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$$K^0 \rightarrow \mu^+ + \mu^-$$ Just like a neutral kaon decays into a pair of pions, can it also decay into a pair of muons? If not, why?

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  • $\begingroup$ How will quarks decay purely into leptons in the Standard Model? $\endgroup$
    – SRS
    Jan 2, 2020 at 5:58
  • $\begingroup$ @SRS But baryon number is conserved since neutral kaon has baryon number zero. But I do get the logic that quarks cannot decay purely into leptons. I am confused, hence the question. $\endgroup$
    – Dirac93
    Jan 2, 2020 at 7:23
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    $\begingroup$ Kaons can decay to leptons. The $K^+$ can decay to $\mu^+ + \nu_\mu$. So the answer to this question seems far from obvious to me. The downvotes seem unwarranted. $\endgroup$ Jan 2, 2020 at 12:44
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    $\begingroup$ This paper suggests the decay to a muon pair is possible. I won't post this as an answer since it's outside my area of expertise. $\endgroup$ Jan 2, 2020 at 12:46
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    $\begingroup$ Note: the Particle Data Group lists nonzero branching ratios for $K^0_L\to \mu\mu\gamma$ and $K^0_L\to\mu\mu\gamma\gamma$, and lists $K^0_S\to\mu\mu$ as a $CP$-violating, strangeness-changing decay mode with a branching ratio below $10^{-9}$. $\endgroup$
    – rob
    Jan 3, 2020 at 15:13

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Yes, this decay is possible, and measured to occur, via diagrams similar to:

enter image description here

involving two W bosons. Note that since it involves one more W boson than the $\rm K^0$ to pion decays, the decay is suppressed pretty strongly.

There are some subtleties involved here regarding CP violation, depending on whether the original particle is a $\rm K^0_L$ or $\rm K^0_S$. But overall this decay can happen.

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This is entirely possible but GIM suppressed. Before the advent of the charm quark, particle physicists were confused as to why this didn't occur more often and theorised the charm quark, which would exactly account for this suppression. The GIM suppression would be perfect if it wasn't for the difference in mass between the up and charm quarks, which makes this process possible, but still highly unlikely.

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Diagram showing two different processes by which this decay can occur. Once the charm was theorised, the $V_{CKM}$ elements (or equivalently Cabibbo elements) can be shown to cancel if these two Feynman diagrams are summed.

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