What determines the behavior of weak interactions in fundamental particles?

[turin]

Can the cross-section of the weak interaction be extended? Are there things that can be done to fundamental particles in order to either increase their likely-hood or range of interacting weakly with a neutrino? What causes a fundamental particle to emit a weak boson anyway?

 

[zefram_c]

Can the cross-section of the weak interaction be extended? Are there things that can be done to fundamental particles in order to either increase their likely-hood or range of interacting weakly with a neutrino?

Nope. Nothing we can do to the cross section between elementary particles: the theory predicts that. Actually that's not entirely true, the cross section varies greatly with the energy of the incident particle - but generally decreases with higher energy. The only thing we can do to increase the likelihood of a neutrino interaction is to provide more targets (more nucleons) - ie use a lot of heavy water, maybe with some dissolved salts.

What causes a particle to emit a weak boson? In the naive picture, there is simply a probability for the particle to do so (quantum fluctuations).

 

[turin]

Can we recede the detector at relativistic speeds (barring practical considerations for the moment) and thereby effectively reduce the incident energy of the particles?

 

[zefram_c]

Then you run into other problems: if you don't have enough incident energy available, you don't have the energy for charged current interactions since you need to produce the outgoing electron's rest mass. As for neutral weak currents, those are pretty darn weak. The best energies to operate at (theoretically) are the resonances corresponding to the W and Z masses, where the propagator of those mediators (which is what kills it otherwise) nearly vanishes. See http://www.ps.uci.edu/~silvestri/thesis/THESIS/node35.html for the low energy behavior. Note how the cross section goes to zero as the available energy approaches the rest mass of the particles produced.

 

[turin]

... the cross section goes to zero as the available energy approaches the rest mass of the particles produced.

Say wha-? This seems so counter-intuitive, at least if I have understood your point about resonance. Can you elaborate?

 

[zefram_c]

A resonance is a particular interaction energy at which the particles like to interact. You see this all the time when you collide electrons and positrons: every time you approach the rest mass of some highly unstable particle (like the J/Psi), the cross section shows a sharp increase and decrease.

 

[arivero]

Can the cross-section of the weak interaction be extended? Are there things that can be done to fundamental particles in order to either increase their likely-hood or range of interacting weakly with a neutrino? What causes a fundamental particle to emit a weak boson anyway?

To me the more intriguing phenomena is nuclear beta decay. In principle the weak boson gets its energy from all the nucleus, but really the boson comes from a particular nucleon. And being so massive, its compton radius do not covers the nucleus. So how does it get its energy? You could claim that it is because of De Broglie wavelength, but particle creation is a phenomena of relativistic QM, so not sure if De Broglie has a role there.

 

[turin]

How can the cross-section (or anything, for that matter) show an increase and decrease?

a > b AND a < b?

 

[zefram_c]

Arivero: the deBroglie wavelengths of massive bosons are indeed quite small, and so they usually do not escape the nucleus. In fact the first theory of beta decays proposed a model of a point-like interaction between the nucleons and the two leptons observed in beta decay. This model is valid at low energies (far below the W mass). As far as the energy for the boson is concerned, it need not be there as the mediating W is not on its mass shell - this is the infamous virtual particle mechanism.
Turin: surely you've seen Gaussian curves before? I was certainly not suggesting the cross section both decreases and increases at the same time. However, since our conversation, I have become aware that the cross section of neutrinos does some strange things, so I will defer further posts on this topic until I get some clear information.