Speaker
Description
We present the first lattice QCD calculation of the total gluon helicity contribution $\Delta G_H$ to the spin of $\Lambda$, $\Sigma$, and $\Xi$ hyperons.
The calculation employs the Coulomb-gauge fixed topological current $K^\mu$, whose forward matrix element in the infinite momentum frame yields $\Delta G_H$ without non-trivial perturbative matching.
Using a single $N_f=2+1$ flavor dynamical ensemble with lattice spacing $a\approx 0.105\ \mathrm{fm}$ and pion mass $m_\pi\approx 292\ \mathrm{MeV}$, we extract the bare matrix elements via the Feynman-Hellmann method, with distillation and momentum smearing to control excited-state contamination.
The bare matrix elements are non-perturbatively renormalized in the RI/MOM scheme and subsequently converted to the $\overline{\mathrm{MS}}$ scheme; the renormalization factor $\bar{Z}_{11}^{\mathrm{lat}}$ is employed, whose state-independence is guaranteed by the intrinsic nature of operator ultraviolet divergences.
After infinite-momentum extrapolation and renormalization, we obtain
$\Delta G_{\Lambda} = 0.165(19)_{\rm stat}(19)_{\rm ren}$,
$\Delta G_{\Xi} = 0.160(14)_{\rm stat}(19)_{\rm ren}$, and
$\Delta G_{\Sigma} = 0.232(24)_{\rm stat}(28)_{\rm ren}$
at the $\overline{\mathrm{MS}}$ scale $\mu^2 = 10\ \mathrm{GeV}^2$, corresponding to approximately
$37(5)_{\rm stat}(4)_{\rm ren}\%$,
$33(3)_{\rm stat}(4)_{\rm ren}\%$, and
$48(5)_{\rm stat}(6)_{\rm ren}\%$ of the hyperon total spin, respectively.
The temporal and spatial components of $K^\mu$ yield consistent results, confirming Lorentz covariance of the approach beyond the nucleon sector.
These first-principles results reveal the impact of flavor-symmetry breaking on gluon polarization across the baryon octet.
