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Why measure the top quark mass ? June 6, 2006

Posted by dorigo in news, physics, science.

This morning Sven Heinemeyer gave a nice talk on the importance of a precise determination of the top quark mass. Of course, he spent lots of time discussing the plot of top mass versus W boson mass. Here is the plot:

The plot shows graphically the inner consistency with measured data of two particle theories: the Standard Model, and an extension called "Minimal SuperSymmetric Model". Most everybody who does Higgs Hunting these days has this plot stuck to their office wall. So let me explain a little bit what is in there.

The top quark mass and the W boson mass are inextricably linked to the unknown mass of the Higgs boson; however, while in the Standard Model (red band) there is a direct connection between these three parameters – and the arrow near the lower left shows what the Higgs boson mass has to be if you pick one particular value for Mt and Mw – in the MSSM (green band) you can accommodate different values of top and W mass by varying other parameters: the mass of the supersymmetric particles (arrow near the right boundary). But in that case the lightest Higgs boson has to be lighter than 135 GeV. 

The red band is constrained from above by the direct limit, MH>114 GeV, obtained by the LEP II experiments at CERN; the green band is only constrained by the inner consistency of the theory. You could extend it a bit upwards if you assumed extreme values for some free parameters of MSSM theory; and downwards, if you added Higgs bosons – but in that case you would be into real SUSY theories, and no longer into the "minimal" model.

We do not know what the Higgs boson mass is, nor do we know if there are supersymmetric particles, let alone their mass. So, this plot is of some guidance to us: the better we measure what we observe – top and W boson masses, x and y axis – and the more we can discriminate the two theories, SM and MSSM.

Right now, the two measurements constrain physics to within the blue ellipse: there is a 68% probability that the true value of Mt and Mw is withing the ellipse, given what we observed experimentally. We cannot yet say whether the pure SM is favored, or whether MSSM is the better candidate as a particle theory. We can say, however, that the Higgs boson is light: detailed computations find it consistent with measurements only if the Higgs boson mass is lower than about 175 GeV. This bodes well for the near future of the Tevatron, which has a better chance to discover the Higgs if the mass of that particle is near to the experimental limit.  


1. Better BetterSearch - June 6, 2006

inextricably ..how?

2. dorigo - June 6, 2006

Great question, bettersearch.

The fact is, if you have a Higgs boson that propagates in space, it will emit and reabsorb top quarks, W bosons, or other particles. These are “virtual” processes, in the sense that they happen because of quantum fluctuations. They, however, have an observable consequence: they affect the measured mass of the Higgs boson.

Yes, that is right: the heavier the top quark, the heavier the Higgs boson has to be (once you fix other parameters) because of the way it couples to the Higgs boson and because of the way virtual loops of top quarks affect the propagation of a Higgs boson. On the other hand, the lighter the W is, the heavier the Higgs, for the same reason and yet with an opposite effect.

I can explain more quantitatively the matter if you wish… Just ask.

3. Fred Altieri - June 6, 2006

Eventually, what type of practical application will be derived from this research?

4. dorigo - June 7, 2006

Hi Fred,

at order zero, none!

That is, let me qualify my statement. We measure fundamental parameters of our theory to check its internal consistency. If it is not the right theory, for instance, the Standard Model will fail to predict the observed value of top, W, and Higgs masses, as in the plot I showed above the three will not match.
There are no practical applications of knowing that the Standard Model is not the right theory of particle physics. However, by studying fundamental physics one occasionally learns things that allow new technological developments. You cannot say before you open a door to a unknown room what you will find inside.
Roentgen did not know what would happen if he accelerated electrons in a vacuum tube, but a week later a bone was fixed with the newly discovered x rays!


5. Eggsino - June 10, 2006

It looks like that the pure SM Higgs particle is almost ruled out. I hadn’t realized that. You couldn’t find that statement in a textbook.

So what measurements need to be made to completely rule out a pure SM Higgs? (That would be the sign of `new physics’ — even SUSY is `new physics’ because no one has seen it.)

I suppose not finding a light enough Higgs would rule out both SM and MSSM Higgs sectors … what is the upper limit for MSSM light Higgs? 135 GeV?

6. dorigo - June 10, 2006

Hi Eggsino,

well, its a little early for textbooks! That plot is fresh out of press… With results that are less than a month old.

Yes, absence of a Higgs is death to the SM. But beware, the blue ellipse represents 68% of the probability for the two masses of top and W to lie therein. So that plot does not rule out much… yet.

For the MSSM, yes, above 135 GeV the lightest Higgs would make little sense, or none at all.


7. Michael Schmitt - June 11, 2006

Hi Tommaso, this is an interesting and useful post. As you’ve seen here and elsewhere, other people like it, too.

Now I don’t quite have the same opinions as you do, though I agree with the gyst of your comments.

I do hope that the Tevatron data will show the Standard Model (SM) to be unviable before the Tevatron is turned off. The consistency of the SM with precision electroweak observables is not so good at present (perhaps Sven Heinemeyer commented on this?). But the real point comes out clearly on the plot you posted – the current values of the W and top masses are “uncomfortable” for the SM (and apparently perfectly OK for the MSSM).

As you know, we have yet to obtain a new value for the W mass from the Tevatron data, so we do not know where that error ellipse will fall in the future. It could move downward or upward – it is not likely to stay where it is. And the size of the ellipse will shrink significantly. So, depending on Nature and statistical fluctuations, the SM could be disfavored at the couple of percent level, unless the ellipse moves downward significantly.

Furthermore, the Tevatron program will eventually add to what we know about a SM-like Higgs boson. It will take a lot of inspired hard work and a lot of data, but people expect that CDF + D0 could extend the excluded range of a Higgs boson upward toward 130 or even 135 GeV (and also cover some small mass range around 160 GeV, too) – provided that there is no Higgs in that mass range.

So, if the error ellipse shrinks and stays where it is, or moves upward, and if the bound on the mass of a SM-like Higgs moves upward from 114 GeV to, say, 130 GeV, then the SM will be in trouble. One might not argue that it is not fully “ruled out” – but then we don’t expect the SM to survive for all measurements and all energies, do we? Eventually new physics, whatever it is, has to enter the kind of quantum fluctuations that you described above.

Now, if the ellipse moves down, and a signal for the Higgs boson is found, then we will not be killing the SM at the Tevatron. But we will certainly celebrate long and hard, having discovered the (first) fundamental scalar…

8. Eggsino - June 11, 2006

Hi TD,

Yes, of course it’s too early for textbooks! I meant that I didn’t know how close to ruling out the SM Higgs things were.

I’ll be guessing that LHC will rule out a single scalar Higgs (pure SM Higgs). That’ll be fun!

9. dorigo - June 11, 2006

Hi Michael,

I have to agree – the Tevatron has the potential of moving the ellipse around where it makes things more interesting, and of moving down the experimental limit on the lightest scalar.

The SM is tough to kill, but as you note it cannot live forever. I do doubt it will be killed by this plot alone, but you are right, it could be put in a awkward situation by it…


10. dorigo - June 11, 2006

Hi Eggsino,

we all hope for some sort of earthquake in HEP these days… If none occurs, we might be closing the shop soon!


11. vivacious photon - November 24, 2006

I guess that your posts allows some of us to enjoy the (part of the) beauty of elementary particle searches without the nightmare of data monitoring, crashing jobs at endless queues, redoing histos, not to mention awfull trailers… thanks…

One of your comments caught my attention: “Yes, absence of a Higgs is death to the SM (6. dorigo – June 10, 2006)…”.. how to interpret such sentence? I would guess that you mean that the existence of a Higgs boson is then a logical necessary consequence of the Standard Model.. however, quite often you could find in literature that the Higgs boson is a mechanism, that explains the presence of mass, not a necessary consequence. I may be wrong, but I do not recall any deduction of the Higgs existence from the SM. It is more a field that you add to the Lagrangian, and then you get the masses… but if there is not higgs.. what is wrong?

12. dorigo - November 25, 2006

Hi photon,

I think the absence of a standard higgs would revolutionize much of the standard model, because we would then have to read our calculation of radiative corrections and related observables (and there’s twoscores of them) in a totally new way – they are sensitive to the presence of that particle and their value is what we measure by force of the higgs being what we think it is. The fact that we do not at present have an alternative mechanism nor a different reading key of the observable values in the standard model does not imply that the higgs mechanism is the right theory, but it makes everything very interconnected. The SM would become something else with no higgs, in some way.


13. michael - August 31, 2007

You say “The red band is constrained from above by the direct limit, MH>114 GeV, obtained by the LEP II experiments at CERN”.
How does this constraint come about?
What is the consequence if, for example, the Higgs boson is 112GeV?

14. dorigo - August 31, 2007

Hello michael,

the constraint is due to the searches performed by electron-positron collisions at LEP II. The associated ZH production was expected by running the machine at a total energy exceeding M_z + M_h , roughly. They did not see it, so they set a limit. The limit is very stringent: although it says “we exclude a SM higgs boson if its mass is below 114.4 GeV, at 95% confidence level”, the probability they can have missed it if its mass is 112 GeV is about zero. That is because of the steep behavior of their probability of observing the particle as a function of the mass.


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