Thursday, October 09, 2008

Kobayashi, Maskawa and Quarks

This year's Nobel Prize in Physics has been jointly awarded to Yoichiro Nambu, (for his work on spontaneous symmetry breaking) and to Makoto Kobayashi and Toshihide Maskawa, for their 1973 prediction that there are 3 generations of quarks. This prediction was intimately related to the violation of CP symmetry in quark processes involving the weak nuclear force.

A CP transformation is the combined operation which swaps positive charges and negative charges (Charge conjugation), and swaps right-handed particle states and left-handed particle states (Parity reversal). Given a left-handed, negatively charged particle, the corresponding antiparticle is a right-handed, positively charged particle. CP-violation occurs when particle processes are not invariant under a CP transformation.

At the time of Kobayashi and Maskawa's work, it was believed that there were 2 generations of quarks. The first generation of quarks contains the up and down quarks, the second contains the charm and strange quarks. However, Cronin and Fitch had already discovered in 1964 that quark processes involving the weak nuclear force violate CP-symmetry, and it transpired that if there were only 2 generations of quarks, then CP-symmetry would be preserved. Ergo, there must be more than 2 generations of quarks. The quarks in the third generation, the top and bottom quarks, have now been experimentally detected.

Note carefully, however, that the presence of 3 quark generations is merely a necessary condition for CP-violation. Weak force interactions permit something called quark mixing, which enables quarks of one generation to transmute into a quark from another generation, (accompanied by the emission of a W gauge boson, the so-called 'interaction carrier' of the weak force). The amplitudes of the various quark mixing is specified by something called the Cabibbo-Kobayashi-Maskawa (CKM)-matrix, an array of nine numbers. If all the numbers in this matrix can be real numbers, then CP-symmetry is preserved, but if some of the numbers must be complex numbers, then CP-violation occurs. With 2 quark generations, the numbers can always be real, but with 3 quark generations, there is no such guarantee. The experimental detection of CP-violation entails that complex values unavoidably enter the CKM-matrix in our universe, but the mere presence of 3 generations does not itself entail this.

I note at this point that my own book, The Structure and Interpretation of the Standard Model, can now be found on Google Books, and those wishing to develop a deeper understanding of the Standard Model could do far worse...

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