## Wednesday, June 19, 2013

### Clarification

I should not post late at night.

A few things might make the 4-quark post a little clearer.

Quantum mechanics assumes that an object can be described by a linear combination of states, where a state can be such things as:

• an electron and a positron orbiting each other with a specific angular momentum
• an up quark and an anti-up quark orbiting each other with that specific angular momentum
• a neutrino and an anti-neutrino orbiting each other with that specific angular momentum
• an electron and a positron and a photon, with the photon going between the two
• a top quark and an anti-top quark orbiting each other with that specific angular momentum
• a neutron and an anti-neutron orbiting each other ditto
• other combinations that have the same quantum numbers (charge, angular momentum, etc)

The experienced reader will have noticed that the masses of these combinations seem a little disproportionate: the top quark is perhaps a hundred billion times heavier than a neutrino. Can it be in the same mix? Yes: but its contribution will be correspondingly tiny. Or if you want to try to interpret that statement, you might say something like: "It only exists a little bit there, or it only exists for a tiny amount of time."

Interpretations are controversial, and these are no exception. But one way to understand it goes like this. Particles that only exist for a small amount of time have (thanks to the Uncertainty Principle) some fuzziness in their energy. For a big fuzziness in energy/mass (being "off the mass shell"(*)) the particle can only exist for a proportionately tiny amount of time. (δE δT > h).

If a particle is unstable, it typically winds up in a final state based on one of those component states. If possible. One way to think of a positive pion (mass 140 MeV/c^2) is as a combination of a proton (mass 938 MeV/c^2) and an anti-neutron (mass 940 MeV/c^2). That is handy for describing some of its interactions, but you'll notice the mass numbers don't add up--it is the proverbial gallon of frogs in a pint jar--so it never decays into a proton and neutron. It doesn't decay into a positron and electron neutrino either, but instead into a positive muon and muon neutrino, but that's a topic for another day.

(*) The term "mass shell" comes from the description of the possible particle momenta in momentum 4-space (Px,Py,Pz,Energy). For a particle of known mass, the possible momenta are restricted to a 3-dimensional "cone" or shell in the 4-space. If there's fuzziness in the mass because of the Uncertainty Principle, the momentum can be away from that cone/shell: "off the mass shell."