Question

Quarks carry spin $\mathbf{1}\mathbf{/}\mathbf{2}$. Three quarks bind together to make a baryon (such as the proton or neutron); two quarks (or more precisely a quark and an antiquark) bind together to make a meson (such as the pion or the kaon). Assume the quarks are in the ground state (so the orbital angular momentum is zero).

(a) What spins are possible for baryons?

(b) What spins are possible for mesons?

Short answer

(a) Spin $\frac{1}{2}$or $\frac{3}{2}$

(b) Spin 1 or 0

Step-by-step solution

Definition of baryon and meson

The subatomic particles having large mass and are the combination of three quarks are known as baryons.

The existence quark and an antiquark in a subatomic particle are termed Meson

(a) Determination of possible spins for baryon

Combine two quarks,$\frac{1}{2}$and$\frac{1}{2}$.

Spin 1 (If they are parallel),

$\left(\frac{1}{2}+\frac{1}{2}\right)or\left(\frac{-1}{2}+\frac{-1}{2}\right)$

Zero (If they are antiparallel),

role="math" localid="1658124052031" $\left(\frac{1}{2}+\frac{-1}{2}\right)or\left(\frac{1}{2}+\frac{-1}{2}\right)$

Combine the result with the third quark for the case to get spin1, $\frac{1}{2}$ and1.

$\frac{3}{2}$(if they are parallel),

$\left(\frac{1}{2}+1\right)\mathrm{or}\left(\frac{-1}{2}-1\right)$

$\frac{1}{2}$(if they are antiparallel),

role="math" localid="1658123797200" $\left(\frac{-1}{2}+1\right)\mathrm{or}\left(\frac{1}{2}-1\right)$

For the case to get zero, only $\frac{1}{2}$ is there only.

Thus, the possible spins for baryons are $\frac{1}{2}$and $\frac{3}{2}$.

(b) Determination of possible spins for mesons

Combine two quarks, $\frac{1}{2}$ and $\frac{1}{2}$.

Spin 1 (if they are parallel),

$\left(\frac{1}{2}+\frac{1}{2}\right)or\left(\frac{-1}{2}+\frac{-1}{2}\right)$

Zero (if they are antiparallel),

$\left(\frac{1}{2}+\frac{-1}{2}\right)or\left(\frac{1}{2}+\frac{-1}{2}\right)$

Thus, the possible spins for mesons are 1 and 0.