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No Z’ below 1 TeV September 7, 2008

Posted by dorigo in news, physics, science.
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New heavy bosons are predicted by several models of physics beyond the standard model. In particular, heavy versions of the Z° boson, called generically Z’ but sometimes distinguished by greek subscripts (Z_\eta, Z_\chi, Z_\psi etc.), might constitute the quickest route to a discovery of superstring-inspired E6 models; and also Kaluza-Klein spin-2 gravitons may appear as a Z’. I won’t describe what those models are about (and besides, I am not the best person to do that), but just mention that many of my colleagues pin their hopes of finding new physics on just such a signature: the production of a new Z’ boson, with its decay to a pair of charged leptons. A pair of muons of several hundred GeV, for instance, is a great discovery channel, because muons cannot easily be mistaken with other final state particles -all collider detectors have an outer shell of drift chambers specifically designed to detect muons, in fact, exploiting the high penetrating power of these particles.

With only a few days separating us from the official start of LHC operations, it is now as good a time as any to take stock with respect to the experimental situation with the search for Z’ bosons. A recent result by CDF, based on 2.3 inverse femtobarns of proton-antiproton collisions produced by the Tevatron accelerator, has pushed the lower limit for the mass of these particles above the TeV. Interestingly, one TeV was a reference point good enough for CMS and ATLAS to produce expectation plots in their technical design reports. Take CMS, for instance: the expected dimuon mass spectrum after just 100 inverse picobarns (about ten times the data that LHC will collect this fall) would present a very narrow, distinctive peak of about 18 events, as shown by the empty histogram over the sharply falling background (shown by the green histogram).

The graph above would be a unmistakable evidence for the production of a new massive neutral particle. Unfortunately, we now know it’s just not going to happen. The CDF result excludes a Z’ boson with mass below 1030 GeV. The analysis is straightforward: having noticed that the mass is measured with the momenta of the two muons, which are obtained from their curvature in the 1.4 Tesla magnetic field, one finds that the mass resolution degrades significantly with dimuon mass, but if one plots the inverse of the mass, this has a fixed relative resolution, making it much easier to search for a signal of unknown mass in a wide range. The data (blue points) is shown in the plot below.

From the very good agreement of all data points with the expectation -which is due to the sum of electroweak production of muon pairs through the so-called Drell-Yan mechanism (yes, that includes the regular Z° boson decay) and background processes due to QCD- it is not too hard to extract direct lower limits on the cross-section times branching-ratio of Z' \to \mu \mu. These are shown below (the red curve) as a function of the hypothetical Z’ mass.

The plot is busy as much as it is colorful. First off, ignore the stretched Brazil flag, and only look at the red curve. That is the upper limit on the cross section, at 95% Confidence Level. That is the result of trying to fit a signal in the histogram of inverse masses, which does not seem to contain any. At 1 TeV, the limit is set at 3.5 femtobarns. Since a SM-like Z’ would have a 4.5 femtobarn cross section, such a particle is excluded. All mass values above 1030 GeV are instead still possible.

The “brazil flag” is then just a prediction of the cross-section limit that CDF could set, a priori computed using the analysis methodology, before looking at the data. The red line wiggles around but stays within the 1-sigma band (yellow).

The phase space of new physics continues to shrink, without any real hint from collider data of the SM becoming inadequate…



1. Luboš Motl - September 7, 2008

It’s good and expected if a light Z’ goes away. I see no rational reason why such a new Z’ should be detectably light.

Your comment that there’s no hint that SM is inadequate sounds ill-informed. The high-precision data favor the Higgs mass around 85 GeV which is pretty well excluded. To compare, regions in the MSSM parameter space favor the mass around 115 GeV which seems just right.

Also, dark matter is not quite consistent with the SM.

2. Alejandro Rivero - September 7, 2008

Actually, the discarding of E6 based models could be the most interesting thing in superstring theory. They went up to E8xE8 because (apart from being more productive) the real thing, to fit the chiral standard model in some Kaluza Klein that moves between 10 and 11 dimensions, was not easy work to do. Of course, the return of Kaluza Klein would not imply to trash (do they trash any?) E8xE8, because this model itself comes from “interiorising” KK modes of 26 dim, and it is possible to exchange some internal gauge with some KK gauge.
But 7 extra dimensions is the unbroken, vector, pure massless Standard Model. So experimental support of the Standard Model can be translated to experimental support of 7 extra dimensions.

3. dorigo - September 7, 2008

Hi Lubos,

the fact that SM fits “favor” 85 GeV means little, once you know that the d(chi^2)/dm curve is quite flat. Much more stringent is the direct limit. I would interpret the situation by saying that the SM fits, once the direct lower limit is taken into account, have a minimum at 115 with a 20 GeV “good” range extending to 135. This is in no conflict with the SM.

Hi Alejandro, I wish I understood better what you mean… Keep trying 😉


4. J - September 8, 2008

Isn’t the 115 limit when Afb(b,0) taken into account which has a pretty strange fluctuation?

5. Luboš Motl - September 8, 2008

Dear Alejandro #2,

having no Z’ around 1 TeV surely doesn’t discard all E6-based models (even though I see no reason why there should be any E6 traces surviving up to low TeV energies, anyway: SO(10) is more than enough). I can’t comment on your other sentences because I don’t understand your point, to put it very mildly.

Dear Tommaso #3,

that’s very cute to take all the evidence including the lower direct bound on the Higgs mass as one package but it doesn’t change the fact that inside this package, a (so far) slight contradiction (between two ways to determine the Higgs mass) lurks.

Your method to handwave the signal of a contradiction away is equivalent to proving that there’s no contradiction between Jesus Christ walking on water and hydrostatics. You would say: When the Jesus signal is taken into account, there is an additional upward force in the equations of hydrostatics with coefficient going from a minimum of 115 pounds per Jesus, extending up to 135 pounds per Jesus. That sounds great but according to other high-precision observations of water, the coefficient should probably be below 115 pounds per Jesus.


6. Guess Who - September 8, 2008

Lubos, before you wax too theological, you may want to cast a quick empirical glance at


and in particular at figure 1 and sections 1 and 2.

Since the spam filter seems to eat comments based on a link/text ratio, I hereby add some utterly superfluous fluff in the hope to increase that ratio sufficiently to pass the spam filter threshold. Let’ s see if it works…

7. Luboš Motl - September 8, 2008

Dear Guess Who, the paper looks great to me. Does it contradict something I wrote? Best wishes, Lubos

8. Guess Who - September 9, 2008

Just a reminder that it may be premature to argue which light Higgs model is the right Higgs model. Plus it has lots of interesting references, so any excuse to link it is good. 🙂

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