The so-called ``spin puzzle" of hadrons, in general, is, simply, an expression of the assumption that the valence quarks interact weakly-which is true at high energies, isn’t true at low energies. How to do the detailed calculation, that is to be compared to experiment, is known, but it’s not easy, since the numerical calculations are very time-consuming. An example is discussed here: Preprint Status on Lattice Calculations of the Proton Spin Decomposition

In fact, since neutron scattering is used much more extensively than proton scattering, it's much easier to understand that the main properties of the neutron's spin are much better known than that of the proton. However in that energy range the structure of the neutron isn't that relevant. The fine details of the spin structure function are needed for establishing backgrounds for discovering new effects. But what's necessary is understanding at what energy range which approximation makes sense.

Dear Stam Nicolis and Preston Guynn

Thank you for your valuable input.

The first ever experiments back at 1970's before the EMC null result have actually shown a 60% contribution thus 0.3ℏ. But these experiments were done at low Q2 energies, meaning the spatial resolution of the collider was small thus a larger area of the proton was probed. However, as collision energies increased in subsequent experiments the contribution of the valance quarks triplet became smaller up to the EMC experiment almost null result of 1988.

But hold on, it is my understanding that by probing essentially with larger magnification, larger Q2 , you loose the big picture since you actually are probing a smaller area in the proton. Would that not mean that you measure only a fraction of the spin contributions? If you cover an area smaller than the triplet area would that not mean that your measurements are not accurate since you increase the chance a muon to totally miss a collision with a quark in the triplet?

Especially if the triplet spatial distribution is asymmetric and not symmetric as assumed? As Preston said it is assumed that the orientation is that of an equilateral triangle π/3. But what if it's not? Then larger magnification, smaller area probed, could be a problem and result to inaccurate measurement of the the spin contribution of the triplet. My research shows that this may be a problem:

Preprint A possible explanation for the proton spin puzzle using a no...

An indication for that the orientation is not symmetrical can be that the down quark has double the mass of the up quark. Just do a simple experiment tie three bowling balls together but the third ball should have double mass and join them with springs in an equilateral triangle orientation. Then spin the triangle with orbital angular momentum. I really doubt that the triplet will maintain its equilateral orientation.

Finally, I'm not so sure in such a high complexity combinatoric particle like the proton if high probing energies will not disturb the whole proton structure and result in measuring nonsense.

They say if the experiment does not verify the theory then the theory is wrong. But what if the experiment method or setup is wrong or the experiment is conceptually wrong? Nobody seems to talk about experimenters doing wrong experiments? Take for example the havoc created when an experiment result from OPERA collaborators in Italy was announced of neutrinos found travelling with speed larger than c ! https://en.wikipedia.org/wiki/Faster-than-light_neutrino_anomaly

For some reason I trust more the 60% measured contribution of the first SLAC experiment back at late 1970s.

There's no need to use analogies, because lattice QCD-as mentioned-can provide the complete and consistent framework.

It's not true that probing shorter distances in the proton implies missing contributions to its spin-it's possible to check that by checking the identities the quantities that are calculated and are measured should satisfy; if anything were ``missing'', the identities wouldn't be satisfied. Indeed, in QCD, it's the other way around, since the strength of the interaction decreases, as the distances become shorter. That's, indeed, how it's possible to understand that the contribution from the valence quarks may not be enough-and that by taking into account the sea quarks and the gluons everything is accounted for.

Regarding experiments, the consistency checks involve controlling the backgrounds.

The bottom line: What was learned, by the so-called ``spin puzzle'' (or ``crisis'') is how the contribution to the proton's spin depends on the energy scale, when the constituents of the proton can be resolved. These constituents aren't, only, the valence quarks, but the ``sea quarks'', as well as the gluons. When the strong interactions are weak-as occurs at high energies-the contribution of the sea quarks and of the valence quarks to processes involving the valence quarks is ``small''; at low energies, when the interactions are stronger, the contributions can't be neglected; once it's taken into account, agreement with experiment is re-established. This, then, provides the background for new experiments.

Something similar occurs with the neutron and any hadron.

Yes but still the dominant contribution to the total proton spin is when the strong interaction aka valance triplet is included measured at low collision energies, right?

So, the discrepancy then is the 60% contribution measured by SLAC of the tripled which probably was lower than predicted at that time. Also we must put into account the orbital angular momentum of the strong interaction contribution and then adding all these small-x contributions.

But are all these side contributions coherent with the proton spin? And in what degree they cancel each other out?

Somehow they cannot bring it to 100% contribution. That is I guess the final puzzle about the proton spin.

Thanks for the tip about lattice QCD. I will investigate if this numeric technique considers all the possible spatial orientations of the valance quarks distribution in the triplet formation.

The dominant contribution depends on the energy scale. The statement `` the valence contribution aka the strong interaction'' is, just, wrong. The statement that the valence contribution is dominant, whatever the energy scale, also.

Once more, there's no ``discrepancy'', because what was measured at SLAC was something else.

All the contributions are consistent with the proton's spin being 1/2, in units of Planck's constant. What is experimentally measured is the final result, the calculation can focus on individual contributions.

There's no puzzle-some people may have thought so and they may have written papers about it, but it suffices to take into account all the contributions and there's no problem of principle. The calculation has become feasible in lattice QCD only recently, that's all. And the reason for that is that there is a range of energies, between ``high'' energies, where the valence quarks' contribution dominates and the ``low'' energies, where the internal structure of the proton can't be resolved at all. It's in this, intermediate, range, where the quarks and gluons can be resolved, but they interact strongly, that the valence quark contribution doesn't dominate. But it's not expected to. The experiment measures a specific quantity and its dependence on the energy scale and only recently has it become possible to compute the same quantity and its dependence on the energy scale, in lattice QCD.

The answer about the valence quarks ad the orbital contribution is affirmative-however what really matters is the total.

From your last enlightening analysis I start wondering what is actually being measured here? The proton at rest or an excited proton by a beam? Is the proton being measured or the interaction of the measurement with the proton?

Here we go again in cycles the classical quantum measurement problem...

For now I go for the low Q2 measurements at least there are less intrusive and natural. Not all the time a proton gets hit by a 20Gev beam.

So there was actually a measurement of the neutron valance quarks contribution that is significantly closer to the predicted value for the nucleus (i.e. proton or neutron) by a SLAC experiment after the EMC proton 1988 reported almost null result (4%-24%). Namely a staggering 60% contribution of the valance quarks to the spin of the neutron with similar collision energies with EMC. However here in this SLAC experiment there were electrons used and not muons we had in the EMC experiment. Neveretheless, the difference of the two measurements for proton and neutron spin valance quarks contribution is about 2σ.

https://inspirehep.net/files/e9ce4a03e531451e76314f12d808a3b2 (see Abstract of linked thesis)

So I guess I was right about my intuition that the two different nucleons may differ in the quarks spin contribution. However, this is not widely known.

This indicates IMO that something is seriously wrong with the methods of measurement used in these experiments or that there is a fundamental difference between the two triplets besides there different quark types the experiments cannot resolve.

Here is the above mentioned E 142 SLAC experiment of 1992 with the analysis of the data finished at 1996 were also the paper was published in PRW:

Published paper: https://tinyurl.com/5n7u6yp7

Thanks Preston Guynn for your insightful comments.

I guess my feeling is that lattice QCD concentrates more on the small-x (i.e. high Q2 ) contributions anyway, which makes the measurement problem more dominant. I prefer the more gentle low Q2 approach.

About the electric dipole moment of the neutron. You have said: "The neutron electric dipole moment is expected to be zero." I am not so sure about that, if it has a magnetic moment then a small asymmetry is possible to exist in its composite cancelling out charge in the near field and possible co linear aligned to the magnetic moment axis.

There is a paper here that reports for the neutron an electric dipole moment of 30MeV/fm and opposite to the spin magnetic moment vector and the magnetic moment of the neutron point in the opposite direction of the spin angular momentum vector. As if the neutron had an negative charge!! (i.e. positive charge fermions have magnetic moment aligned in the same direction as spin angular momentum whereas negative charge fermions antiparallel). Which means that in the neutron the claimed electric dipole moment is parallel to the spin angular momentum vector and antiparallel to the magnetic moment vector, https://en.wikipedia.org/wiki/Neutron_magnetic_moment :

Article A Precision Measurement of the Neutron Twist-3 Matrix Elemen...

These are too complicated for me and do not cover my paycheck :)... see figure.

I myself would expect also a zero electric dipole moment since the neutron has zero charge. However maybe since it is a composite particle, zero electric charge does not mean that it has no charge at all but more likely a composite charge that cancels out in the far field.

Best Regards,

Emmanouil

Yep. These are too complicated for me anyway and do not cover my paycheck :)...

In my mind the explanation is, unfortunately for those who've studied QCD, that the composition of the proton is not quarks but as in my paper, Preprint The Structure of The Proton and the Calculation of Its G-fac...