What are the consequences of breaking the Baryon and Lepton U(1) symmetries?

[ChrisVer]

I am trying to understand the concept of anomalies and the global or gauge symmetry breaking, i.e. the Lepton and Baryon number symmetries.

Could someone explain me, what we mean by saying that the Baryon or Lepton U(1) symmetries are broken? and how is that done?
I've seen the loop diagram - eg a current of B or L coming in and annihilating into two U(1)_Y bosons- and how this leads into non trivial current divergence... But I cannot or didn't see where the factor of energy comes in... (because in low energies, the B,L numbers are "good").

 

[LightHero]

The concept of anomalies, in general, is a quantum mechanical effect that arises due to the non-conservation of certain symmetries of a system. Anomaly resulting from a U(1) symmetry is an example of a global symmetry breaking. This type of anomaly occurs when the divergence of a given current associated with that U(1) symmetry is nonzero, meaning that the corresponding charge is not conserved. In the case of Baryon and Lepton number symmetries, the corresponding currents are called Baryon and Lepton number currents, and if their divergence is nonzero, then it means that they are not conserved. The way this is done is by a process called "loop diagram" in which a current of B or L comes in and annihilates into two U(1)-Y bosons. This process leads to non-trivial current divergence, which implies that the B or L number is not conserved. The factor of energy comes into play because in low energies, the B,L numbers are "good" and the corresponding anomalous processes are suppressed. However, if the energy is high enough, these processes can occur, leading to the breaking of the B,L symmetry.