4 ms·

Would love to have an explanation of statistical vs total uncertainty, how they are quantified and how they are different.

• SaberTail 4y ago
  I haven't read the paper yet, but I can give a general idea based on my experience working on similar experiments. The W boson doesn't live long enough to make it to the detector. All they can see are the decay products. The detector is like an onion, with different layers measuring the energies and/or momentum of different decay products. So what a search like this is trying to do is look at these decay products, figure out which ones came from a W boson, combine the various energy and momentum measurements, and use that and relativity to determine the rest mass. The measurement process always has some error, so you want to combine multiple measurements. This is how you get the statistical uncertainty. As an oversimplified example, imagine averaging multiple measurements. The more measurements you get, the smaller this error gets as your average gets closer to the true value. In actuality they're fitting some distribution to the mass measurements, but the same idea applies. The key thing is that the more data they collect, the smaller the statistical uncertainty gets. But there's also systematic uncertainty. Lots of things contribute to this, and it's effectively an indicator of how well they understand the detector and how well they understand the decay process. For example, the various systems need to be calibrated to convert their measurements to actual energies and momentums. These calibrations aren't perfect, and so the measurements aren't perfect. Or, when they determine which events look like W boson decays, they might be selecting some small fraction of other processes, or rejecting events in a way that biases for higher or lower mass. These will throw off the final measurement. They try to correct for these, but there's never enough data to do so perfectly. The key thing about systematic uncertainties are that no amount of measuring more decays will overcome them. There are other things you can do to bring them down, such as improving your detector simulations and doing additional calibrations. But there's a limit to how much they can bring this down. As an example, imagine trying to measure the height of a building with a long measuring tape. You might measure it many times and then average it, and that would give you some very small statistical error. But you don't know that the measuring tape was printed completely accurately, you don't know that it isn't stretching due to gravity or temperatures, you don't know that you got the tape perfectly lined up with the building. Those are all systematic uncertanties, and so when you report your measurement, those will be included in your total uncertainty.