Hi all. I have a question. What is the behaviour of the polarization vector of a pseudoscalar particle under a parity transformation??(adsbygoogle = window.adsbygoogle || []).push({});

Let me explain my problem. I know for sure that the effective matrix element which links a [itex]D^*[/itex] and a [itex]\pi[/itex] can be written as:

$$

\langle \pi(p)D^*(q,\lambda) | D^*(k,\eta)\rangle=\frac{g}{M_{D^*}}\epsilon_{\alpha\beta\gamma\delta} \lambda^\alpha \eta^\beta p^\gamma q^\delta,

$$

where $g$ is an effective coupling.

What I am trying to prove is that such a matrix element is (as it must be) a scalar. Now if, for example, we put ourselves in the rest frame of the [itex]\pi[/itex] we have just [itex](\vec{\lambda}\times\vec{\eta})\cdot \vec{q}[/itex]. Is that a scalar function?

Thank you very much

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# Pseudoscalar matrix elements

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