**The Theoretical Particle Physics component of the DISCOVERY Center focuses on amplitude computations in gauge theories, structure functions (in particular, small-x physics), and will also explore all possibilities related to the phenomenology of particle physics results from ATLAS. ALICE and the Planck satellite.**

## Amplitude computations in QCD

In order to calculate cross-sections with sufficient precision, amplitudes for QCD processes must be known at least at next-to-leading order. Of great importance are cross-sections for background processes such as four and five jet production at one-loop order, for example proton scatterings resulting in two high-pT quark pairs or electroweak bosons together with high-pT gluons.

In recent years there has been an enormous progress in computations of amplitudes in QCD, but nevertheless many amplitudes still remain undetermined. Perturbative amplitudes in physical theories are traditionally calculated via Feynman diagrams. Calculating loop amplitudes this way is often an extremely cumbersome process when there are many final state particles, since we face factorial growth in complexity as the number of external legs increases. The calculation can involve huge cancellations of diagrams. It is therefore essential to find new computational simplifications that can make cancellations and simplifications in amplitudes manifest from the outset.

This represents a research challenge of significant importance that the DISCOVERY center aims to meet.

## Structure functions and small-x physics

The factorization of hard scattering into perturbatively computable short-distance amplitudes and large-distance structure functions, distribution functions, etc. is one of the cornerstones of perturbative QCD. While the large-distance part is not computable in perturbation theory, the evolution in terms of transverse momentum is. This is an example of one of the predictions of asymptotic freedom, and it has been tested to immense accuracy in a long series of different accelerator experiments. What is new at the LHC is the tremendous change of scale. The theoretical particle physics community is already meeting the challenge by pushing computations deeper into the "small-x" regime probed by the LHC using a combination of all the approaches that are known to tackle the problem.

The cross-section for deep inelastic scattering of neutrinos with energy exceeding 100 GeV is sensitive to small-x gluon dynamics. This is an area of remarkable synergy between nonperturbative QCD and ultra-high energy (UHE) cosmic neutrino physics. The structure functions have been probed at HERA down to x ~ 10^-5 at Q2 ~ 100 GeV^2 and using these, the UHE deep inelastic scattering cross-section can be predicted using the perturbative DGLAP formalism. The forthcoming measurements at the LHC will extend the kinematic range of x and Q^2 further, making the extrapolation far more reliable. When x is sufficiently small so that αslog(1/x) ~ 1, it is necessary to resum these large logarithms using the BFKL formalism.

Whereas such calculations at leading-log suggest an even steeper rise of the gluon structure function at low x (which would imply a higher cross-section), both the DGLAP and the BFKL formalisms neglect non-linear screening effects due to gluon recombination which may lead to saturation of the gluon structure function. A unified BFKL/DGLAP calculation supplemented by estimates of screening and nuclear shadowing effects, predicts a decrease of the cross-section by ~20-100% at very high energies E ~100-10^12 GeV.