Doubts about conservation laws/numbers

Question

I'm new to the forum ( sorry for my bad English, I'm Italian).

I'm new to the study of particle physics and I have some doubts about conservation laws and numbers. For example, I found this exercise in my book.

"Establish which of the following reactions is more or less prohibited, and indicate which numbers and conservation laws are violated."

I know that, generally, 4-impulse, lepton ,fermion and baryon numbers, charge, angular and linear momentums have to be conserved. My question is, in that kind of exercise, where I don't have any information about mass, energy and angular moment, what are the variables should I consider to say what process is forbidden and which not? Just charge and fermyon, baryon and lepton numbers?

Answer 1

Baryon number conservation and individual lepton number conservation are obviously helpful. You will, in general, require more information to consider conservation of angular momentum.

It's possible to consider conservation of 4-momentum, since tables listing the masses of these particles are quite accessible. If a decay is not forbidden, then it should be impossible to find a reference frame in which the decay is forbidden. This constraint is significant when you're trying to figure out if a decay of a single particle into multiple particles is allowed: in the reference frame of the center of mass, the energy before the process is just $E_0=mc^2$, where $m$ is the mass of the particle. In that frame, the energy after the decay is at least $E_1=c^2\Sigma m_i$. This quantity must be less than $E_0$. In other words, a decay mode is forbidden unless the sum of the resultant particles' masses is less than the initial particle's mass.

It may also be relevant to apply additional rules not mentioned in the question, such as parity and CP, but there exist certain processes that violate these conservation laws.