Which of the following reactions and decays are possible?...

Key Concepts

Charge Conservation

The conservation of electric charge is a strict rule in particle physics. No matter what reaction takes place, the sum of the electric charges of all particles in the initial state must equal the sum in the final state. This principle prevents processes that would lead to a net creation or destruction of charge.

Baryon and Lepton Number Conservation

Baryon and lepton numbers are quantum numbers that must be conserved in all standard model processes. Baryon number conservation ensures that the total number of baryons (like protons and neutrons) remains constant, while lepton number conservation requires that the number of leptons (such as electrons and neutrinos) minus antileptons remains unchanged. Violations of these conservation rules indicate forbidden processes.

Conservation Laws

In all particle reactions and decays, certain quantities must remain constant from the initial state to the final state. These include energy, momentum, charge, baryon number, and lepton number. Ensuring these conservation laws are satisfied is a fundamental requirement for any allowed process in particle physics.

Energy-Momentum Conservation

Every reaction or decay must be kinematically allowed, meaning that the total energy and momentum before and after the reaction are conserved. This requirement ensures that the masses and the kinetic energies of all particles involved are consistent with the limits imposed by nature, such as the threshold energy needed for particle production.

Interaction Types (Strong, Electromagnetic, Weak)

Different reactions are mediated by different fundamental forces, each with its own set of selection rules. Strong interactions conserve quantities such as quark flavor and typically occur rapidly, while electromagnetic interactions involve the exchange of photons and maintain charge and other quantum numbers. Weak interactions, on the other hand, can change particle flavor but must still satisfy all overall conservation laws like charge and energy, often resulting in processes like beta decay.

Transcript

00:01 So this problem, we're giving a bunch of different reactions and decay processes.

00:06 And the problem is asking us which of these are possible.

00:09 And the ones that aren't possible list the conservation laws that are violated.

00:16 So this problem's kind of tedious because it isn't enough to find one violation and wants you to find all of them.

00:24 So you have to test all of them.

00:31 Other than strangeness, it doesn't seem to care about anything to do with court.

00:35 So we don't have to look at that kind of stuff.

00:39 So first, we have a negative pion interacting proton reaction turns into a neutron plus an aeta with zero charge.

00:49 So in this case, the energies is 139 .6 plus 938 .3 .3 .3 .3 .3.

01:00 Neutron is 939 .6.

01:07 Ada is 5 .5 .38 .3.

01:09 Neutron is 9 .8 .6.

01:09 47 .5.

01:13 This is mep over c squared.

01:17 So that clearly violates e -conservation.

01:27 Then for spin, so pyon has zero spin, proton has one -half, neutron has one -half, aeta has zero.

01:41 So that checks out.

01:43 Pion has zero barion number, proton has one, neutron has one, aeta has zero, so that works, lepton number, pion and proton have zero lepton number, neutron, and aeta have zero, so strangeness pina is zero, proton has zero, neutron has zero, eta has zero.

02:18 Pyon has negative one charge, proton has plus one charge, neutron has zero, a has zero, so that becomes zero equals zero, so that works.

02:28 So the problem here is that this reaction violates conservation of energy unless you're adding kinetic energy into the system but it doesn't say that you're allowed to do that so we'll go with it violates conservation of energy so then we have positive pylon so that's 139 .6 this is 938 .3 this is 939 .3 this is 939 .6 that is 135 .0.

03:20 So that's only 1 .3 up, but that's 4 .6 down.

03:24 So there's some extra connect energy here, so that's good.

03:30 So spin, 0 plus 1⁄2 equals 1⁄2.

03:40 So that's good.

03:43 Pion has zero bearing on number, proton has 1 plus 0.

03:49 So that's good.

03:51 So charge is plus 1 plus plus 1.

03:59 0.

04:01 So those are both electrically neutral.

04:03 So we've got charged violation.

04:12 Lepton number.

04:14 So pion and proton have zero leptone number, neutron.