Particle theory

Abstract:

© 2020, The Author(s). The Neutrino Mass Ordering (NMO) remains one of the outstanding questions in the field of neutrino physics. One strategy to measure the NMO is to observe matter effects in the oscillation pattern of atmospheric neutrinos above ∼1GeV, as proposed for several next-generation neutrino experiments. Moreover, the existing IceCube DeepCore detector can already explore this type of measurement. We present the development and application of two independent analyses to search for the signature of the NMO with three years of DeepCore data. These analyses include a full treatment of systematic uncertainties and a statistically-rigorous method to determine the significance for the NMO from a fit to the data. Both analyses show that the dataset is fully compatible with both mass orderings. For the more sensitive analysis, we observe a preference for normal ordering with a p-value of pIO= 15.3 % and CL s= 53.3 % for the inverted ordering hypothesis, while the experimental results from both analyses are consistent within their uncertainties. Since the result is independent of the value of δCP and obtained from energies Eν≳5GeV, it is complementary to recent results from long-baseline experiments. These analyses set the groundwork for the future of this measurement with more capable detectors, such as the IceCube Upgrade and the proposed PINGU detector.

Abstract:

We investigate different approaches to machine learning of line bundle cohomology on complex surfaces as well as on Calabi-Yau three-folds. Standard function learning based on simple fully connected networks with logistic sigmoids is reviewed and its main features and shortcomings are discussed. It has been observed recently that line bundle cohomology can be described by dividing the Picard lattice into certain regions in each of which the cohomology dimension is described by a polynomial formula. Based on this structure, we set up a network capable of identifying the regions and their associated polynomials, thereby effectively generating a conjecture for the correct cohomology formula. For complex surfaces, we also set up a network which learns certain rigid divisors which appear in a recently discovered master formula for cohomology dimensions.