Sérgio Carrôlo

A bstract: We study the leading singularities for pure gluon amplitudes obtained by on-shell gluing of three-particle amplitudes for an arbitrary graph in any number of dimensions. By encoding the polarization vector contractions in a graphical way, on-shell gluing “discovers” curves on surfaces, and we find that the leading singularity is determined by a simple combinatorial question: what are all ways of covering the graph with non-overlapping curves such that each edge is covered exactly once? This precisely matches the formula from the surfaceology formulation of gluons, where the leading singularities are given by maximal residues, with the combinatorial problem arising from the linearized form of the u variables. At loop-level we describe how the novelties associated with spin sums (related with the need for ghosts when working off-shell using Lagrangians) can be easily encoded in this combinatorial picture. Matching the leading singularities also lets us settle an open question in the surface formulation of gluons, determining the exponents of the closed curves at any loop order.

We present a symbol-level bootstrap construction of the planar, two-loop six-gluon scattering amplitude for the − − + + + + helicity configuration in quantum chromodynamics (QCD), focusing on the maximal weight pieces—the “most complicated terms” in the sense of Lipatov Building on recent advances in the understanding of the relevant function space, we incorporate as a crucial new ingredient the complete set of leading singularities, obtained from an analysis of on-shell diagrams. The resulting expressions are manifestly conformally invariant and clarify the structure of previous five-particle results. Combining this with the symbol bootstrap, we show that constraints from physical limits are sufficient to determine the answer. We thus obtain the first concrete characterization of two-loop six-gluon amplitudes at symbol level and at highest weight. Remarkably, we find that the effective function space involves only 137 symbol letters—significantly fewer than the full set of 167 possible letters, suggesting a yet-unexplained underlying structure akin to that seen in maximally supersymmetric Yang-Mills theory. From the novel amplitude results we extract previously unknown symbol-level results describing two-loop triple collinear and double soft limits.

There are only six independent types of symmetry-constrained (renormalizable) scalar potentials in the two Higgs doublet model (2HDM). For example, the scalar sector symmetry known as Z 2 ⊗ Π 2 , generated by the simultaneous application of two independent symmetries acting on the scalar fields, and the generalized C P symmetry known as GCP2 yield equivalent 2HDM scalar potentials. A similar situation arises for the scalar sector symmetries known as U ( 1 ) ⊗ Π 2 and GCP3, respectively. In this paper, we show that this “degeneracy” remains when the definitions of the corresponding symmetries are extended to the Yukawa sector with three quark generations. The proof involves the exploration of all possible extensions of the corresponding symmetries to the Yukawa sector, consistent with the phenomenological constraints of nonzero quark masses and a nontrivial quark mixing matrix. Moreover, we find that this result is a peculiarity of a Yukawa sector with three quark generations. In particular, with two quark generations, we find that models based on the extension of Z 2 ⊗ Π 2 to the Yukawa sector are inequivalent with those based on GCP2.

A bstract: In this work, we compute the two-loop result of the null hexagonal Wilson loop with a Lagrangian insertion in planar, maximally supersymmetric Yang-Mills theory via a bootstrap approach. Normalized by the null polygonal Wilson loop itself, the integrand-level result of this observable corresponds to the logarithm of the six-point three-loop amplitude in this theory, while its integrated result is conjectured to match the maximally transcendental part of the six-point three-loop all-plus amplitude in pure Yang-Mills theory. Our work builds on two recent advances. On the one hand, the set of leading singularities relevant to this observable was recently classified. On the other hand, the relevant space of special functions that may in principle accompany these leading singularities was determined at two loops and for six particles by a dedicated Feynman integral calculation. These two ingredients serve as the foundation of our bootstrap ansatz. We fix all indeterminates in this ansatz by imposing physical constraints, such as symmetries, absence of spurious divergences, and correct behavior in soft and collinear limits. Finally, we discuss and verify certain physical properties of our symbol result, including physical singularities, behavior under multi-Regge limit, as well as Steinmann relations between symbol entries. The latter relations are motivated by the correspondence to all-plus amplitudes in pure Yang-Mills theory, and successfully checking them constitutes a consistency check of this conjectured correspondence.

In this work, we compute the two-loop result of the null hexagonal Wilson loop with a Lagrangian insertion in planar, maximally supersymmetric Yang-Mills theory via a bootstrap approach. Normalized by the null polygonal Wilson loop itself, the integrand-level result of this observable corresponds to the logarithm of the six-point three-loop amplitude in this theory, while its integrated result is conjectured to match the maximal transcendental part of the six-point three-loop all-plus amplitude in pure Yang-Mills theory. Our work builds on two recent advances. On the one hand, the set of leading singularities relevant to this observable was recently classified. On the other hand, the relevant space of special functions that may in principle accompany these leading singularities was determined at two loops and for six particles by a dedicated Feynman integral calculation. These two ingredients serve as the foundation of our bootstrap ansatz. We fix all indeterminates in this ansatz by imposing physical constraints, such as symmetries, absence of spurious divergences, and correct behavior in soft and collinear limits. Finally, we discuss and verify certain physical properties of our symbol result, including physical singularities, behavior under multi-Regge limit, as well as Steinmann relations between symbol entries. The latter relations are motivated by the correspondence to all-plus amplitudes in pure Yang-Mills theory, and successfully checking them constitutes a consistency check of this conjectured correspondence.