Next-to-Next-to-Leading Order Evolution of Polarized Parton Densities in the Larin Scheme

In many calculations involving polarized twist-2 parton densities to higher order in the strong coupling constant one uses the Larin scheme to describe chiral effects in dimensional regularization. Upon forming observables, the scheme dependence cancels. Still one needs a corresponding regularization scheme to compute the contributing building blocks, like massless and massive Wilson coefficients, as well as the massive 3-loop operator matrix elements used in the variable flavor number scheme. These are matched to the evolved parton distribution functions in the Larin scheme. Starting with suitable input distributions we provide the solution of scale evolution of the different polarized parton distribution functions in Bjorken $x$ space for a wide range of virtualities $Q^2$ in the Larin scheme, at next-to-leading, and to next-to-next-to-leading order for the first time. We also illustrate the deviation between the parton distributions in the Larin and $\overline{\rm MS}$ schemes numerically.