Particle Physics: Question 9

Worked solution

Part (a): Checking the total charge

Particle Y contains two up quarks and one strange quark. Summing their charges: $Q = \left(+\frac23e\right) + \left(+\frac23e\right) + \left(-\frac13e\right)$

Adding the two up quark charges: $\frac23e + \frac23e = \frac43e$

Subtracting the strange quark’s contribution: $\frac43e - \frac13e = \frac33e = +1e$

This matches the measured total charge of $+1e$, so the $uus$ composition is consistent with the measurement.

Part (b): Why Particle Y is a baryon

Particle Y is composed of three quarks ($uus$). A particle built from exactly three quarks is classified as a baryon. (A meson, by contrast, is built from a quark-antiquark pair. Only two constituents.)

Part (c): Why Particle Y is not a proton

The proton is also a baryon with total charge $+1e$, composed of two up quarks and one down quark ($uud$). At first glance, Particle Y ($uus$) looks similar: “two up quarks and one other quark,” with the same total charge.

However, the third quark is different: Particle Y’s third quark is a strange quark, while the proton’s third quark is a down quark. A strange quark and a down quark happen to carry the same charge ($-\frac13e$ each), which is why the total charges of the two baryons come out equal. But charge is only one property of a quark. flavour (up, down, strange, and so on) is a separate identity, and quarks of different flavour are different particles with different masses. Because Particle Y contains a strange quark where the proton contains a down quark, Particle Y ($uus$) is a genuinely different baryon from the proton ($uud$), even though the two happen to share the same total charge.

Final answers

• (a) $Q = \frac23e+\frac23e-\frac13e = \boxed{+1e}$, consistent with the measured charge.
• (b) A baryon, because it contains exactly three quarks.
• (c) Not a proton. Its third quark is strange, not down; matching total charge does not mean matching quark flavour, so $uus$ and $uud$ are different particles.