The Curious Case of Leading Transcendentality: Three Point Form Factors

Abstract

Form factors are important ingredients to investigate the principle of maximal transcendentality (PMT) and to extract anomalous dimensions of local gauge invariant operators. In this article, we compute several two- and three-point FFs to three- and two-loops, respectively, for three different choices of local gauge invariant operators in $\mathcal{N}=4$ super Yang-Mills (SYM) theory. The operators ${\mathcal{O}}^1$ and ${\mathcal{O}}^2$ are flavour and helicity blind configurations of supersymmetric descendant of the half-BPS and Konishi primary, respectively, and ${\mathcal{O}}^3$ is the energy-momentum tensor. The operators ${\mathcal{O}}^1$ and ${\mathcal{O}}^2$ are composed of non-protected dimension-three (classical) fermionic and scalar components belonging to SU($2|3$) closed sub-sector of $\mathcal{N}=4$ SYM. We analyse the mixing among the non-protected fermionic and scalar components of these operators up to three-loops in perturbation theory and consequently, compute the quantum corrections to the corresponding dilatation operators. The highest transcendental (HT) weight terms of the FFs of ${\mathcal{O}}^1$ are found to be independent of the external on-shell states and, moreover, those are equal to that of half-BPS, however, this does not hold true for the FFs of ${\mathcal{O}}^2$. FFs of the ${\mathcal{O}}^3$ exhibit identical behaviours to that of half-BPS, in concordance with the classical expectations. However, the three-point FFs of ${\mathcal{O}}^3$ violate the PMT while comparing with the corresponding quantity in the standard model, observed for the first time at the level of FF.

arXiv commentSubstantial update of the contents, 36 pages, 1 figure

References in corpus (47)

• Multiloop integrals in dimensional regularization made simple
• Differential Equations for Two-Loop Four-Point Functions
• New features of FORM
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• Numerical evaluation of multiple polylogarithms
• Infrared singularities of scattering amplitudes in perturbative QCD
• Three-loop universal anomalous dimension of the Wilson operators in N=4 SUSY Yang-Mills model
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• On planar gluon amplitudes/Wilson loops duality
• Reduze - Feynman Integral Reduction in C++
• One-Loop Corrections to Five-Gluon Amplitudes
• The su(2|3) Dynamic Spin Chain
• Hexagon Wilson loop = six-gluon MHV amplitude
• Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Multiple polylogarithms and mixed Tate motives
• Reduze 2 - Distributed Feynman Integral Reduction
• Presenting LiteRed: a tool for the Loop InTEgrals REDuction
• Three-Loop Results for Quark and Gluon Form Factors
• Higher-Order threshold effects to inclusive processes in QCD
• Numerical Evaluation of Two-Dimensional Harmonic Polylogarithms
• Two-Loop QCD Corrections to the Helicity Amplitudes for $H\to$ 3 partons
• On the highest transcendentality in N=4 SUSY
• Leading singularities and off-shell conformal integrals
• Form Factors in N=4 Super Yang-Mills and Periodic Wilson Loops
• On Sudakov and Soft resummations in QCD
• Next-to-Leading Order QCD Corrections to the Drell-Yan Cross Section in Models of TeV-Scale Gravity
• Group structure of the integration-by-part identities and its application to the reduction of multiloop integrals
• On form factors in N=4 sym
• The last of the simple remainders
• DGLAP and BFKL evolution equations in the N=4 supersymmetric gauge theory
• Cutting through form factors and cross sections of non-protected operators in N=4 SYM
• Pseudo-scalar Form Factors at Three Loops in QCD
• The SU(2|3) dynamic two-loop form factors
• $\text{Tr}(F^3)$ supersymmetric form factors and maximal transcendentality Part I: $\mathcal{N}=4$ super Yang-Mills
• Higgs amplitudes from $\mathcal{N}=4$ super Yang-Mills theory
• Three-loop universal structure constants in N=4 susy Yang-Mills theory
• Analytic Two-Loop Higgs Amplitudes in Effective Field Theory and the Maximal Transcendentality Principle
• Operator mixing in N=4 SYM: The Konishi anomaly revisited
• Konishi Form Factor at Three Loop in $\mathcal{N}=4$ SYM
• Hidden Analytic Relations for Two-Loop Higgs Amplitudes in QCD
• Two-Loop QCD Corrections to the Higgs plus three-parton amplitudes with Top Mass Correction
• Two-Loop QCD Correction to massive spin-2 resonance $\to$ 3 gluons
• Three loop form factors of a massive spin-2 particle with nonuniversal coupling
• Second order splitting functions and infrared safe cross sections in $\mathcal{N}=4$ SYM theory
• QCD Radiative Corrections to Higgs Physics

Cited by in corpus (3)

• Two-Loop QCD Corrections to the Higgs plus three-parton amplitudes with Top Mass Correction
• Two-loop amplitudes for di-Higgs and di-pseudo-Higgs productions through quark annihilation in QCD
• Hidden Analytic Structure of Higgs Amplitudes and Maximal Transcendentality Principle