Today I was in the mood of cleaning up some areas of my labyrintic hard drive, after having performed a periodic backup of its contents. I thus came across some pieces of text that had been sitting in a remote folder, waiting to be used for a project now obsolete. I was about to just dump these files in the trash bin, when it occurred to me that this was stuff that had taken me some good time to put together, and maybe there was a better use for it.

Indeed, I have a blog ! This blog is in some sense a kind of "trash bin" of my thoughts, which I happily share with whomever is willing to read them. Now, the text I decided to save from oblivion is not particularly good, and it is obsolete because it talks of an era now gone - the pre-Higgs-discovery time when we could still speculate on whether the Higgs was actually a "fairy field", as a friend of mine would call it. However, it does transport us back to the pre-discovery time and it describes in simple terms the situation, in a way that might be of benefit to some of you.

So I am offering it below, with the caveat emptor clause that of course things have changed ! Not everything, however: the statements about the standard model being incomplete, and the mysteries surrounding the fermion masses, are still all the rage today...


Despite the continuing failure to find a Higgs boson, which the theory cannot do without, the standard model has been overwhelmingly successful in the last thirty years. It is maybe ironical that the Higgs boson, despite being the cornerstone of the whole theoretical construction, is affecting so little the observed phenomenology of sub-nuclear processes; if its influence were stronger, physicists might at least obtain an indirect evidence of its existence, but Nature has chosen otherwise. Even with no knowledge of the Higgs boson mass –a quantity that the model itself cannot predict- the standard model provides the tools to compute extremely accurate predictions for the observable features of electroweak processes. The availability of collider data probing the properties of weak bosons has allowed a verification of those predictions, and the result has always been a near-perfect match.

The best example of the new discipline flourished in the late eighties, called “precision tests of electroweak theory”, is the corpus of results obtained by the four experiments at the LEP synchrotron of the CERN laboratories in Geneva, and by the one at the Stanford Linear Accelerator Center in California. By colliding 45-GeV electron and positron beams in the core of the Aleph, Delphi, L3, and Opal detectors at CERN, and the SLD detector at SLAC, several million Z bosons were produced through the picture-perfect production process of electron-positron resonant annihilation. The created Z particles immediately decayed into fermion-antifermion pairs with different rates which depend on the details of the theory: the simplest precision test was thus just comparing the observed and predicted rates of the different kind of events.

With millions of Z decays, the LEP and SLD experiments could examine in exquisite detail the predictions of the standard model concerning not just the relative rates of decays of the Z boson into different final states, but also the angular distributions of the produced particles, the asymmetries resulting from the intrinsic properties of the particles involved in the reactions, etcetera. Literally thousands of man-years of studies and analysis have gone in that effort, such that the Particle Properties data book, the bible of experimental particle physicists and a compendium of all the human knowledge of the properties of sub-nuclear particles, contains a hundred pages of summarized results, none of which exhibits a significant deviation from the model predictions. No anomalies there: the model is successful.

Using the mass of data acquired at LEP and SLAC, plus the additional information coming from several other particle physics experiments throughout the world, it is indeed possible to try and discern the elusive influence of Higgs particles in the studied reactions. Everything seems to consistently point to the existence of that new neutral boson, whose mass should not be far from that of its electroweak W and Z cousins. Few particle physicists doubt that a Higgs boson with a mass in the 100-200 GeV range will be discovered in the next year or two by the new experiments at the Large Hadron Collider at CERN. Otherwise, the surprise will be even bigger.

And physicists would love to be surprised. Anything new and unexpected can be used as a tool with which to make way into new unexplored territory. In the case of the standard model, however, there is an additional bonus from anything not contained there: physicists know that regardless of its beauty and the precision of its predictions, the standard model is incomplete, and to some extent unsatisfactory. For sure, it cannot be the final word on the theory of matter and interactions. The model does not include gravity, it does not provide a straightforward means to unify the four forces together, and it presents at least one or two nagging technical issues. But these issues are complex, and they are out of scope here.

Instead, even without looking at the big problems mentioned above, which are given no solution within the existing framework, for an experimentalist or for a bystander the most nagging issue making the standard model not totally satisfactory is probably of more down-to-earth nature. This is the observation that the theory contains over twenty parameters whose value is only known through experiment: there are no ways to calculate them from first principles. The presence of twenty-something numbers that have a unexplained value is annoying in a theory so beautiful and successful.

Among the unexplained parameters of the standard model the ones we would love the most to explain are the fermion masses. It would be so nice if we could know just why the muon is two-hundred times heavier than the electron! We do not know why that is so. This leaves us to wonder what it is that is really being hidden from our view. To Rabi’s question “Who ordered the muon?”, we are compelled to add “and why the heck is it so heavy?”. Similar questions of course surround each of the fermions. Note that the Higgs boson, with its coupling to fermions proportional to the fermion mass, does not “explain” in any way the different values that these masses have. The explanation is deeper, if one exists; but we have not found it yet.

We are thus led to believe that the standard model needs to be replaced by a deeper, more fundamental theory. And we can only hope that this new theory will give answers to all our questions, rather than answering just a few while adding new, more impenetrable ones.