Comment on the Matrix Element of $O_{11}$

TL;DR

This paper critically examines the matrix element of the gluon dipole operator $O_{11}$, highlighting discrepancies with previous estimates and emphasizing the importance of accurate calculations in SUSY models.

Contribution

It provides a reassessment of the matrix element of $O_{11}$, comparing it with earlier estimates and clarifying its numerical accuracy.

Findings

The commonly used matrix element estimate is roughly numerically accurate.

Previous estimates may be coincidentally close due to dimensional analysis.

The paper emphasizes the need for precise calculations in SUSY-related operators.

Abstract

The gluon dipole operator, $O_{11}$, has received much attention recently because it can have a large coefficient in some SUSY extensions of the standard model. We find that the commonly used matrix element of $O_{11}$ of Bertolini, Eeg and Fabbrichesi is in rough (but accidental) numerical agreement with an estimate based on dimensional analysis.