In the Standard Model, with the introduction of the CKM matrix, we have that quark mixing between different generations is possible via a charged current (W boson).

My question is if this also implies that a given quark can change flavour (oscillate), auto-interacting with itself via a W boson.

For example, $$u \rightarrow W^{+} + d \rightarrow c$$ flavor oscillation Feynman diagram

  • $\begingroup$ In what sense is any quark in your diagram “auto-interacting with itself”? Are you considering the six flavors of quarks to be one quark? $\endgroup$
    – Ghoster
    Sep 25, 2022 at 4:25
  • $\begingroup$ Yes it was an abuse of notation, because this is like the self energy correction to the quark propagator. $\endgroup$ Sep 25, 2022 at 13:18

1 Answer 1


Yes, this type of oscillation is possible. Your specific example is forbidden because there are no charmed baryon states whose masses overlap with the nucleon, so the $u\to c$ diagram you’ve drawn would have to be followed by a second weak loop to get you back to the initial zero-charm state.

However, the simpler virtual charged-current states,

$$ u\longrightarrow W^+s\longrightarrow u \\ d\longrightarrow W^-c\longrightarrow d $$

will contribute to the strangeness and charm of the virtual-quark “sea.”

  • $\begingroup$ So the problem here is that, for the conservation of 4-momentum, the initial state must have the same mass as the final state. So, in principle, if all “up” quarks of the various generations would be degenerate in mass (same for “down) these change in flavor should then be possible, right? Or the problem is with the “strangeness” etc. quantum number? (I don’t recall it as a fundamental quantum number of weak interactions) $\endgroup$ Sep 25, 2022 at 4:01
  • $\begingroup$ And it should also be the same with top and bottom quarks as intermediate states (but a lot less probable), right? $\endgroup$ Sep 25, 2022 at 4:03
  • $\begingroup$ A virtual fluctuation can include states with larger rest masses than the “real” particle. For example, vacuum polarization arises in part because a photon “spends some of its time as” an electron-positron pair. The heavy flavor quantum numbers are only changed by the charged current, unless you count hand-wringing over flavor-changing neutral currents, so only the W can contribute to heavy-flavor virtual states. $\endgroup$
    – rob
    Sep 25, 2022 at 4:26
  • $\begingroup$ In natural word, we don't see single "free" quark, and $u$ quark is a component of proton and neutron. If their exist super high energy free $u$ quark, like in LHC, why $u\rightarrow W^+ +d \rightarrow c$ don't happen? In low energy natural world, quarks are confined within nucleon, from energy conservation we can't create on-shell $c$ quark. $\endgroup$
    – Daren
    Sep 25, 2022 at 4:32
  • $\begingroup$ @Daren The process illustrated in this question has two weak vertices, and must compete against much faster processes with one or zero weak vertices. Any uncharmed system heavy enough for $u\to c$ has flavor-preserving strong-interaction channels available, analogous to $\Delta^{++}\to p\pi$. The same goes for a system where $d\to Wc$ is energetically allowed. In accelerators, charmed particles come almost entirely from strong or electromagnetic interactions whose $\bar cc$ products get separated. $\endgroup$
    – rob
    Sep 25, 2022 at 12:32

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