Wednesday, July 12, 2017

Higgs Mass Increases Slightly After Run 2 At LHC

The Status Quo

At the end of Run-1 at the Large Hadron Collider (LHC), the combined estimate of the Higgs boson mass from all sources was 125.09 +/- 0.24 GeV.

The New Results

New measurements from ATLAS and CMS (the two main experimental groups at the LHC) of the Higgs mass were announced this week, and the error weighted average of those mass measurements is now 125.14  +/- 0.17 GeV, a global best fit value that is about 29% more accurate than the previous state of the art measurement after LHC Run 1. The error in the new Higgs boson mass measurement is less than 0.14%. This isn't bad for measurements of the properties of a particle that was only discovered five years ago, although it is less accurately known than some of the other physical constants in the electroweak sector of the Standard Model.

The one sigma margin of error was +/- 0.28 GeV for the ATLAS result and +/- 0.22 GeV for the CMS result. This is based upon an ATLAS measurement of the Higgs boson mass of 124.98 GeV and a CMS measurement of 125.26 GeV.

Evaluation In Light Of A Conjecture About The Fundamental Particle Mass Scales

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 which in turn each equal one half of the square of the Higgs vacuum expectation value.

It has been the case for some time that the measured value of the Higgs boson is a bit heavy relative to this prediction. This theoretical value is about 2.9 sigma away from the current best fit value, which is enough to disfavor this hypothesis, although not enough to definitively rule it out, particularly given the still relatively wide range of different experimental measurements of the Higgs boson mass by different means in the two experiments.

In contrast, as discussed below, the top quark mass has been on the light side relative to this theoretical expectation in recent measurements. The magnitude of the measured Higgs boson mass and top quark mass deviations from the theoretical expectation largely cancel out, however. So the total sum of the square of the pole masses of the fundamental particles of the Standard Model is very close to the square of the Higgs vev, even though the bosons make up just a bit more than half of the total, while the fermions make up just a bit less than half of the total. The main barrier to rigorously confirming the accuracy of this observation, particularly now as the mass of the Higgs boson becomes known more precisely, is the uncertainty in the measured mass of the top quark which is the predominant source of uncertainty in the overall sum of the square of the masses of the fundamental particles of the Standard Model. Indeed, this very slightly broken symmetry between the fermion masses and boson masses is from a theoretical perspective, harder to explain than an exact symmetry of these two quantities.

One possible way to reconcile this hypothesis with the experimental data might be to evaluate the sum of the set of masses at a single energy scale (such as the Higgs vacuum expectation value of ca. 246 GeV), rather than using the pole masses of each particle considered (the pole mass of a particle its its mass evaluated at an energy scale equal to its rest mass).

On the boson side of the equation, the W and Z boson masses are slightly lighter than their pole masses at the Higgs vev scale, so the Higgs boson mass at the scale would have to be slightly greater to fit the equation, and since the Higgs boson mass also deceases somewhat from its pole mass at the Higgs vev energy scale, a slightly higher Higgs boson mass at the Higgs vev scale would translate into an even larger Higgs boson pole mass.

I haven't done the calculations (and to be honest, it would take a couple of weeks for me to get up to speed enough on the calculations of the running masses involved to do them right), but the order of magnitude and direction of the adjustments would be about right.

On the fermion side the the equation, the fundamental fermion masses also get smaller at higher energy scales. To the extent that one is determining the top quark mass by starting with half of the square of the Higgs vev and then subtracting out the square of the masses of the other fundamental fermions, this means that the contribution of the other fundamental fermions is slightly smaller, so the square of the top quark mass has to be slightly greater, and gets greater still when converted from a Higgs vev mass to a top quark pole mass. All of these adjustments are pretty modest, but they are enough to make the predicted value of the top quark mass a bit higher.

This solution is less attractive on the fermion side, where large margins of error in most measurements to data limit the extent to which this hypothesis can be confirmed or ruled out. If the sum of the squares of the fundamental fermion masses evaluated at the Higgs vev equals half of the square of the Higgs vev, and the sum of the squares of the fundamental boson masses evaluated at the Higgs vev also equals half of the square of the Higgs vev.

Using pole masses throughout, the formula predicts a top quark mass of 174.0 GeV. The final Tevatron measurement of the Higgs boson mass was a bit heavier than that at 174.30 +/- 0.65 GeV, which would probably be a good fit to this energy scale hypothesis, but the state of the art top quark mass measurements at the LHC are coming in at the mid- to high- 172 GeV range, which would tend to disfavor this hypothesis.

This also means that the sum of the square of the fundamental particle pole masses (both fermions and bosons) should slightly exceed the square of the Higgs vev, since the pole masses are across the board at lower energy scales than the Higgs vev and hence, are larger.

Another, more ad hoc, was to reconcile the discrepancies between the experimental data and this hypothesis, which might lead to an exact fermion mass sum-boson mass sum symmetry, would be to evaluate the fermion masses at the mass of the heaviest fermion (the top quark) which would only every so slightly reduce the total (the main contribution would come from a slight reduction in the bottom quark mass), while evaluating the boson masses at the mass of the heaviest boson (the Higgs boson) which would also reduce the total for the sum of the square of the boson masses, but less so because the Higgs mass is lighter than the top quark mass. Then, perhaps, the grand total would have to be calculated on the basis of pole masses compare to the Higgs vev which would pretty much fit the existing data.

Other Properties Of the Higgs Boson

The couplings of the Higgs boson to the Standard Model expectation at its measured mass is generally a fairly reasonable given the experimental errors involved in these measurements and is generally getting closer to the theoretically predicted value.

The spin and parity of the Higgs boson have been measured with sufficient precision to completely rule out alternatives to the Standard Model values of those quantum numbers of the Higgs boson.

A fairly tight upper bound on the "width" of the Higgs boson (which is functionally equivalent to its mean lifetime), which is consistent with a much narrower Standard Model prediction, has also been established.

Note: This post was significantly polished and expanded on July 13, 2017.

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