Colloquium

Speaker: Lance Dixon (SLAC, Stanford University)

Title: The DNA of Particle Scattering

Abstract: At the Large Hadron Collider, the copious scattering of quarks and gluons in quantum chromodynamics (QCD) produces Higgs bosons and many backgrounds to searches for new physics.  At short distances, scattering in QCD can be evaluated in perturbation theory and leads to highly intricate, multivariate mathematical functions such as generalized polylogarithms.  To gain further insight, one can study a cousin of QCD called planar N=4 super-Yang-Mills theory.  Some processes in this theory can be computed to eighth order in perturbation theory, versus second or third order in QCD.  The computation and analysis of these results rely on a Hopf algebra coaction on polylogarithms.  Its maximal iteration is called the ‘symbol’, which serves as a ‘genetic code’ for amplitudes.  The symbol is a linear combination of words, sequences of letters analogous to sequences of DNA base pairs.  Understanding the alphabet, and then reading the code, exposes the physics and mathematics of quantum scattering, including bizarre new symmetries.  For example, the two scattering amplitudes that are known to the highest orders in perturbation theory (8 loops) are related to each other by an ‘antipodal duality’, which involves reading the code backwards as well as forwards. A third scattering amplitude, which contains the other two as limits, has an antipodal self-duality which ‘explains’ the other duality.  However, we still don’t know ‘who ordered’ this property, or what it really means.