Theoretical and mathematical physics group



Our research receives funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 725110), Novel structures in scattering amplitudes
This project focuses on developing quantum field theory methods and applying them to the phenomenology of elementary particles. At the Large Hadron Collider (LHC) our current best theoretical understanding of particle physics is being tested against experiment by measuring e.g. properties of the recently discovered Higgs boson. With run two of the LHC, currently underway, the experimental accuracy will further increase. Theoretical predictions matching the latter are urgently needed. Obtaining these requires extremely difficult calculations of scattering amplitudes and cross sections in quantum field theory, including calculations to correctly describe large contributions due to long-distance physics in the latter. Major obstacles in such computations are the large number of Feynman diagrams that are difficult to handle, even with the help of modern computers, and the computation of Feynman loop integrals. To address these issues, we will develop innovative methods that are inspired by new structures found in supersymmetric field theories. We will extend the scope of the differential equations method for computing Feynman integrals, and apply it to scattering processes that are needed for phenomenology, but too complicated to analyze using current methods. Our results will help measure fundamental parameters of Nature, such as, for example, couplings of the Higgs boson, with unprecedented precision. Moreover, by accurately predicting backgrounds from known physics, our results will also be invaluable for searches of new particles.
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Dr. Taushif Ahmed

Taushif Ahmed
After the discovery of the Standard-model-like-­Higgs boson, the high energy physics community is standing on the verge of a crucial era where the new physics may show up as tiny deviations from the predictions of the Standard Model (SM)! To exploit this possibility it is absolutely necessary to make the theoretical predictions, along with the revolutionary experimental progress, to a very high accuracy within the SM and beyond. Multi-loop and multi-leg computations play a crucial role to achieve this golden task. However, the complexity of these computations grows very rapidly with the increase of number of loops and/or external particles. Nevertheless, it has become a reality due to several remarkable developments over the past few decades. My research interests primarily focus on these multi-loop and multi-leg analytic computations in QCD, N=4 SYM, SUSY. I am interested in analyzing the structures of scattering amplitudes, study the UV and infrared/collinear divergences by applying the state-of-the-art techniques. Recently, I have worked along these directions involving the Higgs boson, CP-odd Higgs boson, Drell-Yan and spin-2 particles at 2- and 3-loop level. In addition to these, I am also interested in studying the observables (say, cross-sections/rapidity distributions) under the threshold approximation which often captures the dominant contributions at the LHC.

Dr. Dmitrii Chicherin

Dima
My research topic is concerned with N = 4 supersymmetric Yang- Mills theory, in particular the study of multipoint super-correlation functions and scattering amplitudes in this theory, as well as superspace methods. I also study integrable spin chains and their applications in quantum field theory.

Dr. Vladimir Mitev

Vladimir
Obtaining an analytical understanding of gauge theories at large values of the coupling constant is one of the major challenges of theoretical particle physics. The past twenty years have given us several new tools with which to dissect gauge theories. The first important breakthrough is the gauge/string theory duality, thanks to which one can describe gauge theories by strings moving in a certain curved background. The second one is a series of 4D/2D dualities that relate supersymmetric gauge theories to two dimensional conformal field theories. My research sits at the intersection of these two dualities and seeks to understand supersymmetric gauge theories by deriving exact results for them by using tools such as localization, the conformal bootstrap, topological string theory and various other methods.

Dr. Tiziano Peraro

Tiziano Peraro
My primary research interests are the development and the implementation of algorithms for the solution of problems related to Quantum Field Theory and particle physics phenomenology, with a particular focus on methods for the computation of scattering amplitudes. I work on both numerical and analytic algorithms and calculations, involving techniques such as integrand reduction, generalized unitarity and transverse integration. My recent work focuses on the usage of functional reconstruction techniques based on numerical evaluations over finite fields, as well as their usage for the derivation of complex analytic higher-loop results.

Dr. Maximilian Stahlhofen

Maximilian
The primary objective of my research is to provide precise theoretical predictions for high-energy collider experiments. This typically requires complicated higher-order perturbative calculations in quantum field theory. Many of these computations can be significantly simplified or are even only made possible by using an effective field theory (EFT). EFTs are theories devised to efficiently describe specific phenomena one is interested in, at the cost of losing generality. They can often be derived directly from the underlying quantum field theory and are an indispensable tool in many fields of modern particle physics. In my current work, I am applying recently developed methods for scattering amplitudes to precision calculations within such EFTs in order to improve predictions for processes at the LHC and future colliders like the ILC.

Robin Brüser

Robin
My research interests are higher loop order Wilson line calculations. Not only Wilson lines are interesting objects in quantum field theories by themselves, but they are also closely related to scattering amplitudes and effective field theories. For instance, scattering amplitudes in a certain kinematic limit (Regge limit) can often be described via a Wilson line calculation.

Pascal Wasser

Pascal Wasser
I am working on analytic properties of scattering amplitudes in quantum field theory. One crucial step in the computation of scattering amplitudes is the computation of Feynman integrals, which can be much simplified by finding the right basis of master integrals. One approach to find such a basis is to analyze the analytic properties of the integrands, for example by determining the leading singularities and obtaining a basis of dlog forms.

Simone Zoia

Simone Zoia
Scattering amplitudes represent the bridge between our theoretical understanding of fundamental interactions and experiments. Calculating these objects at ever increasing accuracy is thus essential, if we want to test our comprehension of nature in a significant way. Pursuing this ultimate goal, I am currently studying some recent techniques which, by exploiting the analytic properties of scattering amplitudes, substantially simplify the calculation of multi-loop integrals. To the same end, I am also investigating the possible applications of conformal symmetry. In the past, I have worked in the field of high energy resummation.

Dr. Yang Zhang

Yang Zhang
I am interested in developing new mathematical methods, especially computational algebraic geometry methods, for the computation of multi-loop scattering amplitudes in perturbation QCD and supergravity theories. I am working on 1) using Groebner basis to determine loop integrands from unitarity 2) using syzygies to determine master integrals and IBP identities 3) using complex geometry to study differential equations for Feynman integrals. Besides, I am also working on new computational methods for the Bethe ansatz of integrable spin chains.

Prof. Dr. Emeri Sokatchev

Emery Sokatchev
TBA

Prof. Dr. Johannes Henn

Johannes Henn
Main research interests:
  • Scattering amplitudes in gauge and gravity theories
  • Feynman integrals
  • Collider physics
  • Infrared properties of gauge theories
  • Conformal symmetry and supersymmetry
  • Maximally supersymmetric Yang-Mills theory

  • Selected publications


    Exploring the structure of scattering processes beyond the planar limit

    B. Mistlberger and J.M. Henn,
    ``Four-Gluon Scattering at Three Loops, Infrared Structure, and the Regge Limit``,
    Phys. Rev. Lett. 117 (2016) 17, 171601

    This paper represents a new milestone in theoretically describing scattering processes of elementary particles, by computing a full four particle scattering amplitude at the three-loop order in quantum field theory. Our ability to compute scattering amplitudes at high perturbative order is a crucial ingredient for fully exploiting the wealth of experimental information collected from particle collisions at experiments such as the Large Hadron Collider. At the theoretical level, analytic results are an important catalyst for developments. They help to understand better the underlying structure of quantum field theory, to search for hidden simplicity and symmetries, and they provide a testing ground for novel techniques. While previously results at the three-loop order had only been available in the planar approximation, we now provide for the first time a full, non-planar result. Our result can be used to glean insights into the universal structure of scattering processes, such as high-energy scattering, and important effects due to the emission of soft radiation. In the former case, we provide new data that can be used to test and further develop Regge theory. In the latter case, a recent effective field theory calculation showed that at the three-loop order, non-trivial correlations between four particles exist, violating a previous dipole conjecture. Our calculation provides a first independent confirmation of this important result.

    Figure: non-planar Feynman diagram
    Figure: A prototypical non-planar Feynman diagram contributing to three-loop four-gluon scattering in Yang-Mills theory. Progress in theoretical methods allowed for the first time the analytic evaluation of the corresponding scattering amplitude. The result provides valuable insights into the structure of scattering amplitudes.


    Hidden symmetry: from classical mechanics to quantum field theory

    S. Caron-Huot and J.M. Henn,
    ``Solvable Relativistic Hydrogenlike System in Supersymmetric Yang-Mills Theory``,
    Phys. Rev. Lett. 113 (2014) 16, 161601
    Editor's suggestion in Phys. Rev. Lett.

    This paper shows how a well-known hidden symmetry in classical and quantum mechanics can be realized in quantum field theory, helping to analyze bound-state energy levels of two-particle systems. In the development of physics, symmetry has been an important guiding principle for identifying and understanding the laws of nature. An example is the equivalence principle, which postulates that observers in different reference frames experience the same physical laws. These symmetries, which are not always obvious, can be used to understand important physical models. In classical mechanics, for example, the Kepler problem has a hidden symmetry that explains the stability of planetary orbits; in quantum mechanics, this hidden symmetry allows one to find the energy spectrum of the hydrogen atom. In this paper, we identify the same hidden symmetry within a supersymmetric quantum field theory, which describes systems at even higher energies (or equivalently, at shorter distances), like the particle interactions being explored by the Large Hadron Collider. Identifying this symmetry and applying it to the calculation of the energy levels of hydrogen-like bound states signifies an important step toward the first analytic solution of a bound-state problem in a four-dimensional quantum field theory.

    Outreach article: ``From the Motion of Planets to Quantum Field Theory``
    The Institute Letter Summer 2015


    Groundbreaking new method for Feynman integral computations

    J.M. Henn,
    ``Multiloop integrals in dimensional regularization made simple``,
    Phys. Rev. Lett. 110 (2013) 25, 251601

    In this paper, I proposed a groundbreaking new method allowing for a systematic analytic computation of many previously unknown loop integrals for NNLO virtual corrections. Applications include processes involving top quarks, vector boson production, Bhabha scattering, heavy-quark effective theory (HQET). The results obtained with this method are also conceptionally beautiful and simple: for each problem, defined by the kinematics of the physical scattering process, an alphabet of differential forms is identified. Iterated integrals of the latter are then sufficient to fully describe the solution for the loop integrals, to all orders in the epsilon expansion near integer dimensions. The rules for how to form 'words', i.e. how to write down the explicit solution, is simply encoded in a set of constant N x N matrices, where N is the number of (master) integrals. Using this method, the analytic solution, to any order in epsilon, can be written down by algebraic means.

    This paper has had a profound impact on the field, and the method proposed has become standard in state-of-the-art computations.