# How do you read the spin contributions of proton

This paper reads the number of their results. I'm attaching the how they have included all the spin contributions of quarks to proton.
The contributions are from u, d, s quarks.

How I can tell someone else that what is the approximate contribution? Would it be bad if I say its around $$\approx 12\%$$ ?

• A 1989 paper is not the place to go for this. There was lots of parity violating electron scattering, and other experimental and theoretical work, done since the 90's that added a lot to the proton spin crisis. – JEB Oct 14 at 17:26
• Thanks, I understand. But how would cite their (EMC) result of the quark spin contribution? Would you prefer to round these percentages ? – user193422 Oct 14 at 17:46

The other numbers are uncertainties. In general, when two uncertainties are reported separately like this, one is the "statistical" uncertainty and the other is the "systematic." The statistical uncertainty can be reduced by running your experiment for longer. The systematic uncertainty generally can't be improved without redesigning the experiment (but can sometimes be reduced after the fact, by understanding the apparatus better somehow). The abstract for your paper reports a statistical uncertainty first, so in your quote the $$\pm9\%$$ is statistical and the $$\pm14\%$$ is systematic.
As a commenter points out, a lot has changed in the proton-spin problem in the thirty years since the paper you're reading was published. But you can see why the puzzle was interesting: $$12\pm14$$ was consistent with zero of the proton's spin coming from its valence quarks.
• To drill down on this: "Would it be bad if I say its around $\approx 30\%$?" - yes, this would be bad. You can say that the paper's results are consistent with 30%, but they're also consistent with zero. (They're also consistent with negative values, which indicates that the statistics are likely non-gaussian, and both edges of the confidence interval need to be handled carefully, but that's beside the point.) You report either the central value or the confidence interval in full. Reporting the edge of the confidence interval as if it was the center is nothing short of dishonest. – Emilio Pisanty Oct 14 at 18:16