if supersymmetry is not broken, that the ground state has zero energy and the superpartners have the same energy and thus (using relativity) also the same mass. However as it states in the paper of Edward Witten on page 3 (or page 663) if supersymmetry were to be spontaneoulsy broken this would lead to the ground state having a non-zero energy, which creates an energy difference between the superpartners. Now I don't see how one can derive that the superparnters would have a difference is mass in the context of supersymmetric quantum mechanics?
My second question is the following: As of yet supersymmetry has not been experimentally verified. As Edward Witten says it is because the fermions and bosons we see in nature have different masses. So either supersymmetry is broken at the energy level we are looking at or supersymmetry is just not a real thing I guess? However do we know for example for a electron what mass its superpartner might have in case supersymmetry is indeed broken? Because why can't it be that some other boson (that we observe in nature) with a different mass might be the superpartner of the electron? To me if this is not the case it indicates that we should know what the mass of the electron's superpartner might be.
http://www.damtp.cam.ac.uk/user/tong/susyqm.html (David Tong)
https://doi.org/10.4310/jdg/1214437492 (paper of Edward Witten)
