Particle Physics

We consider the production of strongly interacting, heavy SUSY pairs at the LHC. When the centre of mass energy is close to the production threshold of the pair, the corresponding cross sections receive large higher-loop QCD corrections. These corrections are classified as the so-called soft logarithms and Coulomb singularities and they lead to a break down of the usual perturbation expansion. In this talk I review the origin of these large corrections and explain how they can be resummed by using Effective Field theories. Finally, I will present some resummed results for the pair production cross sections of heavy squarks and gluinos. Based on: arXiv:1202.2260 and 1211.3408.

In the past few years, optical cooling and manipulating of macroscopic objects, such as micro-mirrors and cantilevers has developed into an active field of research. In mechanical systems, the oscillator is attached to its suspension, a thermal contact that limits the motion isolation. On the other hand, when these small objects are levitated using the radiation pressure force of lasers, the excellent thermal isolation even at room temperatures helps produce very sensitive force detectors, and eventually quantum transducers for quantum computation purposes. These new techniques may have a variety of applications for fundamental physics such as short distance tests of gravity and gravitational wave detection at high frequencies. In addition, there are several proposals suggesting that optically levitated dielectrics can be cooled to the ground state of the center of mass motion,
opening the exciting possibility of creating macroscopic matter-wave interferometers.

Hexagon functions are a class of iterated integrals, depending on three variables (dual conformal cross ratios) which have the correct branch cut structure and other properties to describe the scattering of six gluons in planar N=4 super-Yang-Mills theory. We classify all hexagon
functions through transcendental weight five, using the coproduct for their Hopf algebra iteratively, which amounts to a set of first-order differential equations.  As an example, the three-loop remainder function is a particular weight-six hexagon function, whose symbol was determined
previously.

The differential equations can be integrated numerically for generic values of the cross ratios, or analytically in certain kinematics limits, including the near-collinear and multi-Regge
limits.  These limits allow us to impose constraints from the operator product expansion and multi-Regge factorization directly at the function level, and thereby to fix uniquely a set of Riemann-Zeta-valued constants that could not be fixed at the level of the symbol. The near-collinear limits agree precisely with recent predictions by Basso, Sever and Vieira based on integrability.  The multi-Regge limits agree with a factorization formula of Fadin and Lipatov, and determine three constants entering the impact factor at this order. We plot the three-loop remainder function for various slices of the Euclidean region of positive cross ratios, and compare it to the two-loop one.  For large ranges of the cross ratios, the ratio of the three-loop to the two-loop remainder function is relatively constant, and close to -7.