Higher-order NLO initial state QED radiative corrections to e+e− annihilation revisited

Radiative corrections due to initial state radiation in electron-positron annihilation are calculated within the QED structure function approach. Results are shown in the next-to-leading logarithmic approximation up to <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="script">O</a:mi><a:mo stretchy="false">(</a:mo><a:msup><a:mi>α</a:mi><a:mn>4</a:mn></a:msup><a:msup><a:mi>L</a:mi><a:mn>3</a:mn></a:msup><a:mo stretchy="false">)</a:mo></a:math> order, where <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>L</f:mi><f:mo>=</f:mo><f:mi>ln</f:mi><f:mo stretchy="false">(</f:mo><f:mi>s</f:mi><f:mo>/</f:mo><f:msubsup><f:mi>m</f:mi><f:mi>e</f:mi><f:mn>2</f:mn></f:msubsup><f:mo stretchy="false">)</f:mo></f:math> is the large logarithm. Several mistakes in previous calculations are corrected. The results are relevant for future high-precision experiments at <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msup><j:mi>e</j:mi><j:mo>+</j:mo></j:msup><j:msup><j:mi>e</j:mi><j:mo>−</j:mo></j:msup></j:math> colliders. Published by the American Physical Society 2024