The N3LO scheme-invariant QCD evolution of the non-singlet structure functions <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msubsup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi mathvariant="normal">NS</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"><mml:msubsup><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi mathvariant="normal">NS</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math>
J. Blümlein, M. Saragnese
Abstract
We present the scheme-invariant unpolarized and polarized flavor non–singlet evolution equation to N3LO for the structure functions F2(x,Q2) and g1(x,Q2) including the charm- and bottom quark effects in the asymptotic representation. The corresponding evolution is based on the experimental measurement of the non–singlet structure functions at a starting scale Q02. In this way the evolution does only depend on the strong coupling constant αs(MZ) or the QCD scale ΛQCD and the charm and bottom quark masses mc and mb and provides one of the cleanest ways to measure the strong coupling constant in future high luminosity deep–inelastic scattering experiments. The yet unknown parts of the 4–loop anomalous dimensions introduce only a marginal error in this analysis.