Stars as Laboratories for Fundamental Physics - MPP Theory Group

Nonstandard Neutrinos 261
In three-dimensional flavor space one is free to choose any superposition
of states as a basis. It is convenient and common practice to use
the mass eigenstates (vacuum propagation eigenstates) for each column
of Fig. 7.1. Thus by definition the electron is the charged lepton with
the smallest mass eigenvalue, the muon the second, and the tau the
heaviest, and similarly for the quarks.
All fermions interact by virtue of the weak force and thus couple to
the W ± and Z ◦ gauge bosons, the quarks and charged leptons in addition
couple to photons, while only the quarks interact by the strong
force and thus couple to gluons. The W ± (charged current) interaction
has the important property of changing, for example, a charged
lepton into a neutrino as in the reaction p + e − → n + ν e (Fig. 7.3). If
the initial charged lepton was an electron (the lightest charged lepton
mass eigenstate), the outgoing neutrino state is defined to be an “electron
neutrino” or ν e which in general will be a certain superposition of
neutrino mass eigenstates.
Fig. 7.3. Typical charged-current reaction.
This phenomenon of Cabbibo mixing is well established among the
quarks. For example, in the process of Fig. 7.3 the transition among the
quarks is between u and cos θ C d + sin θ C s where cos θ C = 0.975 refers
to the Cabbibo angle. Kinematics permitting, the final-state hadron
will sometimes be uds which constitutes the Λ particle with a mass of
1.116 GeV compared with 0.934 GeV for the neutron (udd).
The superposition of quark states into which u transforms by a
charged-current interaction is commonly denoted by d ′ , charm couples
to s ′ , and top to b ′ while the unprimed states refer to the first, second,
and third mass eigenstates in the d-column of Fig. 7.1. Ignoring the
third family one has
( d
′
s ′ )
=
( ) ( cos θC sin θ C d
− sin θ C cos θ C s
)
. (7.5)
It is only by convention that the mixing is applied to the d-column of
the quarks rather than the u-column or both.