Standard Model of Elementary Particle does not explain the complete subatomic world as it fails to describe gravity. We have to find a new gauge particle "graviton" then we will have a model that explain everything, but even we found a theoretical particle called a graviton, It would not completely explain gravitational force.
The best explanation for gravitation is Einstein's General Theory of Relativity. Why is gravity so difficult to integrate into the Standard Model? Well unlike other forces which can be explain using quantities particles, gravity does not necessarily even need a particle because at its fundamental level it can be explained in geometric terms.
General Relativity is about curvature of space rather than interaction of particles. We can only presume that gravity must have a quantum form but maybe it doesn't, we do not know. The other three forces don't seem to bend space and time, only gravity does. So that is what so far no one can explain and thus incorporate into the standard model.
There are some leading theories that are attempting to put gravity in terms of quantum world namely String Theory and Loop Quantum Gravity. They provide the possibility of a quantum theory of gravity and according to these theories, the graviton must exist but the major problem with these theories is that they don't make predictions that can test.
So for all intents and purposes they may just be random mathematical constructs that happen to model certain parts of nature.
The theory of gravity breaks down to the quantum level so we have no way to explain the singularity of a black hole or the events that led up to the Big Bang but luckily for particle physics when it comes to the minuscule scale of particles, the effect of gravity is so weak that it is negligible. Only when matter is involved at the scale of the human body or of stars and planets, the effect of gravity dominates.
So the Standard Model still works well despite its non explanation of a fundamental force of nature. What we really need is a theory of everything that unites relativity and quantum mechanics. It's possible that space-time itself is not smooth as general relativity presumes but is itself made up of quantum part. We need to come up with a quantum explanation for gravity. Matter-antimatter, Dark matter and dark energy are also not explained by the standard model.
The model predicts that at the beginning of the universe at the Big Bang, there should have an equal amount of both matter and antimatter that totally annihilated each other so the universe would be a massive soup of energy consisting of nothing more than photons. So perhaps the biggest defect with this model is that it predicts that the universe does not exist but we do exist , isn't it ?

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