Just a short post to convey the very sad news that the great Italian physicist Nicola Cabibbo passed away today at the age of 75. I know I’m not alone in thinking that he should have received a share of the Nobel prize in 2008, which was awarded to Yoichiro Nambu (half the prize) and the other half was split between Makoto Kobayashi and Toshihide Maskawa.

As I wrote in 2008:

All three are extremely distinguished physicists and their contributions certainly deserve to be rewarded. But, in the case of Kobayashi and Maskawa, the Nobel Foundation has made a startling omission that I really can’t understand at all and which even threatens to undermine the prestige of the prize itself.The work for which these two were given half the Nobel Prize this year relates to the broken symmetry displayed by weak interactions between quarks. We now know that there are three generations of quarks, each containing quarks of two different flavours. The first generation contains the up (u) and the down (d), the second the strange (s) and the charmed (c), and the third has the bottom (b) and the top (t). OK, so the names are daft, but physicists have never been good at names.

The world of quarks is different to penetrate becauses quarks interact via the strong force which binds them close together into hadrons which are either baryons (three quarks) or mesons (a quark and an anti-quark).



But there are other kinds of particles too, the leptons. These are also arranged in three generations but each of these families contains a charged particle and a neutrino. The first generation is an electron and a neutrino, the second a muon and its neutrino, and the third has the tau and another neutrino. One might think that the three quark generations and the three lepton generations might have some deep equivalence between them, but leptons aren’t quarks so can’t interact at all by the strong interaction. Quarks and leptons can both interact via the weak interaction (the force responsible for radioactive beta-decay).

Weak interactions between leptons conserve generation, so the total number of particles of electron type is never changed (ignoring neutrino oscillations, which have only relatively recently been discovered). It seemed natural to assume that weak interactions between quarks should do the same thing, forbidding processes that hop between generations. Unfortunately, however, this is not the case. There are weak interactions that appear to convert u and/or d quarks into c and/or s quarks, but these seem to be relatively feeble compared to interactions within a generation, which seem to happen with about the same strength for quarks as they do for leptons. This all suggests that there is some sort of symmetry lurking somewhere in there, but it’s not quite what one might have anticipated.

The explanation of this was proposed by Nicola Cabibbo who, using a model in which there are only two quark generations, developed the idea that states of pure quark flavour (“u” or “d”, say) are not really what the weak interaction “sees”. In other words, the quark flavour states are not proper eigenstates of the weak interaction. All that is needed is to imagine that the required eigenstates are a linear combination of the flavour states and, Bob’s your uncle, quark generation needn’t be conserved. This phenomenon is called Quark Mixing. What makes it simple for only two generations is that it can be described entirely by one number: the Cabibbo angle, which measures how much the quark flavour basis is misaligned with the weak interaction basis. The angle is small so the symmetry is only slightly broken.

Kobayashi and Maskawa generalized the work of Cabibbo to the case of three quark generations. That’s actually quite a substantial task as the description of mixing in this case requires not just a single number but a 3×3 matrix each of whose entries is complex. This matrix is universally called the Cabibbo-Kobayashi-Maskawa (CKM) matrix and it now crops up all over the standard model of particle physics.

And there’s the rub. Why on Earth was Cabibbo not awarded a share of this year’s prize? I was shocked and saddened to find out that he’d been passed over despite the fact that his work so obviously led the way. I can think of no reason why he was omitted. It’s outrageous. I even feel sorry for Kobayashi and Maskawa, because there is certain to be such an outcry about this gaffe that it may detract from their success.

But really…