# What is Dalitz decay?

What is Dalitz decay?

I know there are Dalitz $\pi^0 \to e^+ + e^- + \gamma$ decay, $w \to \pi^0 + e^+ + e^-$ decay, may be more. But is there a rule to say which decay is Dalitz and which is not?

Is there a rule to say which particle can decay by Dalitz decay and which does not?

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I've found more examples: $\eta \to e^+ + e^- + \gamma$ decay, $\pi^0 \to e^+ + e^-+ e^+ + e^-$, $K_L^0 \to \mu^+ + \mu^- + \gamma$ and it seems to me that the any 3 and 4 particle decays are called Dalitz decay, since Dalitz plot can be applied to analyze them. –  klm123 Aug 12 '12 at 23:39
that first decay is not allowed by four-momenta conservation, you cannot decay one light-like particle unless its an intermediate stage of a larger decay, it needs to be either zero or two. –  user56771 Aug 12 '12 at 23:49
which first? $\eta$? –  klm123 Aug 12 '12 at 23:52
Presumably @user56771 means that there is no tree-level diagram for it. These decays certainly happen. The PDG gives the $\pi^0$ example a branching ratio of about 1% of all neutral pion decays. –  dmckee Aug 13 '12 at 1:39

After a really brief cursory review of the literature, I think that a Dalitz decay is a meson decay that involves two leptons in the final state, plus a photon. A double Dalitz decay has four leptons in the final state: see this paper and this paper for examples of the usage. The Dalitz decay is when a virtual photon from 2 photon decay of $\pi_0$ internally converts to a real lepton pair before it gets too far, and analogous thing for other meson or Higgs processes (two electrons from an internal photon conversion, plus a neutral object).

I guess that the usage comes from the kinematic decay product phase space is described by a Dalitz plot, hence the name. I don't think it's anything deep.

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Sorry for my pedantry, but could you give me a reference on the definition in a reliable book? What you told was exactly my previous assumption, but I have to be sure. –  klm123 Aug 13 '12 at 3:15
@kim123: I wasn't sure about the previous answer, I just thought of the first thing that came to mind honestly, and I couldn't think of anything else. But I googled for usage, and it always is the decay of a meson into two leptons and something else. A double-Dalitz decay is into four leptons, so that establishes that the usage is for 2 lepton final states. The term Dalitz decay itself is never used without a meson as far as I saw in the search, so I changed my answer. Thanks for keeping me honest, my original answer was probably totally wrong. –  Ron Maimon Aug 13 '12 at 4:12