Quantum chromodynamics is the part of the Standard Model that describes the strong force. Strong interaction dynamics in high-energy collisions typically involves a wide range of energy scales, from the collision energy down to the scale where quarks and gluons are confined to hadrons. Theoretical control over the associated phenomena is a prerequisite for understanding most reactions at colliders. The concepts of factorization and of effective field theories are the keys to separate the dynamics at the different scales, from the perturbative to the nonperturbative domain. They allow for the resummation of the dominant contributions to all orders in perturbation theory, leading to significant improvements in the precision of theoretical predictions.

In proton-proton collisions at high energies, several partons in one proton can undergo a hard scattering with partons in the other proton, each scattering producing particles with large mass or transverse momentum. The effects of such multiparton interactions average out in sufficiently inclusive observables but can have important consequences for the details of the final state. Their theoretical description raises a number of interesting questions, ranging from conceptual issues of factorization to nontrivial aspects of hadron structure and to the phenomenology of pp collisions.

Now that a Higgs-like signal has been observed at the LHC the task is to establish whether the particle is indeed the relic of the electroweak symmetry breaking mechanism, and whether it has the properties predicted by the SM or extensions of it. Specifically the question remains whether one or more Higgs bosons exist in nature, and whether the properties of these new state(s) agree with model predictions. 

The DESY theory group is pursuing work in deriving precise predictions for possible manifestations of the electroweak symmetry breaking mechanism at the LHC. In particular, predictions for Higgs boson masses and couplings, Higgs production processes, decay rates and transverse momentum distributions are studied in different models. Furthermore the phenomenology of more exotic models of new physics is investigated, and the interplay of the Higgs sector with other sectors of the new physics scenarios is analysed.

While the Standard Model has proved to be extremely successful in describing all reactions at colliders, there are experimental as well as theoretical arguments suggesting that the SM cannot be the final theory of nature. In particular, the SM does not have a particle candidate for the dark matter in our Universe and cannot explain the observed asymmetry of baryons and anti-baryons. In addition there is a naturalness problem within the Higgs sector of the SM, suggesting new physics to appear at the TeV scale which is currently being probed at high energy colliders. New physics scenarios are developed within the DESY theory group, including supersymmetric theories, compositeness theories, models with more space dimensions, models for dark matter and more. Deviations from the SM are also studied in the model-independent framework of effective field theories. A close collaboration between theory and experiment as well as an efficient exchange between particle physics and cosmology will be necessary to identify what lies beyond the SM.

There is strong gravitational evidence for the existence of a new form of non-baryonic matter in our Universe. The nature of this dark matter is one of the big questions in science today, with implications for particle physics phenomenology as well as astrophysics and cosmology.  The quest for dark matter is therefore inherently multi-disciplinary, providing a natural strong link between the collider phenomenology and cosmology groups at DESY.  In the collider group special emphasis is put on possible collider signatures of dark matter at the LHC but also at high intensity experiments such as Belle II. In order to link such signatures to cosmological and astrophysical observations, a theory of dark matter is required which is another area of active research within this group.

Monte-Carlo event generators are essential tools in high-energy physics, since they provide fully exclusive predictions, incorporating QCD and electroweak effects at all relevant energy scales. The DESY theory group is involved in the active development of many aspects of Monte Carlo event generators, in particular in the context of the WHIZARD, GENEVA, and DEDUCTOR Monte-Carlo generators. The studied topics include the systematic improvement of the theoretical precision of Monte-Carlo generators by matching to NLO and NNLO as well as higher-order resummed calculations, multi-leg matrix elements, new parton-showers algorithms, and more efficient phase-space algorithms. The research also extends to more IT-related topics like massive parallel computing and virtual machines.

While there is solid gravitational evidence for the existence of dark matter (DM), its particle physics properties are unknown.
In many beyond the Standard Model theories, such as in the simplest supersymmetric models, the dark matter candidate corresponds to a weakly interacting massice particle (WIMP) with only a negligible self scattering. Such collisionless cold DM successfully explains cosmological structure formation at large scales. In recent years however there has been an increasing interest in self-interacting DM, which has been invoked to ameliorate tensions between N-body simulations and astrophysical observations on small scales. Within the DESY Cosmology group models for self-interacting DM as well as potential astrophysical signatures are developed. In addition more classical signatures of dark matter at underground direct detection experiments as well as at colliders and telescopes (especially high-energy ones) are studied, creating strong links to the Collider Phenomenology group at DESY and to the astro groups at DESY Zeuthen and at Hamburg University.

In the DESY theory group different mechanisms for the generation of the cosmological matter-antimatter asymmetry are studied: electroweak baryogenesis at the scale of electroweak symmetry breaking, and leptogenesis, which is based on the properties of Majorana neutrinos. In both cases techniques from nonequilibrium quantum field theory are used to obtain a description of baryogenesis beyond the classical Boltzmann equations. A relatively new developement is hereby the attempt to link baryogenesis to flavor model building.

The large scale structure of the Universe are formed by the gravitational collapse of dark and baryonic matter. While this highly non-linear problem is mostly studied by simulations, the largest scales are eventually accessible to analytic methods. These are often based on the resummation of perturbative results or consist of relations that are based symmetry arguments.
 

Inflation, a likely phase of exponential expansion of the universe, provides a successful description of the initial conditions for the present state and of the cosmic microwave background data. However many conceptual problems are still unsolved, especially in the embedding of inflation in wider particle physics models beyond the Standard Model. Particularly promising appear string theories with its "landscape" of vacua. An important prediction of inflation and cosmological phase transitions are primordial gravitational waves. These are observable in the polarization data of the CMB or with space-based interferometers.

Axion-like particles and WISPs (Weakly-Interacting Sub-eV Particles) are predicted in many extentions of the Standard Model and in particular in String Theory. They have the common feature of being very light particles, so they do not need a high energy to be produced, but they are nevertheless very difficult to produce and detect due to their very weak couplings. The main door to investigate this type of particles is via their coupling to the photons, as in light-shining-through-the-wall experiments like ALPS, and via their cosmological consequences. Additional directions involving the coupling to gluons are also being explored.

Supersymmetry and grand unification in four and more dimensions are interesting concepts for embedding the Standard Model of particle physics into a more fundamental theory. These ideas are pursued in the context of heterotic string compactifications, supergravity models in six dimensions and F-theory compactifications.

Gauge theory provides the theoretical framework with which we describe the world we live in. It is very successful as long as particles interact weakly, however, in the strong coupling regime, major theoretical challenges remain unsolved. Our understanding of non-perturbative phenomena, such as confinement, is very limited (see here for a description of the problem), majorly due to the lack of a quantitative understanding of the theory in regimes with strong interactions among gluons and quarks. Supersymmetric gauge theories provide a theoretical laboratory within which we can explore the strong coupling regime of gauge theories and quantitatively understand non-perturbative phenomena. In many cases they even provide examples of theories or observables with can be solved exactly (see here for recent review). What is more, supersymmetric gauge theories are intimately related to string theory. Gauge theories can emerge as low-energy limits of string theories, and string theories can describe gauge theories at strong coupling providing us qualitative tools. This profound interplay is investigated and exploited in our research in order to learn more about gauge theory and string theory in regimes which are very hard to access by more conventional methods.

Scale invariant theories are ubiquitous in the study of quantum field theories, arising naturally in their low energy behaviour. Most physically relevant scale invariant theories are invariant under a larger symmetry, exhibiting conformal symmetry. The study of Conformal Field Theories (CFTs) is also connected with that of string theory in anti-de-Sitter space through a holographic duality (see for example here). The DESY string theory group is actively studying CFTs from different fronts. One such approach is through the so-called conformal bootstrap approach to CFTs, both in two dimensions and beyond, with the latter having seen much progress in recent years (see here for a review of the recent progress on the subject). In short, these are revivals of the old idea that symmetry constraints, allied with general consistency requirements, could be powerful enough to solve theories. The special case of two-dimensional CFTs allows for rich connections to mathematics, and is also an active subject of research, in close collaboration with the mathematics department at the Hamburg University (see here for a recent guide to two-dimensional CFTs).

Exact results in physics are precious, they give us a deeper understanding of the dynamics of a theory, together with strong analytical control. Integrability refers to the presence of additional, often hidden symmetries. Integrable theories turn out to be exactly solvable due to the enhanced symmetry. Such exactly solvable structures appear both in quantum field theory and string theory. Although integrable structures have played an important role in low-dimensional systems, since the early 2000s impressive progress has been made in the uncovering of integrability in higher dimensional field theories. For this reason, the paradigmatic example of 4d maximally supersymmetric Yang-Mills theory has been dubbed “the harmonic oscillator of the 21st century” (see here for a review). The DESY theory group is active in integrability research, with a particular emphasis on bridging the gap to other areas of modern physics, like the theory of scattering amplitudes and the conformal bootstrap program.

Scattering amplitudes form a bridge connecting theoretical particle physics with the real world of collider experiments, yielding the probability of specific outcomes when quantum particles interact. Although their computation by means of Feynman diagrams quickly becomes prohibitive, and is only valid when the particles are interacting weakly, members of the DESY String theory group are making significant progress addressing these shortcomings, also in close contact with their Phenomenology group colleagues: By exploiting the mathematical structure and analytic behavior of amplitudes, as well as the integrability and dual string description of simple gauge-theoretic models, they develop new efficient methods for their computation, all the way from weak to strong interaction strength (see here for a review).