I have a comment on:
"Extensions of the standard model imply new symmetries and new particle states....... .From this viewpoint, cosmology is sensitive to the most fundamental properties of micro-world, to the conservation laws reflecting strict or nearly strict symmetries of particle theory" page 4:
"So, electron is absolutely stable owing to the conservation of electric charge, while the stability of proton is conditioned by the conservation of baryon charge. The stability of ordinary matter is thus protected by the conservation of electric and baryon charges" page 5:
Yes, as you said the lepton number L (Electric number charges Le plus Muon number charges LВµ) is conservation in Beta Decay :
n >> p + e- + ve
L : 0 = 0 + 1 -1
BUT in case of Louis Michel Decay there are violations of the lepton number (Electron number or Muon number) conservation laws:
Вµ- >> e- + ve + vВµ
L : 1 = 1 + 1 -1 Lepton number conservation ( L = Le + LВµ )
Le : 0 1 + 1 + 0 Electron number violation
LВµ : 1 0 + 0 -1 Muon number violation
In this case, we search for new conservation law for this decay , so a new symmetry must introduce to explain this decay, hence a simple extension model for the Standard Model has been introduced. B - L model (baryon charges B minus lepton charges L) is the difference between the baryon number (B) and the lepton number (L).
If Bв€'L exists as a symmetry, it gives heavy right handed neutrinos and new heavy neutral gauge boson Z' and new heavy Higgs boson rather thans SM- Higgs
p >> ПЂ0 + e+
p (B=1 ; L=0) >> ПЂ0 (B=0 ; L=0) + e+ (B=0 ; L=в€'1)
Baryon charge: 1 = 0 + 0 No conservation
Lepton charge: 0 = 0 - 1 No conservation
B -L charge: 1 = 0 + 1 Conservation
This quantum number (B-L charge) is the charge of U(1) symmetry B-L model, and called U(1)B-L. Unlike baryon number alone or lepton number alone, this hypothetical symmetry would not be broken by chiral anomalies or gravitational anomalies, as long as this symmetry is global, which is why this symmetry is often invoked.
If B в€' L exists as a new symmetry, it must be spontaneously broken to give the heavy right-handed neutrinos if we assume the seesaw mechanism.
In the case of a gauged B в€' L, the gauge boson associated with this symmetry will Z' boson as a new force carriers rather than Z0 of SM weak force
The anomalies that break baryon number B conservation and lepton number L conservation individually cancel in such a way that B в€' L is always conserved.
As we discussed the above hypothetical example of proton decay where a proton (B = 1; L = 0) would decay into a pion (B = 0, L = 0) and positron (B = 0; L = в€'1) and the conservation will be for B -L charge 1 = 0 + 1.
So via B-L model which is a simple extension of SM we get a new conservation (symmetry) quantum number B-L (the difference between the baryon charges (B) and the lepton charges (L) ) and an associated new force via Z' boson.