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# Phenomenology of Elementary Particles

at Particle Colliders

The physics program of the LHC does not only intend to answer some of the most pressing open questions in elementary particle physics, but will also significantly impact other fields such as astroparticle physics, cosmology, and mathematical string theory. A planned future e+e- linear collider, also called International Linear Collider (ILC), offers high-precision studies within a clean environment of a lepton collider and will deepen our understanding of the physics discovered at the LHC. On the road to an understanding of the origin of matter and its interactions the LHC will for sure deliver answers or new insight in the following key questions:

• What are the constituents of matter and which properties do they have?

The presently known periodic system of elementary particles comprises three generations of quarks and leptons, which interact by exchanging gauge bosons, the carriers of strong and electroweak forces. The deeper reason for this particle spectrum and, in particular, the existence of three generations still remains a mystery, in spite of the success of the Standard Model (SM) which describes the strong and electroweak interactions empirically very well. A theory that is supposed to be more fundamental than the SM has to explain the number of generations and to some extent also the mass pattern of the matter constituents. The LHC will deepen our knowledge on the conceivable existence of further generations and on the relevant particle properties (masses and mixing parameters). Specifically, the LHC will act as a top-quark factory, so that the properties of the heaviest known particle, the top-quark, can be determined with high precision. The top-quark is expected to play a key role in any fundamental theory of flavour physics.

• What is the origin of mass?

The guiding principle in the construction of successful theories for the strong and electroweak interactions is provided by the notion of local gauge invariance. Formulated as quantum field theories, these gauge theories predict spin-1 vector bosons as mediators of the interactions. However, in its puritanical formulation the gauge theory predicts such gauge bosons to be massless; even fermionic matter should be massless if parity (the mirror symmetry'') is not respected, as it is observed in the weak interaction. To conform with the experimental results that the weak gauge bosons $W^\pm$ and $Z^0$ are massive and that chiral massive fermions exist, we are forced to assume that the underlying gauge symmetry of electroweak interaction is spontaneously broken down to the electromagnetic gauge symmetry. A deeper reason for this is not known. In the SM, electroweak symmetry breaking is modelled by the Higgs mechanism, where particles receive mass upon interacting with the omnipresent vacuum expectation value of the postulated Higgs field. At the same time, the theory requires that this Higgs field can be excited in particle modes, i.e. a physical Higgs boson is predicted. In July 2012 the LHC experiments discovered a new particle which is (to this date) compatible with the SM Higgs boson. The experimental results coming from the LHC in the next years will show whether this Higgs boson looks perfectly SM like or provides evidence for physics beyond the SM. Since any trace of a new structure beyond the SM seems to hide in small and subtle effects, "precision" in theory and experiment will be the key to uncover it.

• What are the underlying symmetries that govern particle interaction, is there a unification of electroweak and strong forces?

Up to particle energies of the electroweak scale, which is of the order of the heaviest known elementary particles (top-quark, $Z^0$ and $W^\pm$ bosons), the underlying gauge symmetries of the strong and electroweak interactions look independent. The analogy in the underlying symmetry principles as well as the behaviour of the coupling strengths with rising energies suggest a unification of these forces in the framework of a larger gauge symmetry at a much higher energy scale. The larger symmetry and its realization cannot be predicted, but various types of models can be constructed. All these models predict further heavy gauge bosons, such as heavier copies of the $W$ and $Z$ bosons (known as $W'$ and $Z'$) or more exotic lepto-quarks'', which can turn leptons into quarks and vice versa. As a particle collider at the energy frontier, the LHC will enormously extend our knowledge on the (non-)existence of such particles up to energies of several TeV and will, thus, favour or disfavour different roads to the unification of forces.

• What is the space-time structure at small distances?

The SM, which reflects our empirical understanding, ignores effects of gravity in particle interactions and assumes that both (internal) gauge symmetries and the space-time symmetry are mathematically realized by ordinary groups. The question inhowfar, or whether at all, these assumptions hold are fundamental. In fact it is mathematically conceivable that more than four space-time dimensions exist that do not extend to macroscopic distances, but have a finite extension that is seen only by elementary particles at high energies. The LHC is able to probe such models of extra dimensions and, thus, has a great impact on unified theories that include gravity. On the other hand, the realization of space-time symmetry via the Poincar\'e group can be generalized by allowing for supersymmetry'', where a new symmetry relation between bosons and fermions is introduced. The LHC will be able to widely establish or to rule out at least the minimal supersymmetric extension of the SM, where the particle content of the SM is roughly doubled. The question of whether our world is supersymmetric or not is essential in the construction of fundamental unified theories, as for instance aimed at in string theory.

• What is the nature of dark matter?

Astrophysical observations of recent years established a significant deviation to expectations based on the standard theories of particle physics, gravity, and cosmology. Galactic observations, from rotations of spiral galaxies to the formation of clusters of galaxies, cannot be explained by gravitational effects of the visible matter alone, but strongly support the existence of dark matter''. Thus, particle physics models beyond the SM should provide a dark matter candidate: an electrically neutral, colourless, heavy particle. For instance, supersymmetric extensions, such as the above-mentioned minimal model, provide such candidates at least if appropriate assumptions on underlying symmetries are made. If dark matter particles have masses of the order of the TeV scale, the LHC will surely discover them. Only their production in a controllable environment of accelerator experiments can reveal the true nature of dark matter particles.

To answer all these questions with measurements made at the LHC, i.e. within the extremely complicated environment of a high-energy hadron collider, is highly ambitious. On the experimental side, the reconstruction of any interesting'' particle is like the famous search for the needle in a haystack, but with blinded eyes. On the theoretical side, precise predictions both for the aimed signal processes and for the corresponding background reactions are mandatory, together with the corresponding error estimates. Predictions that are merely based on the leading perturbative order are of only qualitative nature, while quantitative results require the inclusion of higher perturbative orders. At least corrections of next-to-leading order (NLO) in the strong coupling constant have to be included in solid predictions, but for several important reactions NLO electroweak and next-to-next-to-leading order (NNLO) QCD corrections are required. Since practically all interesting particles are unstable, their production processes (signal and background) lead to many-particle final states, representing another theoretical complication. In spite of the great theoretical progress achieved in perturbative calculations in recent years and decades, we are not yet in the position that all necessary predictions for the LHC can be carried out with present tools and concepts up to the necessary precision. On the one hand, we have to further develop existing and to work out new techniques to algebraically and numerically evaluate radiative corrections fast and reliably. On the other hand, these goals can only be reached if our general understanding of quantum field theory can be pushed to a higher level.

In our working group we cover the following phenomenological issues:

• Precision physics with electroweak gauge bosons at the LHC and ILC
• Higgs boson production at the LHC and ILC
• Electroweak and QCD radiative corrections
• NLO corrections to multi-particle processes
• Phenomenology of supersymmetric theories