# How is time measured in particle experiments?

I was reading about the half life measurements and was curious to understand the experimental setups that allows so minute measurements to be captured. Specifically looking into half life of Higgs boson. I am looking to understand one example method of measuring Higgs boson half life. Please feel free to explain any one setup

• Do you have an example of a specific experiment? It would be hard to answer without that. Nonetheless I would be interested in the answer as well. Jul 5 at 22:42
• Often, even different experiments measuring the same thing use different methods. So currently the question may not be answerable. You would have to show us a specific paper, or an article referring to a specific experiment that some people did. Or you could just ask for any one example of a method which could measure the half life of a higgs boson, for example. Jul 5 at 23:01
• I just added requesting one example, any other suggestions Jul 5 at 23:19
• I have used my mod superpower to reopen this question, which survived its first trip through the close review queue and which was improved after two of three close votes were cast. The answer by tobi_s is an exceptionally fine bit of physics explication. If the community feels my unilateral action is inappropriate because I also answered the question, please raise a flag to summon another moderator, or we can have discussion in Physics Chat or on Physics Meta.
– rob
Jul 7 at 22:13

The Higgs is a challenging example because the tabulated quantity is the decay width $$\Gamma$$, from which a mean life $$t≈\hbar/\Gamma$$ is inferred. That is, nobody starts a clock when the Higgs is born and then stops it $$10^{-22}$$ seconds later. Instead, the short lifetime of the Higgs contributes an intrinsic uncertainty to its mass, and those variations in the masses of “Higgs events” show up in energy measurements.

Sub-nanosecond timing is a solved problem — consider that you are probably reading this post on a computer whose processor is driven by a sub-nanosecond (multi-gigahertz) clock. For picosecond-level timing, you have to account for the fact that electromagnetic signals travel no faster than 0.3 millimeters per picosecond, about the size of a flake of pepper. So you can’t do reliable picosecond timing on a signal that’s gone through a coaxial cable, because the propagation time through the cable might vary with temperature.

However, if you have a cloud chamber photograph of a relativistic particle, you might be able to measure the distance between two events with sub-millimeter precision, and get picosecond timing from your position data. Modern detectors don’t take photographs of vapor trails, but instead collect ionization from relativistic particles on an array of wires. The position and timing resolutions of modern detectors are the subject of lots of PhD theses.

You can use $$\hbar≈6\times10^{-4}\rm\,eV\,ps≈0.6\,eV\,fs$$ to do your own conversions between energy width and lifetime (though there’s a $$\ln2$$ floating around if you want half-life). The Higgs width is $$\Gamma≈4\,\rm MeV$$.

• Where do the 0.6 eV fs come from? Wikipedia says it's closer to 0.6582 eV fs. Jul 7 at 11:59
• Right, that’s a 9% difference, which would have been a 6% difference if I had rounded the single digit up instead of down. At the level of this answer, I don’t care. My concern was getting the decimal point in the right place.
– rob
Jul 7 at 14:54

The shortest lifetime that was directly measured is that of the neutral pion, or $$\pi^0$$, the lightest meson at a mass of $$m=135\,\textrm{MeV}$$. It decays to (predominantly) two photons and it has a lifetime of $$\tau=8.1\times 10^{-17}\textrm{s}$$. As such, it is both lighter and longer-lived than the Higgs by orders of magnitude, so much actually that particle physicists call it a stable particle. Nevertheless, it is interesting how such a lifetime could be measured. There is only one such measurement, performed in 1985 Phys. Lett. B 158 (1) 1985, pp. 81-84.

Let's discuss the principle of the measurement, but leaving aside some of the auxiliary difficulties. The idea is quickly told: at high energies $$E$$, the (observed) lifetime of the neutral pion increases by the usual dilation factor $$\gamma=E/m$$. Assume the neutral pion is produced by a beam incident on a thin foil of a dense material. Then to a very good approximation, the point of production will be equally distributed over the thickness of the foil and the total number of pions will be proportional to the thickness of the foil. Additionally, secondary hadronic reactions can be neglected for a thin enough foil. Two things can happen: the pion flies out of the foil and decays there, or the pion decays inside the foil. If it decays inside the foil, there is a chance for one or both of the decay photons to undergo pair conversion. The resulting electron/positron pairs are counted.

Let's have a look at some numbers. For ease of calculation, let's assume that $$\gamma = 1000$$ meaning an energy of $$135\,\textrm{GeV}$$, not uncommon in experiment. Then the lifetime will increase by a factor 1000, so $$\gamma\tau\approx 8.1\times 10^{-14}\textrm{s}$$. At these energies the velocity of the pion will be indistinguishable from the speed of light, i.e. (in useful units) $$30\textrm{cm}/\textrm{ns}$$, allowing the pion to propagate $$25\mu\textrm{m}$$. A foil of this thickness is technically feasible, e.g. Rutherford's famous experiment used a $$4\mu\textrm{m}$$ gold foil.

The experiment now proceeds by using foils of different thickness. The total number of pions produced is then proportional to the thickness of each foil. Once the foil becomes thicker than the speed of light times the (dilated) lifetime of the pion, the number of pair conversion will increase significantly, and the exact relation can be modeled as function of the neutral pion's lifetime. Fitting the model to the data gives the lifetime.

• Particle physicists don't call the pi0 stable -- even in collisions in the detectors at the LHC it decays into two photons before it reaches the calorimeters Jul 6 at 10:42
• @Andre Holzner a stable particle as opposed to a resonance. Historically, the terminology comes from nuclear physics, and so the definition is "crosses a distance larger than a nucleus before decaying." BTW just a funny observation: the EM calorimeter wouldn't really be important to the $\pi^0$ if it managed to reach it. Jul 7 at 0:14
• Note: I corrected the propagation length, I had lost a factor 10 when I was doing the math in my head. I was thinking that $3\mu$ was too thin, so I redid the math on paper, and now it's more in line with what I remember from when we discussed redoing the experiment a few years back. Jul 7 at 0:27
• I'm tempted to add a another answer that discusses what the lifetime of the Higgs means, but I see how this would be an encyclopedia article in itself. I already refrained from adding how the $\pi^0$ lifetime is indirectly measured. That would only need 1) relation width ⇄ lifetime 2) crossing symmetry 3) off-shell (virtual) photons and 4) photon-induced reactions. The short answer would be that when particle physicists talk about lifetime of short-lived particles (everything shorter than the $\pi^0$) they mean inverse width and assume that the physics connecting the two is correct. Jul 8 at 3:39