Hierarchy problem is the statement of why the weak force is much stronger than gravity. In terms of coupling constant, weak force (Fermi coupling) is much larger than gravity (Newton's constant).
I want to know how supersymmetry can be a solution to Hierarchy problem.
Answer
It is all about appropriate cancellations in the expansions when calculating the Feynman diagrams:
The hierarchy problem
Supersymmetry close to the electroweak scale ameliorates the hierarchy problem that afflicts the Standard Model. In the Standard Model, the electroweak scale receives enormous Planck-scale quantum corrections. The observed hierarchy between the electroweak scale and the Planck scale must be achieved with extraordinary fine tuning. In a supersymmetric theory, on the other hand, Planck-scale quantum corrections cancel between partners and superpartners (owing to a minus sign associated with fermionic loops). The hierarchy between the electroweak scale and the Planck scale is achieved in a natural manner, without miraculous fine-tuning.
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