Study of the Running Coupling Constant αs(q2) of π– Mesons and Protons from p + p and p + C Interactions at 4.2 GeV/c

This paper is dedicated to the study of the running coupling constant $${{\\alpha }_{s}}({{q}^{2}})$$ of $${{\\pi }^{ - }}$$ meson and protons from $$p + p$$ and $$p + C$$ interactions at 4.2 GeV/c. It is a well known fact that the more correct value of the cut parameter $${{\\Lambda }_{{{\\text{QCD}}}}}$$ in the formula of $${{\\alpha }_{s}}({{q}^{2}})$$ plays a very important role in obtaining the right values of this strong coupling constant $${{\\alpha }_{s}}({{q}^{2}})$$ . In calculations, the value of $${{\\Lambda }_{{{\\text{QCD}}}}}$$ obtained previously by the authors [1], was used: $${{\\Lambda }_{{{\\text{QCD}}}}} = (c\\hbar ){\\kern 1pt} \\,{\\text{GeV}} = 0.197{\\kern 1pt} \\,{\\text{GeV}}.$$ The values of $${{\\alpha }_{s}}({{q}^{2}})$$ obtained with this cut parameter are compared to the QCD predictions.