- #1
Einj
- 470
- 59
Hi all. I have a question. What is the behaviour of the polarization vector of a pseudoscalar particle under a parity transformation??
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
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