# Is kaon decay to muons possible?

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

• How will quarks decay purely into leptons in the Standard Model? – SRS Jan 2 '20 at 5:58
• @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. – Dirac93 Jan 2 '20 at 7:23
• 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. – John Rennie Jan 2 '20 at 12:44
• 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. – John Rennie Jan 2 '20 at 12:46
• 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 $10^{-9}$. – rob Jan 3 '20 at 15:13

## 1 Answer

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