${\rm SU}(5)$ doublet-triplet splitting problem and disagreement with phenomenology

Question

The statement from Wikipedia about ${\rm SU}(5)$ Georgi–Glashow seems very puzzling to me.

Here are the text from https://en.wikipedia.org/wiki/Georgi–Glashow_model#Decomposition:

It is the Higgs fields $5_H$ and $\overline{\mathbf{5}}_H$ which are interesting. On $5_H$ and $\bar{5}_H$ $$ \begin{pmatrix} (3,1)_{-\frac{1}{3}}\\ (1,2)_{\frac{1}{2}} \end{pmatrix} ??? \begin{pmatrix} (\bar{3},1)_{\frac{1}{3}}\\ (1,2)_{-\frac{1}{2}} \end{pmatrix} $$

The two relevant superpotential terms here are $5_H \bar{5}_H$ and $<24>5_H \bar{5}_H$. Unless there happens to be some fine tuning, we would expect both the triplet terms and the doublet terms to pair up, leaving us with no light electroweak doublets. This is in complete disagreement with phenomenology. See doublet-triplet splitting problem for more details.

It says: in complete disagreement with phenomenology. Can some experts fill in why this is the case? How are doublet-triplet splitting problem and fine tuning best understood so far?

This post imported from StackExchange Physics at 2020-11-30 15:24 (UTC), posted by SE-user annie marie heart