Combining results carefully

Combining chemicals in the wrong way can be disastrous. We have to be just as careful with physics data, or we could get an incorrect result.

There are two ways to make a scientific discovery. The first is a serendipitous observation of something that wasn’t predicted. This is rare in modern particle physics. While we still expect the unexpected, a more common approach is that we try to verify a theoretical prediction that fits well into the existing theory, but hasn’t been confirmed. For discoveries of this kind, a single measurement isn’t enough.

In particle physics, the easy questions have already been answered. The more difficult questions have subtle answers, usually swamped by more common collisions that make the desired phenomenon hard to observe. When observing new phenomenon, you need to be certain that you’re not being fooled by lookalikes. If all of the measurements tell the same story, it’s more likely that the observation is a new phenomenon.

Take the discovery of the top quark. Commonly produced in a quark/antiquark pair, top quarks decay quickly into a bottom quark and a W boson. The unstable W bosons decay into two particles, but the method varies. In all, there are ten distinct decay patterns for top quarks.

When the top quark was discovered in 1995, both CDF and DZero observed top quarks in at least five different ways. All five ways were similar enough to give us confidence in the discovery. Specific decay patterns are often investigated using more than one algorithm.

The problem arises when we take those five (or more) different measurements and combine them into a single result. A combination gives a more precise result, as it provides more evidence that the measured value is not a fluke. If many measurements tell the same story, it is more likely that your measurement isn’t accidental. It is rather easy to combine totally independent measurements, but multiple measurements from one experiment are not entirely independent. Each measurement uses the same detector, and if the detector is even slightly miscalibrated, the miscalculation will be true for all measurements. Also, we use the same programs to simulate detector performance and ordinary, expected phenomena.

When we combine these quasi-independent measurements, we need to account for the correlations between those common elements. This is tricky and requires a diverse range of expertise to make sure the combination is accurate. An upward fluctuation in one measurement is not indicative of how the fluctuation will behave in another measurement. It could be a bigger or smaller upward fluctuation or even a downward fluctuation. Understanding how these fluctuations are interrelated takes substantial care.

Mulitple experiments at one accelerator, like DZero and CDF or CMS and ATLAS, or even experiments at different laboratories, can combine results for a more precise measurement. With measurements properly combined, we are much more confident when we announce a result.

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—Don Lincoln