Search arXivSearch

arXiv · 2606.27928

$\texttt{SMaSH}$ : Simplify Massive Spinor Helicity

Abstract

We present $\texttt{SMaSH}$, a $\texttt{Mathematica}$ package to do spinor helicity computations in four spacetime dimensions $\href{https://github.com/aakash-kmr/SMaSH}{\text{(github)}}$. It can handle massive spinor helicity computations with explicit little group indices which is a novel feature. It can also handle massless as well as off-shell spinor helicity variables. It is designed to compute perturbative computations; it comes with predefined three point amplitudes and propagators for any masses and spins (arXiv:1709.04891). It can implement the high energy limit over an expression, check the discrete $\tt{C,P,T}$ transformations, compute contact terms and impose gauge invariance for any scattering process. We have shown the usage of such functions for computing gauge invariant Weinberg minimal amplitudes (arXiv:2506:12431, arXiv:2504:06343). The package can also generate both real and complex numerical kinematics for any $n$-point scattering for arbitrary masses and energy scales by implementing the $\tt{RAMBO}$ algorithm. It is also rich with basic spinor helicity manipulations like Schouten simplification, Clifford algebra manipulation, conversion between spinor helicity and Lorentz vectors, derivative w.r.t. spinors and their scalars, helicity scaling etc.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Aakash Kumar, Arnab Rudra, Rahul Shaw. 2026-06-26. $\texttt{SMaSH}$ : Simplify Massive Spinor Helicity. https://arxiv.org/abs/2606.27928

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Six Easy Pieces: interplays among dualities in 4d, 3d and 2d

In this paper we consider 4d $\mathcal{N}=1$ $\mathrm{SU}(N)$ gauge theories with $N+1$ fundamentals, five antifundamentals and a conjugate two index antisymmetric tensor. The model has been shown to be in a mixed phase in the IR, splitting in an interacting non-Abelian Coulomb phase and a free magnetic phase. Through tensor deconfinement, we show that baryonic deformations lead to a non-Abelian free magnetic phase. Along the analysis we obtain a duality with symplectic SQCD that can be further reduced to 3d and 2d. In the 3d case the analysis of the three sphere partition function allows one to obtain dualities between $\mathrm{SU}(N)$ with a two index symmetric tensor and $\mathrm{SO}(N)$ theories. On the other hand, in 2d we recover dualities already known in the literature and propose new ones between special unitary and symplectic gauge theories.

hep-th

Flat holography for spinor fields

We extend the hyperbolic Milne-slicing construction of flat holography in four-dimensional Minkowski spacetime from scalar fields to massless spin-$\frac{1}{2}$ fields. We solve the massive mode equation and restrict the boundary source-response analysis to the massless sector. Decomposition into harmonics on three-dimensional hyperbolic space, labeled by a continuous principal-series parameter, yields a separated-point nonlocal kernel up to the action normalization and local contact terms. The kernel has the universal form required by two-dimensional conformal covariance for spin-$\frac{1}{2}$ principal-series primaries. Then we construct regular source-normalized conformal-primary wavefunctions in planar and global coordinates on the celestial sphere $S^2$. We show that the planar source-response kernel is naturally identified with the spin-$\frac{1}{2}$ shadow transform, while inverse shadowing recovers the angular delta-function structure of the unshadowed basis. We also analyze radial renormalization by analytic continuation from the principal-series problem to a real-mass AdS$_3$ problem.

hep-th

Off-shell recursion for all-loop planar integrands in Yang-Mills theory

In this paper, we develop in detail the off-shell recursion for planar loop integrands in Yang-Mills theory. Starting from the classical equations of motion solved with the perturbiner method, we derive an exact transfer-matrix representation of the pure-gluon sector. We then include the ghost contributions to the loop kernels based on \cite{Tao:2025fch}. Finally, as an example, we work out the two-loop recursion in detail and conclude a general recursion strategy for two-loop planar integrands whose external legs are gluons.

hep-th