Figure 39.34 shows a Feynman diagram for the fundamental process involved in the decay of a free

Figure 39.34 shows a Feynman diagram for the fundamental...

Key Concepts

Hadronic Decays

Hadronic decays involve the transformation of hadrons—particles made of quarks—into other hadrons, often accompanied by mesons. These decays might occur via either the strong or weak interaction, depending on the specific change in quark flavors and the conservation laws involved. They are key to understanding the dynamics within baryons and mesons and the processes by which quark rearrangements occur.

Quark Flavor Change

Quark flavor change refers to the process in which one type of quark transforms into another, typically mediated by the weak interaction. Such transitions are fundamental to various particle decay processes, as they enable the conversion of neutrons to protons or the decay of strange quarks within mesons and baryons. This concept is vital for understanding the underlying mechanisms of many subatomic decay processes depicted in Feynman diagrams.

Virtual Particles

Virtual particles are transient, intermediate particles that arise during particle interactions as represented in Feynman diagrams. They do not exist as free particles but contribute to the forces and transitions between real particles. In many weak interaction processes, virtual W bosons act as mediators, effectively connecting initial and final states even though they cannot be directly observed.

Feynman Diagrams

Feynman diagrams are pictorial representations in quantum field theory that depict the interactions between particles. They provide a visual shorthand for complex mathematical expressions, showing the flow of particles, the vertices where interactions occur, and the propagators for intermediate states. These diagrams help in understanding, analyzing, and calculating the probabilities of particle processes in both the Standard Model and beyond.

Weak Interaction

The weak interaction is one of the four fundamental forces and is responsible for processes that involve changes in the flavor of quarks and leptons. It is mediated by massive W and Z bosons, which allow for transitions such as a down quark converting to an up quark or a muon decaying into an electron and neutrinos. Its short range and unique properties make it crucial in describing particle decays like beta decay or leptonic decay processes.

Leptonic Decays

Leptonic decays involve transformations where leptons (such as electrons, muons, and neutrinos) are produced. These processes often proceed through the weak interaction, where a heavier lepton decays into lighter leptons by emitting a virtual W boson. Understanding leptonic decays is critical as they help probe the structure of the weak force and test the predictions of the Standard Model.

Transcript

00:01 Hello, and in this question here, we want to draw the fine line diagrams for the following reactions.

00:06 Okay, so we start off with a muon, okay? and that muon must emit a w minus particle, okay? now, the w minus has a charge of minus one, the muon has a charge of minus one, so charge is conserved.

00:23 And in order to conserve lepton number, or muon lepton number, we must it emit out of muon neutrino.

00:33 Okay.

00:34 Now this is the one vertex and the second vertex we must have, okay? we must have this w minus boson, which is a boson for the weak interaction.

00:45 We must have this decaying into, well, it decays into an electron, and to conserve electron number, it also must declay into an anti -electron neutrino.

00:58 Okay.

00:59 So that there, we see that the initial product is a muon and the final products as a muon neutrino, an electron, an anti -electron neutrino as required and that is the feynman diagram.

01:10 In the next case it's a very similar process.

01:13 We begin with a ta -one, okay? this ta -one must emit a w -minus boson, okay? to conserve charge, it's a minus, so charge is conserved.

01:25 And in order for leptone number to be conserved, this particle here must be a tau on neutrino.

01:32 Now, this w minus must can decay and one of the possible decays, so last time it decayed into an electron and anti -electronutrino, this time we're going to let it decay into anti -up and a down quark.

01:49 Okay? now, these two quarks together, okay, they comprise, they make up pi minus.

01:56 So we have here that a tau -on decays into an anti, a tau -on decays into a tau -on retrinos and a pi -minus.

02:07 In the next decay, we have delta plus -plus decaying into positive pi -on and a proton.

02:18 Okay.

02:19 So we have, so this is u -u -u -u -d -u -d - sorry, that should be.

02:26 U -u -d, the quark composition of the proton, and u and t -d.

02:32 Okay, so that's the quark composition.

02:36 We have an up, an up, and an up, okay? and we have, let's say, our final up, okay? this is our last up here.

02:47 That up there will change into a down, okay? so this will change into a down, so that remains an up and up and a down.

02:54 And by changing into a down we need to emit a w minus so we have it's a flavor changing quark okay this is a flavor changing process it changed from the up flavor into the down flavor by emitting a w minus okay and sorry no no sorry it should be a w plus okay it's a w plus because the total the charge of the up quark is two or three the charge of the down so we need the final charge of it to be to 2 over 3.

03:27 The charge of the w plus has a charge of 1...

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