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I'm currently checking some reactions if they are allowed. One of them is $$\nu_\mu p\to\mu^-\Delta^{++}$$

Since this is a weak interaction I've checked the Baryon and Lepton number, Spin and the charge. It seems that the reaction is allowed. Is that really possible?

Some of my colleagues argued that the lepton number is not conserved. But I can not agree with them. Did I make a mistake?

LHS: Lepton number: +1 RHS: Lepton number: +1

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Look at this link with inclusive crossection plots. The reaction is the first on the left part of the figure 48.3

neutrinoinclusive

The delta ++ will be in the bunch around 1 (~1.2 GeV) , note the logarithmic scale. As you can see the errors are too large to be able to say something from this plot, but certainly the channel is there.

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