New methods for precision predictions at the LHC

Experiments carried out during the first phase of the Large Hadron Collider (LHC) have produced one of the most fundamental discoveries in recent times through the observation of the Higgs boson. Predicted more than 50 years ago this last missing ingredient of the Standard Model offers an explanation for the origin of mass and electro-weak forces. Despite this, the origins of the Standard Model and it's place within models for cosmological and astrophysical observations remain unclear.

The second phase of the LHC, which runs until 2018 at twice the energy of phase one, aims to study the properties of this new boson and uncover the true structure of the electro-weak symmetry breaking scale. Astrophysical and cosmological observations predict new forms of matter and energy as yet unexplained by the Standard Model and there are many conjectured theories which point towards new physics around the electro-weak scale at an energy of 1-2 TeV.

Studies of the data from run I of the LHC indicate the expected signals of new physics may be harder to find than originally hoped and it is for this reason that precision predictions and detailed analyses will become the focus for future LHC experiments. The project "New methods for precision predictions at the LHC" addresses the need for new theoretical tools which currently limit our ability to make precision predictions at hadron colliders like the LHC.

Hadron colliders produce huge amounts of strongly interacting radiation that must be precisely modelled if we hope to find the tiny signatures that high energy models of new physics predict. This is an extremely challenging task within the framework of Quantum-Chromo-Dynamics (QCD), our model for the strong interaction, where even perturbative approximations quickly run into areas pushing the boundaries of mathematics and computational power. Owing to the relatively large size of the strong coupling constant, high order expansions within QCD are required in order to keep the theoretical uncertainties under control and in line with the experimental errors.

Despite these challenges remarkable progress has been made in recent years that now allow predictions at next-to-leading order in the pertubative expansion to be made for a wide variety of different processes. A particular highlight of these developments is the ability to look at high multiplicity processes which give access to much more flexible analyses. However, these methods are restricted to an accuracy of between 10 and 20% which is above the projected precision expected from phase two collisions. In order to make sure the theory is ready to handle the new data we must now focus on finding new solutions for higher multiplicity QCD predictions at higher order in perturbation theory and push predictions towards 5% precision.

New mathematical methods developing through formal studies of super-symmetric theories can offer elegant solutions to the problems of computational complexity. To apply these techniques to the QCD environment requires significant extensions however and high degrees of automation and we will develop state-of-the-art analytic tools to compute the necessary amplitude level ingredients. Elements of algebraic geometry and number theory are finding their first applications outside pure mathematics in these studies and the research gives us the opportunity for fruitful discussions between the two disciplines.

A small group will be established within the expert theory group at the University of Edinburgh to study the application of new mathematical techniques in QCD and SM theory. These ideas will be implemented inside public codes that can be used in future experimental analyses when interfaced to Monte-Carlo event generators use to simulate the collisions. By focusing on the theoretical and mathematical techniques now we will be able to perform flexible phenomenological studies of the Standard Model and beyond in the next decade of LHC experiments.

Research into fundamental science has an important affect in a wide context since it forces us to ask
difficult questions. The solutions are often remarkable and can have unexpected consequences beyond
the direct scientific benefits. In the following points I identify an number of more specific ways
in which this project may impact other areas of research on a larger scale.

Firstly, the project offers students an opportunity to work at the cutting edge of high energy physics
which helps to attract bright young students into mathematical fields. The problem solving skills and
technical ability learned of the course of their studies are suitable for a wide range of careers outside
of academia.

High energy physics research is a very international field that often demands a high degree
of collaboration between scientists from different areas. Communications with experimental high energy
physicists are essential for our work and both parties develop their ideas on what can be achieved
based on these discussions.

A unique part of the current proposal is the link between research into pure mathematics and applications
in collider physics. This link has been an interesting development in the last few years as researchers
in algebraic geometry and number theory have discovered physicists trying to apply their methods. Questions
from both sides have affected the development of integral calculus and and understanding of the special
functions the appear in quantum field theory amplitudes. Conferences and workshops that allow the two
fields to meet and discuss will play an important role in the development of the project.

Another area of potential impact is in the development of high performance computing software. Since
QCD simulations push the boundaries of available computing resources testing new technologies to their
limit is often a part of our research. This project has a strong focus on computer algebra software
which has rather different requirements to the high level of parallelization utilised by the experimental
simulations.