Registration

Welcome

• Lorenzo Tancredi (TUM)
• Nikolaos Syrrakos (TUM)
• Christoph Nega (TUM)

Welcoming words and introduction to the workshop

Non-factorizable QCD corrections in hadron collider processes

• Kirill Melnikov

I will discuss the recent progress with describing the non-factorizable QCD corrections to Higgs boson production in weak boson fusion and single-top production at the LHC, focusing on effects that arise beyond the leading eikonal approximation.

Integral reductions and computer algebra for amplitudes

• Andreas von Manteuffel

Integration-by-parts reductions of Feynman integrals and methods from computer algebra play an important role in the calculation of multiloop scattering amplitudes. In this talk, I will review modern methods based on finite field arithmetics and polynomial ideal theory.

Multiscale Amplitudes for Colliders: Tools and Perspectives

• Ben Page

In recent years, we have seen great progress in our ability to compute two-loop amplitudes describing the scattering of multiple particles. In this talk, we review the status of these calculations, the tools that made them possible as well as open questions and future directions.

Analytic computation of 2-loop scattering amplitudes for phenomenological applications

• Ekta Chaubey

Analytic computation of multi-loop Feynman integrals is crucial for the current era of precision physics. These analytic computations often bring us to intriguing algebraic structures which help in establishing deep connections with Mathematics. In this talk I will talk about some analytic computations of 2-loop Feynman integrals with their phenomenological applications in mind.

Mathematical Structures in Massive Operator Matrix Elements and Wilson Coefficients

• Johannes Blumlein

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IBP Reduction with Gröbner bases

• Robin Bruser

In this talk we investigate how Gröbner bases theory can be used to perform integration-by-parts (IBP) reductions of loop integrals. The first part of the talk serves as brief introduction to Gröbner bases. In the second part we discuss the main idea on the example of one-loop bubble and one-loop box integrals. We see that the IBP relations form a left ideal in a rational double-shift algebra. The IBP reduction of loop integrals then amounts to computing normal forms of shift operators of the rational double-shift algebra with respect to a Gröbner basis of the left ideal. Finally, in the last part we discuss an ansatz based on linear algebra to simulate the computation of normal forms. This approach can be used for complicated problems, when obtaining the Gröbner basis is computationally too expensive.

Canonical differential equations for six-point two-loop Feynman integrals

• Julian Miczajka

It is well known, that the problem of calculating a particular family of Feynman integrals can often be solved most efficiently by finding a basis of master integrals which satisfies a differential equation in so-called canonical form. In this talk, we discuss recent progress in finding such a canonical basis for two families of Feynman integrals with six external particles at two loops in an arbitrary number of space-time dimensions. We also demonstrate how the resulting differential equation makes it straightforward to extract the identities that the integrals satisfy when the external kinematics lie in a four-dimensional space.

Feynman integrals, geometries and differential equations

• Stefan Weinzierl

In this talk I will review recent developments in the field of analytical Feynman integral calculations. In particular, I will discuss Feynman integrals related to non-trivial geometries like an elliptic curve, or more general a Calabi-Yau manifold, and methods how to compute these Feynman integrals.

On extended topological quantum field theory

• Ilka Brunner

Topological quantum field theories (TQFT) are very simple models of quantum field theories. They allow for a mathematically rigorous definition and treatment. Physically, they are relevant since they describe subsectors of supersymmetric theories and also have applications in condensed matter. I will review some aspects of TQFT.

The complex simplicity of cosmological correlators

• Ivo Sachs

I will review some aspects of the position space calulation of cosmological correlators in the in-in formalism. In some cases they can be mapped to AdS correlators, by double Wick rotation, that are simpler than the compuation of the cosmological wave function.

Fishnet Amplitudes and Quantum Volumes of Calabi-Yau and Picard Varieties

• Albrecht Klemm

2d conformal graphs can be drawn on the regular tilings of the plane. The corresponding amplitudes are solutions of the Yangian integrable symmetry operators convoluted with the symmetry group of the graph. To each graph we can associate a Calabi Yau variety defined by double or triple cover constructions. The latter case corresponds to the trivalent lattice and in this case the Calabi-Yau geometry is related to Picard varieties. The integrable structure implies flatness of the Gauss Manin connection of the geometry and amplitudes can be efficiently evaluated as the quantum volume of the associated geometries.

Scattering of spinning black holes at NNNLO

• Jan Plefka

The need for high precision predictions of the general relativistic two-body problem for the future generation of gravitational wave detectors has opened a new window for the application of perturbative quantum field theory techniques to the domain of classical gravity. In this talk I will show how observables in the classical scattering of black holes and neutron stars can be efficiently computed in the post-Minkowskian expansion using a world-line quantum field theory; thereby importing multi-loop Feynman integration technology to this field. Here, the black holes or neutron stars are modelled as point particles in an effective field theory sense. Fascinatingly, the intrinsic spin of the black holes is captured by a supersymmetric extension of the world-line theory, enabling the computation of the far field wave-form and scattering angle including spin to highest precision. With a view towards the audience I will sketch our recent state-of-the-art NNNLO computation (4PM order) of Kerr-Black Hole scattering and the challenges and opportunities ahead.

Symbol Alphabets from the Landau Singular Locus

• Georgios Papathanasiou

We provide evidence through two loops, that rational letters of polylogarithmic Feynman integrals are captured by the Landau equations, when the latter are recast as a polynomial of the kinematic variables of the integral, known as the principal A-determinant. Focusing on one loop, we further show how to also obtain all non-rational letters with the help of Jacobi determinant identities. We verify our findings by explicitly constructing canonical differential equations and comparing with the existing literature, and finally extend the proof of the Cohen-Macauley property of one-loop integrals to a broader range of their kinematics.