Strong Force Coupling Constant And Quark Masses Measured With High Precision

Imprecision in the measurement of the strong force coupling constant is the single greatest barrier to precision predictions in QCD, so every new, independent precision determination will boost every single QCD prediction going forward.

We present a determination of the strong coupling constant αs(mZ) based on the NNPDF3.1 determination of parton distributions, which for the first time includes constraints from jet production, top-quark pair differential distributions, and the Z pT distributions using exact NNLO theory. Our result is based on a novel extension of the NNPDF methodology - the correlated replica method - which allows for a simultaneous determination of αs and the PDFs with all correlations between them fully taken into account. We study in detail all relevant sources of experimental, methodological and theoretical uncertainty. At NNLO we find αs(mZ)=0.1185±0.0005(exp)±0.0001(meth), showing that methodological uncertainties are negligible. We conservatively estimate the theoretical uncertainty due to missing higher order QCD corrections (N3LO and beyond) from half the shift between the NLO and NNLO αs values, finding Δαths=0.0011.

Richard D. Ball, et al., "Precision determination of the strong coupling constant within a global PDF analysis" (February 9, 2018).

More specifically, the NNLO result is: α_s^NNLO(m_Z) = 0.11845 ± 0.00052 (0.4%) and the combined measurement, combining all sources of error is 0.1185 ± 0.0012, which matches the precision of the Particle Data Group global average value for this constant as of 2017 which is 0.1182 +/- 0.0012. As noted below, this error estimate is probably an overestimate.

From the Introduction to the paper:

The value of the strong coupling constant αs (mZ) is a dominant source of uncertainty in the computation of several LHC processes. This uncertainty is often combined with that on parton distributions (PDFs), with which it is strongly correlated. However, while PDF uncertainties have reduced considerably over the years, as it is clear for example by comparing the 2012 [1] and 2015 [2] PDF4LHC recommendations, the uncertainty on the αs PDG average [3] remains substantially unchanged since 2010 [4]. As a consequence, the uncertainty on αs is now the dominant source of uncertainty for several Higgs boson production cross-sections [5]. 

Possibly the cleanest [6, 7] determinations of αs come from processes that do not require a knowledge of the PDFs, such as the global electroweak fit [8]. These are free from the need to control all sources of bias which may affect the PDF determination and contaminate the resulting αs value. A determination of αs jointly with the PDFs, however, has the advantage that it is driven by the combination of a large number of experimental measurements from several different processes. This is advantageous because possible sources of uncertainties related to specific measurements, either of theoretical or experimental origin, are mostly uncorrelated amongst each other and will average out to some extent in the final αs result. In addition to the above, the simultaneous global fit of αs and the PDFs is likely to be more precise and possibly also more accurate than individual determinations based on pre-existing PDF sets, many of which have recently appeared [9–15]. This is due to the fact that it fully exploits the information contained in the global dataset while accounting for the correlation of αs with the underlying PDFs.

From the Conclusion:

The main limitation of our result comes from the lack of a reliable method to estimate the uncertainties related to missing higher order perturbative corrections. Theoretical progress in this direction is needed, and perhaps expected, and would be a major source of future improvement. For the time being, even with a very conservative estimate of the theoretical uncertainty, our result provides one of the most accurate determinations of αs (mZ) available, and thus provides valuable input for precision tests of the Standard Model and for searches for new physics beyond it.

The quark masses are another set of critical constants in the Standard Model, and in QCD in particular, which are not known particularly precisely and except in the case of the top quark, cannot be measured directly. A new paper also makes progress on that front:

We calculate the up-, down-, strange-, charm-, and bottom-quark masses using the MILC highly improved staggered-quark ensembles with four flavors of dynamical quarks. We use ensembles at six lattice spacings ranging from a≈0.15 fm to 0.03 fm and with both physical and unphysical values of the two light and the strange sea-quark masses. We use a new method based on heavy-quark effective theory (HQET) to extract quark masses from heavy-light pseudoscalar meson masses. Combining our analysis with our separate determination of ratios of light-quark masses we present masses of the up, down, strange, charm, and bottom quarks. 

Our results for the MS¯¯¯¯¯¯¯-renormalized masses are  

mu(2 GeV)=2.118(38) MeV,  

md(2 GeV)=4.690(54) MeV,  

ms(2 GeV)=92.52(69) MeV,  

mc(3 GeV)=984.3(5.6) MeV, and  

mc(mc)=1273(10)  MeV, with four active flavors, and

  

mb(mb)=4197(14) MeV with five active flavors. 

We also obtain ratios of quark masses mc/ms=11.784(22), mb/ms=53.93(12), and mb/mc=4.577(8). 

The result for mc matches the precision of the most precise calculation to date, and the other masses and all quoted ratios are the most precise to date. Moreover, these results are the first with a perturbative accuracy of α4s. 

As byproducts of our method, we obtain the matrix elements of HQET operators with dimension 4 and 5: Λ¯¯¯¯MRS=552(30) MeV in the minimal renormalon-subtracted (MRS) scheme, μ2π=0.06(22) GeV2, and μ2G(mb)=0.38(2) GeV2. The MRS scheme [Phys. Rev. D97, 034503 (2018), arXiv:1712.04983 [hep-ph]] is the key new aspect of our method.

A. Bazavov, et al., "Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD" (February 12, 2018).

The global average PDG values as of 2017 are:

Up quark mass (2 GeV) 2.2 + 0.6 - 0.4 MeV

Down quark mass (2 GeV) 4.7 + 0.5 - 0.4 MeV

Strange quark mass (2 GeV)  96 +8 -4 MeV

Charm quark mass (at charm quark energy scale) 1,280 +/- 30 MeV

Bottom quark mass (at bottom quark energy scale) 4,180 + 40 -30 MeV

The ratios from PDG are:

Charm mass/strange mass: 11.72 +/- 0.25

Bottom mass/charm mass: 4.53 +/- 0.05

The new results are consistent with the PDG values but more precise.
+0.6+0.6

The imprecision in the strong force coupling constant value is one of the main sources of the imprecision in the non-top quark mass estimates, which has to be inferred from the behavior of bound quarks in composite particles made up of quarks bound by gluons called hadrons. The masses of scores of hadrons have been measured with spurious accuracy that are exact for the practical purpose of determining quark masses but without a more precise measurement of the strong force coupling constant, the precise measurements of the hadron masses can't be translated into equally precise measurements of the quark masses.

Ultimately, there are also uncertainties in the determinations of all of these constants that arise, both directly and indirectly, from truncating infinite series formulas in the QCD calculations involved that are usually done to NNLO or NNNLO in this kind of study. This accounted for half of the error in the most recent strong force coupling constant determination, and is also an independent source of error in addition to the indirect effect on the strong force coupling constant determination, on the quark mass determinations. There are methodologies that can minimize the additional error due to calculation imprecision by, for example, comparing pairs of hadrons whose mass calculations are identical in most respects except for a residual attributable to the mass difference between otherwise identical quarks, however, which is why the percentage error in the mass ratios of the quark masses is lower than the percentage error in the absolute quark masses.

Meanwhile, the diphoton Higgs boson decay channel signal strength predicted by the Standard Model is now an almost perfect match to run two data from the ATLAS experiment at the LHC has been collected:

The global signal strength measurement of 0.99±0.14 improves on the precision of the ATLAS measurement at s√=7 and 8 TeV by a factor of two. . . . The cross section for the production of the Higgs boson decaying to two isolated photons in a fiducial region closely matching the experimental selection of the photons is measured to be 55±10 fb, which is in good agreement with the Standard Model prediction of 64±2 fb.

This observable is purely function of the Higgs boson mass in the Standard Model, together with the spectrum of Standard Model particles in the Standard Model:

The dominant source of error in the Higgs diphoton decay signal study is statistical, which means that the precision of these measurements will increase significantly as more data is collected at the LHC.