# Why is lepton flavour violation suppressed in the standard model?

I know neutrinos cant oscillate in the SM due to lack of mass but why are other processes forbidden? Ie. $\mu\rightarrow e\gamma$

• What do you mean by lack of mass? – Mockingbird Apr 25 '17 at 8:36
• Neutrino oscillation is an emergent phenomenon of lepton mixing, which requires non-degenerate neutrino mass eigenstates (i.e. massive neutrinos). In the Standard Model, $\mu \to e \gamma$ is forbidden for the same reason neutrino oscillation is. @Mockingbird: "lack of mass" refers to the fact that neutrinos are massless in the Standard Model. Neutrino oscillation is technically BSM physics. – dukwon Apr 25 '17 at 12:19
• @dukwon That would make a nice answer. – rob Apr 25 '17 at 13:24
• @dukwon can you expand on your explanation? I dont get what you mean when you say mu to e gamma is forbidden for the same reason – Arland Apr 25 '17 at 14:00
• @Arland because diagrams like this need lepton mixing. i.imgur.com/8VLEl38.png Think of an equivalent transition with quarks, e.g. $b \to s \gamma$. This is only allowed due to quark mixing i.e. the CKM matrix has non-zero off-diagonal terms. – dukwon Apr 25 '17 at 20:32

The standard model has conservation laws which are derived from a large number of obsrvations and experiments:

In developing the standard model for particles, certain types of interactions and decays are observed to be common and others seem to be forbidden. The study of interactions has led to a number of conservation laws which govern them. These conservation laws are in addition to the classical conservation laws such as conservation of energy, charge, etc., which still apply in the realm of particle interactions. Strong overall conservation laws are the conservation of baryon number and the conservation of lepton number. Specific quantum numbers have been assigned to the different fundamental particles, and other conservation laws are associated with those quantum numbers.

Different lepton numbers are assigned to the three generations of leptons, tau, mu, e and this has the consequence that conserving them in the decay means that in muon decay a muon neutrino has to be there to conserve muon lepton number. That is the true state of the standard model.

but why are other processes forbidden?

It is a consequence of imposing the observational fact that lepton number is conserved

Neutrino oscillations are beyond the standard model because they have masses and the reaction μ--> e γ could happen with very small probability through a neutrino oscillation diagram. See my answer here and the limits in this experiment.

• Has a contradiction to particle physics conservation laws ever been discovered? – Mockingbird Apr 26 '17 at 9:28
• I am asking this because may be 'all' possible baryon, lepton reactions are not tested. Do you think there can be a contradiction! – Mockingbird Apr 26 '17 at 9:30
• there are an enormous amount of data, and limits are given for many non standard model possible decays, because people are searching for beyond the standard model physics. The "forbidden" by the SM is because the model is successful 99 percent of the time to describe and predict the data. The particular reaction may go through a small extension of the SM, as seen in the last link I gave, people are looking but are not yet finding inspirehep.net/record/930966?ln=en – anna v Apr 26 '17 at 10:31
• they just give limit for the channel arxiv.org/abs/1605.05081 – anna v Apr 26 '17 at 10:33