I had to split my answer in two, and clumsily posted them in the wrong order—some of this refers to an ‘above’ which is actually below. I suggest reading in chronological rather than page order. :)
Am I right in thinking that the tau lepton is only theorized in order to explain an in-between decay state?
Well no, you get a specific resonance in hadron energy spectra, as described above.
If you don’t know, do you know of anything related to any other fermions (or hadrons) that only exist as a theoretical in-between?
There’s the notorious sigma and kappa resonances, which are basically there only to explain a structure in the pion-pion and pion-kaon scattering spectrum. Belief in these as particles proper, rather than some feature of the dynamics, is not widespread outside the groups that first saw them. (I have a photoshopped WWII poster somewhere, captioned “Is YOUR resonance needed? Unnecessary particles clutter up the Standard Model!) I see the PDG doesn’t even list them in its “needs confirmation” section. I’m aware of them basically because I used them in my thesis just as a way to vary the model and see how the result varied—I had all the machinery for setting up particles, so a more-or-less fictional particle with some motivation from what others have seen was a convenient way of varying the structure.
How were the masses of the tau lepton and the top quark determined? If the methods are different for the charm quark, how was the mass of the charm quark determined?
So quark masses are a vexed subject. The problem is that you cannot catch a quark on its own, it’s always swimming in a virtual soup of gluons and quarks. So all quark masses are determined, basically, by taking some model of the strong interaction and trying to back-calculate the observed hadron and meson masses. And since the strong interaction is insanely computationally intractable, you can’t get a very good answer.
For the tau lepton it’s rather simpler: Wait for one to decay to charged hadrons, calculate the four-momentum of the mother particle, and get the peak of the mass distribution as described above.
Does the weak interaction cause any sort of movement, or hold anything together, or does it only act as a trigger for decay?
I don’t believe anyone has observed a bound state mediated purely by the weak force. In fact one of the particles in such a state would have to be a neutrino, since otherwise there would be other forces involved; and observing a neutrino is hard enough without adding the requirement that it be a bound state. However, I suppose that in inverse-beta-decay, or neutrino capture, the weak force causes some movement at the final movement, to the extent that it’s meaningful to speak of movement at these scales.
Why is it considered a field energy?
Because it can be quantised into carrier bosons, presumably.
When detecting gamma radiation, how much background is there to extract from?
This is really hard to give a general answer for. In the BaBar detector, photons are reconstructed by the EMC, the electromagnetic calorimeter. My rule of thumb for this instrument is that photons with energy less than 30 MeV are worthless; such energies can easily be faked by the electronic noise and ambient radiation. Above 100 MeV you have to be fairly unlucky for an EMC hit to be background. I don’t know if this is helpful; perhaps you can give me a better idea of the context of your question?
Does the process of extracting from the background require performing hundreds of iterations of the experiment?
Again, this is really dependent on context. Can you be more specific about what sort of experiment you’re asking about?
Since you know quite a lot about it, and since the majority of my knowledge comes from Wikipedia, what does “fitting distributions in multiple dimensions” mean? What is the possibility of error of this process?
Have a look at my answer to magfrump. As for errors, our search algorithm does rely on the log-probability function being reasonably smooth, and can give misleading answers if that’s not true. It can get caught in local minima; we try to avoid this by starting from several different points and checking that we converge to the same place. In some cases the assumption of symmetric errors can mislead you, so we often look at asymmetric errors as well. Most insidiously, of course, you can get the physics just wrong, but right enough to mimic the data within the limits of the fit’s accuracy.
Oh, and lastly, do you know of any chart or list anywhere that details the known possible decay paths of bosons and fermions?
I had to split my answer in two, and clumsily posted them in the wrong order—some of this refers to an ‘above’ which is actually below. I suggest reading in chronological rather than page order. :)
Well no, you get a specific resonance in hadron energy spectra, as described above.
There’s the notorious sigma and kappa resonances, which are basically there only to explain a structure in the pion-pion and pion-kaon scattering spectrum. Belief in these as particles proper, rather than some feature of the dynamics, is not widespread outside the groups that first saw them. (I have a photoshopped WWII poster somewhere, captioned “Is YOUR resonance needed? Unnecessary particles clutter up the Standard Model!) I see the PDG doesn’t even list them in its “needs confirmation” section. I’m aware of them basically because I used them in my thesis just as a way to vary the model and see how the result varied—I had all the machinery for setting up particles, so a more-or-less fictional particle with some motivation from what others have seen was a convenient way of varying the structure.
So quark masses are a vexed subject. The problem is that you cannot catch a quark on its own, it’s always swimming in a virtual soup of gluons and quarks. So all quark masses are determined, basically, by taking some model of the strong interaction and trying to back-calculate the observed hadron and meson masses. And since the strong interaction is insanely computationally intractable, you can’t get a very good answer.
For the tau lepton it’s rather simpler: Wait for one to decay to charged hadrons, calculate the four-momentum of the mother particle, and get the peak of the mass distribution as described above.
I don’t believe anyone has observed a bound state mediated purely by the weak force. In fact one of the particles in such a state would have to be a neutrino, since otherwise there would be other forces involved; and observing a neutrino is hard enough without adding the requirement that it be a bound state. However, I suppose that in inverse-beta-decay, or neutrino capture, the weak force causes some movement at the final movement, to the extent that it’s meaningful to speak of movement at these scales.
Because it can be quantised into carrier bosons, presumably.
This is really hard to give a general answer for. In the BaBar detector, photons are reconstructed by the EMC, the electromagnetic calorimeter. My rule of thumb for this instrument is that photons with energy less than 30 MeV are worthless; such energies can easily be faked by the electronic noise and ambient radiation. Above 100 MeV you have to be fairly unlucky for an EMC hit to be background. I don’t know if this is helpful; perhaps you can give me a better idea of the context of your question?
Again, this is really dependent on context. Can you be more specific about what sort of experiment you’re asking about?
Have a look at my answer to magfrump. As for errors, our search algorithm does rely on the log-probability function being reasonably smooth, and can give misleading answers if that’s not true. It can get caught in local minima; we try to avoid this by starting from several different points and checking that we converge to the same place. In some cases the assumption of symmetric errors can mislead you, so we often look at asymmetric errors as well. Most insidiously, of course, you can get the physics just wrong, but right enough to mimic the data within the limits of the fit’s accuracy.
You could try the PDG’s summary tables.