Which of these two decays is more likely using the CKM matrix?

[InsertName]

Homework Statement

I'm trying to get familiar with how to use the CKM matrix when tackling such questions as "which of these two decays is more likely".

My example question is:

Which is more likely c$$\bar{d}$$ ---> s$$\bar{d}$$ or c$$\bar{d}$$ ---> d$$\bar{d}$$

Homework Equations

The relationship between the weak eigenstates, the CKM matrix and the mass eigenstates:
($$\acute{d}$$) (V_ud V_us V_ub) (d)
($$\acute{s}$$) = (V_cd V_cs V_cb) (s)
($$\acute{t}$$) (V_td V_ts V_tb) (t)

The Attempt at a Solution

I don't actually know where to start because I'm not sure how to use the CKM matrix in this way.

Here's my best guess:

The difference between the two interactions is that one has c--->s and the other has c--->d and the value of the element V_cd < V_cs so the most likely is c--->s so the most likely decay is c$$\bar{d}$$ ---> s$$\bar{d}$$.

Any help with this is much appreciated.

 

[grey_earl]

Just add absolute values to your inequality (since the entries in the CKM matrix are generally complex), and you should be fine.

 

[InsertName]

Cool, thanks.