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Consider a neutrino with a Dirac mass [tex] m_\nu [/tex] and the weak interaction

[tex]{\cal{L}}=\frac{g}{2 \sqrt{2}} \sum_l[{W_{\mu}^+ \cdot \bar{\psi}_{\nu_l} \gamma^{\mu}(1-\gamma_5)\psi_l + W_{\mu}^- \cdot \bar{\psi}_{l} \gamma^{\mu}(1-\gamma_5)\psi_{\nu_l} }\right{]} + \frac{g}{4 \cos(\theta_w)}

\sum_l Z_{\mu}[ \bar{\psi}_{\nu_l} \gamma^{\mu}(1-\gamma_5)\psi_{\nu_l} +\bar{\psi}_{l} \gamma^{\mu}(a+b\gamma_5)\psi_{l} ] [/tex]

Why this interaction doesn't change the helicity of the neutrino? It is true?

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# Weak interaction and helicity

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