I have some doubts regarding the CKM matrix in the quark sector and PMNS matrix in the leptonic sector. Let us call $(d^\prime, s^\prime, b^\prime)$ the weak basis for quarks and $(d,s,b)$ the mass basis in the quark sector. In the leptonic sector $\nu_e,\nu_\mu,\nu_\tau$ are the weak basis ans $\nu_1,\nu_2,\nu_3$ represent the mass basis.

  1. All the weak processes involving quarks are written in terms of the mass basis. For example, $$d\rightarrow u,\hspace{0.5cm} d\rightarrow s$$ etc. But in the leptonic sector the weak processes involving neutrinos are written in terms of weak basis. Why is this difference? Does it mean the physical particles in the quark sector are the mass eigenstates and those in the leptonic sector are the weak states? Isn't it strange?

  2. What about the crucial matter of production and detection of neutrinos and quarks? It is said that neutrinos are produced in one of the weak states and I presume they are also detected as weak state. But what happens in the quark sector? Processes like $d\rightarrow u$ or $d\rightarrow s$ seems to imply that quarks are produced in mass eigenstates.

  3. If there is the phenomenon of oscillation of neutrino weak states, from $\nu_e\rightarrow \nu_\mu$ (say, for example), why is there no such oscillation observed in the quark sector form $d^\prime\rightarrow s^\prime$?

  • $\begingroup$ 1. "But in the leptonic sector the weak processes involving neutrinos are written in terms of weak basis." - What, exactly, do you mean by this? Perhaps give an example/reference? 2. Why do you think there is a single type of state they are produced in? When you write $d\to u$, you're interested in the amplitude of the process where a $d$ mass state turns into a $u$ mass state, but you could as well examine the amplitude for producing another non-mass state, it's quantum mechanics after all. $\endgroup$
    – ACuriousMind
    Oct 9, 2015 at 13:11
  • 1
    $\begingroup$ Have a look at the answers on a similar question here physics.stackexchange.com/q/22151 $\endgroup$
    – anna v
    Oct 10, 2015 at 4:22
  • $\begingroup$ Related 76804. $\endgroup$ Apr 29, 2017 at 13:26

1 Answer 1


1) You can of course write down these amplitudes in any basis you choose, as long as you take into account matrix elements of the CKM and PMNS matrix.

2) There is indeed a difference here, neutrinos are produced exclusively by the weak interaction, whereas quarks can be pair produced by the strong (or electric) force, or produced by weak decays.

3) in principle hadronic states can oscillate, $K-\bar{K}$ and $B-\bar{B}$ oscillations have been studied in great detail. Also, interference effects in weak decays certainly exist. There are some difficulties, however, with observing''$d-s$'' oscillations: i) Quarks are confined, so the actual oscillation would have to be $\pi-K$. ii) But pions and kaons are (typically) produced as strong (mass) eigenstates. iii) The mass difference is quite large, and the oscillation length would be very short. iv) Kaons are unstable (not necessarily a problem, they live sufficiently long to observe kaon-anti-kaon oscillations).


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.