How many W mesons required for D+ decay?

[genloz]

Homework Statement

The decay
$$D^{+} \rightarrow D^{0} \pi^{+}$$
is not possible via a weak interaction which involves one virtual W+ meson. How many virtual W mesons are required?

Homework Equations

D0 has quark content c-ubar
Pi+ has quark content u-dbar
I'm not sure what D+ has...

The Attempt at a Solution

Assuming D+ has c-dbar...
how do you determine whether a virtual meson is involved or not and how many? Is it energy based?

 

[malawi_glenn]

Have you tried do a feynman diagram on parton level ?
If you don't know what the D+ meson has, try google it, perhaps here:

http://en.wikipedia.org/wiki/List_of_mesons

How does the W bosons work? Now here you can get lot of hints:
http://en.wikipedia.org/wiki/W_and_Z_bosons
http://hyperphysics.phy-astr.gsu.edu/hbase/particles/expar.html#c4

The W+ boson takes away 1positive charge from a quark

But the question is tricky, there is more eneryg after the decay than before.

 

[genloz]

thanks very much!
so D+ has c-dbar...
D+ = 1869MeV
D- = 1865MeV
pi+ = 139.6MeV

So that means both a W+ and a W- boson are required to keep the charge at +1 on both sides? And have energy greater than 139.6-5?

 

[malawi_glenn]

Even though you had more W bosons involved, i say that it violates energy.

 

[genloz]

okay, thanks... so a trick question? An even number of bosons would be required to conserve charge, but energy will never be conserved so it can't happen...

 

[malawi_glenn]

Hmm ONE W+ boson also conserve charge.

In each vertex, charge, lepton number etc are conserved.

imagine the following:
In the D+ , the W+ turns the d-bar quark to an u-bar quark, and latter decays into something.

The thing is that you have less mass on the RHS of the eq, W+ can decay into one pion + meson. so there is no problem besides energy.

I THINK that you have made a misstake, that it should be the $$D^x _S$$ Meson instead, then you have more mass (maybe correct mass for it to be allowed energetically). I might be wrong, but that is one desperate way =)