Since SUSY has been brought up in this thread with respect to the serious problem in the SM (Standard Model) of fine tuning the Higgs boson mass; it is worthwhile exploring this in greater detail.
Before proceeding we need to define mass from a Quantum Field Theory perspective.
First there is the concept of bare mass of a particle such as an electron which is simply its mass stripped of its electric field.
The bare mass is not a constant; it can be zero or even a negative value depending on the energy of the surrounding field(s).
When a particle such as electron and its field interact with fields of other particles, things get complicated as the measured electron mass turns out to being a combination of the electron’s bare mass and the interaction of the fields.
This interaction of the fields results in mass correction terms.
The mass of an electron is the bare mass plus mass correction terms.
It is found that for electromagnetic interactions the mass correction term is a logarithmic function and therefore the electron mass is of the
general form:
(The expanded mathematics leading to the general form is horrendously more complicated).
m is the bare mass of the electron, klog(Λ) is the mass correction term where k is a constant that can be positive or negative and depends on the field and Λ is the energy scale.
Note that even if the energy scale Λ is large the logarithm of a large number is still small hence the mass correction term for the electron will remain small.
The smaller the mass correction term the easier it is to perform renormalization as discussed in a previous post.
Now let’s look at the Higgs boson.
Unlike an electron which is a half spin fermion, the Higgs is a zero spin scalar boson.
A property of zero spin scalars is their mass correction terms are particularly sensitive to high energy scales.
In this case the mass of the Higgs boson is of the
general form:
Here μ is the bare mass of the Higgs boson.
Note there is no longer a logarithmic term defining the mass correction term.
Λ can be of the order of up to 10¹⁹ GeV which is the Planck mass, hence the mass correction term alone can be extremely large.
Given that the predicted mass range of the Higgs boson was in the region of 1-2000 GeV which was settled at 125 GeV at the time of its discovery, the mass correction term could be far greater than the Higgs mass.
There are two possible arguments in solving this dilemma.
The first is the Higgs cannot interact at high energy scales, which is admitting the SM is wrong and new physics is required.
The second is to preserve the SM by claiming that whatever the mass correction term is, the bare mass term will always be at a value such that the difference between the terms equals the mass of the Higgs boson.
This is the fine tuning argument.
An obvious objection to this argument is that it comes across as the case of adjusting the theory to get the desired result you are looking for.
Fine tuning is well known in Cosmology and particle physicists can take a leaf from the Cosmology handbook by invoking the
Anthropic principle.
There is a third possibility by proposing the existence of SUSY (Supersymmetry).
In this case for every fermion there exists a corresponding boson and vice versa.
The mass correction terms for fermion/bosons are equal in magnitude but of opposite signs and therefore cancel out.
For the simplest and most ideal version of SUSY where supersymmetry isn’t broken, the Higgs boson mass and bare mass are the same, and the problem of fine tuning vanishes.
Unfortunately SUSY isn’t that simple.
Supersymmetry isn’t perfect and it is believed at higher energy scales the symmetry is broken as the fermion/ boson counterparts will have unequal masses.
In this case the general equation takes the form.
In this case the mass correction term is still small and fine tuning is therefore minimized.
In fact there are a number of SUSY models in existence such as
MSSM and
NMSSM but none of the theorized fermions/bosons have been detected.