No abstract

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

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 the interpretation of individual Feynman integrals as correlators in the massless fishnet theory introduced by Gürdoğan and Kazakov. Here we seek for an analogous interpretation of the integrability of massive Feynman integrals. We contrast two approaches to define simple massive quantum field theories in four dimensions. First, we discuss spontaneous symmetry breaking in the massless bi-scalar fishnet theory. We then propose an alternative route to a massive fishnet theory by taking a double-scaling limit of $$ \mathcal{N} $$ N = 4 SYM theory on the Coulomb branch. Both approaches lead to a massive extension of the massless fishnet theory, differing in how masses enter into the propagators. In the latter theory, planar off-shell amplitudes are in one-to-one correspondence with precisely those massive Feynman integrals that were shown to be invariant under the Yangian. This suggests a re-investigation of Coulomb branch $$ \mathcal{N} $$ N = 4 SYM theory with regard to integrability. Finally, we demonstrate that in the case of spontaneous symmetry breaking, the original conformal symmetry leads to soft theorems for scattering amplitudes in the broken phase.

The question of whether classically conformal modifications of the standard model are consistent with experimental obervations has recently been subject to renewed interest. The method of Gildener and Weinberg provides a natural framework for the study of the effective potential of the resulting multi-scalar standard model extensions. This approach relies on the assumption of the ordinary loop hierarchy λ s ∼ g 2 g of scalar and gauge couplings. On the other hand, Andreassen, Frost and Schwartz recently argued that in the (singlescalar) standard model, gauge invariant results require the consistent scaling λ s ∼ g 4 g . In the present paper we contrast these two hierarchy assumptions and illustrate the differences in the phenomenological predictions of minimal conformal extensions of the standard model.

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