Deciphering the maximal transcendentality principle via bootstrap

• Published in: The journal of high energy physics 2022-10, Vol.2022 (9), p.161-71, Article 161
• Main Authors: Guo, Yuanhong, Jin, Qing jun, Wang, Lei, Yang, Gang
• Format: Article
• Language: English
• Subjects: Classical and Quantum Gravitation; Elementary Particles; Fermions; Form factors; Gauge theory; Gluons; Higgs Production; High energy physics; Integrals; Physics; Physics and Astronomy; Principles; Quantum chromodynamics; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quarks; Regular Article - Theoretical Physics; Relativity Theory; Scattering Amplitudes; Statistical methods; String Theory; Supersymmetric Gauge Theory; Theoretical physics
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP09(2022)161

A bstract We prove the principle of maximal transcendentality for a class of form factors, including the general two-loop minimal form factors, the two-loop three-point form factor of tr( F 2 ), and the two-loop four-point form factor of tr( F 3 ). Our proof is based on a recently developed bootstrap method using the representation of master integral expansions, together with some unitarity cuts that are universal in general gauge theories. The maximally transcendental parts of the two-loop four-gluon form factor of tr( F 3 ) are obtained for the first time in both planar N = 4 SYM and pure YM theories. This form factor can be understood as the Higgs-plus-four-gluon amplitudes involving a dimension-seven operator in the Higgs effective theory. In this case, we find that the maximally transcendental part of the N = 4 SYM result is different from that of pure YM, and the discrepancy is due to the gluino-loop contributions in N = 4 SYM. In contrast, the scalar-loop contributions have no maximally transcendental parts. Thus, the maximal transcendentality principle still holds for the form factor results in N = 4 SYM and QCD, after a proper identification of the fundamental quarks and adjoint gluinos as n f → 4 N c . This seems to be the first example of the maximally transcendental principle that involves fermion-loop contributions. As another intriguing observation, we find that the four-point form factor of the half-BPS tr( ϕ 3 ) operator is precisely a building block in the form factor of tr( F 3 ).