I am trying to find out whether the following baryons can exist:
$$ |X\rangle = \frac{|u u u\rangle + |d d d\rangle + |s s s\rangle}{\sqrt{3}} $$ $$ |Y\rangle = \frac{|u u u\rangle + |d d d\rangle - 2|s s s\rangle}{\sqrt{6}} $$
I haven't found in any baryon-list such a quark-configuration, but I don't know of any reason why it shouldn't exist either.
The question is motivated by the $\eta$-Mesons which have a quark representation in the following way: $$ |\eta'\rangle = \frac{|u \bar{u}\rangle + |d \bar{d}\rangle + |s \bar{s}\rangle}{\sqrt{3}} $$ $$ |\eta\rangle = \frac{|u \bar{u}\rangle + |d \bar{d}\rangle - 2|s \bar{s}\rangle}{\sqrt{6}} $$
However, of course each of their terms in the superposition has the same electric charge and strangeness content.
Edit: Frobenius pointed out that my $|X\rangle$ and $|Y\rangle$ are superpositions of states with different electric charge and strangeness. This is a very good point. However it is not completly clear to me why such a superposition should not exist, given that there are many examples of states that exist in superpositions of different properties/quantum numbers.
For example, in atom physics, electrons can exist in superposision of different angular momentum quantum numbers; in particle physics states can exist in superposition of different masses (for example $|\eta\rangle$), in quantum optics photons can be in superpositions of different energies (frequencies). What makes electric charge and strangeness special?
Edit2: Cosmas Zachos pointed out that there exist particles without a well-defined strangeness, namely Kaons (more precisely $K_0^S$ and $K_0^L$). Why shouln't baryons without well-defined charge exist?
Edit3: Cosmas Zachos explains that electric charge conservation is general, in contrast to strangeness conservation. That makes me wonder, does such a state exist:
$$ |Z\rangle = \frac{|d d d\rangle + |s s s\rangle + |b b b\rangle}{\sqrt{3}} $$ (where $d$ is down, $s$ is strange and $b$ is beaty-quark) Which has an electric charge of C=-1e.