A new measurement of the proton mass is three times more precise and 3.3 standard deviations lighter than the previous state of the art measurement recognized in 2014. This leaves open hope that other tiny, but statistically significant discrepancies in physical constant measurements like the muon magnetic moment (muon g-2), and the muonic hydrogen radius may be resolved with similar feats of increased experimental precision, rather than new physics. The new value for the proton mass reduces tensions between several other theoretically predicted values and experiments.

We report on the precise measurement of the atomic mass of a single proton with a purpose-built Penning-trap system. With a precision of 32 parts-per-trillion our result not only improves on the current CODATA literature value by a factor of three, but also disagrees with it at a level of about 3 standard deviations.Fabian Heiße, et al., "High-precision measurement of the proton's atomic mass" (June 21, 2017).

The key passage of the paper is as follows:

[W]e calculate the proton mass in atomic mass units:

mp = 1.007 276 466 583(15)(29) u.

Here, the two numbers given in brackets are the statistical and systematic uncertainties of the measurement, respectively. Thus, our value of mp has a relative precision of 32 ppt [part per trillion], which is three times more precise than the current CODATA value but shows a deviation from the literature value by more than three standard deviations. . . .

Using our result, the proton-electron-mass ratio can be determined with a relative precision of 43 ppt, where the uncertainty arises nearly equally from the proton and the electron mass. This is a factor of two more precise compared to the current value:

mp/me = 1 836.152 673 346(81).

The shifted proton mass also impacts the 3He “mass puzzle”, which indicated a possible inconsistency of the existing determination of the mass of the HD+ molecule compared to 3He+. The inconsistency of 4 σ is reduced by a factor of around two using our measurement result. By applying our measurement scheme also with the deuteron, we will be able to further address the 3He+ inconsistency.

Furthermore, mp affects the atomic mass of the neutron, but results in a shift of smaller than 1 σ, due to the dominant uncertainty in the deuteron’s binding energy.

The influence on the Rydberg constant R∞ is currently small, since its error is dominated by the charge radius of the proton. However, the more precise value for R∞ that could be extracted from the muonic hydrogen experiment once the proton radius puzzle can be resolved will be significantly influenced by our result.The authors close by resolving to improve their experiment in various technical ways which should improve the accuracy of their measurement in the future.

The CODATA (2014) value of the proton mass was 938.272 081 3(58) MeV/c2 =

1.672 621 898(21)×10−27 kg =

1.007 276 466 879(91) u

This was 0.000 000 000 296 u heavier than the new result.

The CODATA (2014) value of the electron mass me is 0.510 998 9461(31) MeV/c2 =

9.109 383 56(11)×10−31 kg

The CODATA (2014) value of the proton/electron mass ratio mp/me was 1836.152 673 89(17). Thus, the proton mass is 0.000 000 554 electron masses lighter in the current measurement than in the previous one.

A layman's description of the new result can be found in the New Scientist.

The proton mass is in theory a function primarily of the up quark mass, the down quark mass and the strong force coupling constant, and secondarily the other quark masses and a few other physical constants. But, the up and down quark masses are known only with a precision of +/- 50%-100% and the strong force coupling constant is known only with a precision of about 1%. So first principles calculations are far less precise than the experimental measurements (by a factor of hundreds of millions).

Of course, we could use the incredibly precisely known masses of composite particles like the proton to calculate the quark and strong force coupling constant masses to much greater precision if only we could make more precise calculations using the relevant QCD equations. But, current methods of making calculations with the relevant QCD equations can take years to conduct with high powered computers only to produce predictions with a mere 1% accuracy, because the equations give answers in the form of an infinite series of terms that does not converge quickly.

It is worth the effort, however, because once your theoretical accuracy is high enough to determine the physical constants relevant to QCD more accurately from a handful of precisely measured observables, those more accurate constants increase the accuracy of all QCD calculations made from first principles.

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