Rare B meson decays - mathieu trocmé

II- Physical Background 9
This combination of operations looking invariant reassured all the community, but a
new surprise arose. In 1964, still in K mesons, Cronin and Fitch discovered the first laboratory
evidence of CP violation [9].
Nowadays, only the combination of the three symmetry operations all together (the
‘CPT combination’) is believed to be invariant. That is, the backwards observation of a
phenomena filmed through a mirror in an antimatter universe would be indistinguishable than
the same phenomena observed in ‘natural’ conditions [10].
II.2- CP Violation in the Standard model:
One of the first attempts to explain CP violation came from Wolfenstein in 1964 [11].
His theory was implying a new unknown force, the “weak superforce”. Although simple and
elegant, it was abandoned, not being able to explain new phenomena. It was only in 1973 that
a valid explanation, based on the work of Cabibbo [12], was proposed by Kobayashi and
Maskawa [13]. Cabibbo first realised that the weak interaction does not ‘see’ the flavour of
the then 4 known quarks (u/d, c/s) as the electromagnetic or the strong interactions do.
Instead, it feels a mixture of quarks. To express his idea, he so created a 2x2 matrix (still only
4 quarks) comprising a real parameter θ c – today known as the Cabibbo angle – that must be
found by experiment.
⎛d
'⎞
⎛V
⎜ ⎟ = ⎜
⎝ s'
⎠ ⎝V
ud
cd
V
V
us
cs
VCabibbo
⎞⎛d
⎞ ⎛ cos( θ c )
⎟⎜
⎟ = ⎜
⎟ ⎜
⎠⎝
s ⎠ ⎝−
sin( θ c )
d'
= (cosθ
). d + (sinθ
). s
c
s'=
( −sinθ
). d + (cosθ
). d
c
sin( θ ⎞⎛d
c ) ⎞
⎟
⎜ ⎟
cos( θ ⎠⎝
s c ) ⎠
where the dashed letters represent the quark eigenstates seen by the weak interaction (called
flavour eigenstates), and the undashed ones the ‘normal’ quark eigenstates as felt by the
electromagnetic or the strong interaction (the mass eigenstates).
c
c