I’ve got a lot of questions I just thought of today. I am personally hoping to think of a possible alternative model of quantum physics that doesn’t need anything more than the generation 1 fermions and photons, and doesn’t need the strong interaction.
What is the reason for the existence of the theory of the charm quark (or any generation 2-3 quark)? What are some results of experiments that necessitate the existence of a charm quark?
Which of the known hadrons can be directly observed in any way, as opposed to theorized as a mathematical in-between or as a trigger for some directly observable decay?
Am I right in thinking that the tau lepton is only theorized in order to explain an in-between decay state? 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?
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?
Does the weak interaction cause any sort of movement, or hold anything together, or does it only act as a trigger for decay? Why is it considered a field energy?
When detecting gamma radiation, how much background is there to extract from? Does the process of extracting from the background require performing hundreds of iterations of the experiment?
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?
Oh, and lastly, do you know of any chart or list anywhere that details the known possible decay paths of bosons and fermions?
That’s all for now. I SO hope you can answer any of these questions; because Wikipedia can’t :’(
(as someone who enjoys theory, I find it annoying when Wikipedia can neither confirm nor deny my conjectures, despite the fact that the information is certainly out there somewhere, and someone knows it.)
Ok, that’s a lot of questions. I’ll do my best, but I have to tell you that your quest is, in my opinion, a bit quixotic.
What is the reason for the existence of the theory of the charm quark (or any generation 2-3 quark)? What are some results of experiments that necessitate the existence of a charm quark?
Basically the strange quark is motivated by the existence of kaons, charm quarks by the D family of mesons (well, historically the J/psi, but I’m more familiar with the D mesons), and beauty quarks by the B family. As for truth quarks, mainly considerations of symmetry. Let’s take kaons, the argument being the same for the other families. If the kaon were to decay by the strong force, it would be extremely short-lived, because it could go pretty immediately to two pions; there would certainly be no question of seeing it in a tracking detector, the typical timescale of strong decays being 10^-23 seconds. Even at lightspeed you don’t get far in that time! We therefore conclude that there is some conservation principle preventing the strong decay, and that the force by which the kaon decays does not respect this conservation principle. Hence we postulate a strange quark, whose flavour (strangeness) is conserved by the strong force (so, no strange-to-up (or down) transition at strong-force speeds) but not by the weak force.
I should note that quark theory has successfully predicted the existence of particles before they were observed; you might Google “Eightfold Path” if you’re not familiar with this history, or have a look at the PDG’s review. (Actually, on closer inspection I see that the review is intending for working physicists familiar with the history—it’s not an introduction to the Eightfold Path, per se. Probably Google would serve you better.)
Which of the known hadrons can be directly observed in any way, as opposed to theorized as a mathematical in-between or as a trigger for some directly observable decay?
For this I have to digress into cross-sections. Suppose you are colliding an electron and a positron beam, and you set up a detector at some particular angle to the beam—for example, you can imagine the detector looking straight down at the collision point:
___detector
e+ -----> collision <------- e-
Now, the cross-section (which obviously is a function of the angle) can be thought of as the probability that you’ll see something in the detector. If electron and positron just glance off each other without annihilating (at relativistic speeds this can easily happen—they have to get pretty close to interact, and our control of the beams is only so good), we call that Bhabha scattering, and it has a particular cross-section structure. For obvious reasons, the cross-section is highest at small angles; that is, it is really quite unlikely for the electron and positron to dance past each other in the exact way that throws them out at a ninety-degree angle to their previous paths; but it’s pretty easy for them to give each other a one-degree kick. If you calculate the cross-section at some particular angle as a function of the total beam energy, you’ll see that the higher the energy, the lower the cross-section, and indeed experiment confirms this.
What if the electron and positron do annihilate, creating a virtual photon that then decays to some other pair of particles—for example, a charm-anticharm pair? Well, again, the cross-section is highest near the beam (basically to conserve the angular momentum—you have to do spin math) and decreases with energy.
So we have this cross-section that decreases monotonically with energy. However, as you run your beam energy up, at very specific energies you will see a sharp increase and drop-off, in a classic Breit-Wigner shape. In other words, at some particular energy it suddenly becomes much more likely that your decay products get kicked away from the beam. Why is that? We refer to these bumps in the spectrum as resonances, and explain them by appealing to bound states—particles, in other words. What happens is that with an intermediate bound state, there are additional Feynman paths that open up between the initial state “electron and positron” and the final state “hit in detector at angle X”. Additional paths through parameter space gives you additional probability unless you’re very unlucky with the phases, hence the bump in the cross-section—the final state becomes more likely. (Additionally, for reasons of spin math that I won’t go into here, the decay products from a bound state of two quarks are produced much more isotropically than back-to-back quark-antiquark pairs.)
Here’s a different way of looking at it. Suppose you have a detector that encloses the collision space, so you can reconstruct most of the decay products; and you decide to take all pion pairs and calculate “If these two particles came from a common decay, what was the mass of the particle that decayed?” Then this spectrum will basically be flat, but you will get an occasional peak at specific masses. Again, we explain this by appeal to a bound state.
It occurs to me that this may not actually differ from what you call “mathematical in-betweens”; I have answered as though this phrase refers to virtual particles, which are indeed a bit of a convenient fiction. Anyway, this is why we believe in the various hadrons and mesons.
(I’m getting “comment too long” errors; splitting my answer here.)
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’ve got a lot of questions I just thought of today. I am personally hoping to think of a possible alternative model of quantum physics that doesn’t need anything more than the generation 1 fermions and photons, and doesn’t need the strong interaction.
What is the reason for the existence of the theory of the charm quark (or any generation 2-3 quark)? What are some results of experiments that necessitate the existence of a charm quark?
Which of the known hadrons can be directly observed in any way, as opposed to theorized as a mathematical in-between or as a trigger for some directly observable decay?
Am I right in thinking that the tau lepton is only theorized in order to explain an in-between decay state? 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?
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?
Does the weak interaction cause any sort of movement, or hold anything together, or does it only act as a trigger for decay? Why is it considered a field energy?
When detecting gamma radiation, how much background is there to extract from? Does the process of extracting from the background require performing hundreds of iterations of the experiment?
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?
Oh, and lastly, do you know of any chart or list anywhere that details the known possible decay paths of bosons and fermions?
That’s all for now. I SO hope you can answer any of these questions; because Wikipedia can’t :’( (as someone who enjoys theory, I find it annoying when Wikipedia can neither confirm nor deny my conjectures, despite the fact that the information is certainly out there somewhere, and someone knows it.)
Ok, that’s a lot of questions. I’ll do my best, but I have to tell you that your quest is, in my opinion, a bit quixotic.
Basically the strange quark is motivated by the existence of kaons, charm quarks by the D family of mesons (well, historically the J/psi, but I’m more familiar with the D mesons), and beauty quarks by the B family. As for truth quarks, mainly considerations of symmetry. Let’s take kaons, the argument being the same for the other families. If the kaon were to decay by the strong force, it would be extremely short-lived, because it could go pretty immediately to two pions; there would certainly be no question of seeing it in a tracking detector, the typical timescale of strong decays being 10^-23 seconds. Even at lightspeed you don’t get far in that time! We therefore conclude that there is some conservation principle preventing the strong decay, and that the force by which the kaon decays does not respect this conservation principle. Hence we postulate a strange quark, whose flavour (strangeness) is conserved by the strong force (so, no strange-to-up (or down) transition at strong-force speeds) but not by the weak force.
I should note that quark theory has successfully predicted the existence of particles before they were observed; you might Google “Eightfold Path” if you’re not familiar with this history, or have a look at the PDG’s review. (Actually, on closer inspection I see that the review is intending for working physicists familiar with the history—it’s not an introduction to the Eightfold Path, per se. Probably Google would serve you better.)
For this I have to digress into cross-sections. Suppose you are colliding an electron and a positron beam, and you set up a detector at some particular angle to the beam—for example, you can imagine the detector looking straight down at the collision point:
___detector
e+ -----> collision <------- e-
Now, the cross-section (which obviously is a function of the angle) can be thought of as the probability that you’ll see something in the detector. If electron and positron just glance off each other without annihilating (at relativistic speeds this can easily happen—they have to get pretty close to interact, and our control of the beams is only so good), we call that Bhabha scattering, and it has a particular cross-section structure. For obvious reasons, the cross-section is highest at small angles; that is, it is really quite unlikely for the electron and positron to dance past each other in the exact way that throws them out at a ninety-degree angle to their previous paths; but it’s pretty easy for them to give each other a one-degree kick. If you calculate the cross-section at some particular angle as a function of the total beam energy, you’ll see that the higher the energy, the lower the cross-section, and indeed experiment confirms this.
What if the electron and positron do annihilate, creating a virtual photon that then decays to some other pair of particles—for example, a charm-anticharm pair? Well, again, the cross-section is highest near the beam (basically to conserve the angular momentum—you have to do spin math) and decreases with energy.
So we have this cross-section that decreases monotonically with energy. However, as you run your beam energy up, at very specific energies you will see a sharp increase and drop-off, in a classic Breit-Wigner shape. In other words, at some particular energy it suddenly becomes much more likely that your decay products get kicked away from the beam. Why is that? We refer to these bumps in the spectrum as resonances, and explain them by appealing to bound states—particles, in other words. What happens is that with an intermediate bound state, there are additional Feynman paths that open up between the initial state “electron and positron” and the final state “hit in detector at angle X”. Additional paths through parameter space gives you additional probability unless you’re very unlucky with the phases, hence the bump in the cross-section—the final state becomes more likely. (Additionally, for reasons of spin math that I won’t go into here, the decay products from a bound state of two quarks are produced much more isotropically than back-to-back quark-antiquark pairs.)
Here’s a different way of looking at it. Suppose you have a detector that encloses the collision space, so you can reconstruct most of the decay products; and you decide to take all pion pairs and calculate “If these two particles came from a common decay, what was the mass of the particle that decayed?” Then this spectrum will basically be flat, but you will get an occasional peak at specific masses. Again, we explain this by appeal to a bound state.
It occurs to me that this may not actually differ from what you call “mathematical in-betweens”; I have answered as though this phrase refers to virtual particles, which are indeed a bit of a convenient fiction. Anyway, this is why we believe in the various hadrons and mesons.
(I’m getting “comment too long” errors; splitting my answer here.)
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.