For each of the following reactions establish whether it is allowed or not; if it is not, give t

For each of the following reactions establish whether it is...

Key Concepts

Weak Interaction Processes and Selection Rules

Many of the reactions involving neutrinos and charged leptons are mediated by the weak interaction, which is responsible for processes like beta decay. The weak force introduces specific selection rules, including the allowed changes in quantum numbers such as charge and lepton family number. These rules determine which transitions are permitted, and any reaction that violates the weak interaction’s selection criteria is forbidden. This concept underpins the analysis of reactions involving neutrino and lepton emissions or absorptions.

Kinematic Constraints and Energy-Momentum Conservation

For any reaction to occur, it must satisfy not only the conservation laws for quantum numbers but also the conservation of energy and momentum. The masses, kinetic energies, and momenta of the particles must be such that the process is energetically possible, taking into account the available energy in the system and ensuring that energy and momentum are balanced throughout the reaction.

Conservation of Baryon Number

Baryon number is a quantum number assigned to baryons (such as protons and neutrons) that must be conserved in nuclear and particle reactions. For a reaction to be allowed, the total baryon number on the initial side must equal that on the final side. This rule prevents transformations that would spontaneously change the number of baryons in the absence of corresponding processes.

Conservation of Charge

In any particle reaction, the total electric charge must remain constant. This means that the sum of the charges of all particles before the reaction must equal the sum of the charges after the reaction. Checking charge conservation helps determine whether a reaction is allowed, as any imbalance would render the process forbidden.

Conservation of Lepton Number and Lepton Family Number

Lepton number conservation requires that the total number of leptons (electrons, muons, tau particles, and their corresponding neutrinos) remains unchanged in a reaction. Often, this conservation applies separately to each lepton family (e.g., electron family, muon family), imposing additional constraints on processes that involve neutrinos and charged leptons. This concept is crucial in assessing whether a given reaction proceeds without violating these separate conserved quantities.

Transcript

00:01 Hello, and in this question here, we want to determine if these reactions can occur.

00:06 And the way we're going to determine that is by looking at conservation laws.

00:11 And if one of these processes disobey one of the conservation laws, then the reaction cannot occur.

00:18 Okay? so the first process, we have a muon plus a proton reacting to given neutron and an anti -mewon neutrino.

00:30 The reason why this process cannot occur is due to breaking conservation of muon leptone number.

00:37 Okay? so muon lepton number, okay? we're going to initially have a muon number of 1, okay, muon lepton number of 1 from the muon plus 0 from the proton, okay? we have a contribution of 0 from the neutron and a contribution of minus 1 from the muon anti -mu -on neutrino.

01:00 So this means the mu -1 number goes from 1 to minus 1, and hence this is not conserved, and therefore this reaction cannot occur.

01:08 Okay? so this here cannot concur, cannot occur, cannot occur because it breaks mu -1 conservation number.

01:14 However, by contrast, if we look at the mu -1 number in this case here, well, we have 1 plus 0 as before, and this goes to 0, but it's a plus 1 now as a muon neutrino has a muon number of plus one.

01:32 Okay? so this means one goes to one and muon number is conserved.

01:36 Now, is any of the other conservation laws broken? well, barian number is that conserved? well, we have one barian on the left hand side, and one barian on the right hand side.

01:46 So barion number is conserved.

01:48 Is charge conserved? the right hand side has a charge of zero.

01:52 And the left hand side has a charge of zero due to a contribution of minus 1 from the muon and plus 1 from the proton.

02:02 So 0 goes to 0.

02:04 That is conserved 2.

02:06 And every single conservative, well, you can look at all of them.

02:09 And if you go through the process, that's the main ones anyway, you can see here that this reaction doesn't break any conservation laws.

02:18 And therefore, we would expect it to see it in nature.

02:21 Now, our next reaction here.

02:23 This cannot occur and the reason for that is we're going to look at new on, sorry, electron lepton number.

02:33 So this initially on the left hand side has a number, an electron number of minus one from the positron and zero from the proton.

02:45 And this goes into, no, sorry, i wrote down this equation wrong...

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