# I Higgs Boson Mass Trending Down At ICHEP

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1. Aug 5, 2016

### ohwilleke

The latest measurement of the Higgs boson mass from the ICHEP conference (based upon four lepton events measured by CMS) was 124.5 +0.48/-0.46 GeV. This is less than the current global average of about 125.09 +/- 0.24 GeV, which is statistically consistent with the global average but will probably drag down a new global average somewhat, although there is a considerable range of data points that contribute to that global average.

The current combined estimate of the Higgs boson mass (from the link to that value above) 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

So, after this new CMS data point, the new global average should be roughly 124.82 GeV with a pretty similar margin of error, before accounting for any new ATLAS results with its wealth of new data.

The new CMS data point also makes the ATLAS diphoton data point look like an outlier relative to the other three measurements (a more than four sigma tension), which suggests that we may expect the combined average is more likely to fall than to rise when ATLAS releases its next Higgs boson diphoton decay based mass measurement, which would bring the combined average even lower.

My quick scan of the ATLAS Higgs papers from ICHEP suggests that we won't be getting any new Higgs boson mass measurements from ATLAS at ICHEP.

Some of the prior Higgs boson mass measurements at the LHC (by date of publication, some of which were used in the current combined average) include the following:

* ATLAS diphoton mass 125.98 +/- 0.42 +/- 0.28 (June 15, 2014)
* ATLAS four lepton mass 124.51 +0.52 +/- 0.06 (June 15, 2014)
* CMS diphoton number 124.7 +/- 0.31 +/- 0.15 (July 2, 2014)
* CMS four lepton mass 125.6 +/- 0.4 +/- 0.2 (September 10, 2014)

The new CMS four lepton mass measurement is very close to the June 15, 2014 ATLAS four lepton mass measurement.

One notable coincidence of this trend is that the combined average Higgs mass is trending towards a value (124.65 GeV) which would cause the sum of the square of the fundamental boson masses in the Standard Model equal to half of the square of the Higgs vev. The 124.65 GeV value is within one sigma of the combined Higgs boson mass post-ICHEP.

This is particularly notable because the sum of the square of the fundamental fermion masses in the Standard Model would also be equal to half of the square of the Higgs vev at a top quark mass of about 174.04 +/- 0.1 GeV which is within 1 sigma of the current global average measurement of the top quark mass. The latest top quark mass estimate from ATLAS (pre-ICHEP at least) is 172.99 +/- 0.91 GeV. The latest combined mass estimate of the top quark (excluding the latest top quark mass measurement estimate from ATLAS) is 173.34 +/- 0.76 GeV.

This balance between fermion masses and boson masses in the Standard Model suggests a supersymmetric-like balance implicit in the Standard Model, although in a much more subtle way than in SUSY theories.

Last edited: Aug 5, 2016
2. Aug 5, 2016

### RGevo

Hi ohwilleke,

Can you provide formula and input mass choices for the values you using?

Are you using on-shell scheme values for all the quark and fermion masses?

What is the value of the on-shell vev value?

Would you use one/two loop relations to extract these values? Like the vev from muon decay etc.

The reason I ask, is that these details will presumably alter how close the numerology is. In addition, these "SM" values (extraction of these on-shell parameters from measurements) will also receive BSM contributions. Will these be consistent?

3. Aug 5, 2016

4. Aug 5, 2016

### Dr.AbeNikIanEdL

Could you explain what you mean by "supersymmetric-like balance"?

5. Aug 5, 2016

### Staff: Mentor

How is 126.02 +/- 0.51 GeV 4 sigma (2 GeV) above ~124.8 GeV? Looks like 2.4 sigma to me.

I wouldn't try to find any physics in 1 sigma fluctuations. It is what you expect, after all, if the values would scatter less something would be wrong with the uncertainty estimates.

6. Aug 5, 2016

### ohwilleke

The new combined value is about 124.82 (crude linear estimate that would be tweaked slightly with weighting proportionate to margin of error, particle data group style). The margin of error of the new combined value is assumed to be similar to the current margin of error of 0.24 GeV for the combined value because the margin of error of the old CMS four lepton entry and the new CMS four lepton entry are about the same. 126.02-124.82=1.20 GeV/0.24 = 5 which is greater than 4 (the conservative number used to allow some wiggle room in the margin of error in the new combined value).

Honestly, that exact quantification of the tension isn't the point and there are different conventions that you could use to quantify it. The point is that if you have three values that are within the range 124.6 +/- 0.1 and you have one value that is 1.3 GeV higher than the other three, and it is more than a two sigma gap by any margin of error you choose to use, then there is tension in the measurement and the outlier is probably wrong.

7. Aug 5, 2016

### Staff: Mentor

That calculation doesn't make sense.
The uncertainty on the difference between a given channel and the average is mainly driven by the uncertainty on this given channel, and if this channel does not contribute too much to the average you can add the uncertainties in quadrature.

If you know that a physical parameter is 1 +- 0.1 and a new measurement is 5 +- 5, then this new measurement is less than 1 standard deviation away (and perfectly compatible), and not 40.

Unrelated: the new combination should have a smaller uncertainty. You absolutely have to use different weights to get any reasonable result. And how did you take correlated systematic uncertainties into account? This os crucial for Higgs mass combinations.

8. Aug 5, 2016

### ohwilleke

First off, I recognize that this has a numerology flavor and I am merely advancing the factual coincidence as an observation, rather than making an real theoretical conclusion about it. It has been noted in the literature, although to be fair, I didn't learn that until after I had figured it out for myself. Obviously, all of these are rest masses and are taken from reliable third party sources. I didn't go out and measure of calculate the Z boson mass myself. I used an Xcel spreadsheet to make the calculations.

(1) The formula on the boson side is (Higgs vev squared)/2=(W boson mass squared)+(Z boson mass squared)+(Higgs boson mass squared)+(Photon mass squared, i.e. zero)+(Gluon mass squared, i.e. zero).

The value I used for the Higgs vev (per the particle data group, I think, or some other standard reference if I did not use it, I don't recall which) is 246.2279579 +/- 0.0000010 GeV.
The value I used for the W boson mass is 80.385 +/- 0.015 GeV from pdg. I also considered a W boson mass of 80.376 GeV from an electroweak global fit.
The value I used for the Z boson mass is 91.1876 +/- 0.0021 GeV.

(Put another slightly more technical way, the hypothesis is that the sum of the thee boson couplings to the Higgs field converted to Yukawa form because the way that those couplings are expressed on the boson side is a little different, is 1.)

It turns out that the Higgs boson mass when you solve for it from the other three constants is robust to either of the values for the W boson and any variation within the one sigma margin of error in the W and Z boson masses because the Higgs boson contribution to the total is much larger than either the W or Z boson contributions.

(2) The formula on the fermion side is (Higgs vev squared)/2=(top pole mass squared)+(bottom pole mass squared)+(charm pole mass squared)+(strange quark pdg value squared)+(down pdg mass squared)+(up pdg mass squared)+(tau mass squared)+(muon mass squared)+(electron mass squared)+(neutrino mass 1 squared)+(neutrino mass 2 squared)+(neutrino mass 3 squared).

(Put another slightly more technical way, the hypothesis is that the sum of the fermion Yukawas is 1.)

I used the same Higgs vev value as above.

The top mass was to solve for in this context. The vast majority of the uncertainty in the total on the fermion side is from the top (which makes sense because its Yukawa is almost 1 and the critical differences are in mass squared which emphasized larger values).

With regard to the other values I used the more recent QCD study values rather than the pdg values for the bottom and charm quark masses. But, the terms other than the bottom, charm and tau masses make a pretty negligible contribution to the total. So, the distinction between MS values at 1 GeV and hypothetical pole values for the light quarks is immaterial, and the difference between including or leaving out the neutrino masses is likewise immaterial to the result. The charged lepton masses are pole values per notes to the pdg. The differences between the bottom and charm pdg values and those from more recent QCD studies also have a very negligible contribution to the total.

I also did an error analysis using the high end and low end of one sigma error bars to see if it would materially effect the end result (which it did only slightly to the tune of about 0.01 GeV in the final top quark mass target).

The other values used were:
* The bottom quark mass is 4.18 +/- 0.03 GeV (per the Particle Data Group). A recent QCD study has claimed, however, that the bottom quark mass is actually 4.169 +/- 0.008 GeV.
* The charm quark mass is 1.275 +/- 0.025 GeV (per the Particle Data Group). A recent QCD study has claimed, however, that the charm quark mass is actually 1.273 +/- 0.006 GeV.
* The strange quark mass is 0.095 +/- 0.005 GeV (per the Particle Data Group).
* The up quark mass and down quark mass, are each less than 0.01 GeV with more than 95% confidence, although the up quark mass and down quark pole masses are ill defined and instead are usually reported at an energy scale of 2 GeV.
* The tau charged lepton mass is 1.77682 +/- 0.00016 GeV (per the Particle Data Group).
* The muon mass is 0.1056583715 +/- 0.0000000035 GeV (per the Particle Data Group).
* The electron mass is 0.000510998928 +/- 0.000000000011 GeV (per the Particle Data Group).
* Each of the three Standard Model neutrino mass eigenstates (regardless of the neutrino mass hierarchy that proves to be correct) is less than 0.000000001 GeV.

Last edited: Aug 5, 2016
9. Aug 5, 2016

### ohwilleke

I am sure that you are correct, but in this particular case, a more rigorous approach would only slightly tweak the bottom line number.

But, for a back of napkin order of magnitude estimate where the margin of error in the new CMS four lepton result and the old CMS four lepton result is almost the same and has the same sources of systemic error, conservatively assuming that the margins of error in the new combined value are the same as in the old combined value is probably reasonable and pretty close. I've looked at several cases of global averages being updated for new data points and its impact on margin of error, and the impact on the margin of error is usually pretty modest when the margin of error of the old entry and the new entry are similar. I suspect that the new margin of error computed rigorously is probably in the 0.21-0.23 GeV range.

Also, in this instance, the margin of errors for three of the four entries (including the replaced one) are all about the same, so weighting by margin of error when doing the combination of the best fit values would just slightly increase the weight of the CMS diphoton result which wouldn't change much because that value is pretty close to the new CMS four lepton value and the ATLAS four lepton value. I suspect that the inaccuracy is on the order of 0.01-0.02 GeV in the combined value.

10. Aug 5, 2016

### ohwilleke

I don't understand your question. Of course a new measurement of the Higgs boson mass can have a smaller value than the old global average of the Higgs boson mass.

UPDATED: Are you questioning the "global average" when all the data points comes from two experiments at one facility? Yeah, whatever.

Last edited: Aug 5, 2016
11. Aug 5, 2016

### ohwilleke

Supersymmetry assumes that there is a symmetry between fundamental fermions and fundamental bosons in a model of particle physics.

Ordinary SUSY theories do so in a direct and crude way by assuming into existence a new boson superpartner particle for each existing fundamental fermion particle, and assuming a new fermion superpartner particle for each fundamental boson particle - even in SUSY this is then obscured somewhat as some superpartners mix with each other.

But, there could also be symmetries between the fundamental fermions of the Standard Model and the fundamental bosons of the Standard Model that are less obvious and a balance in their couplings to the Higgs field addresses the hierarchy problem in a similar way and forms a kind of fermion-boson symmetry. Because there appears to be a quite precise fermion-boson symmetry in the Standard Model in Higgs field couplings, but it is not done SUSY style, calling it a "supersymmetric-like" balance seems like a reasonable description of apparent relationship.

12. Aug 5, 2016

### ohwilleke

To illustrate, it is helpful to show the numbers calculated to two decimal points or one significant digit, whichever is less, using the central values considered (but omitting the error analysis):

Higgs vev squared is 60,628.20 GeV^2. Half of that amount is 30,314.10.
Z boson mass squared is 8,315.17.
W boson mass squared at 80.385 GeV is 6,461.75 and at 80.376 GeV is 6,460.30.

The sum of the two squared masses is 14,776.96 at the high end and 14,775.47 at the low end. Half of the Higgs vev squared less this amount is 15,537.14 (square root 124.648) to 15,538.63 (square root 124.654). Hence, the Higgs boson mass that solves the equation is 124.65 GeV. This is about 0.17 GeV from the new combined average Higgs boson measurements from ATLAS and CMS of about 124.82 which is within one sigma of the calculated value.

The crude average of the non-outlier Higgs boson mass measurements is 124.57 GeV and if the 124.7 GeV CMS diphoton measurement of the Higgs boson mass with the lowest margin of error were weighted more heavily it would be closer to 124.6 GeV.

A bottom quark mass of 4.18 GeV squared is 17.47 and at 4.169 GeV squared is 17.38.
A charm quark mass of 1.275 GeV squared is 1.63 and of 1.273 GeV squared is 1.62.
A strange quark mass of 0.095 GeV squared is 0.01.
An up or down quark mass squared is less than 0.0001 (omitted)
A tau lepton mass of 1.77682 squared is 3.16.
A muon mass of 0.1056583715 squared is 0.01.
An electron mass of 0.000510998928 squared is .0000003 (omitted)
Each of the neutrino mass eigenstates is less than 0.00000000000000001 (omitted).

The sum of the non-quark squared fermion masses is 22.28 at the high end and 22.18 at the low end. Half of the Higgs vev squared less this amount is 30,291.02 (square root 174.043) to 30,291.92 (square root 174.046). Hence, the top quark mass that solves the equation is in the range of 174.04 GeV to 174.05 GeV. This is within one sigma of the current pdg estimate for the top quark mass which is 173.34 +/- 0.76 GeV.

It is also appropriate to note that since the current measured value of the Higgs boson is a bit high, and the current measured value of the top quark is a bit low, the fit is even better to the more general proposition that the sum of the square of the masses of the fundamental particles in the Standard Model is equal to the square of the Higgs vev. The sum of the square of the masses using purely pdg values (including the pdg value for the Higgs boson) is 60,493.36. This differs from the Higgs vev squared of 60,628.20 by just 0.22% of the Higgs vev squared.

Last edited: Aug 5, 2016
13. Aug 6, 2016

### RGevo

Hi ohwilleke,

Thanks for providing all the numbers, formulas and input values. I appreciate its quite a bit of work posting them in.

For the sum of the fermion masses, I would rather use b and c values:
4.5+/- 0.2 b
1.5+/- 0.2 c

These are pole mass values you would get converting the msbar values that the pdg quotes (and you used above). You get these from one-loop qcd conversion of the msbar results. The errors are inflated because the conversion isn't really that well defined for the charm in particular. (They suffer from a renormalon ambiguity)

If you use these values, probably the preferred top mass is closer to the experimental value.

14. Aug 6, 2016

### Staff: Mentor

Please stop with that numerology, unless there is a peer-reviewed paper discussing that.

It has a relevant impact on the uncertainty.
If that would be true, there would be no point in adding new measurements.

If you add two completely independent measurements of similar sensitivity, the uncertainty goes down by a factor sqrt(2). The uncertainty would stay the same if the measurements are 100% correlated (then the two values have to agree exactly as well), but as they come from different data at least the statistical component (the dominant uncertainty in the previous combination) is independent.

If you add two measurements with notably different sensitivity, the final result will be close to the one with a better sensitivity.

Let's make a better estimate:

Previous combination: $125.09 \pm 0.21 ( stat. ) \pm 0.11 ( syst. )$
CMS 4l: $124.50 \pm 0.46 (stat) \pm 0.12 (syst)$

A simple weighted average (weights 0.80 and 0.20) gives $124.97 \pm 0.19 \pm 0.09 \approx 124.97 \pm 0.21$ assuming uncorrelated measurements. The systematic uncertainty of the new CMS study is negligible, so this number won't change if we take correlations into account.

The ATLAS diphoton measurement is 2 standard deviations above that average, so what.

15. Aug 9, 2016

### ohwilleke

Published discussion of the relationship I've discussed is found at:
Relation between masses of particles and the Fermi constant in the electroweak Standard Model
G. Lopez Castro, J. Pestieau
http://arxiv.org/abs/1305.4208

This paper only notes the existence of the tight empirical relationship, just as I do, without drawing a theoretical conclusion about its source. Pestieau has several earlier papers that also explore possible relationships among Standard Model fundamental constants. Castro has only one other paper on the topic, co-authored with Pestieau shortly before this one.

The relationship has also been discussed by others in the literature, but Lopez Castro and Pestieau's paper is the most neutral and least speculative of the presentations that I have seen. Some people call the relationship the LC&P relationship in honor of this paper.

The global electroweak fit for the W boson mass comes from 2013 Moriond Conference presentation slide that in turn cites its sources. http://moriond.in2p3.fr/QCD/2013/ThursdayAfternoon/Baak.pdf

The study with the precision estimate of the bottom quark mass is from 2014. http://arxiv.org/abs/1401.7035
Another precision estimate of the bottom quark mass from 2013 or 2014 by a different group of researchers estimated the bottom quark mass at 4,166 +/- 43 MeV but unfortunately I put the wrong link to that result in a blog post I did on the study at the time and can't find it it any longer.

The study with the precision estimate of the charm quark mass is from 2013. http://arxiv.org/pdf/1312.1556v1.pdf

I'm aware of the issues involved in using MS masses v. masses determined by other means which leads to a significant discrepancy between the directly measured top quark decay masses and other estimates of the top quark mass established in the MS scheme. The discrepancy is surely smaller in absolute magnitude at least for lighter quarks, but is harder to test definitively as we can't directly measure the b quark or c quark masses the way that we can the top quark mass.

pdg doesn't consider this issue for its charm quark mass estimate http://pdglive.lbl.gov/DataBlock.action?node=Q004M
But, it does make a separate evaluation for its bottom quark estimate (4.66 GeV +/ 0.3 GeV). http://pdglive.lbl.gov/DataBlock.action?node=Q005M and considering that adjustment would make the predicted value of the top quark mass 174.03 rather than 174.04.

Last edited: Aug 9, 2016
16. Aug 9, 2016

### ohwilleke

Are you removing the old CMS 4l result which it appears from the new CMS 4l paper is superseded by the new one from the previous combination? The old CMS 4l result was very similar to the ATLAS diphoton, but with it gone, three of the four results are in a tight cluster and the ATLAS diphoton is far afield. I haven't had a chance to read all the new ATLAS papers and honestly, can't find a link where they are posted, so I can determine if there are any new Higgs mass results from ATLAS. If anyone could locate the link for the ICHEP papers from ATLAS, I'd appreciate it.

The other new, but not really new result is that Tevatron has released another updated combined analysis of its measurement of the top quark mass, which if I recall correctly, has the lowest margin of error of any single top quark mass measurement done to date. Tevatron average mass value for the top quark is mt=174.30 ±0.65GeV/c2. The paper is at http://arxiv.org/abs/1608.01881 This is very close to where the LP& C relationship would suggest that it should be.

The previous combined Tevatron estimate is incorporated in the pdg estimate with an appropriate weight. I don't know how much the previous combined Tevatron estimate differs from the current one.

Going forward, we can expect the precision of the Higgs boson mass estimate to improve quite a bit over the next couple of years as a lot of the error in the Higgs boson mass estimates is statistical, and the size of the LHC data sets of both ATLAS (which has made no new estimates using Run 2 data) and CMS (which has not made a new diphoton estimate with Run 2 data) improve over time, and with new data not yet collected or analyzed with will reduce the statistical error in Higgs boson mass estimates significantly. I wouldn't be surprised to see a combined estimate with a 0.1 GeV error margin within a couple of years.

Increasing precision in the top quark mass measurement is going to be slower going because the measurements that we already have are more mature (meaning that the low hanging fruit of quick big reductions in statistical error from just a couple of years more of data aren't available), and because the greater mass means that each new set of data should have fewer top events than Higgs boson events.

Last edited: Aug 9, 2016
17. Aug 9, 2016

### Staff: Mentor

It doesn't seem to be peer-reviewed, and inspire finds exactly 0 citations. That does not count as acceptable source.

Why is it superseded? The old combination was run 1 data, the new result is run 2.

Public ATLAS results concerning the Higgs are listed here. I don't see a run 2 mass measurement.

18. Aug 9, 2016

### ohwilleke

Thanks for the link to the ATLAS results.

19. Aug 9, 2016

### ohwilleke

All the paper does is arithmetic, so a lack of publication or citation isn't a great concern. One doesn't have to be terribly concerned that simple math done by a couple of published professional physicists is correct. It may not be significant enough by itself to be journal publication worthy at 1.5 pages of body text, but honestly, I don't think anyone doubts that they've done their math in the method disclosed correctly and it is an interesting coincidence.

20. Aug 9, 2016

### Staff: Mentor

It is, if the paper is implying any meaning of the arithmetic. If you do it and the paper does not: even worse.

If there is absolutely no meaning implied, then it is pointless.