Main Cause of Proton Spin: What Accounts For It?

[say_physics04]

Hello guys, can you help me on this question:
What accounts most for the spin of protons? I think the quarks only contribute a few percentage for the spin, but I'm wondering if there are new discoveries about the main cause of proton spin

thx!

 

[Meir Achuz]

That is a subject of some controversy.
A combination of quark spin, quark orbital angular momentum,
a quark-antiquark sea (or mesons), relativistic effects, gluon spin and orbital angular momentum, add up to 1/2.
But what proportion of each is the question with no clear answer as yet.
Also the contributions of each effect are different in the proton at rest and in a proton at infinite momentum where QCD sum rules are used.

 

[malawi_glenn]

That is a subject of some controversy.
A combination of quark spin, quark orbital angular momentum,
a quark-antiquark sea (or mesons), relativistic effects, gluon spin and orbital angular momentum, add up to 1/2.
But what proportion of each is the question with no clear answer as yet.
Also the contributions of each effect are different in the proton at rest and in a proton at infinite momentum where QCD sum rules are used.

According to my course book, the sea quarks and gluons quantum numbers add up to zero.

 

[humanino]

A combination of quark spin, quark orbital angular momentum, a quark-antiquark sea (or mesons), relativistic effects, gluon spin and orbital angular momentum, add up to 1/2.

To the best of my knowledge, there is no gauge independent separation between spin and angular momentum contribution for the gluons.

Also the contributions of each effect are different in the proton at rest and in a proton at infinite momentum where QCD sum rules are used.

They do not depend on the referential, rather on the scale of observation. They undergo evolution under renormalisation equations.

 

[humanino]

According to my course book, the sea quarks and gluons quantum numbers add up to zero.

This is an old book, or the discussion has been simplified.

 

[malawi_glenn]

This is an old book, or the discussion has been simplified.

It is from november 2006.. maybe it is simplified.

Particles and nuclei - by pohv; Springer.

States that quantum # of the sea quarks and gluon-"glue" adds up to zero so the quantum # of the nucleon is described by its valance quarks.

 

[humanino]

Particles and nuclei - by pohv; Springer.

Yes, I have this book, it is a good one. I do not think they say that sea-quarks and gluons do not contribute to the angular momentum.

States that quantum # of the sea quarks and gluon-"glue" adds up to zero so the quantum # of the nucleon is described by its valance quarks.

Watch out. The quantum numbers add up correctly indeed. You take the quantum numbers of any partonic state in a Fock decomposition, all of them are the same of course. But in the end, you want the real wave function to compute relevant quantities.

For definiteness, say a u-quark with spin up is denoted by |u(^)> and with spin down by |u(v)>. The proton state can be decomposed as follows.
Call
|VAL> = a1*|u(^)u(^)d(v)> + a2*|u(v)u(^)d(^)> + a3*|u(^)u(v)d(^)>
and (I will note antiquarks with an upper-case... sorry)
|SEA> = b1*|u(^)U(v)> + b2*|d(^)D(v)> + b3*|g(^)G(v)> + ... + b4*|u(^)U(^)g(v)> + ... + b5*|s(^)S(v)> + ...
Then
|p(^)> = |VAL> * ( 1 + |SEA> )

So my point is the following : everything written in |SEA> has the quantum numbers of the vaccuum, indeed it is all fluctuations. But the all wavefunction is not just the valence. And it is very important for some properties, in particular the spin.

edit
let me be even more specific. A nucleon has a valence core and a meson cloud. The $$q\bar{q}$$ configuration typically occur in mesons. They can and do carry angular momentum, which participates in the total sum (the spin)

 

[malawi_glenn]

okay, maybe i misunderstodd. I can show you what page tomorrow, that i meant.

 

[say_physics04]

edit
let me be even more specific. A nucleon has a valence core and a meson cloud. The $$q\bar{q}$$ configuration typically occur in mesons. They can and do carry angular momentum, which participates in the total sum (the spin)

So, is this the main cause of the spin? Or is it really impossible to know what contributes "more" to the spin?

thx!

 

[humanino]

So, is this the main cause of the spin? Or is it really impossible to know what contributes "more" to the spin?

In a partonic language, you can separate the quark and gluon contributions to the nucleon spin. The quark one can straightforwardly be further decomposed into spin and orbital angular momentum contributions. For the gluons, this further decomposition is slightly more tricky. You can define in a gauge invariant manner the total contribution and the spin contribution, so that the orbital angular momentum contribution for the gluon is defined (as of today at least, and as far as I know) as the difference between the total and the spin.

So, all those are defined as operators really, acting on the nucleon states decomposed in a partonic basis. Say you want to know the contribution from the meson cloud. You then have to first project your states on the relevant subspace, namely that would be the quarks located in position space far from the center (valence core), and possibly also in momentum space at low longitudinal momentum fraction (low x_Bjorken). Then once you have projected your states, you can evaluate the expectation value (or the spectrum) of your operators.

To be honnest, I have looked back at the litterature, and failed to find a reference where such a detailed study would be carried on. Usually theoretical calculations focus on integrated quantities, which are more easily accessed experimentally and have not yet been measured with enough accuracy, before starting more complicated predictions which cannot be checked anyway.