Extending the light cone sum rule method to the electromagnetic pion form factor at low momenta using QCD renormalization-group summation

We obtain the electromagnetic pion form factor (emFF) <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>F</a:mi> <a:mi>π</a:mi> </a:msub> </a:math> for spacelike midrange of momentum transfer in quantum chromodynamics (QCD). We use renormalization group (RG) summation within the light cone sum rules (LCSRs) to obtain the QCD radiative corrections to the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>F</c:mi> <c:mi>π</c:mi> </c:msub> </c:math> and involve contributions of the leading twist 2 and, twists 4, 6. The additional conditions to apply here this RG summation are discussed in details. The strong coupling constants in this approach are free of Landau singularities, which allows one to go down to the lower transferred momentum <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msup> <e:mi>Q</e:mi> <e:mn>2</e:mn> </e:msup> </e:math> . The prediction of the calculations performed reproduces the experimental data below/around <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msup> <g:mi>Q</g:mi> <g:mn>2</g:mn> </g:msup> <g:mo>=</g:mo> <g:mn>1</g:mn> <g:mtext> </g:mtext> <g:mtext> </g:mtext> <g:msup> <g:mrow> <g:mi>GeV</g:mi> </g:mrow> <g:mrow> <g:mn>2</g:mn> </g:mrow> </g:msup> </g:math> significantly better than analogous predictions based on a fixed-order power-series expansion in the standard QCD.