Doubly virtual Compton scattering and the beam normal spin asymmetry

We construct an invariant basis for Compton scattering with two virtual photons (VVCS). The basis tensors are chosen to be gauge invariant and orthogonal to each other. The properties of the corresponding 18 invariant amplitudes are studied in detail. We consider the special case of elastic VVCS with the virtualities of the initial and final photons equal. The invariant basis for VVCS in this orthogonal form does not exist in the literatur. We furthermore use this VVCS tensor for a calculation of the beam normal spin asymmetry in the forward kinematics. For this, we relate the invariant amplitudes to the helicity amplitudes of the VVCS reaction. The imaginary parts of these latter are related to the inclusive cross section by means of the optical theorem. We use the phenomenological value of the transverse cross section $\sigma_T\sim0.1$ mbarn and the Callan-Gross relation which relates the longitudinal cross section $\sigma_L$ to the transverse one. The result of the calculation agrees with an existing calculation and predicts the negative values of the asymmetry $B_n$ of the order of 4-6 ppm in the energy range from 6 to 45 ppm and for very forward angles.Comment: 13 pages, 2 figures, revtex, submitted to Phys. Rev. C; new version: two figures added, typos correcte

Leptonic contribution to the effective electromagnetic coupling constant up to three loops

In this note the leptonic contribution to the running of the electromagnetic coupling constant is discussed up to the three-loop level. Special emphasize is put on the evaluation of the double-bubble diagrams.Comment: 5 pages (Latex) 2 figure

IST Austria Thesis

In this thesis we present a computer-aided programming approach to concurrency. Our approach helps the programmer by automatically fixing concurrency-related bugs, i.e. bugs that occur when the program is executed using an aggressive preemptive scheduler, but not when using a non-preemptive (cooperative) scheduler. Bugs are program behaviours that are incorrect w.r.t. a specification. We consider both user-provided explicit specifications in the form of assertion statements in the code as well as an implicit specification. The implicit specification is inferred from the non-preemptive behaviour. Let us consider sequences of calls that the program makes to an external interface. The implicit specification requires that any such sequence produced under a preemptive scheduler should be included in the set of sequences produced under a non-preemptive scheduler. We consider several semantics-preserving fixes that go beyond atomic sections typically explored in the synchronisation synthesis literature. Our synthesis is able to place locks, barriers and wait-signal statements and last, but not least reorder independent statements. The latter may be useful if a thread is released to early, e.g., before some initialisation is completed. We guarantee that our synthesis does not introduce deadlocks and that the synchronisation inserted is optimal w.r.t. a given objective function. We dub our solution trace-based synchronisation synthesis and it is loosely based on counterexample-guided inductive synthesis (CEGIS). The synthesis works by discovering a trace that is incorrect w.r.t. the specification and identifying ordering constraints crucial to trigger the specification violation. Synchronisation may be placed immediately (greedy approach) or delayed until all incorrect traces are found (non-greedy approach). For the non-greedy approach we construct a set of global constraints over synchronisation placements. Each model of the global constraints set corresponds to a correctness-ensuring synchronisation placement. The placement that is optimal w.r.t. the given objective function is chosen as the synchronisation solution. We evaluate our approach on a number of realistic (albeit simplified) Linux device-driver benchmarks. The benchmarks are versions of the drivers with known concurrency-related bugs. For the experiments with an explicit specification we added assertions that would detect the bugs in the experiments. Device drivers lend themselves to implicit specification, where the device and the operating system are the external interfaces. Our experiments demonstrate that our synthesis method is precise and efficient. We implemented objective functions for coarse-grained and fine-grained locking and observed that different synchronisation placements are produced for our experiments, favouring e.g. a minimal number of synchronisation operations or maximum concurrency

SS-arithmetic (co)homology and pp-adic automorphic forms

We study the $S$-arithmetic (co)homology of reductive groups over number fields with coefficients in (duals of) certain locally algebraic and locally analytic representations for finite sets of primes $S$. We use our results to construct eigenvarieties associated to parabolic subgroups at places in $S$ and certain classes of supercuspidal and algebraic representations of their Levi factors. We show that these agree with eigenvarieties constructed using overconvergent homology and that for definite unitary groups they are closely related to the Bernstein eigenvarieties constructed by Breuil-Ding.Comment: 85 pages. Comments are welcom