particle-physicsquarksstandard-model
Protons and neutrons, which are found in everyday matter around us, compose of up and down quarks. Are the other two generations of quarks, i.e. $c,s,t,b$ quarks found in everyday matter around us?
I am learning about these fundamental particles and would like to know how they relate to our daily life. Are they mostly irrelevant to our daily life except in extreme physical conditions, like in the particle colliders?
The question: "I'm wondering if there is some good reason why the universe as we know it has to have twelve particles rather than just four."
The short answer: Our current standard description of the spin-1/2 property of the elementary particles is incomplete. A more complete theory would require that these particles arrive in 3 generations.
The medium answer: The spin-1/2 of the elementary fermions is an emergent property. The more fundamental spin property acts like position in that the Heisenberg uncertainty principle applies to consecutive measurements of the fundamental spin the same way the HUP applies to position measurements. This fundamental spin is invisible to us because it is renormalized away. What's left is three generations of the particle, each with the usual spin-1/2.
When a particle moves through positions it does so by way of an interaction between position and momentum. These are complementary variables. The equivalent concept for spin-1/2 is "Mutually unbiased bases" or MUBs. There are only (at most) three MUBs for spin-1/2. Letting a particle's spin move among them means that the number of degrees of freedom of the particle have tripled. So when you find the long time propagators over that Hopf algebra you end up with three times the usual number of particles. Hence there are three generations.
The long answer: The two (more or less classical) things we can theoretically measure for a spin-1/2 particle are its position and its spin. If we measure its spin, the spin is then forced into an eigenstate of spin so that measuring it again gives the same result. That is, a measurement of spin causes the spin to be determined. On the other hand, if we measure its position, then by the Heisenberg uncertainty principle, we will cause an unknown change to its momentum. The change in momentum makes it impossible for us to predict the result of a subsequent position measurement.
As quantum physicists, we long ago grew accustomed to this bizarre behavior. But imagine that nature is parsimonious with her underlying machinery. If so, we'd expect the fundamental (i.e. before renormalization) measurements of a spin-1/2 particle's position and spin to be similar. For such a theory to work, one must show that after renormalization, one obtains the usual spin-1/2.
A possible solution to this conundrum is given in the paper:
Found.Phys.40:1681-1699,(2010), Carl Brannen, Spin Path Integrals and Generations
http://arxiv.org/abs/1006.3114
The paper is a straightforward QFT resummation calculation. It assumes a strange (to us) spin-1/2 where measurements act like the not so strange position measurements. It resums the propagators for the theory and finds that the strange behavior disappears over long times. The long time propagators are equivalent to the usual spin-1/2. Furthermore, they appear in three generations. And it shows that the long time propagators have a form that matches the mysterious lepton mass formulas of Yoshio Koide.
Peer review: The paper was peer-reviewed through an arduous process of three reviewers. As with any journal article it had a managing editor, and a chief editor. Complaints about the physics have already been made by competent physicists who took the trouble of carefully reading the paper. It's unlikely that someone making a quick read of the paper is going to find something that hasn't already been argued through. The paper was selected by the chief editor of Found. Phys. as suitable for publication in that journal and so published last year.
The chief editor of Found. Phys. is now Gerard 't Hooft. His attitude on publishing junk is quite clear, he writes
How to become a bad theoretical physicist
On your way towards becoming a bad theoretician, take your own immature theory, stop checking it for mistakes, don't listen to colleagues who do spot weaknesses, and start admiring your own infallible intelligence. Try to overshout all your critics, and have your work published anyway. If the well-established science media refuse to publish your work, start your own publishing company and edit your own books. If you are really clever you can find yourself a formerly professional physics journal where the chief editor is asleep. http://www.phys.uu.nl/~thooft/theoristbad.html
One hopes that 't Hooft wasn't asleep when he allowed this paper to be published.
Extensions: My next paper on the subject extends the above calculation to obtain the weak hypercharge and weak isospin quantum numbers. It uses methods similar to the above, that is, the calculation of long time propagators, but uses a more sophisticated method of manipulating the Feynman diagrams called "Hopf algebra" or "quantum algebra". I'm figuring on sending it in to the same journal. It's close to getting finished, I basically need to reread it over and over and add references:
http://brannenworks.com/E8/HopfWeakQNs.pdf
The analysis of the phase structure of gauge theories is a whole field. Some major breakthroughs were the t'Hooft anomaly matching conditions, the Banks-Zaks theories, Seiberg duality, and Seiberg Witten theory. There is a lot of controversy here, because we don't have experiment or simulation data for most of the space, and there is much more unknown than known.
The first thing to note is that when the Higgs field vacuum expectation value is zero, the Higgs doesn't touch the low energy physics. You can ignore the Higgs at energy scales lower than it's mass, and if this mass is much greater than the proton mass, the result is indistinguishable qualitatively from the Higgsless standard model. So I'll describe the Higgsless standard model.
Even without the Higgs, electroweak symmetry is broken anyway by QCD condensates. When the Higgs VEV is zero, the W and Z do not become completely massless, although they become much much lighter.
The reason is that QCD has a nontrivial vacuum, where quarks antiquark pairs form a q-qbar scalar fluid that breaks the chiral symmetry of the quark fields spontaneously. This phenomenon is robust to the number of light quark flavors, assuming that there aren't so many that you deconfine QCD. QCD is still asymptotically free with 6 flavors, and it should be confining even with 6 flavors of quarks. So I have no compunctions about assuming the confinement mechanism still works with 6 flavors, and all 6 are now like the up and down quark. Assuming the qualitative vacuum structure is analogous to QCD is plausible and consistent with the anomaly conditions, but if someone were to say "no, the vacuum structure of QCD with 6 light quarks is radically different from the vacuum structure of QCD", I wouldn't know that this is wrong with certainty, although it would be strange.
Anyway, assuming that QCD with 6 light quarks produces the same sorts of condensates as QCD with 3 light quarks (actually 2 light quarks and a semi-light strange quark), the vacuum will be filled with a fluid which breaks SU(6)xSU(6) chiral rotations of quark fields into the diagonal SU(6) subgroup. The SU(6) is exact in the strong interactions and mass terms, it is only broken by electroweak interactions.
The electroweak interactions are entirely symmetric between the 3 families, so there is a completely exact SU(3) unbroken to all orders. The SU(6)xSU(6) breaking makes a collection of massless Goldstone bosons, massless pions. The number of massless pions is the number of generators of SU(6), which is 35. Of these, 8 are exactly massless, while the rest get small masses from electroweak interactions (but 3 of the remaining 27 go away into W's and Z's by Higgs mechanism, see below). The 8 massless scalars give long-range nuclear forces, which are an attractive inverse square force between nuclei, in addition to gravity.
The hadrons are all nearly exactly symmetric under flavor SU(6) isospin, and exactly symmetric under the SU(3) subgroup. All the strongly interacting particles fall into representation of SU(6) now, and the mass-breaking is by terms which are classified by the embedding of SU(3) into SU(6) defined by rotating pairs of coordinates together into each other.
The pions and the nucleons are stable, the pion stability is ensured by being massless, the nucleon stability by approximate baryon number conservation. At least the lowest energy SU(3) multiplet
The condensate order-parameter involved in breaking the chiral SU(6) symmetry of the quarks is $\sum_i \bar{q}_i q_i$ for $q_i$ an indexed list of the quark fields u,d,c,s,t,b. The order parameter is just like a mass term for the quarks, and I have already diagonalized this order parameter to find the mass states. The important thing about this condensate is that the SU(2) gauge group acts only on the left-handed part of the quark fields, and the left-handed and right handed parts have different U(1) charge. So the condensate breaks the SU(2)xU(1) gauge symmetry.
The breaking preserves a certain unbroken U(1) subgroup, which you find by acting the SU(2) and U(1) generators. The left handed quark field has charge 1/6 and makes a doublet, so for the combination $I_3+Y/2$ where I is the SU(2) generator and Y is the U(1) generator, you get a transformation of 2/3 and 1/3 on the top and bottom component, which is exactly the same as $I_z + Y/2$ on the singlets (since they have no I). So this combination isn't chiral, and preserves the vacuum. So the QCD vacuum preserves the ordinary electromagnetic subgroup, which means it makes a Higgs, just like the real Higgs, which breaks the SU(2)xU(1) down to U(1) electromagnetic, with W and Z bosons just like in the standard model.
This is not really as much of a coincidence as it appears to be--- a large part of this is due to the fact that QCD condensates in our universe are not charged, so that they don't break electromagnetism, because u-bar and u have opposite electromagnetic charge transformation. This means that a u-bar u condensation leaves electromagnetism unbroken, and it isn't a surprise that it doesn't leave any of the rest of SU(2) and U(1) unbroken, because it's a chiral condensate, and these are chiral gauge transformations.
The major difference is that there are 3 separate Higgs-like condensates, one for each family, each with an identical VEV, all completely symmetric with each other under the global exact SU(3) family symmetry.
The W's and Z's get a mass from an arbitrary one of these 3, leaving 2 dynamical Higgs-like condensates. The main difference is that these scalar condensates don't necessarily have a simple distinguishable higgs-boson-like oscillation, unlike a fundamental scalar Higgs. The result of this is that the W's and Z's acquire QCD-scale masses, so around 100 MeV for the W's and Z's, as opposed to approximately 100 GeV in the real world. The ratio of the W and Z mass is exactly as in the standard model.
The low energy spectrum of QCD is modified drastically, due to the large quark number. The 8 massless pions and 24 nearly massless pions (three of the pions are eaten by the W's and Z's to become part of the massive vectors) include all the diquark degrees of freedom that we call the pions,kaons and certain heavy quark mesons. There will still be a single instanton heavy eta-prime from the instanton violated chiral U(1) part of U(6)xU(6). There should be 35 rho particles splitting into 8 and 27 and 35 A particles splitting into 8 and 27 effectively gauging the flavor symmetry.
The 6 quarks could be thought of as getting a mass from their strong interaction with the Higgs-like condensates, of order some meVs, but since the mass of a quark is defined at short distances, from the propagator, it might be more correct to say the quarks are massless. Some of the particles you see in the data-book, the sigma(660), the f0(980) should disappear (as these are weird--- they might be the product of pion interactions making some extremely unstable bound states, something which wouldn't work with massless pions)
The electron and neutrino will be massless except for nonrenormalizable quark-lepton direct coupling, which would couple the electron to the Higgslike chiral quark condensate. This effect is dimension 6, so the compton wavelength of the electron will be comparable to the current radius of the visible universe. The neutrino mass will be even more strongly suppressed, so it might as well be exactly massless.
The massless electron will lead the electromagnetic coupling (the unHiggsed U(1) left over below the QCD scale) to logarithmically go to zero at large distances, from the log-running of QED screening. So electromagnetism, although it will be the same subgroup of SU(2) and U(1) as in the Higgsed standard model, will be much weaker at macroscopic distances than it is in our universe.
Nuclei should form as usual at short distances, although Isospin is now a nearly exact SU(6) symmetry broken only by electromagnetism, and not by quark mass, and with an exact SU(3) subgroup. So all nuclei come in SU(6) multiplets slightly split into SU(3) multiplets. The strong force will be longer ranged, and without the log-falloff of the electromagnetic force, because the pions quickly run to a free-field theory, since the pion self-interactions are of a sigma-model type. The pion interactions will look similar to gravity in a Newtonian approximation, but scalar mediated, so not obeying the equivalence principle, and disappearing in scattering at velocities comparable to the speed of light.
The combination of a long-ranged attractive nuclear force and a log-running screened electromagnetic force might give you nuclear bound galaxies, held at fixed densities by the residual slowly screened electrostatic repulsion. These galaxies will be penetrated by a cloud of massless electrons and positrons constantly pair-producing from the vacuum.
Best Answer
Every nucleon has what are called sea quarks in it, in addition to the valence quarks that define the nucleon as a proton or neutron. Some of those sea quarks, especially the strange quarks, have some secondary relevance in practical terms regarding how the residual strong nuclear force between protons and neutrons in an atomic nucleus is calculated from first principles and how stable a free neutron is if you calculate that from first principles. Strange quarks are also found in the $\Lambda^0$ baryon (which has quark structure $uds$), which is present at a low frequency in cosmic rays, but has a mean lifetime of only about two tenths of a nanosecond and is only indirectly detected in the form of its decay products.
Strange quarks are also relevant at a philosophical level that could impact your daily life, because mesons including strange quarks called kaons, are the lightest and most long lived particles in which CP violation is observed; thus, strange quarks are what made it possible for us to learn that the laws of physics at a quantum level are not independent of an arrow of time.
You could do a lot of sophisticated engineering for a lifetime without ever knowing that second or third generation quarks existed, even nuclear engineering. Indeed, the basic designs of most nuclear power plants and nuclear weapons in use in the United States today were designed before scientists knew that they existed. The fact that protons and neutrons are made out of quarks was a conclusion reached in the late 1960s and not widely accepted until the early 1970s, although strange quark phenomena were observed in high energy physics experiments as early as the 1950s. Third generation fermions were discovered even later. The tau lepton was discovered in 1974, the tau neutrino in 1975, the b quark in 1977, and the top quark in 1995 (although its existence was predicted and almost certain in the 1970s).
Otherwise, these quarks are so ephemeral and require such concentrated energy to produce, that they have no real impact on daily life and are basically never encountered outside of high energy physics experiments, although some of them may be present in and influence to properties of distant neutron stars. Second and third generation quarks also definitely played an important part in the process of the formation of our universe shortly after the Big Bang.
The only second or third generation fermion in the Standard Model with significant practical engineering applications and an impact on daily life and on technologies that are used in the real world are muons (the second generation electron). Muons are observed in nature in cosmic rays (a somewhat misleading term since it doesn't include only photons) and in imaging technologies similar to X-rays but with muons instead of high energy photons. Muons are also used in devices designed to detect concealed nuclear isotypes. Muons were discovered in 1937, although muon neutrinos were first distinguished from electron neutrinos only in 1962, and the fact that neutrinos have mass and that different kinds of neutrinos have different masses was only established experimentally in 1998.