Updated Physical Constant Measurements

There are two main scientific collaborations that summarize the state of current experimental data on the physical constants of the Standard Model and hadron physics: the Particle Data Group (PDG) and the Flavour Lattice Averaging Group (FLAG). 

The bottom lines of the two collaborations are largely consistent, with FLAG claiming smaller uncertainties, although there are some moderate tensions between the averages in CKM matrix element values.

FLAG has just published its 2021 update. Don't read the whole thing (it's 418 pages long).

The values of most of the Standard Model physical constants that aren't evaluated by FLAG (the three charged lepton masses, the W and Z boson masses, the Higgs boson mass, Fermi's constant, the electromagnetic force coupling constant, and Planck's constant) are already known to similar or higher precision than the most precisely determined physical constants that it evaluates. The top quark mass isn't very amenable to lattice QCD methods and is better measured directly. 

FLAG also doesn't evaluate the PMNS matrix elements (applicable to neutrino oscillation) and neutrino mass physical constants.

Results 

When more than one numbers is quoted, I use MS scheme values for the most complete model. I also quote the comparable PDG values, which are consistent with the FLAG values, except as noted in bold.

Quark Masses

* Up quark mass at 2 GeV = 2.14(8) MeV 

(PDG is 2.16 + 0.49-0.26 MeV)

3.7% relative uncertainty

* Down quark mass at 2 GeV = 4.70(5) MeV

1% relative uncertainty

(PDG is 4.67 + 0.48-0.17 MeV)

* Strange quark mass at 2 GeV = 93.44(68) MeV 

0.7% relative uncertainty 

(PDG is 93 + 11 - 5 MeV)

* Charm quark mass at c quark energy = 1278(13) MeV

0.1% relative uncertainty

(PDG is 1,270 ± 20 MeV) 

* Bottom quark mass at b quark energy = 4203(11) MeV

0.26% relative uncertainty

(PDG is 4,180 + 30 -20 MeV)

* Average of up and down quark mass at 2 GeV = 3.410(43) MeV

1.26% relative uncertainty

(PDG is 3.45 + 0.55 -0.15 MeV)

Ratios

* Ratio of up quark to down quark mass = 0.465(24)

5.16% relative uncertainty

(PDG is 0.47 + 0.06 - 0.07)

* Ratio of strange quark mass to average of up and down quark mass = 27.23 (10)

0.37% relative uncertainty

(PDG is 27.3 + 0.7 -1.3)

* Ratio of c quark mass to s quark mass = 11.768(34)

0.29% relative uncertainty

(PDG is 11.72 ± 0.25)

A technical detail regarding the quark masses

FLAG also quotes masses for the Renormalization Group Independent (RGI) scheme, which is arguably a better benchmark. But this scheme is less familiar and less useful for comparisons from other sources, so I omit them here. Generally, speaking those results are approximately proportionately more massive.

CKM Matrix Elements

FLAG also updated is CKM matrix element values determined individually (as opposed to with global SM fits):

* V(us) = 0.2248(7)

The consistent stand alone PDG value is 0.2245(8). The PDG global fit value is 0.22650(48) which is in 2.4σ tension with the FLAG result.

Treating the discrepancy as true uncertainty, however, the relative uncertainty is still about 0.7%.

* V(ud) = 0.97440(17). 

This compared to a stand alone PDG value of 0.97370(14) which differs by ≈ 3.2σ from the FLAG value. The PDG global fit value is 0.97401(11) which is consistent with the FLAG value.

Treating the discrepancy as true uncertainty, however, the relative uncertainty is still about 0.07%.

Strong Force Coupling Constant

FLAG updates its estimate of the strong force coupling constant value, at the Z boson mass, in five flavor QCD:

* α(s) = 0.1184(8). 

0.68% relative uncertainty

The PDG is 0.1179(10).

My Summary From June 4, 2021