4
$\begingroup$

Virtual $W^-$ boson may decay into $\bar{u}$ and $d$ quarks, $\bar{c}$ and $s$ quarks, $e$ and $\bar{\nu}_e$, $\mu$ and $\bar{\nu}_{\mu}$, $\tau$ and $\bar{\nu}_{\tau}$. Decay into $\bar{u}$ and $s$, $\bar{u}$ and $b$, $\bar{c}$ and $d$, $\bar{c}$ and $b$ are CKM suppressed. Also, as these hadrons ($\Lambda$, $\Xi$, $\Omega$ baryon, $K^{-}$) consist of $u$, $d$ &/or $s$ quarks, so decay of virtual $W^{-}$ boson (emitted by any of these quarks in these hadrons) into $\bar{c}$ and $s$ is kinematically forbidden but what makes the decay of this virtual $W$ boson into $\bar{u}$ and $d$ more probable than decay into $e^-$ and $\bar{\nu}_e$.

$\endgroup$

1 Answer 1

-1
$\begingroup$

I think that you are looking for the helicity suppression, this is simpler to understand for the decay of a $\pi$.

In leptonic decays you can separate the hadronic part and the leptonic one. You will get for the matrix element something like that: $ M \propto f_{\pi}p_{\mu}^{\pi}\bar{u}_{\nu_l}\gamma^{\mu}(1-\gamma_5)v_l \\ f_{\pi}\bar{u}_{\nu_l}\require{cancel}({\cancel{p}}_{\nu_l}+{\cancel{p}}_{l})(1-\gamma_5)v_l \\ \bar{u}_{\nu_l}\require{cancel}{\cancel{p}}_{\nu_l} = 0 ~ (\text{massless}) \\ {\cancel{p}}_{l}v_l = m_l v_l ~ (\text{lepton mass} ) \\ m_lf_{\pi}\bar{u}_{\nu_l}(1+\gamma_5)v_l $

The mass term produces the helicity suppression.

You can see that also thinking about the back to back decay, you have a left current, so the spins of the product would be directed in the same directions, but it's impossible because you have a pseudoscalar particle to start, so you have to do a spin flip but it costs the lepton mass term.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.