  We present the first chiral-continuum extrapolated up, down and strange quark
spin contribution to the proton spin using lattice QCD. For the connected
contributions, we use eleven ensembles of 2+1+1-flavor of Highly Improved
Staggered Quarks (HISQ) generated by the MILC Collaboration. They cover four
lattice spacings $a \approx \{0.15,0.12,0.09,0.06\}$ fm and three pion masses,
$M_\pi \approx \{315,220,135\}$ MeV, of which two are at the physical pion
mass. The disconnected strange calculations are done on seven of these
ensembles, covering the four lattice spacings but only one with the physical
pion mass. The disconnected light quark calculation was done on six ensembles
at two values of $M_\pi \approx \{315,220\}$ MeV. High-statistics estimates on
each ensemble for all three quantities allow us to quantify systematic
uncertainties and perform a simultaneous chiral-continuum extrapolation in the
lattice spacing and the light-quark mass. Our final results are $\Delta u
\equiv \langle 1 \rangle_{\Delta u^+} = 0.777(25)(30)$, $\Delta d \equiv
\langle 1 \rangle_{\Delta d^+} = -0.438(18)(30)$, and $\Delta s \equiv \langle
1 \rangle_{\Delta s^+} = -0.053(8)$, adding up to a total quark contribution to
proton spin of $\sum_{q=u,d,s} (\frac{1}{2} \Delta q) = 0.143(31)(36)$. The
second error is the systematic uncertainty associated with the chiral-continuum
extrapolation. These results are obtained without model assumptions and are in
good agreement with the recent COMPASS analysis $0.13 < \frac{1}{2} \Delta
\Sigma < 0.18$, and with the $\Delta q$ obtained from various global analyses
of polarized beam or target data.
