关于$J^P=\frac{3}{2}^+$重子为何不存在$\Delta^{--}=|\bar u\bar u\bar u\rangle$的问询

Great question! Let's unpack this—this gets into some key rules of how quark-based particles (hadrons) behave, plus the practical challenges of detecting rare short-lived particles.

First, let's clear up a naming point: The particle you're describing (three anti-up quarks with $J^P = 3/2^+$) would technically be the anti-particle of the $\Delta^{++}$, since the $\Delta^{++}$ is $|uuu\rangle$ with charge +2. Its anti-particle would have charge -2, so calling it $\Delta^{--}$ makes sense as a shorthand.

Now, why do we not observe this particle? Let's break it down into theory and experiment:

1. Theoretical Allowance (It is allowed by the rules) #

First, let's address the Pauli Exclusion Principle, which is often the first thought here. For fermions (like quarks and anti-quarks), the total wavefunction must be antisymmetric.

• For the $\Delta^{++} = |uuu\rangle$: The three up quarks have identical flavor and spin (all aligned to make $J=3/2$), and the ground-state spatial wavefunction is symmetric (s-wave, $L=0$). To satisfy the exclusion principle, the color wavefunction must be fully antisymmetric (a color singlet: the antisymmetric combination of red, green, blue). This makes the total wavefunction antisymmetric, which is allowed.
• For $|\bar{u}\bar{u}\bar{u}\rangle$: Anti-quarks are also fermions. The same logic applies: identical flavor, symmetric spin, symmetric spatial wavefunction—so we need an antisymmetric color wavefunction (this time, the antisymmetric combination of anti-red, anti-green, anti-blue, a color anti-singlet). This also gives a fully antisymmetric total wavefunction, so the state is theoretically allowed.

2. Practical Experimental Challenges (Why we don't see it) #

The real issue isn't that the particle can't exist—it's that detecting it is extremely hard:

• Low production probability: To make three anti-up quarks come together to form this anti-baryon, you need high-energy collisions (like proton-antiproton collisions in accelerators) that produce large numbers of anti-quarks. The chance that three anti-up quarks will simultaneously form a bound state is tiny compared to producing more common particles.
• Extremely short lifetime: Like all $\Delta$-baryons, this anti-particle would have a lifetime of around $10^{-23}$ seconds—far too short to travel any measurable distance. It would decay almost instantly into an anti-proton ($|\bar{u}\bar{u}\bar{d}\rangle$) and a $\pi^-$ meson ($|\bar{u}d\rangle$), for example.
• Background noise: Detecting the decay products to infer the original anti-baryon is tricky. The collision environments where these particles are produced have huge numbers of other particles, making it hard to pick out the specific signature of this rare decay.

3. Context of our universe #

In ordinary matter, baryon number is conserved (we don't have naturally occurring anti-baryons), so this particle can't exist in the world around us. We can only create it temporarily in lab settings, and even then, it's fleeting and hard to spot.

内容的提问来源于stack exchange，提问作者Buh