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Movable Type 3.2-ja-2



2008年10月30日

The birth of the Kobayashi-Maskawa mechanism of CP violation

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This is based on a chat I had with Prof. Maskawa
on Feb 9, 2001 (Fri).

Maskawa-san was about 5 years senior of Kobayashi-san.
Maskawa-san was a joshu at Nagoya which expired in 3 years
and then moved to Kyoto U. At about the same time,
Kobayashi-san was hired at Kyoto as a joshu also.

The quark mixing in weak interaction that Cabibbo introduced
in 1963 had been extended to a credible 4-quark theory
by Glashow, Iliopoulos, and Maiani in 1970. Since then,
many people had been working on 4-quark models.
The 4-th quark, charm, was not discovered yet. Maskawa-san
and Kobayashi-san were also working on 4-quark models,
but their focus was to explain the CP violation that had been
observed in the decay of neutral Kaon several years earlier.
QCD was not established yet, and if the strong interaction
violated SU(4), then CP violation could occur in 4-quark model.
The first correct choice was to assume that the strong
interaction did not contribute to CP violation, and that
CP violation would occur in the framework of the gauge theory
of weak and electromagnetic interactions. It then became
clear that there could be no CP violation in the 4-quark models.

The mode of operation was that Maskawa-san came up with
various models which Kobayashi-san would examine and kill.
Kabayashi-san was so able and also knowledgeable about
experimental constraints that most models were rejected
one after another.

It was clear that if the number of quarks were increased,
then there could be CP violation. However, it looked quite
adventurous to propose a 6 quark model when the 4th quark
had not even been found yet. At one night in the bath tab,
Maskawa-san was resigned that probably the point of the paper
should be that there would be no CP violation within 4-quark models.
Then, when he got up from the tab, he thought maybe they should
emphasize that there would be CP violation with 6-quark models.
A slight shift of focus. But it was not the only ingredient that led to
the discovery of so-called Kobayashi-Maskawa mechanism of
CP violation.

The quark mixing matrix, which is called
the Cabibbo-Kobayashi-Maskawa (CKM) matrix, is a product of
two unitary matrixes that diagonalize left-handed up-type quarks
and left-handed down-type quarks. The diagonalization is
performed by bi-unitary transformations where the unitary
transformations of right-handed quarks also participate
but do not get included in the CKM matrix.
Bi-unitary transformation was not too well known, but
Maskawa-san had studied the chiral transformation of pions
where each of two indexes transforms by a separate matrix.
He was thus well prepared to tackle the topic of quark mixing
matrix and figure out how a CP-violating complex phase
could sneak into the weak interaction of quarks.
On the other hand, Kobayashi-san was able to quickly figure out
what forms of interaction could and could not lead to the observed
CP violation. When it was combined with the mathematical ability
of Maskawa-san, the result was that the standard theory of
CP violation is now called the ‘Kobayashi-Maskawa mechanism.’
Yes, there existed good reasons why they were the first.

Hitoshi Yamamoto(Tohoku University)

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