- #1
GWSguy
- 3
- 0
I'm studying the \tau \rightarrow \rho \; \nu_{\tau} decay. I'm asked to calculate the decay width, using a parameterization of the matrix element of the hadronic current. I actually find a matrix element of the form:
\left<\rho |\; \bar{u} \gamma^{\mu} \left( 1-\gamma^{5} \right ) d \; | 0\right>
in which I have both the vector and the axial current (u and d are up and down quarks). The \rho meson is a spin 1 vector meson, so I expect that only the term from the vector current survives. I've infact verified this statement in many articles which report:
\left<\rho |\; \bar{u} \gamma^{\mu} d \; | 0\right> = f_{\rho} m_{\rho} \epsilon ^{\mu}
with \epsilon ^{\mu} the polarization vector of the meson.
The problem is that I'm not able to demonstrate it. How can I formally demonstrate it? Is there any parity argument which allows me to exclude the axial term?
\left<\rho |\; \bar{u} \gamma^{\mu} \left( 1-\gamma^{5} \right ) d \; | 0\right>
in which I have both the vector and the axial current (u and d are up and down quarks). The \rho meson is a spin 1 vector meson, so I expect that only the term from the vector current survives. I've infact verified this statement in many articles which report:
\left<\rho |\; \bar{u} \gamma^{\mu} d \; | 0\right> = f_{\rho} m_{\rho} \epsilon ^{\mu}
with \epsilon ^{\mu} the polarization vector of the meson.
The problem is that I'm not able to demonstrate it. How can I formally demonstrate it? Is there any parity argument which allows me to exclude the axial term?
