How is time measured in particle experiments?

Question

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

Answer 1

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 $\Gamma≈4\,\rm MeV$.

Answer 2

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.