Question

There is no known meson with charge quantum number $\mathbf{q}\mathbf{=}\mathbf{+}\mathbf{1}$and strangeness $\mathbf{S}\mathbf{=}\mathbf{-}\mathbf{1}$or with $\mathbf{q}\mathbf{=}\mathbf{-}\mathbf{1}$and .$\mathbf{S}\mathbf{=}\mathbf{+}\mathbf{1}$Explain why in terms of the quark model.

Short answer

Mesons with strangeness $\mathbf{S}\mathbf{=}\mathbf{-}\mathbf{1}$ can have charge$\mathbf{q}\mathbf{=}\mathbf{-}\mathbf{1}\mathbf{,}\mathbf{0}$ and those strangeness role="math" localid="1663136410092" $\mathbf{S}\mathbf{=}\mathbf{+}\mathbf{1}$ can have charge$\mathbf{q}\mathbf{=}\mathbf{1}\mathbf{,}\mathbf{0}$

Step-by-step solution

Given data

No meson has charge $q=+1$and strangeness $S=-1$ or charge$q=-1$ and strangeness.$S=+1$

Quantum numbers of quarks

The up, charm and top quarks and charge$q=2/3$ and the down, strange and bottom quarks have charge $q=-1/3$. The anti quarks have negative charges with magnitude same as those of the respective quarks. Only the strange quark has strangeness$S=-1$ and the anti strange has strangeness.$S=1$ The rest of the quarks have zero strangeness.

Determining the reason why mesons don't have charge q=+1  and strangeness S=-1  or chargeq=-1   and strangeness  S=+1

A meson is made up of one quark and one anti-quark. For a meson to have strangeness,$S=-1$it must have a strange quark. The accompanying anti-quark can be anything except an anti-strange. If the anti-quark is an anti-up, anti-charm or anti-top, the net charge of the meson will be.$-\frac{2}{3}-\frac{1}{3}=-1$If the anti-quark is an anti-down or anti-bottom the net charge of the meson will be.$\frac{1}{3}-\frac{1}{3}=0$Thus, charge $q=+1$and strangeness $S=-1$ is not possible.

For a meson to have strangeness$S=1$, it must have an anti-strange quark. The accompanying quark can be anything except a strange quark. If the quark is a up quark, a charm or a top, the net charge of the meson will be$\frac{2}{3}+\frac{1}{3}=1$. If the quark is a down or a bottom the net charge of the meson will be$-\frac{1}{3}+\frac{1}{3}=0$. Thus, charge$q=-1$ and strangeness is $S=+1$not possible.