I understand that we can find the energy of a bosonic field in its vacuum state via
$E_{vac}^{(B)} = \sum_{\vec{k},s} \frac{1}{2}\hbar\omega_{\vec{k},s}^{(B)}$
and a fermionic one similarly,
$E_{vac}^{(F)} = \sum_{\vec{k},s} -\frac{1}{2}\hbar\omega_{\vec{k},s}^{(F)}$
since anticommutators and commutators are as a rule swapped for fermionic fields.
If these fields have masses $m_B$ and $m_F$ respectively, we can estimate the total energy density of both fields in their vacuum state from dimensional arguments as
$\Lambda \propto m_B^4 - m_F^4$
As I understand it, part of the appeal of unbroken supersymmetry is that if each excitation has a partner of opposite statistics/spin ("commutativity"?) but identical mass, then $\Lambda = 0$.
But experimentally, we don't observe equal-mass superpartners, or even similar mass ones, so I see no reason $\Lambda$ is required to be "small".
The current lower bound on the selectron mass is on the order of $10$ GeV, so it seems to me that this contribution is still required to be some $10^{51}$ orders of magnitude too larger than the value known value from cosmology, which is admittedly better than $10^{120}$ but still not very convincing.
How is spontaneously broken supersymmetry salvaged?