Modern Foundations of Scattering Amplitudes - Kickoff Meeting DFG Research Unit

5 Nov 2025, 12:00 → 7 Nov 2025, 21:00 Europe/Berlin

Seminar Room bctp (Bethe Center for Theoretical Physics)

Wednesday 5 November

13:00 Coffee & Registration

1 Scalar-scaffolded Yang-Mills amplitudes: minimal basis, a planar expansion and derivatives

The scaffolding description of Yang-Mills amplitudes via the planar variables originally introduced in the curve integral formalism, naturally captures the planar structure of color-ordered gluon amplitudes and offers a unique expression at fixed multiplicity. In this talk, we study the derivatives of tree-level Yang-Mills amplitudes with respect to these variables and derive a systematic rule for constructing differential operators that generate individual scalar cubic diagrams. Interestingly, in some cases, straightforward generalizations of these operators yield results that incorporate gluon insertions, although in certain instances the naive generalizations fail. We also show that the number of linearly independent mixed amplitudes of $r$ scalars and $n-r$ gluons is given by the Catalan number $\mathcal{C}_{r-2}$. This leads to a planar version of the universal expansion of Yang-Mills amplitudes.

Speaker: Jin Dong

2 Unlocking higher spin effects in black hole and neutron star binaries with supersymmetry

In this talk, I will present the recently introduced higher spin extension of the Wilson line approach to classical gravitational scattering. Wilson lines, abundant in theoretical physics, can be suitably generalized to subleading powers in the soft expansion to capture the soft dressing of asymptotic states in scattering amplitudes. By appropriately choosing the topology for these Wilson lines, the eikonal phase emerges as their correlator, which in turn enables the computation of observables in the scattering process from the eikonal.
Since Wilson lines can be derived from worldline actions, spin can be elegantly captured through worldline supersymmetry. While no-go theorems previously suggested limitations—specifically, that supersymmetry can not describe spin effects beyond second order—I will show that considering non-minimal coupling can overcome these limitations. This insight opens a rich framework for obtaining Hamiltonians and scattering amplitudes for spinning particles. To illustrate the potential of this approach, I will present two new solutions to the supersymmetry algebra: firstly, the supersymmetric action for Kerr black holes accurate to all orders in spin, and secondly, the cubic in spin action for neutron stars in d dimensions.

Speaker: Johannes Pirsch

3 On QED Self-Energies at Higher Loop Orders and Canonical Differential Equations

The self-energies in Quantum Electrodynamics (QED) are not only fundamental physical quantities, but also well-suited for investigating the mathematical structure of perturbative Quantum Field Theory. In this talk, I will discuss the computation of the QED self-energies through differential equations up to the fourth loop order, where increasingly complicated Calabi-Yau geometries appear. In particular, I will consider contributions to the electron self-energy at four loops, involving a Calabi-Yau threefold, and give an overview of some insights, challenges and open questions.

Speaker: Felix Forner

16:30 Reception

Thursday 6 November

4 Hypergeometry from Phat-Symmetry

We study position-space Feynman integrals with generic propagator powers in one and two dimensions. We show that track integrals at any loop order are completely fixed by the recently found Phat-symmetries of Yangian type, and we prove that these symmetries can be derived from the framework of Aomoto–Gelfand hypergeometric functions. We also show that a ‘spectral transform’ from the integrability toolbox is particularly efficient for the direct evaluation of position-space tree integrals in lower dimensions. We demonstrate the method’s applicability to conformal integrals. Finally, we provide a straightforward recipe to read off the 2D integrals from their 1D counterparts.

This talk is based on arXiv:2509.26305, written with F. Loebbert, A. Pitters, and S.F. Stawinski.

Speaker: Gwenaël Ferrando

5 Infrared exponentiation at integrand level in N=4 sYM

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Speaker: Dimitri Corradini

11:20 Lunch Break

PI Meeting

16:00 Coffee Break

6 From Geometry to Scattering Amplitudes (and beyond)

In recent years it has become clear that particular geometric structures, called positive geometries, underlie various observables in quantum field theories. In this talk I will review these concepts, with a particular focus on scattering amplitudes in N=4 super Yang-Mills. I will also present some new related ideas for ABJM and cosmological correlators.

Speaker: Livia Ferro

18:30 Dinner

Friday 7 November

7 When ε-Factorisation Goes Bananas: Peeling Back the Geometry

I present the computation of the three-loop banana integral with four unequal masses in dimensional regularisation. This integral is associated to a family of K3 surfaces, thus representing an example for Feynman integrals with geometries beyond elliptic curves.
We evaluate the integral by deriving an ε-factorised differential equation, for which I rely on the algorithm presented in a recent publication. Equipping the space of differential forms in Baikov representation by a set of filtrations inspired by Hodge theory, I first talk about how to obtain a differential equation with entries as Laurent polynomials in ε. Via a sequence of basis rotations the non-epsilon factories terms are removed. This procedure is algorithmic and at no point relies on prior knowledge of the underlying geometry.

Speaker: Toni Teschke

8 Numerical Evaluation of Iterated Integrals

Iterated integrals provide a powerful language to express the solutions of Feynman integrals. We discuss a novel approach to evaluate iterated integrals numerically. This approach is based on the conversion of an iterated integral to a system of ordinary differential equations, which in turn is solved numerically. Further, we describe how in this numerical context the tangential base point regularisation can be performed algorithmically. Thus important classes of special functions like (elliptic) multiple polylogarithms can easily be evaluated.

Speaker: Gideon Baur

9 Calabi--Yau(CY) Periods and Feynman Integrals

The maximal cuts of Feynman integrals have been identified in certain cases as the periods of CY manifolds. Motivated by string theory,
powerful tools have been developed to analyze their period geometry,
which, in turn, can lead to an epsilon factorized form of the differential equation. I will explain how to identify underlying geometries from the analytic structure of the integral and comment on special properties of their motives.

Speaker: Paul Blesse

12:00 The End