Of course I know about up and down quarks, but I cannot seem to find that much about the other four (of course being eight if we're including antiquarks). Is mass the only difference between the quarks? Can the other quarks form hadrons of their own? Is there some interesting matter or reaction or anything that any of them can make or do, or are they really as boring as the Internet has been telling me?

# [Physics] Top, bottom, charm, and strange

particle-physicsquarks

#### Related Solutions

* 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.

http://www.phys.uu.nl/~thooft/theoristbad.htmlIf you are really clever you can find yourself a formerly professional physics journal where the chief editor is asleep.

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 residual strong force […] is mediated by pions exchanged between protons and neutrons.

This is a pretty big oversimplification of the strong nuclear force. The pion, as the lightest member of the meson spectrum, can be associated with the longest-range part of the residual strong force. But if you’re also interested in the phenomenon that nuclear matter has constant density, you already have to go further up in the meson spectrum than the pion to find a repulsive interaction. In many-body systems or in high-energy interactions, the meson-exchange picture rapidly stops being a useful way to make quantitative predictions.

Your question about “all hadrons” suggests you are also curious about long-range interactions between mesons. That’s basically impossible to measure directly, because all mesonic hadrons are short-lived. It’s one thing to build an accelerator that makes a beam of pions or kaons; it’s a different thing altogether to make two such accelerators and point the beams at each other. Beam-beam interaction experiments, like the Large Hadron Collider, make use of stored beams of stable particles. (A possible exception was a neutron-neutron scattering length measurement which used the simultaneous detonation of two nuclear bombs in the same underground cavity. Its results were never published; I have heard variously that a blast door failed and the DAQ was destroyed, that the experiment was proposed but never attempted, and that the whole thing is an extremely niche urban legend.)

To the extent there *are* residual meson-meson interactions, virtual mesons will participate in them as well, and those meson-meson interactions show up as modifications to your model of the meson-mediated nuclear force. That recursive relationship gets messy fast. For a taste of how complicated it is, look for literature about whether the “fictitious $\sigma$” (renamed $f_0(500)$ in the current PDG) is a “real” meson or a two-pion bound state.

Long-lived baryons absolutely participate in the nuclear force, illustrated most clearly by hypernuclei made of protons, neutrons, and exotic baryons. (In practice there’s just one hyperon, for the same reason as the absence of meson-meson colliders.)

For short-lived baryons, it’s not clear whether the meson-mediated approximation would be useful under any circumstances. The effective range of the pion-mediated force is related to the pion’s mass:

$$ r_\pi = \frac{\hbar c}{m_\pi c^2} \approx 1.3\rm\,fm \approx r_\text{nucleon} $$

An unstable state with lifetime $\tau$ has an intrinsic uncertainty $\Gamma$, or width, in its total energy,

$$ \Gamma \tau \approx \hbar $$

which you can think of as a kind of energy-time version of the uncertainty principle. If we use $\hbar = c = 1$ units so that energy, mass, (inverse) time, and (inverse) distance are all measured in the same units, you might say that a particle whose decay width is larger than the pion mass, $\Gamma > m_\pi$, will probably have already decayed in the time it takes for light to cross a nucleon. It’s not clear (to me) what it would mean to “interact” with a particle which has already decayed before you finish touching it.

## Best Answer

Wikipedia does a good job of explaining the quarks, but really all you need to know is in the handy Standard Model particle chart:

Quarks come in three generations and two different electrical charges, $+2/3$ and $-1/3$. Like the up and down quarks, which differ in electric charge and therefore in how they can combine to make integer-charge baryons and mesons, the charm/strange and top-bottom quarks work slightly differently with respect to the kinds of combinations they can form. However, that is essentially it, and in particular the up / charm / top and down / strange / bottom triplets behave identically as far as which interactions they're able to take part in.

On the other hand, the masses are different from generation to generation, and that is not just some random property that you jot down and forget: the mass of a particle is (via $E=mc^2$) the energy that it can contribute to a reaction, and the more massive the particle, the more energy it can bring in, and the wider the array of reaction products that can come out.

Thus, if you start with, say, a Lambda baryon, you have enough energy to produce, say, a $\Delta^+$ baryon, which has $uud$ quark content with all their spins aligned (instead of two anti-aligned), and can therefore be seen, roughly, as an excited state of the proton system. On the other hand, if you start with a proton, you would need to provide some significant energy to excite it into the $\Delta^+$ state.

I should also mention that for each of the given quarks there is a quantum number known as flavour, or more specifically strangeness, charm, topness and bottomness, which can be used to characterize the particle content of the reaction at any given state. Unlike electric charge and baryon number, which are always conserved, the individual flavour numbers are only weakly conserved: many processes (and in particular strong-force and electromagnetic interactions) will respect them, but weak-force interactions don't.

Thus, as an example, the strong and electromagnetic interactions forbid the decay of the $\Sigma^+$ baryon (quark content $uus$) into a proton's $uud$, as that would decrease the strangeness of the state, so the process is relatively unlikely, as only weak-force routes can mediate the decay.