A bstract We compute three families of two-loop six-point massless Feynman integrals in dimensional regularization, namely the double-box, pentagon-triangle, and hegaxon-bubble family. This constitutes first analytic computation master with eight scales. use method canonical differential equations. describe corresponding integral basis uniform transcendentality, relevant function alphabet, boundary values at a particular point Euclidean region up to fourth order regularization parameter ϵ ....

In the context of planar holography, integrability plays an important role for solving certain massless quantum field theories such as N=4 super Yang-Mills theory. this Letter, we show that also features in building blocks massive theories. At one-loop order prove all n-gon Feynman integrals generic spacetime dimensions are invariant under a Yangian symmetry. two loops similar statements can be proven graphs built from n-gons. loop conjecture cut regular tilings plane with propagators on...

We derive the full system of canonical differential equations for all planar two-loop massless six-particle master integrals, and determine analytically boundary conditions. This fully specifies solutions, which may be written as Chen iterated integrals. argue that this is sufficient information evaluating any scattering amplitude in four dimensions up to finite part. support claim by reducing, most complicated integral topologies, integrals with typical Yang-Mills numerators. use analytic...

A bstract The state-of-the-art in current two-loop QCD amplitude calculations is at five-particle scattering. Computing six-particle processes requires knowledge of the corresponding one-loop amplitudes to higher orders dimensional regulator. In this paper we compute analytically hexagon integral via differential equations. particular identify its function alphabet for general D -dimensional external states. We also provide representations all integrals up weight four. With this, basis ready...

We extend the study of recently discovered Yangian symmetry massive Feynman integrals and its relation to momentum space conformal symmetry. After proving statements in detail at one two loop orders, we employ constraints bootstrap various one-loop examples integrals. In particular, explore interplay between hypergeometric expressions considered Based on these conjecture single series representations for all dual D spacetime dimensions with generic propagators.

A bstract We extend the recently developed Yangian bootstrap for Feynman integrals to Minkowski space, focusing on case of one-loop box integral. The space invariants is spanned by Bloch-Wigner function and its discontinuities. Using only input from symmetries, we constrain functional form integral in all 64 kinematic regions up twelve (out a priori 256) undetermined constants. These need be fixed other means. do this explicitly, employing two alternative methods. This results novel compact...

A bstract We derive and study Yangian Ward identities for the infinite class of four-point ladder integrals their Basso-Dixon generalisations. These symmetry equations follow from interpreting respective Feynman as correlation functions in biscalar fishnet theory. Alternatively, presented can be understood anomaly a momentum space conformal symmetry. The take form inhomogeneous extensions partial differential defining Appell hypergeometric functions. employ manifestly tensor reduction order...

A bstract Recently, infinite families of massive Feynman integrals were found to feature an unexpected Yangian symmetry. In the massless case, similar integrability properties are understood via interpretation individual as correlators in fishnet theory introduced by Gürdoğan and Kazakov. Here we seek for analogous integrals. We contrast two approaches define simple quantum field theories four dimensions. First, discuss spontaneous symmetry breaking bi-scalar theory. then propose alternative...

The question of whether classically conformal modifications the standard model are consistent with experimental observations has recently been subject to renewed interest. method Gildener and Weinberg provides a natural framework for study effective potential resulting multiscalar extensions. This approach relies on assumption ordinary loop hierarchy ${\ensuremath{\lambda}}_{\mathrm{s}}\ensuremath{\sim}{g}_{\mathrm{g}}^{2}$ scalar gauge couplings. On other hand, Andreassen et al. argued that...

A bstract We compute all 2 → 5 gluon scattering amplitudes in planar $$ \mathcal{N} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 super-Yang-Mills theory the multi-Regge limit that is sensitive to non-trivial (“long”) Regge cut. provide through four loops and logarithmic accuracy at leading power, terms of single-valued multiple polylogarithms two variables. To obtain these results, we leverage function-level results for Steinmann cluster...

We compute three families of two-loop six-point massless Feynman integrals in dimensional regularization, namely the double-box, pentagon-triangle, and hegaxon-bubble family. This constitutes first analytic computation master with eight scales. use method canonical differential equations. describe corresponding integral basis uniform transcendentality, relevant function alphabet, boundary values at a particular point Euclidean region up to fourth order regularization parameter $\epsilon$....

We evaluate the three-loop five-point pentagon-box-box massless integral family in dimensional regularization scheme, via canonical differential equation. use tools from computational algebraic geometry to enable necessary reductions. The boundary values of equation are determined analytically Euclidean region. To express final result, we introduce a new representation weight six functions terms one-fold integrals over product weight-three with weight-two kernels that derived Our work paves...

An overview of the massive generalization Yangian symmetry for Feynman integrals is given. We illustrate relation to a fishnet theory defined as double-scaling limit Coulomb-branch N=4 SYM theory.

The state-of-the-art in current two-loop QCD amplitude calculations is at five-particle scattering. Computing six-particle processes requires knowledge of the corresponding one-loop amplitudes to higher orders dimensional regulator. In this paper we compute analytically hexagon integral via differential equations. particular identify its function alphabet for general $D$-dimensional external states. We also provide representations all integrals up weight four. With this, basis ready...

An overview of the massive generalization Yangian symmetry for Feynman integrals is given. We illustrate relation to a fishnet theory defined as double-scaling limit Coulomb-branch N=4 SYM theory.