All quarks have spin (1)/(2). Explain why baryons have spin (1)/(2) or 3 / 2 but mesons all have

All quarks have spin (1)/(2). Explain why baryons have spin...

Key Concepts

Intrinsic Spin

Intrinsic spin is a fundamental quantum property of particles that characterizes their intrinsic angular momentum. For quarks, this spin is 1/2, meaning each quark carries a quantum angular momentum of 1/2, which plays a crucial role in determining the total spin of any composite particle they form.

Angular Momentum Addition

Angular momentum addition is the quantum mechanical rule that describes how the spins of individual particles combine to yield the total spin of a composite system. When adding spins of particles with spin 1/2, the possible results depend on the number of particles involved and their relative orientations. The addition rules explain why combinations of three spin 1/2 particles (typical of baryons) yield total spins of either 1/2 or 3/2, while a quark and an antiquark (as in mesons) can combine to form spin 0 (or even spin 1 in excited states).

Composite Particle Structure

The structure of composite particles like baryons and mesons is central to understanding their spin. Baryons are made up of three quarks, and due to the combination of three spin 1/2 particles, only half-integer total spins (1/2 or 3/2) are permitted by quantum statistics. In contrast, mesons consist of a quark-antiquark pair whose spins typically align in opposite directions in the ground state, resulting in a total spin of 0. This structural difference underpins the distinct spin values of these particles.

Fermions versus Bosons

The classification of particles into fermions and bosons is deeply connected to their total spin. Quarks, as fermions with spin 1/2, combine in ways that retain their half-integer or integer characteristics when forming composite particles. Baryons, being composed of an odd number of quarks, are fermionic and hence must have half-integer spins (like 1/2 or 3/2). On the other hand, mesons, as quark-antiquark pairs, are bosonic and typically exhibit integer spins (with the ground state usually having spin 0), consistent with the requirements of quantum statistics.

Transcript

00:01 Hello, and in this question here, we want to explain the potential spins for mesons and barons.

00:07 Okay, so mesons are composed of two quarks and barons are composed of three quarks, okay? and a quark has a spin of one half, okay? so let's just raise that for now, actually.

00:21 So it's a spin of one half.

00:25 Now when we say one half, we are being lazy in the sense we're saying it's one half.

00:30 Times the unit of angular momentum, which is h bar.

00:34 So it's one half times h bar is the actual spin.

00:38 But if you just see one half or one or whatever, you know that this is in units of h bar.

00:43 So the actual spin is h bar over two.

00:47 So if we have two quarks, let's look at mesons first.

00:51 If we have two quarks, okay, and we're going to look at the spin in the z direction.

00:57 So the spin can either be in the z direction.

01:00 So the spin subscript z.

01:01 Can either be in the along the z direction or against the z direction okay and we're just using the z direction arbitrarily we could use the x y or any other axes we want to define but in any case the spin can either be along it or anti -alonged or anti -aligned so the spin can be plus hbara 2 or minus h bar 2 okay so in the mezon okay we could have the spins along the z direction well, what situations could we have? we could have the case where the spins are pointing in the same direction, or we could have the case where the spins are pointing in opposite directions.

01:40 Okay? that's the only two situations we could have.

01:43 If they're pointing in the opposite direction, this means the total spin is h bar over 2, minus h bar over 2, which is equal to 0...

Please give Ace some feedback