Power corrections to heavy-quark spin correlations in small-$x$ deep-inelastic scattering

Abstract

Heavy-quark spin correlations in small-$x$ deep-inelastic scattering receive corrections beyond the back-to-back limit. For a rotationally symmetric target at leading power, the target dependence cancels from the normalized spin density matrix after full azimuthal averaging, for fixed kinematics and spin axes related by transverse light-front boosts. We calculate the first nonvanishing correction at tree level for finite quark mass and finite $N_c$ in a homogeneous Gaussian target. The expansion through fourth order in the dipole sizes includes logarithms, contact terms and all interference contributions at that order. Comparison with the improved transverse-momentum-dependent approximation separates kinematic corrections from terms with additional insertions of the target current. Numerical integration of the unexpanded Gaussian kernel tests the approximation at 28 parameter points. Spin correlations differ between the two targets in all 12 kinematic comparisons; in one comparison both spin states remain separable. At fixed photon virtuality, the leading large-$P$ behavior of the fourth-order correction to the normalized transverse spin state is generically proportional to $m\ln P/P^3$. We also compare two fixed Gaussian targets using unpolarized momentum distributions and joint spin measurements. For a purely transverse photon, three narrow momentum bins and an ideal measurement of both spins along the common quark-momentum axis defined by the light-front boost, spin information adds 3.5-3.7 percent to the expected log likelihood ratio after the overall normalization is fitted. This increase depends on the spin analyzing power and bin selection. The calculation establishes a model-dependent effect, rather than an experimental sensitivity prediction.