Precision Hadron Mass Measurement

The bottom lambda baryon is a short lived (its mean lifetime is roughly 1.41*10^-12 seconds), heavy hadron (only eight baryons and one meson have heavier measured masses, although many more which have not been produced and measured in experiments are predicted to be heavier) made of an up quark a down quark and a bottom quark.  Its existence is predicted by the Standard Model, and it has all of the properties that it is predicted to have in the Standard Model.

A new paper describing some of its (completely expected) properties, including its mass, is mostly exceptional for the precision of the mass measurement which has a margin of error of less than half an electron mass (the combined error is +/- 0.24 MeV/c², while the electron mass in the same units is 0.511), which is one part in 23,515.  (The relative frequency of the rare branching fractions examined are measured to a precision of roughly 5%).

M(Λ⁰_b)=5619.65±0.17±0.17 MeV/c²

What's Special About The Λ⁰_b?

The mass of a hadron can be decomposed into the sum of the quark rest masses and the mass-energy of the gluon fields binding the quarks together (with a small adjustment for electro-weak fields between the quarks).  Since all quarks have a color charge of the same magnitude, the gluon field contribution is, to first order, roughly the same in all hadrons with the same number of quark and the same spin and electric charge.  This isn't a perfect approximation (the gluon field in a Λ⁰_b has roughly 50% more mass-energy than the gluon field in a neutron which is identical to it, except that the bottom quark is replaced by a down quark), but it is a good starting point heuristically to think about the question.

The Λ⁰_b is special in terms of comparing measurement to theory, because in hadrons with a bottom quark, the quark rest masses make up a majority of the mass (unlike protons and neutrons where the sum of the quark rest masses make up less than 2% of the total mass).  Since the precision of the measurements is roughly the same in absolute terms regardless of the mass of the hadron measured, heavier hadrons can be measured with greater precision on a percentage basis than lighter hadrons.

Still, even measured in terms of absolute accuracy, for which 1 MeV is the norm, 1/4 of an MeV is still excellent. As the paper notes at page 10: "This is the most precise measurement of any b-hadron mass reported to date. . . . Previous direct measurements of the Λ⁰_b mass by LHCb were made using the decay Λ⁰_b → J/ψΛ⁰ and are statistically independent of the results of this study. The combination obtained here is consistent with, and more precise than, the results of these earlier studies." Also notably:

From the value of the Λ⁰_b mass . . . and a precise measurement of the mass difference between the Λ⁰_b and B⁰ hadrons reported in Ref. [6], the mass of the B⁰ meson is calculated to be:

M(B⁰) = 5279.93 ± 0.39 MeV/c², 

where the correlation of 41% between the LHCb measurements of the Λ⁰_b mass and the Λ⁰_b–B⁰ mass splitting has been taken into account. This is in agreement with the current world average of 5279.61 ± 0.16 MeV/c².

A neutral B meson is a two quark composite particle which (to oversimplify) is made up of a bottom quark and an anti-down quark.

QCD Still Has Great Experimental Accuracy And Poor Theoretical Accuracy

The precision of the experimental measurement is much greater than the precision of the theoretically predicted mass of the baryon which is in the vicinity of one part per 100 to one part per 1000.

We can get predictions for hadron masses that rival the accuracy of state of the art first principles QCD by playing around with linear regression models of existing hadron mass data sets (including a few non-linear terms of the properties in the equation, such as the square of the quark masses and dummy variable for factors like hadron spin), although the best predictions using either approach don't rival the precision of the measurements themselves. And, knowing what parts of a first principles calculation are important isn't an obvious thing that often implicates factors that are only discernible after the fact.

The theoretical estimates are imprecise because, while we have the exact equations of QCD that are used to determine it* and have more than enough high precision calibration points in the form of measurements of myriad hadron properties (for example, we know the proton and neutron masses with a precision of roughly one part per 100,000,000), the relevant QCD calculations are extremely difficult to conduct even with supercomputers.

While this is most obvious in the imprecision of the QCD coupling constant, the imprecision in that constant is almost entirely due to the imprecision in QCD theoretical calculations, as opposed to measurement error.  Since quarks are confined, the only way to measure the QCD coupling constant is to calculation hadron properties as a function of the QCD coupling constant and then to calibrate the results against the measured hadron properties.

The hadron measurements are very precise, but the theoretical calculations from which the QCD coupling constant can be reverse engineered using the measured hadron properties have great uncertainties because you have to calculate the values of gillions of path integral terms to get to even a several loop level and the infinite series that give the exact QCD value doesn't converge very rapidly. The most precise QCD calculations these days done from scratch are done numerically, rather than analytically, to a two to four loop level, and use one of several simplifications of the full QCD calculations.

We could increase the accuracy with which we know the QCD coupling constant to the same accuracy as the theoretical calculation, if we could calculate just one experimentally well calibrated hadron property to that level of accuracy theoretically.  And, this would also greatly improve our ability to precisely measure the quark masses, since one of the inputs into the equation would be much more precisely known.  But, even if we were able to improve the precision of these constants due to an isolated highly symmetric or cancellation prone setup, our generalized QCD calculation precision would improve only a little, because the main limiting factor is our inability to add in a sufficient number of terms to the slowly converging infinite series approximation and not the imprecision with which we know the physical constants.

* This is a widely held belief of physicists who do QCD and of Standard Model particle physics more generally, for a variety of reasons, some theoretical and some because we haven't seen the kind of systemic deviations from their predictions that we would expect if they were wrong.  We know it to be true to the level of precision that we can do the calculations.  For all practical purposes, a theoretical calculation precision of one part in 1,000,000 or less (i.e. a 1,000 to 10,000 fold improvement in precision) would be exact relative to current experimental precision. Any adjustment due to the admittedly ignored adjustments for gravity between the particles would be smaller than that level of precision.