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Latest global fits to SM observables: the situation in March 2009 March 25, 2009

Posted by dorigo in news, physics, science.
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A recent discussion in this blog between well-known theorists and phenomenologists, centered on the real meaning of the experimental measurements of top quark and W boson masses, Higgs boson cross-section limits, and other SM observables, convinces me that some clarification is needed.

The work has been done for us: there are groups that do exactly that, i.e. updating their global fits to express the internal consistency of all those measurements, and the implications for the search of the Higgs boson. So let me go through the most important graphs below, after mentioning that most of the material comes from the LEP electroweak working group web site.

First of all, what goes in the soup ? Many things, but most notably, the LEP I/SLD measurements at the Z pole, the top quark mass measurements by CDF and DZERO, and the W mass measurements by CDF, DZERO, and LEP II. Let us give a look at the mass measurements, which have recently been updated.

For the top mass, the situation is the one pictured in the graph shown below. As you can clearly see, the CDF and DZERO measurements have reached a combined precision of 0.75% on this quantity.

The world average is now at M_t = 173.1 \pm 1.3 GeV. I am amazed to see that the first estimate of the top mass, made by a handful of events published by CDF in 1994 (a set which did not even provide a conclusive “observation-level” significance at the time) was so dead-on: the measurement back then was M_t=174 \pm 15 GeV! (for comparison, the DZERO measurement of 1995, in their “observation” paper, was M_t=199 \pm 30 GeV).

As far as global fits are concerned, there is one additional point to make for the top quark: knowing the top mass any better than this has become, by now, useless. You can see it by comparing the constraints on M_t coming from the indirect measurements and W mass measurements (shown by the blue bars at the bottom of the graph above) with the direct measurements at the Tevatron (shown with the green band). The green band is already too narrow: the width of the blue error bars compared to the narrow green band tells us that the SM does not care much where exactly the top mass is, by now.

Then, let us look at the W mass determinations. Note, the graph below shows the situation BEFORE the latest DZERO result;, obtained with 1/fb of data, and which finds M_W = 80401 \pm 44 MeV; its inclusion would not change much of the discussion below, but it is important to stress it.

Here the situation is different: a better measurement would still increase the precision of our comparisons with indirect information from electroweak measurements at the Z. This is apparent by observing that the blue bars have width still smaller than the world average of direct measurements (again in green). Narrow the green band, and you can still collect interesting information on its consistency with the blue points.

Finally, let us look at the global fit: the electroweak working group at LEP displays in the by now famous “blue band plot”, shown below for March 2009 conferences. It shows the constraints on the Higgs boson mass coming from all experimental inputs combined, assuming that the Standard Model holds.

I will not discuss this graph in details, since I have done it repeatedly in the past. I will just mention that the yellow regions have been excluded by direct searches of the Higgs boson at LEP II (on the left, the wide yellow area) and the Tevatron ( the narrow strip on the right). From the plot you should just gather that a light Higgs mass is preferred (the central value being 90 GeV, with +36 and -27 GeV one-sigma error bars). Also, a 95% confidence-level exclusion of masses above 163 GeV is implied by the variation of the global fit \chi^2 with Higgs mass.

I have started to be a bit bored by this plot, because it does not do the best job for me. For one thing, the LEP II limit and the Tevatron limit on the Higgs mass are treated as if they were equivalent in their strength, something which could not be possibly farther from the truth. The truth is, the LEP II limit is a very strong one -the probability that the Higgs has a mass below 112 GeV, say, is one in a billion or so-, while the limit obtained recently by the Tevatron is just an “indication”, because the excluded region (160 to 170 GeV) is not excluded strongly: there still is a one-in-twenty chance or so that the real Higgs boson mass indeed lies there.

Another thing I do not particularly like in the graph is that it attempts to pack too much information: variations of \alpha, inclusion of low-Q^2 data, etcetera. A much better graph to look at is the one produced by the GFitter group instead. It is shown below.

In this plot, the direct search results are introduced with their actual measured probability of exclusion as a function of Higgs mass, and not just in a digital manner, yes/no, as the yellow regions in the blue band plot. And in fact, you can see that the LEP II limit is a brick wall, while the Tevatron exclusion acts like a smooth increase in the global \chi^2 of the fit.

From the black curve in the graph you can get a lot of information. For instance, the most likely values, those that globally have a 1-sigma probability of being one day proven correct, are masses contained in the interval 114-132 GeV. At two-sigma, the Higgs mass is instead within the interval 114-152 GeV, and at three sigma, it extends into the Tevatron-excluded band a little, 114-163 GeV, with a second region allowed between 181 and 224 GeV.

In conclusion, I would like you to take away the following few points:

  • Future indirect constraints on the Higgs boson mass will only come from increased precision measurements of the W boson mass, while the top quark has exhausted its discrimination power;
  • Global SM fits show an overall very good consistency: there does not seem to be much tension between fits and experimental constraints;
  • The Higgs boson is most likely in the 114-132 GeV range (1-sigma bounds from global fits).


1. Sven - March 25, 2009

It might be interesting to note that the GFitter group (that also produced the last plot in this post) produced their *own* *unofficial* average of M_W,
M_W = 80.399 +- 0.023 GeV, which is just the old value, but with a 9% smaller error. This should simply ‘sharpen’ the blue band a bit.

2. mandeep gill - March 25, 2009

T- good, informative post, and i had one quick q for you (that you may have answered in previous posts, in which case you can just point me to the link) — in most scenarios, all these limits apply equally to the lowest mass MSSM Higgs (i believe the neutral CP-even one, though i’m not certain), if this version of SUSY is ‘out there’, correct..?

Also, could you remind me of how much you have wagered so far on the discovery of the Higgs actually happening at the LHC, and the conditions on that bet — it should be pretty interesting to follow this, the next couple of years!

thx, M

3. Daniel de França MTd2 - March 25, 2009

Hi Tommaso,

Why NuTeV is so broken?

4. chris - March 25, 2009

hi Tomaso,

thanks for the very nice post!

i always find it a bit confusing to see the gfitter plot where one fit never touches delta-chi^2=0 line.

well, anyways. it’s getting really tight for the SM higgs now. and most interestingly (for me) the region around 170GeV is now really disfavored. that’s the region where you could run the SM up to M_GUT without hitting any inconsistencies and have that huge dessert in between.

and now clues are accumulating that it’s not a desert after all – horay!

5. dorigo - March 25, 2009

Hi Mandeep, yes, in much of the parameter space the lightest MSSM Higgs boson is very similar to the SM one; branching ratios are in principle different (it depends on a parameter of the MSSM giving the ratio of vacuum expectation values to up- and down-type fermions) but before one can realize which Higgs one has bagged, it will take many years at the LHC…

I have wagered 1000 dollars that the LHC will NOT find supersymmetry or new exotic phenomena within two years of collecting 10/fb/exp. It now seems a long time away before I can cash that bet!

Daniel, NuTeV determines the W mass from the ratio of NC/CC neutrino interactions. Systematics due to our understanding of the nucleon structure are sizable. My understanding is that the result is not usually averaged with the direct determinations, because of those uncertainties and other model-dependent assumptions.

Chris, yes, the black line does touch the delta chi2=0 line, but the one without theory uncertainties stands above, which may sound odd until you realize that reducing uncertainties your denominator in the chisquared will decrease, and the chisquare increases.


6. Tony Smith - March 25, 2009

Tommaso, I sort of apologize for asking about 1-sigma stuff, but you said, about the Gfitter graph shown above:
“… From the black curve in the graph you can get a lot of information. For instance, the most likely values, those that globally have a 1-sigma probability of being one day proven correct,
are masses contained in the interval 114-132 GeV. …”.

However, in your blog post of 13 March 2009 Tevatron excludes chunk of Higgs masses Chris (comment 16) said, about the Tevatron LLR graph shown in that post:
“… what i [Chris] find most interesting is that the former peak at around 115 GeV seems to have vanished. ah, the joys of sub-1-sigma statistics …”
you [Tommaso] replied (comment 19):
“… yours [Chris] is a meaningful observation, but unfortunately the Tevatron data is still not enough to provide a meaningful hint yet. …”.

Do you have any intuitive feeling about what is the physical difference between
the indirect electroweak events underlying the Gfitter graph
the Tevatron events underlying the Tevatron LLR graph
explains why the indirect electroweak Gfitter seems to like low (125 GeV or below) Higgs
the Tevatron LLR seems to dislike that region (125 GeV or below)

For example,
does the difference come from differences between the two sets of modeling sausage-machines,
does the difference come from differences between the two sets of input events, such as selection/trigger cut differences ?

Again, I realize that at current 1-sigma levels the questions may not be easily answerable, but my curiosity got the better of me so I asked anyway.

Tony Smith

7. dorigo - March 25, 2009

Hi Tony,

the GFitter inputs are both indirect (EWK observables from LEP and SLD, top mass, W mass, W width), and direct (LEP II limit, Tevatron limit). I mean to say that ALL the information from the Tevatron exclusion plot, i.e. the LLR plot you quote, goes into the GFitter input. You can sort of see it if you realize that the black line is a parabolic growing line, to which an addition of some chisquared units is provided in the region investigated by the Tevatron, and an addition of almost infinite chisquared for masses below the LEP II limit, due to the very sharp limit that those experiments could set.


8. Amos - March 26, 2009

Hold on a second… The LEP EWWG calculation (based on the latest W and top mass estimates) is 90 +36-27 (63-127). But the bulk of that range is below 114.4 GEV, and therefore excluded by LEP direct searches.

So, if there is a SM Higgs, then the W mass measurement has to be pretty close to the edge of the current reported experimental margin of error (on the lighter side), and in fact outside the margin of error reported by combined CDF and D0.

So, although it is not excluded, the current weight of the evidence (to one’s statistical confidence in the measurement of the W mass) is against the existence of an SM Higgs.

(It seems, though, that the LEP EWWG calculation method may be different from the one in the plot that started this discussion. On that plot, when I drew the error margins for W and top mass, I got a box located entirely lighter than the 114 diagonal.)

I accept that I am misreading or misinterpreting something. What?

9. dorigo - March 26, 2009

Amos, the answer to your question lies in the second plot of the post above, where it is shown the world average W mass from direct measurements (green band) compared to the W mass inferred from electroweak global fits (which exclude W mass measurements), the last blue bar at the bottom.

There, you can see that direct and indirect measurements go along pretty well together.

In other words, the fact that the inferred M_h is in the range 63-126 GeV (at 1-sigma level), does not “exclude” anything. In fact, the limit at 114 GeV only shows that a part of that 1-sigma band is impossible, but a sizable chunk of it remains. The compatibility of the two observations is good, as long as you do not try to fit in a higgs mass well above 130-140 GeV. That is exactly what the last graph shows.


10. Sven - March 26, 2009

Hi Mandeep and Dorigo,
on the one hand it is correct that for ‘large parts’ of the MSSM parameter space the lightest CP-even Higgs is very SM-like. On the other hand, the fits for the Higgs mass (e.g. the blue band plot from the LEPEWWG) do *not* apply to the MSSM. The reason is twofold. First, there are additional contributions to the precision observables, see the last post. Second, the mass of the lightest Higgs is not a free parameter as in the SM, but predicted in terms of the other MSSM parameters. There is only one analysis doing something very similar to the blue band plot for the MSSM, see http://arxiv.org/abs/0707.3447, fig. 3. The analysis was done in the Constrained MSSM and added some more observables to the blue band analysis (dark matter, g-2_mu, b -> s gamma). Interestingly, the central value for the lightest Higgs mass came out substantially higher than in the blue band plot.🙂
This issues was also discussed in this blog about a year ago.

11. dorigo - March 26, 2009

Hi Sven,

that is right. And sorry for not having linked to your paper before…
As for fig.3 in your paper, I must say that while the central value is higher than that of the SM, the slope with chi2 is much steeper, so that it is not too clear which model has the higher integrated probability… Or am I misinterpreting that plot ?


12. Sven - March 26, 2009

Hi Tommaso,
you are right with your description of the ‘red band’. However, at least at the time of that analysis (with m_t = 170.9 +- 2.1 GeV), the compatibility of the CMSSM Higgs mass with the direct searches was somewhat better than the one of the SM (check p.7-8 of the paper). How this looks with the new m_t
value of 173.1 +- 1.3 GeV has not been analyzed.

13. dorigo - March 26, 2009

Ok, thanks for the clarification!


14. chris - March 26, 2009


if you go back in history a bit you will see that the situation was even worse with LEP preliminary data. i remember that about ’99 the central value for m_H from EW fits was about 50 and a zero value for the Peskin-Takeushi parameters S and T (i.e. the standard model) was on the edge of the 68% contour.

15. Amos - March 26, 2009


OK… let me see if I understand… I think what you are saying is that there is an overlap between the world-average direct measurement of W mass, and the predicted W mass based on electroweak precision tests. That overlap (well, the range generated by performing some statistical magic on the two ranges) (which is on the light end of the world-average W mass range, and outside Tevatron’s error range), when combined with the top mass to predict a range of acceptable SM Higgs values, allows a SM Higgs weighing between 114 and 126 Gev.

But, if there is an SM Higgs, this means that the Tevatron’s estimate of the W mass is off by a sigma or two. (Or, alternatively, if the Tevatron’s W mass estimate is right, then the SM Higgs is, in fact, excluded.)

Did I get that right?


I can accept on an intellectual level that sigmas really do mean something, and one time in 20 something excluded at the 95% confidence level turns out to exist. But I’m not a scientist, and so I don’t “feel” these statistical points the way you experimentalists do. I accept that this is my limitation.

16. dorigo - March 26, 2009

Amos, yes, direct and indirect determinations of the W mass agree. This does not necessarily say that the direct W mass measurements agree with direct bounds on the Higgs mass. However, they happen to agree. There is no 2-sigma difference. Maybe one sigma, but one sigma is nothing. Not even worth discussing, really, especially since there are a few assumptions in the fits.


17. Low Math, Meekly Interacting - March 27, 2009

Thanks so much for these wonderful posts. They’ve really helped me understand a great deal, and I’m grateful.

18. pligg.com - March 31, 2009

Latest global fits to SM observables: the situation in March 2009…

A recent discussion in this blog between well-known theorists and phenomenologists, centered on the real meaning of the experimental measurements of top quark and W boson masses, Higgs boson cross-section limits, and other SM observables, convinces me …

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