The Hierarchy Problem
Problem statement
Radiative corrections to the Higgs mass scale quadratically with the cutoff,
$$\delta m_H^2 \sim \frac{\Lambda^2}{16\pi^2},$$
so keeping $m_H \approx 125\,\text{GeV}$ against a Planck-scale cutoff requires enormous fine-tuning.
Why is the electroweak scale so far below the Planck scale? Supersymmetry and compositeness were expected to help, but the LHC has found no new states so far.
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