The Particle Data Group value for the mass of the charged pion has a precision of ± 2.5 parts per million. A new experiment has improved the precision of the charged pion mass measurement by almost 50% to ± 1.3 part per million.
The newly measured value of the charged pion which is more accurate than any previous measurement to date is 139.57077±0.00018 MeV/c^2. Put another way, this is a more or less perfect measurement to the nearest 1000 electron volts/c^2, and is between 1,000 and 10,000 times more precise than the experimental precision of a typical newly discovered hadron.
This experimentally measured value is more than a thousand times more precise than the theoretical value that can be determined from first principles using QCD in the Standard Model, even though, in principle, the Standard Model with sufficiently accurately measured physical constants contains everything needed to determine this mass to this level of precision and more.
Our experimental measurements of the charged pion mass matched the precision of our current theoretical prediction of the charged pion mass in the year 1954 (62 years ago).
(This is also a good point to make a general observation about particle physics. Many measurements in particle physics are of fundamental or composite particles which are perfectly interchangeable parts which once measured accurately never need to be measured again. If you do dozens of different experiments that measure the mass of a charged pion to this level of precision, you will get a distribution of results will that is consistent with a Gaussian distribution with a mean close to the true value of the charged pion mass and a standard deviation with a 1 part per million margin of error. The true value is going to be the same every time even at this immense level of precision which rivals that of pretty much any precision piece of equipment ever made by man.)
Why is the theoretically calculated value so much less precise?
One immediate source of this limitation is that the quark masses and strong force coupling constant aren't known to sufficient precision. But, the deeper source of the lack of precision is that we lack the computational power to determine the formula into which the constants would be added to a sufficient number of terms to provide the required theoretical accuracy.
What would be possible if we could calculate a greater number of terms in the relevant QCD formulas?
If we could calculate the formula out to enough terms to make the theoretical error small enough, we could compare the half dozen or dozen most accurately measured hadron masses (such as the charged pion, proton and neutron) to the experimentally measured results and use them to determine the masses of the light quarks and the strong force coupling constant to comparable degrees of precision. We could then use those constants in turn to determine with masses of the heavier quarks with more precision by using the most accurately measured masses of hadrons containing heavy quarks and the newly determined more accurate constants.
More accurate knowledge of those physical constants, in turn, would allow us to make far more accurate predictions of all forms of QCD processes (e.g. particle decays and scattering processes at high energies). And, more accurate measurements of physical constants would also provide a more meaningful test of hypothetical mathematical relationships between those physical constants which could elucidate the deeper theory that gives rise to the Standard Model's physical constants.
Why is this approach attractive as an area to spend fundamental physics research funds?
The most attractive thing about this avenue of research, despite its somewhat dry nature, is that we have exact rules telling us how to calculate the relevant formulas in QCD to any desired degree of precision, so this approach is guaranteed to produce more accurate knowledge of Standard Model constants and the associated advances in science, even if we never do another measurement of a QCD observable ever again. It would even allow us to reanalyze past QCD observations in a manner that would increase their precision as well.
Right now, it can take many months to several years with super-computers to come up with a formula necessary to get even four or five digit precision in the result. But, for the most part, the time it takes to come up with the answer is scalable with increased computer power.
In other words, if we spent $5 billion on computers to do QCD calculations instead of $500 million today (these are purely hypothetical numbers, I don't know how much we actually spend right now on computers to do QCD calculations), we could do calculations that now take 5 years in 6 months, and could do calculations that would take 50 years to do now in a much more tolerable 5 years, increasing the precision of the formula significantly.
There aren't many areas of physics where you can pretty much guarantee scientific advances just by spending more money on more and more powerful computers. But, QCD and by association, the whole of Standard Model fundamental physics, is one area where spending more money in this way can guarantee scientific advances.