Abstract: Motivated by the Goldbach conjecture in number theory and the Abelian bosonization mechanism on a cylindrical two-dimensional space-time, we study the reconstruction of a real scalar field as a product of two real fermion (so-called prime) fields whose Fourier expansion exclusively contains prime modes. We undertake the canonical quantization of such prime fields and construct the corresponding Fock space by introducing creation operators b(p)(dagger) – labeled by prime numbers p – acting on the vacuum. The analysis of our model, based on the standard rules of quantum field theory and the assumption of the Riemann hypothesis, allows us to prove that the theory is not renormalizable. We also comment on the potential consequences of this result concerning the validity or breakdown of the Goldbach conjecture for large integer numbers.

Abstract: We argue that the quantum nature of matter and gravity should lead to a discretization of the allowed states of the matter confined in the interior of black holes. To support and illustrate this idea, we consider a quadratic extension of general relativity (GR) formulated a la Palatini and show that nonrotating, electrically charged black holes develop a compact core at the Planck density which is nonsingular if the mass spectrum satisfies a certain discreteness condition. We also find that the area of the core is proportional to the number of charges times the Planck area.

Abstract: Recent experimental results and developments in the theoretical treatment of neutrino-nucleus interactions in the energy range of 1-10 GeV are discussed. Difficulties in extracting neutrino-nucleon cross sections from neutrino-nucleus scattering data are explained and significance of understanding nuclear effects for neutrino oscillation experiments is stressed. Detailed discussions of the status of two-body current contribution in the kinematic region dominated by quasielastic scattering and specific features of partonic nuclear effects in weak DIS scattering are presented.

Abstract: We discuss constraints on the coefficient A(MSW) which is introduced to simulate the effect of weaker or stronger matter potential for electron neutrinos with the current and future solar neutrino data. The currently available solar neutrino data leads to a bound A(MSW) = 1.47(+0.54)(-0.42)((-0.82)(+1.88)) at 1 sigma (3 sigma) CL, which is consistent with the Standard Model prediction A(MSW) = 1. For weaker matter potential (A(MSW) < 1), the constraint which comes from the flat B-8 neutrino spectrum is already very tight, indicating the evidence for matter effects. However for stronger matter potential (A(MSW) > 1), the bound is milder and is dominated by the day-night asymmetry of B-8 neutrino flux recently observed by Super-Kamiokande. Among the list of observables of ongoing and future solar neutrino experiments, we find that (1) an improved precision of the day-night asymmetry of B-8 neutrinos, (2) precision measurements of the low-energy quasi-monoenergetic neutrinos, and (3) the detection of the upturn of the B-8 neutrino spectrum at low energies are the best choices to improve the bound on A(MSW).

Abstract: This Letter presents a search for magnetic monopoles with the ATLAS detector at the CERN Large Hadron Collider using an integrated luminosity of 2.0 fb(-1) of pp collisions recorded at a center-of-mass energy root s = 7 TeV. No event is found in the signal region, leading to an upper limit on the production cross section at 95% confidence level of 1.6/epsilon fb for Dirac magnetic monopoles with the minimum unit magnetic charge and with mass between 200 GeV and 1500 GeV, where epsilon is the monopole reconstruction efficiency. The efficiency epsilon is high and uniform in the fiducial region given by pseudorapidity vertical bar eta vertical bar < 1: 37 and transverse kinetic energy 600-700<E-kin sin theta< 1400 GeV. The minimum value of 700 GeV is for monopoles of mass 200 GeV, whereas the minimum value of 600 GeV is applicable for higher mass monopoles. Therefore, the upper limit on the production cross section at 95% confidence level is 2 fb in this fiducial region. Assuming the kinematic distributions from Drell-Yan pair production of spin-1= 2 Dirac magnetic monopoles, the efficiency is in the range 1%-10%, leading to an upper limit on the cross section at 95% confidence level that varies from 145 fb to 16 fb for monopoles with mass between 200 GeV and 1200 GeV. This limit is weaker than the fiducial limit because most of these monopoles lie outside the fiducial region.