Vacuum expectations of the high dimensional operator and their contribution in Bjorken and Ellis-Jaffe sum rules

TL;DR

This paper introduces a method to estimate high-dimensional vacuum averages using a self-consistent factorization hypothesis, enabling improved calculations of their contributions to key sum rules in particle physics.

Contribution

It presents a novel estimation technique for high-dimensional vacuum averages, enhancing the accuracy of their contributions to sum rules.

Findings

Estimated vacuum averages of dimensions 7 and 10.

Quantified contributions to Bjorken and Ellis-Jaffe sum rules.

Provided a new approach for high-dimensional operator analysis.

Abstract

The method of estimation of the unknown high-dimensional vacuum averages is offered. This method is based on the idea of self-consistence of the factorization hypothesis. So it appears possible to evaluate all vacuum averages of dimension 7 and also get some estimations for vacuum averages of dimension 10. Obtained results are used to calculate high dimensional operator contribution to Bjorken and Ellis-Jaffe sum rules.