Why is the decay of Ds*+(2110) → Ds+(1969)π0 forbidden?

[sunrah]

Homework Statement

Why is D^*+(2010) → D⁺(1869)π⁰ allowed via the strong interaction but D_s^*+(2110) → D_s⁺(1969)π⁰ forbidden.

The numbers in the brackets are masses in MeV.

Homework Equations

The Attempt at a Solution

My guess was that mass was not conserved, but if π⁰ is 135 MeV then it is. Strangeness is also conserved. Charge is also conserved. Isospin is also conserved. What else is there to consider?

 

[sunrah]

ok so I see that for the allowed process we have:

$|c\bar{d}\rangle \longrightarrow |c\bar{d}\rangle|d\bar{d}\rangle$
for example and for the forbidden process we have:

$\\ |c\bar{s}\rangle \longrightarrow |c\bar{s}\rangle|d\bar{d}\rangle$

my question is does the first process conserve quarks? if so how? I think that the strong interaction can create a quark-antiquark pair from either an up or down quark. But the antidown on the left could create a π⁺ particle but where does the other down quark come from to make the D⁺ meson? thanks

 

[sunrah]

here is a stab at answering my own question.
in the first allowed process, the D^*+ particle decays producing a $d\bar{d}$

pair via a gluon and then the $\bar{d}$ joins with the charm quark forming D^*+ and the $d$-quark with

the $\bar{d}$-quark from the left hand side forming the pion. is that right?

but i still don't know why the second process is not allowed. i think it is allowed under the weak force but why and why not under the strong

thanks