Form factors with two operator insertions and the principle of maximal transcendentality

Taushif Ahmed,Pulak Banerjee,Prasanna K. Dhani,V. Ravindran,Amlan Chakraborty

doi:10.1103/physrevd.102.061701

Abstract

We present the first calculations of two-point two-loop form factors (FFs) with a two identical operators insertion in maximally supersymmetric Yang-Mills theory. In this article, we consider the supersymmetry protected half-BPS primary and unprotected Konishi operators. Unlike the FFs of a single operator insertion of the half-BPS primary, the FFs involving two half-BPS operators are found to contain lower transcendentality weight terms in addition to the highest ones. Moreover, in contrast to Sudakov FFs, the highest weight terms of the FFs of a double half-BPS no longer match with that of a double Konishi. We also find that the principle of maximal transcendentality, which dictates the presence of identical highest weight terms in the scalar FFs of half-BPS and quark/gluon FFs in QCD, does not hold true anymore for insertions of two identical operators. We discover the absence of any additional ultraviolet counterterm that could arise from the contact interaction between two composite operators.

Highlights

A generic quantum field theory is entirely specified by the knowledge of on shell scattering amplitudes and off shell correlation functions
We find that the principle of maximal transcendentality, which dictates the presence of identical highest weight terms in the scalar form factors (FFs) of half-BPS and quark/gluon FFs in QCD, does not hold true anymore for insertions of two identical operators
We present the form factors with the insertions of two identical local gauge invariant operators to two loops in N 1⁄4 4 sYM theory by performing a state-ofthe-art computation

Summary

INTRODUCTION

A generic quantum field theory is entirely specified by the knowledge of on shell scattering amplitudes and off shell correlation functions. The two-point or Sudakov FFs of primary half-BPS operator belonging to the stress-energy supermultiplet is observed [1,3,11] to exhibit the UT property to three loops; they are composed of only highest transcendental (HT) terms with weight 2L at loop order L This is a consequence of the existence of an integral representation of the FFs with every Feynman integral as UT [11]. [22] that the HT weight parts of every two-point minimal FFs (the presence of an equal number of fields in the operator and external on shell state) are identical, and those are equal to that of a half-BPS, OBrtPS This conjecture is verified to four-loops order in Ref. We find that the PMT does not hold true

COMPUTATION OF TWO-LOOP FORM FACTOR

PRINCIPLE OF UNIFORM TRANSCENDENTALITY

PRINCIPLE OF MAXIMAL TRANSCENDENTALITY

REGGE AND COLLINEAR LIMIT

CONCLUSIONS