Verification of the tenth-order QED contribution to the anomalous magnetic moment of the electron from diagrams without fermion loops
Tatsumi Aoyama, Hayakawa Masashi, Akira Hirayama, M. Nio
Abstract
A discrepancy of approximately <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mn>5</a:mn> <a:mi>σ</a:mi> </a:mrow> </a:math> exists between the two known results for the tenth-order QED contribution to the anomalous magnetic moment of the electron, calculated from Feynman vertex diagrams without fermion loops. To investigate this, we decomposed this contribution into 389 parts based on a self-energy diagram representation, enabling a diagram-by-diagram numerical comparison of the two calculations. No significant discrepancies were found for individual diagrams. However, the numerical differences of the 98 diagrams sharing a common structure were not randomly distributed. The accumulation of these differences resulted in the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mn>5</c:mn> <c:mi>σ</c:mi> </c:mrow> </c:math> discrepancy. A recalculation with increased statistics in the Monte Carlo integration was performed for these 98 diagrams. By replacing the old values with the new ones for these 98 integrals, we have obtained a revised result of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mn>6.800</e:mn> <e:mo>±</e:mo> <e:mn>0.128</e:mn> </e:math> , thereby resolving the discrepancy.