Soft scalar-mass sensitivity ($\delta m_H^2\sim \frac{|y{|}^2}{16{\pi }^2}{m}_{\mathrm{soft}}^2\log (\Lambda /m_{\mathrm{soft}})$)

Soft supersymmetry breaking removes quadratic ultraviolet sensitivity but can leave scalar-mass corrections proportional to the soft squared masses and logarithms of scale ratios. The high-momentum difference of a paired scalar and fermion propagator falls as their squared-mass splitting divided by momentum to the fourth power. Heavy soft partners can therefore still create a tuning problem through logarithmic and finite thresholds even though the original quadratic hierarchy problem has been controlled.