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How are quarks and leptons (including subatomic particles) detected in the laboratory,especially when most hadrons and leptons have a lifespan for a considerable small amount of time?Also how do we measure the extremely small lifespans with great accuracy?

Any answers or links will be helpful.

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  • $\begingroup$ Special relativity tells you that if these particles are accelerated to a very high speed v (close to c), as it is the case in the LHC, then the lifetime of these particles, in the reference frame of the laboratory, is $\tau=\gamma(v)\tau_0$ (where $\tau_0$ is the proper lifetime of the particle, and $\gamma(v)\ge 1$ is the Lorentz factor). In other words, due to time dilation at high velocities, the particle in the accelerator will appear to exist for a longer period of time. $\endgroup$ – Demosthene Jan 19 '15 at 18:17
  • $\begingroup$ Is it observed in experiments that acceleration causes time dilation or is it still a theory?And by acceleration, do you mean change in direction or accelerating in a straight line since i guess the latter would need a lot of distance to travel even in a short time and we can't make an instrument that big on earth. $\endgroup$ – user65445 Jan 19 '15 at 18:31
  • $\begingroup$ You can see in the bubble chamber picture I have in my answer the low energy muon decaying while the high energy one goes straight out of the picture. And it is high velocity that slows time, not acceleration. $\endgroup$ – anna v Jan 19 '15 at 20:07
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Leptons are easy and have been seen for many decades

leptons

A "textbook" picture from the BEBC bubble chamber. A neutrino interacts with a proton in the liquid hydrogen to produce a negative muon, a proton and an excited charmed meson (D*). The D* decays to a charmed D0 meson plus a positive pion and the D0 itself decays to a negative kaon and another positive pion. After stopping in the liquid the kaon interacts with another proton to produce a hyperon.

Using energy and momentum conservation one can solve for the masses. [Neutrinos using algebra and from missing energy and momentum, electrons and muons from direct observation. Taus from algebra and energy momentum conservation. The new experiments use sophisticated electronics to measure the curvatures which will give the momenta and the programs do the fit event per event.

Quarks have only been seen as quark jets, because they are never free.

enter image description here

Top quark and anti top quark pair decaying into jets, visible as collimated collections of particle tracks, and other fermions in the CDF detector at Tevatron.

The CERN teaching materials will be a help for those interested. Particularly these.

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Among all elementary particles, only $e^\pm$, $\mu^\pm$ and $\gamma$ are detected directly in the modern detectors. For, $e^\pm, \gamma$, calorimeters are used: these particles interact with material having a large atomic numbers creating many more electrons and photons producing what is called an electromagnetic shower. For muons, gas detectors are usually used in association with a tracker (that can be made with silicon detectors) that can measure the trajectory of charged particles thanks to a powerful magnet.

All the other elementary particles are detected through their decay products by combining their energy/momentum in order to measure the invariant mass of the decay products. The comparison of the invariant mass with the nominal mass of the particle give a good indication of the nature of the particle.

In case of the $\tau$ lepton, the lifetime is large enough, so that they can fly a few mm before decaying. Hence, by detecting the primary vertex (source of the collision) where the $\tau$ has been produced and the decay vertex, we can measure their time of flight. The combination of the time of flight and the invariant mass of the decay products are a good way to identify the $\tau$.

Quarks cannot fly freely and are necessarily "dressed" into hadrons (pions, proton etc). If the energy of the quark is large enough (and this is the case with modern experiment), 1 single quark will produce a large number of hadrons flying roughly in the same direction as the initial quark. This will form a jet of hadrons. Now $b$ quark and to a lesser extent c quark produce respectively B and charmed hadrons that can fly few mm. So again, a jet of hadrons not pointing to the primary vertex is a sign of $b$ or $c$ quark. For $u,d,s$ quarks, they produce jets that cannot be really distinguished (at least with the high energy collisions of nowadays). Gluons produce same kind of jets (but slightly broader). top quark is a bit special: its lifetime is so short that it decays immediately into a b quark plus a $W$. So the association of a $b$-jet with a $W$ (see later) is a sign of a $t$ quark. Hadrons contained in the jets are detected with hadron calorimeters.

$Z$ and $W$ bosons have a very short lifetime and decay as soon as they are produced. However their mass is huge compared to (almost) all the other elementary particles. $Z$ can have a clear signature via their leptonic decay $Z\to e^+ + e^-, \mu^+ + \mu^-, \tau^+ + \tau^-$. When they decay into quarks $q \bar{q}$, they produced 2 jets that can be combined to measure the invariant mass (but with a much less good accuracy that with leptonic channel). For $W$, they can decay into a neutrino and a charged lepton or into $q \bar{q'}$ producing 2 jets. The neutrinos are not detected and so will appear as a missing energy flow by comparison with the initial energy of the collision. The combination of the magnitude of this missing energy and its direction with the charged lepton give an approximate mass spectrum with a shape that can be used to track the $W$. With the W hadronic decay (into jets), the combination of jets give also access to the invariant mass.

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  • $\begingroup$ This is a good answer, but you make some statements about the selection of detector elements that are only true in the high-energy collider world. Other kinds of PID than calorimetry are widely used at lower energies. $\endgroup$ – dmckee --- ex-moderator kitten Jan 25 '15 at 5:31

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