From Euler's play with infinite series to the anomalous magnetic moment

During a first St. Petersburg period Leonhard Euler, in his early twenties, became interested in the Basel problem: summing the series of inverse squares (posed by Pietro Mengoli in mid 17th century). In the words of Andre Weil (1989) "as with most questions that ever attracted his attention, he never abandoned it". Euler introduced on the way the alternating "phi-series", the better converging companion of the zeta function, the first example of a polylogarithm at a root of unity. He realized - empirically! - that odd zeta values appear to be new (transcendental?) numbers. It is amazing to see how, a quarter of a millennium later, the numbers Euler played with, "however repugnant" this game might have seemed to his contemporary lovers of the "higher kind of calculus", reappeared in the analytic calculation of the anomalous magnetic moment of the electron, the most precisely calculated and measured physical quantity. Mathematicians, inspired by ideas of Grothendieck, are reviving the dream of Galois of uncovering a group structure in the ring of periods (that includes the multiple zeta values) - applied to the study of Feynman amplitudes.Comment: v.2: minor corrections, references adde

Constraining SUSY models with Fittino using measurements before, with and beyond the LHC

We investigate the constraints on Supersymmetry arising from available precision measurements using a global fit approach. When interpreted within minimal supergravity (mSUGRA), the data provide significant constraints on the masses of supersymmetric particles, which are predicted to be light enough for an early discovery at the Large Hadron Collider (LHC). We provide predicted mass spectra including, for the first time, full uncertainty bands. The most stringent constraint is from the measurement of the anomalous magnetic moment of the muon. Using the results of these fits, we investigate to which precision mSUGRA and more general MSSM parameters can be measured by the LHC experiments with three different integrated luminosities for a parameter point which approximately lies in the region preferred by current data. The impact of the already available measurements on these precisions, when combined with LHC data, is also studied. We develop a method to treat ambiguities arising from different interpretations of the data within one model and provide a way to differentiate between values of different digital parameters of a model. Finally, we show how measurements at a linear collider with up to 1 TeV centre-of-mass energy will help to improve precision by an order of magnitude.Comment: submitted to EPJ