# Researchers solve the problem of the dimensions of space-time in theories relating to the Large Hadron Collider

Researchers at the universities of Valencia and Florence propose an approach to the experimental data generated by the Large Hadron Collider that solves the infinity problem without breaching the four dimensions of space-time.

The theories currently used to interpret the data emerging from CERN’s Large Hadron Collider (LHC), which have so far most notably led to the discovery of the Higgs boson, are poorly defined within the four dimensions of space-time established by Einstein in his Theory of Special Relativity. In order to avoid the infinities resulting from the calculations that these theories inspire, new dimensions are added in a mathematical trick which, although effective, does not reflect what we now know about our Universe.

Now though, a group of researchers at the Institute of Corpuscular Physics (IFIC, CSIC-UV) in Valencia has devised a way to side-step the infinity issue and keep the theory within the bounds of the four standard dimensions of space-time.

The crux of the issue lies in the fact that it is theoretically possible for particles with zero energy to be produced in LHC collisions, not to be confused with another problematic theoretical outcome of zero particle emissions. A similar issue arises when two particles are produced in exactly the same direction: they are indistinguishable from a single particle. Another of the problems with existing theories derives from the need to apply quantum corrections to their calculations, which requires the validity of the theories to be extrapolated to infinite energies, never reached in a particle accelerator. However, these situations are hard to reconcile with the theory and doing so has a price: the issue of infinity in the four dimensions of space-time. Infinities do not work well with theoretical predictions.

As mentioned above, the solution, found in 1972 by Nobel Prize winners Gerardus’ t Hooft and Martinus J. G. Veltman, was to alter the dimensions of space-time. Known as Dimensional Regularization, it consists of defining the theory in a space-time that has more than four dimensions. That way, the infinities that emerge in four dimensions become contributions that depend on their dimensional difference with respect to four. It is a mathematical trick that deals with these infinities in the intermediate stages of the calculations, allowing predictions to be made that would otherwise be impossible.

But today, a group of researchers from the University of Valencia, led by Germán Rodrigo, has devised a new approach that redefines the theory in a way that avoids the infinity issue and keeps it within the bounds of the four standard dimensions of space-time. It entails a fundamental change in the way the predictions used to interpret LHC experimental data are obtained, simplifying the underlying calculations and solving one of the main problems faced by particle physicists when moving from theory to experiment.

Their approach is based on establishing a direct correspondence between different Feynman diagrams that generate infinities. These diagrams, proposed by Nobel Prize winner Richard P. Feynman in 1965, are used by physicists to pictorially represent the collisions produced between subatomic particles at very high energies in large particle accelerators like the LHC.

Known as the ‘loop-tree duality’, this new relationship of correspondence developed by IFIC researchers, in collaboration with a University of Florence research group led by Stefano Catani, unifies quantum states which, for theoretical purposes, are different but which experimentally are not, like those commented above.

The new algorithm was presented by IFIC researcher Germán Sborlini at the top particle physics conference, ICHEP 2016, held early last August in Chicago. It has also been published in *Journal of High Energy Physics*.

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