Quantum Flavordynamics (Weak Nuclear Force)
- This is basically the decay of a neutron into a proton by the emission of a W- boson.
- The up and down part of quarks is known as their flavour, they can effectively change flavours, in this case it is a down quark into an up quark.
- The W- has to be emitted for the flavour of the quark to change but it does not last long until it decays into an electron (e-) and an anti-electron neutrino (ν
- The W- boson (80GeV) is roughly 80x heavier than the neutron (1GeV) it decayed from meaning that it takes a lot of energy for this to happen so is seen happening inside stars which is basically just a big burning ball of protons.
- The energy for this change can also be borrowed from the vacuum provided the energy is paid back, to do this we refer to Heisenberg’s uncertainty principle:
ΔE x Δt<h
(amount of energy borrowed from vacuum) x (amount of time borrowed for) < Plancks constant
- This shows that the energy debt has to be paid back in 1e-25 seconds in which time the W- boson can move the distance of part a proton before it decays.
- This process is represented by the special unitary matrix two dimensional su(2) in mathematics. It is 2D because it is only changing ups and downs.
I have a deep and abiding love of high energy physics.
Weak physics is great! I have a few things to add/critique about the original post.
While p —> n + e + ν is characteristic of the weak interaction, it is but a raindrop in a downpour of others. There are entire classes of weak-mediated processes that I think deserve mention as well.
- Charged Current Interactions: These are processes by which the lowest order decay is carried out by the charged and massive W+ or W− bosons. These processes typically involve an overall change of particle flavor. Flavor is a fancy word that describes the different types of particles. Thus these is an up quark flavor, a down quark flavor, an electron flavor, an electron neutrino flavor, etc. Flavor is a quantum number just like spin.
- Neutral Current Interactions: These processes are mediated by a the neutral and massive Z boson. Unlike the charged current interactions, the Z boson cannot change flavor on its own. Thus (to lowest order) the standard model says there are no flavor changing neutral currents.
My point is that weak interactions come in a huge number of forms. They let the neutron decay into a proton (a semileptonic decay, because it involves quarks AND leptons), sure, but they also mediate the decay of a muon into an electron (a leptonic decay) and the decay of a kaon into pions (a hadronic decay). In fact, flavor may not change at all, like in Z-mediated electron-neutrino scattering!
Additionally, I think there’s some confusion in the original post between external particles and virtual particles. An external particle is one which goes into or out of the process in question, i.e. can be measured in principle. This is like the proton, neutron, electron, or antineutrino in the OP’s post. External particles are on-shell: that is, they have the mass you’d expect them to have and their energy content is consistent with Einstein’s energy-momentum relation: m^2 = E^2 - p^2. A virtual particle on the other hand, need not obey that relation. Virtual particles are those that appear between the initial and final particles in a Feynman diagram, like the W- boson in the OP’s post.
Virtual W-bosons need not have their mass "on-shell", so you don’t need the energy of a sun to produce them. In fact, any propagating particle is emitting and reabsorbing virtual W-bosons all the time. Hell, I can leave a sample of oxygen-14 sitting on a table (i.e. with hardly any energy at all) and it will readily decay. Kinetic energy is produced in rest-frame decays, not spent. Carbon dating—for instance—is useful because carbon-14 decays spontaneously.
Furthermore, it’s always to be emphasized that conservation of energy is a statistical phenomenon. Even when an on-shell virtual W-boson is produced, energy conservation isn’t violated because energy conservation doesn’t apply there in the first place. That’s what the time-energy uncertainty relation is all about. Energy becomes a good conserved quantity only when enough time has elapsed to consider the system statistically stable.
Another important thing to remember is that in these processes we don’t measure the intermediate particles. In a lot of ways, virtual particles are more mathematical niceties than physical realities. The only thing we see in the lab is the overall p —> n + e + ν. Feynman diagrams like the one above (wherein we see specific intermediate processes) are really pictures describing terms in an infinite sum. We only obtain what’s going on when they’re all added together. No diagram is correct on its own.
Finally, a comment about the SU(2) group. The elements of SU(2) are 2 by 2 complex matrices which are “special” (determinant = 1) and unitary (look like rotations of a complex vector). Because of those conditions, the 8 real parameters of a general 2 by 2 complex matrix are brought down to 3 real parameters. SU(2) is three-dimensional in the sense that we need 3 parameters to describe any element of the group. A representation of a group is a collection of matrices that behaves the same way as the group being represented. Thus, any element of a representation of SU(2) can be described by 3 parameters just like in SU(2). When a representation is utilized to describe the symmetry group of some particles, the number of rows/columns in the matrix representation determines how many particles the representation can simultaneously describe. That means I can describe the mixing of 2 nucleons, the mixing of 3 spin states of a massive vector boson, and even larger groups of particles using different representations of the same SU(2). There is an important difference between the dimension of a symmetry group and the dimension of a representation of the symmetry group.