Calculating Light Meson Masses From First Principles In QCD

How good are current Standard Model calculations at predicting the experimental values of the light meson masses?

A new paper that makes that attempt for all light mesons under 1.5 GeVs of mass. And, its results are finally starting to do a pretty good job of describing the meson mass spectrum which has been an elusive target for decades, even for axial vector mesons.

As explained in the introduction:

In the present work we employ the procedure described above to compute the masses of relatively light mesons, namely mesonic states no heavier than about 1.5 GeV. Specifically, for mesons composed of u and ¯d quarks, we compute the masses of π±, ρ(770), b1(1235), a1(1260), π±(1300), and ρ±(1450). For the strange sector, we calculate the masses of the states K±, K∗(890), K1A, K1B, and K±(1460). 

In general, the computed masses are in good agreement with the experimental values. In fact, our findings represent a definite improvement over the results obtained within the standard rainbow-ladder truncation [84], where the masses of axial-vector mesons and radially excited states tend to deviate considerably from the observed values.

Notably, this omits the f(0)(500) scalar meson a.k.a. the sigma meson and seven other true scalar mesons with masses under 1.5 Gev. The other omitted scalar mesons are the f(0)(980), f(2)(1270), f(1)(1285), f(0)(1370), f(1)(1420), f(2)(1430) and f(0)(1500). This may be because their internal structures are less well understood.

The actual procedure used is too technical for this blog.

The money chart is as follows:

With the exception of spin-1 kaons (where the relationship is inverted for some reason), the experimental values (in red) tend to be at the very high end of the theoretically predicted values using their methods (in blue), and their predictions, in turn, tend to be more massive than those made using a previous "rainbow ladder" truncation method (in green).

The predictions (and measurements) of excited state light meson masses are much less precise than the predictions (and measurements) of ground state light meson masses.