Is it because of the difficulty of forming muonic hydrogen or making measurements before the decay?
To get the money to do this, you have to apply for government grants that may take up to a year to get approved. And no government wants to fund it so you need an 'in' with the lab, because they'll be the ones that sponsor your application for it to have a chance of success, and you'll need to know people from a whole load of other countries to collaborate with and prove your bona fides. And the people writing all these grant applications and doing most of the middle management are distracted by teaching literally hundreds of students every week during term time, so they can't even work full-time on it.
There are other experimental ways of doing this (e.g. measure correlated form factors and parton distribution functions from elastic scattering and extrapolate to zero momentum transfer), but they're all harder. They'll probably be done within the next 30 years. Probably. This particular effort is likely the work of 30-50 PhDs working for five or more years (at 50% of the salary they'd earn working for commercial companies), discounting any of the commercially available technology like electronics developed by CAEN or detector components developed by the likes of ElJen or Hamamatsu. And I would be surprised if they didn't mint another 10-15 PhDs during the effort. And I haven't covered the highly trained technicians and electronic engineers that are usually needed to build a lot of the custom experimental equipment.
I dislike that it has a strong feeling of not-invented-here syndrome where it could include dependencies on well tested code, e.g. the gnu scientific library, but instead rewrites everything. And up until about 6 months ago the default plot styles were damned ugly, although this has gotten a lot better. There seem to be three different math libraries that each implement some subset of mathematical functions independently and a lot of the graphics stuff makes little sense to me (take a look at how to ensure platform-independent type face size in a plot, for example). The CINT interface almost seemed designed to ensure that when students were learning, they learned ROOT and not C or C++, which is great for productivity in the short term, and incredibly sucky in the medium to long term.
I understand that a lot of this is legacy cruft (and even made sense at the time!) and that I could contribute patches for it, but I'm busy doing my actual job. I'm impressed that a lot of my objections are being worked on too - I was heavily dependent on the framework for my PhD about 5 years ago and a lot of my frustration stems from then. It often feels like the ROOT team learn-by-doing; they want to understand something, so they make it in ROOT. Which is a fine way to learn, but not the best way to develop stable code that should be used by thousands and thousands of people. In some senses ROOT is an amazing achievement and I still find myself using it on occasion. But I've now mostly replaced what I use it for with matplotlib and the GSL and my life is easier.
breathes
I also dislike the way that it seems partially to have enabled physics to go in a direction where we pump out PhDs who don't understand code or physics, but act as worker-drones for the large collaborations. But that's not really ROOT's fault, and is a whole 'nother topic.
For Mainz experiment, we have or own code base. Not pretty, but because it's a lot more specialist, less confusing. I am working now on OLYMPUS, and we are using ROOT for that. I created a Framework for the analysis based on ROOT, trying to hide the most problematic areas and making it easier for use by the other collaboration members. Also trying to make them write programs, not ROOT macros. Every time I look up a new feature, I'm surprised that they managed to find a non standard way of doing it. My pet peeve? TH1D is a 1-d historgram class. What does TH1D.Clear do?
Wrong! It clears the histogram title and name, not the histogram itself. For that, you need Reset. It makes kind of sense if you know the class hierarchy, TNamed and all. But who remembers that? I saw this mistake in the wild a lot.
Protip: Gnuplot. While also a little bit arcane in its command language, it's for me the best tool to produce paper-ready plots. With the tikz terminal you can include it in your Latex flow, and with some Makefile trickery you can have e.g. \cites resolve correctly in plot labels. With numbering correctly reflecting the position of the plot in the paper!
Lol! It's Jan. The world is small.
On the electron scattering side, ROOT is more common, but the experiments which are most relevant for the radius either predate ROOT or are known to not work with ROOT. Doesn't mean the software used has no errors, quite the contrary, however since all the results from different measurements with different software agree, I think a programming error is not the culprit.
But there are other problems too. For example, you need to measure the frequency of the light. Since the (quite recent) invention of frequency combs, this is possible with astounding precision. While this experiment is not the most complicated in this regard, it is still a challenge.
Also, even after you have measured the level difference, you need quite a lot of theory to get the radius out, which had to be developed first, as you need to know where to look.