Relations between Spin Structure Functions and Quark Mass Corrections to Bjorken Sum Rule

The power correction, surviving the zero quark mass limit and found earlier to restore the validity of Burkhardt-Cottingham sum rule, provides the contribution to the Bjorken sum rule as well. The leading perturbative correction to the Bjorken sum rule is increased by the factor 4/3 for light quarks and 5/3 for heavy quarks. The resulting value for the Bjorken sum rule for light quarks is in excellent agreement with the most precise SLAC data. The same correction should appear in the case of the Gross-Llewellyn Smith sum rule. It completely removes the observed deficit of this sum rule within the experimental errors.