Friday, December 16, 2016

More Top Quark Mass Measurement Data From The LHC

The News

The latest top quark mass data:
The combined ATLAS result from the √ s = 7 TeV dileptonic and semileptonic tt¯ measurements yields a value of mtop = 172.99 ± 0.48 (stat) ± 0.78 (syst) GeV. Additional precision is to be expected with the inclusion of √ s = 8 TeV measurements. The combined CMS result of mtop = 172.44 ± 0.13 (stat) ±0 .47 (syst) GeV is based on all √ s =7 and 8 TeV measurements performed in the three standard tt¯ decay channels. The results of both experiments are in good agreement. 
While future measurements at √ s = 13 TeV will recognizably benefit from higher statistics, the reduction of several theoretical uncertainties would further allow for improved precision in both the indirect measurements from the production cross-sections and those analyses which avoid employing jets in the construction of an observable sensitive to mtop.
From the conclusion of this preprint.

A previous low precision CMS report using a hadronic channel not included in the CMS average above is here. It reported a top quark mass of 173.5 ± 3.13 GeV.

The final Tevatron mass measurement for the top quark was 174.30 ± 0.65 GeV.

The combined ATLAS error is ± 0.92 GeV. The combined CMS error is ± 0.49 GeV. The range of the independent average top quark mass measurements is 1.86 GeV.

The most recent previous ATLAS report is here. A summary of recent Higgs and top quark mass are here.

Global Average Top Quark Mass

Currently, the Particle Data Group bases its top quark mass estimate on the Tevatron data without resorting to the LHC data, but that will probably change in the 2017 edition.

The inverse error weighted average of the three main results plus the CMS hadronic channel is 173.20 GeV. 

Excluding the CMS hadronic channel (which there is no good reason to do in an error weighted measurement), the inverse error weighted average is 173.18 GeV.

All of the leading results cited above are consistent with this global average at the two sigma level, although I can't easily work out the precise new margin error for the global average myself.

Theoretical Conjecture Expectations For The Top Quark Mass

If the the sum of the square of the boson masses equals the sum of the square of the fermion masses equals one half of the Higgs vacuum expectation value, the implied top quark mass is 174.03 GeV if pole masses of the quarks are used, and 174.05 GeV if MS masses at typical scales are used. The pole mass is really more fundamental, so the 174.03 GeV expected top quark mass is probably the better one to use (but the MS masses for the non-top quarks in the measurement are more precise).

This is 0.83 GeV and 0.85 GeV, respectively, above the complete global average, and 0.85 GeV and 0.87 GeV, respectively, above the global average of the precision measurements. Of these for differences, I suspect that the 0.83 GeV discrepancy value is most meaningful.

The expected value of the top mass from the formula that the sum of the square of each of the fundamental particle masses equals the square of the Higgs vaccum expectation value (a less stringent condition because the fermion and boson masses don't have to balance), given the global average Higgs boson mass measurement (and using a global fit value of 80.376 GeV for the W boson rather than the PDG value) is 173.73 GeV. The top quark mass can be a little lighter in this scenario because the global average measured value of the Higgs boson mass is a bit heavier than under the more stringent condition.

This is 0.53 GeV above the complete global average and is 0.55 GeV above the global average of the precision measurements, but this discrepancy will increase if the Higgs boson value falls.

All of these values are consistent at the two sigma level with the global average of both all an all of the precision the top quark mass measurements.

Thus, it is my prediction that the new ATLAS √ s = 8 TeV measurements, and eventually the new ATLAS and CMS √ s = 13 TeV measurements will tend to push up the global average by some amount less than 0.83 GeV.  The ATLAS results, due to the higher statistical error and higher systemic error are more likely to be significantly different than the old data points than the CMS results (whose error margins, quite frankly, look unrealistically low and may be underestimated).

A Footnote On The Higgs Mass and Theoretical Conjecture Expectations For It

For convenience, I'll recap my prior posts on the Higgs boson mass in this post even though this post contains no new information on the Higgs boson mass.

The current global average of the Higgs boson mass 125.09 +/- 0.24 GeV is based upon the following data points:

* ATLAS diphoton mass 126.02 +/- 0.51 GeV
* ATLAS four lepton mass 124.51 +/- 0.52 GeV
* CMS diphoton mass 124.7 +/- 0.34 GeV
* CMS four lepton mass 125.59 +/- 0.45 GeV

The latest measurement of the Higgs boson mass (based upon four lepton events) by CMS, which is not included in that global average, was 124.5 +0.48/-0.46 GeV.  So, after this new CMS data point, the new global average should be roughly 124.82 GeV with a very similar margin of error (perhaps 0.25 GeV since the new CMS four lepton measurement isn't quite as precise as the old value), before accounting for any new ATLAS results. 

The new CMS data point also makes the ATLAS diphoton data point look like an outlier relative to the other three measurements, which suggests that the combined average is more likely to fall than to rise when ATLAS releases its next Higgs boson diphoton decay based mass measurement. A new ATLAS diphoton result will most likely bring the global average Higgs boson mass to something between 124.65 GeV and 124.82 GeV.

A Higgs boson mass of 124.65 GeV is theoretically notable because it is the value of the Higgs boson mass if if the the sum of the square of the boson masses equals the sum of the square of the fermion masses equals one half of the square of the Higgs vacuum expectation value.

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