Wednesday, November 28, 2018

The Latest On Top Quark Mass And Properties

ATLAS and CMS have also come out with a combined review of top quark property measurements at the LHC. Like the Higgs boson review released yesterday, the data aren't particularly new.

In principle, the top quark is fully described in the Standard Model when you know its mass and the relevant components of the CKM matrix (which is itself a function of four parameters). All other top quark properties are predicted by the Standard Model (sometimes with the assistance of other Standard Model parameters like the strong force coupling constant), so the experimental results can be compared to Standard Model predictions to constrain extensions of the Standard Model involving "new physics" and to calibrate numerical and analytical approximation methods for ascertaining Standard Model predictions.
The top quark mass, mtop is a key parameter in the SM and is the major contributor to the Higgs boson mass (mH) through radiative corrections. Therefore, the accuracy on both mtop and mH measurements is quite crucial for the consistency tests of the SM. Starting from the Tevatron experiments, the top quark mass has so far been measured with increasing precision using multiple final states, as well as with different analysis techniques. Two of the most recent mtop measurements from CMS and ATLAS experiments are presented here. 
ATLAS has recently performed a top quark mass measurement [21] in lepton+jets final states using a 20.2 fb−1 dataset at √ s = 8 TeV. The full event reconstruction is performed using a likelihood based kinematic fitter, KLFITTER [22]. The t¯t → lepton+jets event selection is further optimized through the usage of a boosted decision tree [23]. The top quark mass (mtop) together with the jet energy scale factor (JSF) and b-jet energy scale factor (bJSF) is then simultaneously extracted using the template fit technique. The template fit results in terms of mtop and mW are shown in Fig. 7. The measurement yields a top quark mass of 172.8±0.39(stat)±0.82(syst) GeV, where the dominant uncertainties are driven by theoretical modeling and systematics. 
The latest mtop measurement [25] from CMS is based on a 35.9 fb−1 dataset at √ s = 13 TeV. The full t¯t → lepton+jets event reconstruction is performed using a kinematic fit of the decay products. A 2-D ideogram fitting technique [24] is then applied to the data to measure the top quark mass simultaneously with an overall jet energy scale factor (JSF), constrained by mW (through W → qq¯ 0 decays); the fit results in terms of mtop and mW are shown in Fig. 8. The ideogram method measures an mtop value of 172.25 ± 0.08(stat) ± 0.62(syst) GeV, in consistency with the Run 1 CMS measurements at √ s = 7 and 8 TeV. The measurement results in a precision of ∆mtop/mtop ≈ 0.36% where the leading uncertainties originate from MC modeling, color reconnection, parton showering, JES, etc. The most recent individual mtop measurements from the LHC experiments, along with the world average value for mtop are summarized in Fig. 9.
The Particle Data Group reports that the global average value for the top quark mass (including measurements from Tevatron as well as the LHC and also the one CMS Run 2 result) is 173.0 ± 0.4 GeV.

Either analysis of speculative theoretical predictions of what the top quark mass should be to fit various assumptions can be found in a March 20, 2014 post at this blog. Some highlights:
An extended Koide's rule estimate of the top quark mass using only the electron and muon masses as inputs, predicted a top quark mass of 173,263.947 ± 0.006 MeV. . . .  
The dominance of any imprecision in the top quark mass to overall model fits is further amplified in cases where the quantities compared are the square of the masses rather than the masses themselves (e.g. comparing the sum of squares of the Standard Model particle masses to the almost precisely identical square of the vacuum expectation value of the Higgs field). . . . About 72% of this imprecision is due to the top quark mass and about 99.15% of the imprecision is due to the top quark mass and Higgs boson masses combined. . . . What is the best fit value for the top quark mass? Answer: 173,112.5 ± 2.5 MeV . . . The value of the top quark mass necessary to make the sum of the squares of the fermion masses equal to the sum of the square of the boson masses would be about 174,974 MeV under the same set of assumptions[.]
That analysis assumed a 125,955.8 MeV mass for the Higgs boson, which is high (the current best estimate is 125.18 ± 0.16 GeV), so the top quark mass estimates in both cases should be higher than estimated given those assumptions. As previously noted in a December 16, 2016 blog post at this blog:
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 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.
One property of the top quark predicted by the Standard Model is its "decay width" (which has a one to one correspondence with its half-life). A particle's half-life is inversely proportional to its decay width, so a particle with a very large decay width, like the top quark, has a very short half-life. The quantity αs referred to in the text is the strong force coupling constant strength at the Z boson mass.
Top Decay Width 
Being quite heavy the top quark has a large decay width (Γt). Within the SM, the Next-to-next-to-leading-order (NNLO) calculations predict Γt of 1.322 GeV for a top quark mass (mtop) of 172.5 GeV and αs=0.1189 [15]. 
CMS has recently utilized the t¯t → dilepton events from 12.9 fb−1 of the Run 2 dataset (at √ s = 13 TeV) to constrain the total decay width of the top quark through direct measurement. . . . the likelihood fit provides an observed (expected) bound of 0.6 < Γt < 2.5 (0.6 < Γt < 2.4) GeV at 95% confidence level [16]. [Ed. although expressed differently, this is roughly equivalent to a value of 1.5 +/- 0.45 GeV which is actually a smaller MOE and a mean value closer to the predicted value than the ATLAS measurement. The actual fit to the prediction is actually a little better since the error margins are lopsided.]
ATLAS performed a more refined measurement of top quark decay width using the t¯t → lepton+jets events from 20.2 fb−1 of the Run 1 dataset at √ s = 8 TeV. . . . the measurement yields a value of Γt = 1.76±0.33(stat) +0.79 −0.68 (syst) GeV (for mtop=172.5 GeV) [17], in good agreement with the SM predicted value. However, the measurement is limited by the systematic uncertainties from jet energy scale/resolution and signal modeling.


neo said...

has there ever been any explanation for Koide ?

andrew said...

There have been several, in his own works and the works of others, none of which Ive found to be very satisfactory.

What I think is going on is that the the Higgs vev sets a mass scale, and the relative masses are emergent dynamically as W boson interactions reach something like a geometric mean between all of the particles that can turn into that particle, and all of the particles that a particle can turn into, weighed by the probability of each.

You get the clean two-thirds ratio for charge leptons because the transition probabilities are confined to three possibilities and they are democratic -- equally likely controlling for mass-energy limitations. Also, neutrinos are so light that transitions to them have almost no impact on charged lepton masses.

To get the mass of a charm quark, however, you need to know the probability of all possible charm quiark transitions: c <-=-> b, c <==> s, c <==> d, and get a weighted average.

The most Koide-like set of quarks is the t-b-c triple, which makes sense because the t-b possibility is so dominant and b <==> u is such a rare transition and involves such a light quark, it barely influences the triple at all. On the other hand, because the b quark is so massive, even a slight possibility of a u <==> b transition tugs up the u quark mass significantly from the default it would be in a pure u-d-s triple, which would be basically zero. Of course, every possible transition has to be in balance with every other one.

I think that the CKM matrix is logically prior to the dynamical determination of Yukawas for quarks. Indeed, it is possible to do a Wolfenstein parameterization of it with just three parameters instead of four, and two of them mostly pertain to the CP phase. I think it is quite possible that there is really just one true CKM matrix parameter that in the right theory can explain everything but CP violation, and that CP violation actually has a completely independent source from the other driver of the CKM matrix, even though they are always observed in concert with each other.

andrew said...

An new CMS measurement:

"Top quark mass measurement in the tt⎯⎯ all-jets final state with the CMS experiment at s√=13TeV
Johannes Lange (on behalf of the CMS Collaboration)
(Submitted on 13 Dec 2018)
The top quark mass is measured using 35.9 fb−1 of LHC proton-proton collision data collected with the CMS detector at s√=13 TeV in 2016. The measurement uses the tt⎯⎯ all-jets final state, which comprises a total of six jets. A kinematic fit is performed to reconstruct the decay of the tt⎯⎯ system and suppress QCD multijet background. By means of the ideogram method, the top quark mass is determined, simultaneously constraining an additional jet energy scale factor (JSF). The result of 172.34±0.20(stat+JSF)±0.76(syst) GeV for the top quark mass is in good agreement with previous measurements in the same and different final states."

andrew said...

The combined error s 0.79 GeV. It is an ever so slight pull higher compared to the previous Run-1 estimate with all jets but with a somewhat higher MOE. So it doesn't change the CMS average much at all except to give it a bit more weight. So, while it tweaks up the CMS average by a bit less than 0.01, it decreases the global average slightly by giving more weight to a CMS average that is lower than the global average. The LHC combined data are quite a bit lower and fairly consistent with each other relative to the Tevatron data.

andrew said...

"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. . . . "

This is looking increasingly unlikely. The top is a bit light for it to be 50-50 and the Higgs is a bit heavy, although given current uncertainties it can't be entirely discounted. The global fit of the sum of the square of all fundamental particle masses equals the square of the Higgs vev is closer to the data, although still not at the best fit points.

Thus, it seems that we have a slightly boson tilted universe.