The two-loop four-fermion scattering amplitude in QED

We present the analytic evaluation of the two-loop corrections to the amplitude for the scattering of four fermions in Quantum Electrodynamics, $f^- + f^+ + F^- + F^+ \to 0$, with $f$ and $F$ representing a massless and a massive lepton, respectively. Dimensional regularization is employed to evaluate the loop integrals. Ultraviolet divergences are removed by renormalizing the coupling constant in the ${\overline{\text{MS}}}$-scheme, and the lepton mass as well as the external fields in the on-shell scheme. The analytic result for the renormalized amplitude is expressed as Laurent series around $d=4$ space-time dimensions, and contains Generalized Polylogarithms with up to weight four. The structure of the residual infrared divergences of the virtual amplitude is in agreement with the prediction of the Soft Collinear Effective Theory. Our analytic results are an essential ingredient for the computation of the scattering cross section for massive fermion-pair production in massless fermion-pair annihilation, i.e. $f^- f^+ \to F^- F^+$, and crossing related processes such as the elastic scattering $f F \to f F$, with up to Next-to-Next to Leading Order accuracy.Comment: 5 pages, 2 figures, 1 table + supplemental materia

Two-Loop Four-Fermion Scattering Amplitude in QED

We present the first fully analytic evaluation of the transition amplitude for the scattering of a massless into a massive pair of fermions at the two-loop level in quantum electrodynamics. Our result is an essential ingredient for the determination of the electromagnetic coupling within scattering reactions, beyond the currently known accuracy, which has a crucial impact on the evaluation of the anomalous magnetic moment of the muon. It will allow, in particular, for a precise determination of the leading hadronic contribution to the (g−2)μ in the MUonE experiment at CERN, and therefore can be used to shed light on the current discrepancy between the standard model prediction and the experimental measurement for this important physical observable

A portal of educational resources: providing evidence for matching pedagogy with technology

The TPACK (Technology, Pedagogy and Content Knowledge) model presents the three types of knowledge that are necessary to implement a successful technology-based educational activity. It highlights how the intersections between TPK (Technological Pedagogical Knowledge), PCK (Pedagogical Content Knowledge) and TCK (Technological Content Knowledge) are not a sheer sum up of their components but new types of knowledge. This paper focuses on TPK, the intersection between technology knowledge and pedagogy knowledge – a crucial field of investigation. Actually, technology in education is not just an add-on but is literally reshaping teaching/learning paradigms. Technology modifies pedagogy and pedagogy dictates requirements to technology. In order to pursue this research, an empirical approach was taken, building a repository (back-end) and a portal (front-end) of about 300 real-life educational experiences run at school. Educational portals are not new, but they generally emphasise content. Instead, in our portal, technology and pedagogy take centre stage. Experiences are classified according to more than 30 categories (‘facets’) and more than 200 facet values, all revolving around the pedagogical implementation and the technology used. The portal (an innovative piece of technology) supports sophisticated ‘exploratory’ sessions of use, targeted at researchers (investigating the TPK intersection), teachers (looking for inspiration in their daily jobs) and decision makers (making decisions about the introduction of technology into schools)

Characterisation of Peptide Microarrays for Studying Antibody-Antigen Binding Using Surface Plasmon Resonance Imagery

BACKGROUND: Non-specific binding to biosensor surfaces is a major obstacle to quantitative analysis of selective retention of analytes at immobilized target molecules. Although a range of chemical antifouling monolayers has been developed to address this problem, many macromolecular interactions still remain refractory to analysis due to the prevalent high degree of non-specific binding. We describe how we use the dynamic process of the formation of self assembling monolayers and optimise physical and chemical properties thus reducing considerably non-specific binding and allowing analysis of specific binding of analytes to immobilized target molecules. METHODOLOGY/PRINCIPAL FINDINGS: We illustrate this approach by the production of specific protein arrays for the analysis of interactions between the 65kDa isoform of human glutamate decarboxylase (GAD65) and a human monoclonal antibody. Our data illustrate that we have effectively eliminated non-specific interactions with the surface containing the immobilised GAD65 molecules. The findings have several implications. First, this approach obviates the dubious process of background subtraction and gives access to more accurate kinetic and equilibrium values that are no longer contaminated by multiphase non-specific binding. Second, an enhanced signal to noise ratio increases not only the sensitivity but also confidence in the use of SPR to generate kinetic constants that may then be inserted into van't Hoff type analyses to provide comparative DeltaG, DeltaS and DeltaH values, making this an efficient, rapid and competitive alternative to ITC measurements used in drug and macromolecular-interaction mechanistic studies. Third, the accuracy of the measurements allows the application of more intricate interaction models than simple Langmuir monophasic binding. CONCLUSIONS: The detection and measurement of antibody binding by the type 1 diabetes autoantigen GAD65 represents an example of an antibody-antigen interaction where good structural, mechanistic and immunological data are available. Using SPRi we were able to characterise the kinetics of the interaction in greater detail than ELISA/RIA methods. Furthermore, our data indicate that SPRi is well suited to a multiplexed immunoassay using GAD65 proteins, and may be applicable to other biomarkers

Measurement of the cosmic ray spectrum above 4×10184{\times}10^{18} eV using inclined events detected with the Pierre Auger Observatory

A measurement of the cosmic-ray spectrum for energies exceeding $4{\times}10^{18}$ eV is presented, which is based on the analysis of showers with zenith angles greater than $60^{\circ}$ detected with the Pierre Auger Observatory between 1 January 2004 and 31 December 2013. The measured spectrum confirms a flux suppression at the highest energies. Above $5.3{\times}10^{18}$ eV, the "ankle", the flux can be described by a power law $E^{-\gamma}$ with index $\gamma=2.70 \pm 0.02 \,\text{(stat)} \pm 0.1\,\text{(sys)}$ followed by a smooth suppression region. For the energy ($E_\text{s}$) at which the spectral flux has fallen to one-half of its extrapolated value in the absence of suppression, we find $E_\text{s}=(5.12\pm0.25\,\text{(stat)}^{+1.0}_{-1.2}\,\text{(sys)}){\times}10^{19}$ eV.Comment: Replaced with published version. Added journal reference and DO

Energy Estimation of Cosmic Rays with the Engineering Radio Array of the Pierre Auger Observatory

The Auger Engineering Radio Array (AERA) is part of the Pierre Auger Observatory and is used to detect the radio emission of cosmic-ray air showers. These observations are compared to the data of the surface detector stations of the Observatory, which provide well-calibrated information on the cosmic-ray energies and arrival directions. The response of the radio stations in the 30 to 80 MHz regime has been thoroughly calibrated to enable the reconstruction of the incoming electric field. For the latter, the energy deposit per area is determined from the radio pulses at each observer position and is interpolated using a two-dimensional function that takes into account signal asymmetries due to interference between the geomagnetic and charge-excess emission components. The spatial integral over the signal distribution gives a direct measurement of the energy transferred from the primary cosmic ray into radio emission in the AERA frequency range. We measure 15.8 MeV of radiation energy for a 1 EeV air shower arriving perpendicularly to the geomagnetic field. This radiation energy -- corrected for geometrical effects -- is used as a cosmic-ray energy estimator. Performing an absolute energy calibration against the surface-detector information, we observe that this radio-energy estimator scales quadratically with the cosmic-ray energy as expected for coherent emission. We find an energy resolution of the radio reconstruction of 22% for the data set and 17% for a high-quality subset containing only events with at least five radio stations with signal.Comment: Replaced with published version. Added journal reference and DO

Measurement of the Radiation Energy in the Radio Signal of Extensive Air Showers as a Universal Estimator of Cosmic-Ray Energy

We measure the energy emitted by extensive air showers in the form of radio emission in the frequency range from 30 to 80 MHz. Exploiting the accurate energy scale of the Pierre Auger Observatory, we obtain a radiation energy of 15.8 \pm 0.7 (stat) \pm 6.7 (sys) MeV for cosmic rays with an energy of 1 EeV arriving perpendicularly to a geomagnetic field of 0.24 G, scaling quadratically with the cosmic-ray energy. A comparison with predictions from state-of-the-art first-principle calculations shows agreement with our measurement. The radiation energy provides direct access to the calorimetric energy in the electromagnetic cascade of extensive air showers. Comparison with our result thus allows the direct calibration of any cosmic-ray radio detector against the well-established energy scale of the Pierre Auger Observatory.Comment: Replaced with published version. Added journal reference and DOI. Supplemental material in the ancillary file