# How many generations and fermions are there in the Standard Model Group?

• A
• shiraz
In summary, the conversation discusses the gauge groups and number of families and fermions in the standard Model Group. It is mentioned that the number of fermions per family in the SM is 15, but some extensions may include a right-handed neutrino, bringing the total to 16. The number of generations affects the beta functions and running of coupling constants.
shiraz
Dear All
The standard Model Group is SU(3)*SU(2)*U(1) i know that there is 3 families and each family contain 16 fermion. I am trying to guess the number of families and fermions from the representation of the concerned group. For example the SO(10) How many generations we have and how may fermions? I will be so thankful if anyone could help me to find a criteria to study that in a simple way

arivero
The gauge groups are totally independent of the number of particles coupled to them. You can decide to couple matter to any representation of the gauge group, and that will change the number of fermions/bosons accordingly.

(There is a demand that there isn't a "gauge anomaly," which rears its head in the Standard Model because of the coupling to chiral fermions. But the Standard Model is not the unique way to cancel a gauge anomaly.)

shiraz
shiraz said:
and each family contain 16 fermion
Just to point out that the SM contains 15 fermions per family:
• 2x3=6 left-handed quarks
• 3 right-handed up type quarks
• 3 right-handed down type quarks
• 2 left-handed leptons
• 1 right-handed charged lepton
6+3+3+2+1 = 5x3 = 15
However, many extensions of the SM also include a right-handed neutrino, making a total of 16, but the RH neutrino is a priori not a part of the SM. These fermions (including the RH neutrino) fit well into the 16 representation of SO(10).

What does change with the number of generations are the beta functions and therefore the running of the coupling constants. For example, if you slam too many (17) fermion generations into QCD, the beta function will no longer be negative (it contains a factor ##11 - 2n_f/3##).

stoomart and shiraz

## 1. How many generations of particles are there in the Standard Model Group?

The Standard Model Group includes three generations of particles, also known as families. These are the electron family, the muon family, and the tau family. Each family consists of two quarks and two leptons.

## 2. What are the names of the fermions in the Standard Model Group?

The fermions in the Standard Model Group are the building blocks of matter and include six types of quarks (up, down, charm, strange, top, and bottom) and six types of leptons (electron, electron neutrino, muon, muon neutrino, tau, and tau neutrino).

## 3. Are there any other types of particles in the Standard Model Group besides fermions?

Yes, in addition to fermions, the Standard Model Group also includes four types of bosons: the photon, the W and Z bosons, and the gluon. These particles are responsible for fundamental forces such as electromagnetism, weak nuclear force, and strong nuclear force.

## 4. How many particles are there in total in the Standard Model Group?

There are a total of 61 particles in the Standard Model Group. This includes 12 fermions and 49 bosons.

## 5. Why are there only three generations of particles in the Standard Model Group?

The exact reason for the three generations of particles in the Standard Model Group is still unknown. However, it is believed that the number of generations is related to the mass of the particles, with each generation being heavier than the previous one. This is known as the hierarchy problem and is an area of ongoing research in particle physics.

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