YOUNGST@RS - Loop-the-Loop: Feynman Calculus and its Applications to Gravity and Particle Physics

Session

Applied Mathematics for Feynman Calculus

12 Nov 2024, 10:30

3. Syzygy method of integration by parts

Rourou Ma

12/11/2024, 10:30

Integration by parts(IBP) plays an important role in the calculation of Feynman integrals. Numerous Feynman integrals can be reduced to a small amount master integrals, as the simpler integral basis of a given Feynman integral family. Compare with traditional IBP, syzygy method can reduce IBP system redundancy, also make IBP reduction more efficient. I will introduce an IBP package "NeatIBP",...

4. Two-loop five-point two-mass Feynman integrals

Simone Zoia

12/11/2024, 11:00

I present the computation of the planar two-loop five-point Feynman integrals with two off-shell external legs. These integrals are relevant, for instance, for the second-order QCD corrections to the production of two heavy vector bosons in association with a jet at hadron colliders. We employ the method of canonical differential equations, boosted by finite-field sampling to tame the...

5. Series expansion approach and application to 2L mixed QCD-EW corrections to Drell-Yan

Tommaso Armadillo

12/11/2024, 11:30

The calculation of higher order corrections to physical observables is becoming essential for matching the theoretical predictions to the experimental precision at present and future colliders. One of the main bottleneck for their evaluation is the computation of the Feynman integrals appearing in the amplitude, due to the number of loops, external legs or internal masses.
In this talk I...

6. Intersecting companion matrices for Feynman integrals

Vsevolod Chestnov

12/11/2024, 13:30

Twisted period integrals play an essential role in theoretical physics and
mathematics, residing in a finite-dimensional vector space with an inner
product known as the intersection number. In this talk, we explore the emerging
tensor structures in intersection numbers within the fibration-based evaluation
scheme. By introducing companion matrices, we reformulate the computation...

7. Twisted Cohomology & Canonical Differential Equations

Franziska Porkert

12/11/2024, 14:00

Interpreting Feynman integrals as periods of (relative) twisted cohomology groups has lead to many interesting and fruitful insight. Recently we explored, what one can learn from the twisted Riemann bilinear relations that these periods satisfy. This led to further insights on a notion of self-duality for maximal cuts and specifically, the form of the intersection matrix for a canonical basis...

8. Recent advancements and hidden structures in intersection numbers for Feynman Integrals

Giulio Crisanti

12/11/2024, 14:30

The intersection number is an inner product that can be defined on the vector space of Feynman Integrals, allowing one to perform integral reductions without using IBPs. In this talk I will review the main ideas behind intersection theory, and present some new computational and advancements in the field. Specifically, I will showcase a prescription for choosing orthogonal bases of differential...

9. Systematically evaluate cosmological correlators by IBP and differential equations

Jiaqi Chen

12/11/2024, 15:30

We generalize the Integration-By-Parts (IBP) and IBP-based differential equations method to general cosmological correlator, including massive correlator and time-derivative interactions cases, and find the factorization property from the perspective of IBP. By our selection of master integrals, we find uniform formulas for iterative reduction and dlog-form differential equations of arbitrary...

10. Minimal Cuts and Genealogical Constraints on Feynman Integrals

Maria Polackova

12/11/2024, 16:00

We introduce an efficient method for deriving hierarchical constraints on the discontinuities of individual Feynman integrals. This method can be applied at any loop order and particle multiplicity, and to any configuration of massive or massless virtual particles. The resulting constraints hold to all orders in dimensional regularization, and complement the extended Steinmann relations --...

11. Progress in Landau Analysis

Mathieu Giroux

12/11/2024, 16:30

We review a recent recursive unitary-based workflow that opens the path further to a systematic treatment of Landau singularities for n-point scattering amplitudes in perturbation theory. For two-particle cut reducible diagrams, our method allows for fast computations of Landau singularities beyond the current state-of-the-art, including examples relevant to two- and higher-loop massive...