High energy physics strives to understand the fundamental building blocks of nature. The masses of elementary particles and the exact strength of the forces between them play a key role in the evolution of the universe from the Big Bang to its appearance today. However, the origin of the mass remains a mystery. Our best assumption today relates the origin of the mass to a yet undiscovered particle, the famous “Higgs boson”.

To solve this riddle, a new collider is presently under construction (LHC at CERN, Geneva) and others are in the planning stage (ILC). However, to fully exploit the scientific potential of these machines, experimentalists need precise predictions from theory. Precise predictions are necessary to dig out signals of new particles and phenomena from the bulk of known physics.

An important tool in phenomenology is perturbation theory: Accurate results often require the inclusion of the second or third term of the perturbative expansion. Beyond leading order in the perturbative expansion, these calculations are highly non-trivial and lead to interesting connections with mathematics and computer algebra.

**Precision calculations in particle physics**

Examples of predictions for specific processes:

- The forward-backward asymmetry in electron-positron annihilation
- 4-jet observables in electron-positron annihilation
- Single top production at hadron colliders
- Top pair production in association with a jet at hadron colliders

Development of tools and techniques:

- NNLO calculations
- Automatization of NLO calculations
- Parton showers

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**Mathematical physics**

Scattering amplitudes reveal interesting mathematical structures:

- Multiple polylogarithms
- Twistor space

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**Computer algebra**

The calculation of loop amplitudes in particle physics is nowadays done with computer algebra and puts special requirements on computer algebra systems: On the one hand large amounts of data need to be handled by the system, on the other hand it has to be possible to program sophisticated algorithms in the language of the computer algebra system. To meet these goals, the dedicated computer algebra system “GiNaC” has been developed at Mainz University. The user community of this program extends now worldwide and far beyond the particle physics community:

- GiNaC
- gTybalt – A graphical font-end to GiNaC
- The nestedsums library – Symbolic expansion of transcendental functions.

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