arXiv subjects

Christoph Bartsch

Publications and source records attributed to Christoph Bartsch.

7 recordsLinked to original sources

arXiv2026

A Surface Integrand for the Inverse KLT Kernel

We propose a loop-level generalization of the inverse string theory Kawai-Lewellen-Tye (KLT) kernel: the planar inverse KLT integrand. The integrand is defined constructively via a novel Berends-Giele-like recursion that exposes the inverse KLT kernel as the simplest toy model of a ``stringy amplitude''. We show that, to all loop orders, the inverse KLT integrand is structurally equivalent to integrands in the cubic scalar tr$ϕ^3$ theory. This simplicity is obscured in the conventional Feynman diagram approach, where the inverse KLT integrand receives contributions from an infinity of infinite towers of contact interactions. The inverse KLT integrand is a rational function of stringified kinematic variables and is naturally defined on the kinematic surface proposed by Arkani-Hamed et al.. It provides an elementary analogue of the surfacehedron integrand for the tr$ϕ^3$ theory involving only scalar resonances and unifies the scattering of cubic scalars and pions in the non-linear sigma model (NLSM) to all loop orders via kinematic $α'$-shifts.

hep-th↗

arXiv2026

Positive Geometry for Stringy Scalar Amplitudes

We introduce a new positive geometry, the associahedral grid, which provides a geometric realization of the inverse string theory KLT kernel. It captures the full $α'$-dependence of stringified amplitudes for bi-adjoint scalar $ϕ^3$ theory, pions in the NLSM, and their mixed $ϕ$/$π$ amplitudes, reducing to the corresponding field theory amplitudes in the $α'\to 0$ limit. Our results demonstrate how positive geometries can be utilized beyond rational functions to capture stringy features of amplitudes, such as an infinite resonance structure. The kinematic $δ$-shift, recently proposed to relate field theory $\mathrm{Tr}(ϕ^3)$ and NLSM pion amplitudes, naturally emerges as the leading contribution to the stringy geometry. We show how the connection between $\mathrm{Tr}(ϕ^3)$ and NLSM can be geometrized using the associahedral grid.

hep-th↗

arXiv2025

Soft Factor Structure of MHV Amplitudes for Massless Charged Particles

We present a simple derivation of MHV amplitudes in massless spinor and scalar electrodynamics. Working with permutationally invariant amplitudes, we show that they are fully determined by their soft photon behavior and admit a simple factorized form in terms of soft factors and lower-point amplitudes. We prove these formulae using recursion relations. Finally, we consider possible extensions of these results by looking at supersymmetric theories, amplitudes beyond the MHV sector, gravity, and theories with charged particles of higher spins.

hep-th↗

arXiv2025

Universality of Colored Scalars from the Stringy KLT Kernel

A new perspective on the inverse string theory Kawai-Lewellen-Tye (KLT) kernel is provided which establishes the universality of scattering amplitudes in the bi-adjoint scalar (BAS) theory, pions in the Non-linear sigma model (NLSM), and mixed amplitudes (NLSM+$ϕ^3$) recently studied in the literature. We show that all these amplitudes can be viewed as equivalent, arising from a single function, the inverse string theory KLT kernel, evaluated at different kinematic points. In this way cubic colored scalars and pions become interchangeable through a procedure we call the $α'$-shift. The latter complements the $δ$-shift proposed by Arkani-Hamed et al., and demonstrates an inherent equivalence of scattering amplitudes in different quantum field theories by embedding them in a common stringy framework.

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arXiv2024

Hidden Amplitude Zeros From Double Copy

Recently, Arkani-Hamed et al. proposed the existence of zeros in scattering amplitudes in certain quantum field theories including the cubic adjoint scalar theory Tr($ϕ^3$), the $SU(N)$ non-linear sigma model (NLSM) and Yang-Mills (YM) theory. These hidden zeros are special kinematic points where the amplitude vanishes and factorizes into a product of lower-point amplitudes, similar to factorization near poles. In this letter, we show a close connection between the existence of such zeros and color-kinematics duality. In fact, all zeros can be derived from the Bern-Carrasco-Johansson (BCJ) relations. We also show that these zeros extend via the Kawai-Lewellen-Tye (KLT) relations to special Galileon amplitudes and their corrections, evincing that these hidden zeros are also present in permutation-invariant amplitudes.

hep-th↗

arXiv2024

An All-loop Soft Theorem for Pions

In this letter, we discuss a generalization of the Adler zero to loop integrands in the planar limit of the $SU(N)$ non-linear sigma model (NLSM). While possible to maintain at one-loop, the Adler zero for integrands is violated starting at the two-loop order and is only recovered after integration. Here we propose a non-zero soft theorem satisfied by loop integrands with any number of loops and legs. This requires a generalization of NLSM integrands to an off-shell framework with certain deformed kinematics. Defining an `algebraic soft limit', we identify a particularly simple non-vanishing soft behavior of integrands, which we call the `algebraic soft theorem'. We find that the proposed soft theorem is satisfied by the `surface' integrand of Arkani-Hamed, Cao, Dong, Figueiredo and He, which is obtained from the shifted ${\rm Tr}ϕ^3$ surfacehedron integrand. Finally, we derive an on-shell version of the algebraic soft theorem that takes an interesting form in terms of propagator renormalization factors and lower-loop integrands in a mixed theory of pions and scalars.

hep-th↗

arXiv2022

Recursion Relations for One-Loop Goldstone Boson Amplitudes

In this letter, we construct the recursion relations for one-loop planar integrands in the SU(N) non-linear sigma model. This generalizes the soft recursions for tree-level amplitudes in a variety of quantum field theories with special soft limits. The main ingredient is the definition of the one-loop planar integrand, which is fixed by cuts in the sense of generalized unitarity and by requiring the Adler zero on all external legs. We show that this does not uniquely fix the integrand, so additional constraints on the soft behavior of the loop momentum have to be imposed. Our work is the first step in extending modern amplitudes methods for loop amplitudes to effective field theories with special soft limits.

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