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Speculations about the Higgs boson mass December 14, 2006

Posted by dorigo in news, personal, physics, science.

I received a long comment by James Graber in a post below, and decided that since I was going to answer his many questions anyway, I could do it here and maybe do a service to some other interested readers. So here it is.

  • How soon is the W mass unblinding likely to occur?

Today, at 3.30PM Chicago time.

  • Does a higher or lower value favor your side of the bet with Watts and Distler?

That depends. If one gives credit to the MSSM, which if found at the LHC would make me lose my bet, then a low value of W mass favors me, since it favors higher values of the lightest scalar higgs in the MSSM, and this cannot be much higher than 135 GeV. Please refer to the plot above, where the top mass is on the x axis and the W mass on the y axis: the green band is the region “allowed” by MSSM theories (in the plot, it stops at about 115 GeV for the higgs mass, but that depends on how much one wishes to twist some parameters of the model). Also note the black arrows which shows the direction of logarithmic increase of the higgs mass (negative y axis – as the W mass decreases –  or positive x axis – as the top mass increases).

On the other hand, if one believes in less minimal SUSY theories, then a higher W mass could also be interesting, because the ellipse would then move away from the region where the Higgs has not been excluded yet (I remind you that LEP II found that Mh>114 GeV). That is to say, if the right theory of nature is SUSY, then the fact that the lowest mass higgs state is non-observable could make things harder for LHC. But that is just a wild speculation, and I can imagine opposite arguments too.  

  • Assuming the Higgs is not an MSSM Higgs, but rather “just” or “only” a standard model Higgs, what mass do you expect it will have?

I expect it to have the mass which is most favored by the global electroweak fits. The information is summarized in the famous “blue band plot, shown below. There, you see as a function of the unknown value of the SM higgs mass the global chisquare per degree of freedom of a fit to all measured electroweak observables, including Tevatron measurements of the top quark mass and W boson mass determinations (of course excluding the still unknown CDF measurement). The blue band represent the effect of theoretical uncertainties on the observables which are fit. Forget delta alpha_5, too technical and not very important. The dotted magenta line shows how the fit moves about if you include the somewhat controversial data from neutrino scattering experiments, which imply a very low mass for the W boson which appears inconsistent with all other determinations.

If taken at face value, the blue band implies that the Higgs boson has a mass of 85 GeV in the standard model, with an asymmetric error bars of -28+39 GeV: that is to say, there is a 68% chance that it lies in the interval [57-124] GeV.

Now for the answer to your question: since I believe electroweak fits, as much as LEP II results, I think the most likely value of the Higgs boson mass is 115 GeV, just above the experimental limit and still within the blue band. 

  • Assuming no Higgs is seen below 130 GeV, do you see that as a big plus for your side of the bet?

No, since I do not believe in the MSSM, and its exclusion would mean little to me. I am more “worried” (would be delighted) by completely unexpected effects than by SUSY particles popping out in numbers the minute LHC turns on its triggers.

  • Even if we see a fairly light Higgs, i.e. below 130 GeV, we still don’t know it’s a supersymmetric Higgs, rather than a standard model Higgs. Correct?

Correct. Cross section determinations helps little. Until other scalars are found, the lightest SUSY Higgs could be indistinguishable from the SM one.

  • Other than seeing a superpartner, or a second higher mass Higgs, are there indirect ways of supporting supersymmetry that we are likely to see?

Well, there are measurements in B-physics which would strongly suggest SUSY is the theory if observed. For instance, a dimuon decay of the B_s meson (a hadron made up of a bottom and a strange quark) is enhanced by the presence of virtual loops of SUSY particles. However, the present determinations of mixing parameters in the B sector are so precise, that it would be very hard for any theory that predicted new particles contributing to virtual diagrams to not spoil the consistency of the picture. That of course could be taken upside down to say that if we were to find inconsistencies in the CP measurement asymmetries then we could well start smelling SUSY rats.

  • What sort of 5 sigma non Standard model effect is Jacques likely to be thinking of?

I think Jacques took the bet because he genuinely believes that supersymmetric particles will be observed at the LHC. But you should ask him.

  • How about a disagreement between the Masses of the Higgs, top, W, and or Z?

 You are basically talking about an inconsistency between electroweak fits and the Higgs mass. Well, yes. That could be evidence of something fishy too. But our knowledge of electroweak observables will hardly improve to the level of creating much tension with a direct Higgs boson mass measurement in the next few years, partly because theory uncertainties are still quite large. 

  • How do you expect to win your bet with Watts and Distler?

I expect to see CMS and Atlas get their 10 fb-1 of data and sit on it, while being unable to find anything screaming at the standard model.

  • Suppose we see something that looks like a standard model Higgs but the mass is way high. Does that count as a 5 sigma discrepancy?

No, that would be suspicious but not impossible to accommodate within the standard model. Of course, if the Higgs mass were found above a few hundred GeV we would enter in some sort of gray zone, where neither me nor Jacques or Gordon could really claim anything for a while.

Sure, but I am not registered there yet… Will do, but not today.


1. James Graber - December 18, 2006

Hi Tomasso,
I hope you are not insulted or angered by my slow responses. Two reasons: I like to think things over before I post, and then there is my family and my day job.
I want to thank you for your detailed response to my questions. As I posted above in the misleading plot thread, I finally figured out that the red green plot does not imply a heavy Higgs in the MSSM. I also finally remembered that it is split supersymmetry that prefers a Higgs near 170 GeV, at least according to slides 6 and 7 of this reference

Click to access TPlehnFreiburg.pdf

I still find the blue band plot hard to understand because the vertical axis is given in terms of delta chi-squared. I have googled around and am still puzzled. Most references to chi-square depend on degrees of freedom. They also frequently mention a Gaussian limit. So is the vertical axis roughly equivalent to sigma?
Or given that mH=115 GeV is about delta chi-squared 1 and mH =175 GeV is about delta chi-squared 4 or 5 (that logarithmic scale is hard to read), then how much more likely is mH = 115 than mH =175, according to this plot?
TIA Jim Graber

2. dorigo - December 19, 2006

Hi James,

take your time! 😉

My comment is that the posted version of the Mt%Mw plot is indeed quite complicated, if not outright misleading. Another instance of a “use with caution” picture… It is used by experts, and by posting it in the blog maybe I committed a sinful act.
The blue band plot is in delta chisquared per degree of freedom, so it is “normalized” in a way. A unit difference of chisquared does imply a decrease of probability in line with 1-sigma deviations. So the answer to your question is yes, but Dchi2=1 is 1-sigma, Dchi2=4 is 2-sigma, Dchi2=9 is 3-sigma.
Be careful that the blue band shows the theory uncertainty, and should be included in one’s eyeballing estimates.
Best is to take the LEP ewwg as a reference… Their latest-greatest result for Mh is 85+39-28 GeV.

3. Big Vlad - January 9, 2008


can someone give me an arxiv reference for the blue band plot above? Where did it first appear?

many thanks,

Big Vlad

4. dorigo - January 9, 2008

Hi Vlad,

you should search the documents in the LEP Electroweak Working Group page. There is all the information you need there, plus more.


5. rebuild credit after bankruptsy - October 1, 2008

rebuild credit after bankruptsy…

deplores!imported!daddy scratcher predicating?…

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