arXiv subjects

Jeffrey V. Backus

Publications and source records attributed to Jeffrey V. Backus.

4 recordsLinked to original sources

arXiv2025

New Recursions for the Canonical Scalar-Scaffolded Yang-Mills Amplitude

The recently-developed "scalar-scaffolding" formulation of gluon amplitudes casts the Yang-Mills (YM) amplitude as a well-defined Laurent series expansion in scalar variables, valid for any spacetime dimension and helicity configuration. In this letter, we exploit this new perspective to develop conceptually novel methods of computing YM tree amplitudes. First, using standard gluon factorization to determine all terms with poles, we show how gauge invariance uniquely fixes the piece with no poles (the "contact term") from only terms that have a single pole. This allows us to write a YM recursion not only for the full amplitude but also for the amplitude up to any order in the Laurent series. Next, by imposing gauge invariance for terms with poles, we write down relations which compute numerators recursively in the amplitude's Laurent series expansion. Starting from an initial set of cuts depending only on the $(n-1)$-point amplitude, these formulae allow us to determine the remaining terms in the $n$-point amplitude. Finally, we use this "Laurent series recursion" to derive a recursion solely for the contact term. We speculate on the possibility that this and analogous recursions for any term in the amplitude may be solved. In attached Mathematica notebooks, we give implementations of these three recursions.

hep-th↗

arXiv2025

Surface Gauge Invariance, Soft Limits and the Transmutation of Gluons into Scalars

Over the past year, the "scalar-scaffolding" formalism has revealed a number of new features of gluon amplitudes. In this paper, we leverage these developments to study two distinct but related questions, linked by the scaffolding statement of gauge invariance. We start by revisiting the soft expansion of gluon amplitudes. The scaffolding picture allows for a precise definition of the soft limit and a canonical way to expand the amplitude. At tree-level, this reproduces the classic Weinberg soft theorem, and at one-loop, using surface kinematics, we derive an extension of this theorem valid at the level of the loop integrand. We then switch gears and describe a new relationship between gluon and scalar amplitudes. The expression of surface gauge invariance naturally suggests a certain differential operator acting on individual external gluons. Remarkably, we find that, both for the tree-level amplitude and the surface one-loop integrand, repeated applications of this operator transmutes gluon amplitudes/integrands into those of Tr$(\phi^3)$ scalars. This is an interesting counterpart to the $\delta$-shift connection that lifts "stringy" Tr$(\phi^3)$ amplitudes to those of gluons.

hep-th↗

arXiv2025

Emergence of Unitarity and Locality from Hidden Zeros at One-Loop Order

Recent investigations into the geometric structure of scattering amplitudes have revealed the surprising existence of "hidden zeros": secret kinematic loci where tree-level amplitudes in Tr$(\phi^3)$ theory, the Non-Linear Sigma Model (NLSM), and Yang-Mills theory vanish. In this Letter, we propose the extension of hidden zeros to one-loop-order in Tr$(\phi^3)$ theory and the NLSM using the "surface integrand" technology introduced by Arkani-Hamed et al. We demonstrate that, under the assumption of locality, one-loop integrands in Tr$(\phi^3)$ are unitary if and only if they satisfy these loop hidden zeros. We also present strong evidence that the hidden zeros themselves contain the constraints from locality, leading us to conjecture that the one-loop Tr$(\phi^3)$ integrand can be fixed by hidden zeros from a generically non-local, non-unitary ansatz. Near the one-loop zeros, we uncover a simple factorization behavior and conjecture that NLSM integrands are fixed by this property, also assuming neither locality nor unitarity. This work represents the first extension of such uniqueness results to loop integrands, demonstrating that locality and unitarity emerge from other principles even beyond leading order in perturbation theory.

hep-th↗

arXiv2023

Toward extracting $γ$ from $B \to DK$ without binning

$B^\pm \to DK^\pm$ transitions are known to provide theoretically clean information about the CKM angle $γ$, with the most precise available methods exploiting the cascade decay of the neutral $D$ into $CP$ self-conjugate states. Such analyses currently require binning in the $D$ decay Dalitz plot, while a recently proposed method replaces this binning with the truncation of a Fourier series expansion. In this paper, we present a proof of principle of a novel alternative to these two methods, in which no approximations at the level of the data representation are required. In particular, our new strategy makes no assumptions about the amplitude and strong phase variation over the Dalitz plot. This comes at the cost of a degree of ambiguity in the choice of test statistic quantifying the compatibility of the data with a given value of $γ$, with improved choices of test statistic yielding higher sensitivity. While our current proof-of-principle implementation does not demonstrate optimal sensitivity to $γ$, its conceptually novel approach opens the door to new strategies for $γ$ extraction. More studies are required to see if these can be competitive with the existing methods.

hep-ph↗