I need a little bit of help in understanding the mu problem in SUSY. As I unders

Question

I need a little bit of help in understanding the mu problem in SUSY. As I understand it, the gist of the problem is that ? must be on the same order of magnitude as the electroweak scale (246 GeV). Thus, ? is much smaller than the Planck scale and we run into problems of naturalness. Correct me if I am wrong, but isn't this basically the same as the hierarchy problem in the SM that SUSY is supposed to help fix? So in SUSY, are we just replacing one hierarchy problem with another?

Furthermore, why is ? constrained to be ~246 GeV in SUSY? Mathematically, or physically, why can't ? be very large?

Explanation / Answer

The difference between the ?-problem and the hierarchy problem is that loop corrections to the value of ? in MSSM are small and convergent, because of supersymmetry, while the loop corrections to m2h in the SM are divergent. So to explain why ? is small, it is enough to explain why its approximate

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