Just a quick question about notation really here. In neutrino oscillation we can calculate a probability of an oscillation occurring between two flavour eigenstates - invariably denoted [itex] P(\nu_{\alpha} \rightarrow \nu_{\beta}) [/itex]. I've got some confusion about what happens to this when we apply operators for P, CP and CPT.(adsbygoogle = window.adsbygoogle || []).push({});

Charge conjugation turns particles to anti-particles, so I'm thinking this transformation would be denoted [itex] P(\nu_{\alpha} \rightarrow \nu_{\beta}) \rightarrow P(\overline{\nu_{\alpha}} \rightarrow \overline{\nu_{\beta}}) [/itex]

Time reversal would presumably be [itex] P(\nu_{\alpha} \rightarrow \nu_{\beta}) \rightarrow P(\nu_{\beta} \rightarrow \nu_{\alpha}) [/itex]

The combination of C and T operations would therefore be [itex] P(\nu_{\alpha} \rightarrow \nu_{\beta}) \rightarrow P(\overline{\nu_{\beta}} \rightarrow \overline{\nu_{\alpha}}) [/itex]

My question is how would the parity transformation be incorporated here?

ie. how would one write [itex] \hat{P} P(\nu_{\alpha} \rightarrow \nu_{\beta}), \hat{C}\hat{P} P(\nu_{\alpha} \rightarrow \nu_{\beta}) [/itex] and [itex] \hat{C}\hat{P}\hat{T} P(\nu_{\alpha} \rightarrow \nu_{\beta}) [/itex] ?

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# P, CP and CPT symmetry in neutrino oscillation? (quick question)

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