Conveners
Methods for amplitudes and integrals
- Stefano Pozzorini (Zurich university)
Methods for amplitudes and integrals
- Simone Zoia (CERN)
Methods for amplitudes and integrals
- Simon David Badger (Istituto Nazionale di Fisica Nucleare)
Methods for amplitudes and integrals
- Matteo Becchetti (Università di Bologna)
The remarkable detection of gravitational waves (GWs) by Ligo-Virgo-Kagra interferometers has opened the new era of multimessenger astrophysics. An analytic understanding of GWs waveform allows us to construct precise GWs templates, which are needed to detect signals via matched filtering analyses.
In this talk, I will combine the observable-based formalism (KMOC), the analytic properties of...
A universal numerical method for computing loop amplitudes would enable precise theoretical predictions for a broad range of phenomenological relevant processes. A major obstacle in developing such methods is the treatment of infrared and ultraviolet singularities, which must be eliminated at the integrand level before numerical integration becomes feasible.
In this talk, I will introduce a...
We present a new method for computing multi-loop scattering amplitudes in Quantum Field Theory (arXiv:2403.18047). It extends the Generalized Unitarity method by constraining not only the integrand of the amplitude but also its full integrated form. Our approach exploits the relation between cuts and discontinuities of the amplitude. Explicitly, by the virtue of analyticity and unitarity of...
The Feynman integral is a critical object in quantum field theory. It is very important in high energy physics. The integration-by-parts (IBP) reduction is one of the bottle-neck steps in the evaluation of multi-loop Feynman integrals. NeatIBP is a program based on the syzygy method of IBP reduction. It generates much smaller sized IBP system compared to traditional Laporta's algorithm. This...
In this talk I will present a calculation of the three-loop four-point master integrals. They come from two three-loop ladder diagrams with two off-shell legs that have identical masses. The talk will mainly consist of two sections. First I will demonstrate the construction of a canonical basis and solve the differential equation it fulfills. Then it goes to the discussion of using the symbol...
Extending the BFKL program beyond next-to-leading logarithms requires high-multiplicity central-emission vertices (CEV) and peripheral emission vertices (PEV). In this talk, I discuss how to conveniently extract these building blocks at tree level from amplitudes in general kinematics using a suitable (minimal) set of kinematic variables. Specifically, we determine all quark and gluon emission...
The availability of high-multiplicity multi-loop scattering amplitudes in QCD provides invaluable data for studying the theory under special kinematic configurations. Recent calculations of two-loop full-colour QCD amplitudes for the scattering of five partons have enabled us to explore their high-energy limit, known as Multi-Regge Kinematics (MRK). In this limit, a universal factorisation...
I will present novel results for non-planar three-loop four-point Feynman integrals with one off-shell leg. The talk will cover various integration techniques, as well as observations on the function space. As a first application, I present an analytic result for a form factor of a local composite operator in maximally supersymmetric Yang-Mills theory.
Feynman integrals can be evaluated in terms of generalized hypergeometric series known as A-hypergeometric functions, which were proposed by Gel'fand-Kapranov-Zelevinsky (GKZ) as a unified approach to hypergeometric functions. Among the properties of A-hypergeometric functions are symmetries associated with the Newton polytope. In ordinary hypergeometric functions these symmetries lead to...
We discuss modern techniques for the numerical computation of master integrals as series solutions of differential equations.
A vital step in multi-loop Feynman integral calculations is tensor reduction. We present an efficient graphical approach to this problem and introduce OPITeR a code that implements this method for arbitrary tensor Feynman integrals. OPITeR can handle integrals of arbitrary loop up to tensor rank 20 with any number of spin indices. We present some applications in the context of R*...
Reduction of Feynman integrals to a basis of linearly independent master integrals is a crucial step in any perturbative calculation, but also one of its main bottlenecks. In this talk I will present an improvement over the traditional approach to IBP reduction, that exploits transverse integration identities. Given an integral family to be reduced, the key idea is to find sectors whose corner...
I will present recent progress in constructing a generic two-loop amplitude reduction algorithm within the computational framework of HELAC. Following the well-known OPP reduction approach at one loop, a two loop amplitude approach is developed. I will also discuss the differences between the 4-2ε and pure 4 dimensional reduction fitting as well as the implications on the so-called rational...
The reduction of Feynman integrals to a basis of master integrals plays a crucial role for many high-precision calculations and Kira is one of the leading tools for this task. Recently, we achieved significant performance improvements. In this talk we discuss those and some of the new features for the next major release.
We present a novel, simplified formulation of the recursive algorithm for
evaluating intersection numbers of differential forms. This approach is
applied to derive the complete decomposition of two-loop planar and non-planar
Feynman integrals in terms of a master integral basis.
The new algorithm extensively utilizes various emerging tensor structures
derived from the polynomial...
The infrared structure of scattering amplitudes offers a natural path to organize bases of Feynman integrals according to their divergence properties. In this talk, I will describe two complementary approaches to this organization: an analytic approach that builds upon the theory of Landau singularities in momentum space, and a geometric approach based on the parametric representation of the...
The Baikov representation of Feynman integrals, and in particular its loop-by-loop variant, has proven itself useful for a number of purposes. Specifically for generalized cuts, twisted cohomology, and the unveiling of geometric structures.
For that reason I have made a package implementing that parametrization. In my talk I will present the package, and discuss some strategies for how best...
Soft singularities of scattering amplitudes are important for both theoretical and practical reasons. It is well known that these singularities are captured by correlators of Wilson lines which follow the classical trajectory of energetic partons participating in the process and intersect at the hard interaction vertex. Such correlators feature ultraviolet singularities, which allow us to...
