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Sanchis-Lozano, M. A., Barbero, J. F., & Navarro-Salas, J. (2012). Prime Numbers, Quantum Field Theory and the Goldbach Conjecture. Int. J. Mod. Phys. A, 27(23), 1250136–24pp.
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.
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Sahin, E. et al, Gadea, A., & Algora, A. (2012). Structure of the N=50 As, Ge, Ga nuclei. Nucl. Phys. A, 893, 1–12.
Abstract: The level structures of the N = 50 As-83, Ge-82, and Ga-81 isotones have been investigated by means of multi-nucleon transfer reactions. A first experiment was performed with the CLARA PRISMA setup to identify these nuclei. A second experiment was carried out with the GASP array in order to deduce the gamma-ray coincidence information. The results obtained on the high-spin states of such nuclei are used to test the stability of the N = 50 shell closure in the region of Ni-78 (Z = 28). The comparison of the experimental level schemes with the shell-model calculations yields an N = 50 energy gap value of 4.7(3) MeV at Z = 28. This value, in a good agreement with the prediction of the finite-range liquid-drop model as well as with the recent large-scale shell model calculations, does not support a weakening of the N = 50 shell gap down to Z = 28.
Keywords: NUCLEAR REACTIONS U-238(Se-82, Ga-81), (Se-82, Ge-82), (Se-82, As-83), E=515 MeV; measured E-gamma, I-gamma (theta), gamma gamma-coin, reaction fragments, (fragment)gamma-coin using PRISMA magnetic spectrometer, gamma after deexcitation using Ge Compton-suppressed detectors of CLARA array, thin and thick target; deduced sigma(theta), levels, J, pi; calculated levels, J, pi using shell model
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Romanets, O., Tolos, L., Garcia-Recio, C., Nieves, J., Salcedo, L. L., & Timmermans, R. G. E. (2012). Charmed and strange baryon resonances with heavy-quark spin symmetry. Phys. Rev. D, 85(11), 114032–30pp.
Abstract: We study charmed and strange baryon resonances that are generated dynamically by a unitary baryon-meson coupled-channel model which incorporates heavy-quark spin symmetry. This is accomplished by extending the SU(3) Weinberg-Tomozawa chiral Lagrangian to SU(8) spin-flavor symmetry plus a suitable symmetry breaking. The model produces resonances with negative parity from s-wave interaction of pseudoscalar and vector mesons with 1/2(+) and 3/2(+) baryons. Resonances in all the isospin, spin, and strange sectors with one, two, and three charm units are studied. Our results are compared with experimental data from several facilities, such as the CLEO, Belle or BABAR collaborations, as well as with other theoretical models. Some of our dynamically-generated states can be readily assigned to resonances found experimentally, while others do not have a straightforward identification and require the compilation of more data and also a refinement of the model. In particular, we identify the Xi(c)(2790) and Xi(c)(2815) resonances as possible candidates for a heavy-quark spin symmetry doublet.
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Roca, L., & Oset, E. (2012). Scattering of unstable particles in a finite volume: The case of pi rho scattering and the a(1)(1260) resonance. Phys. Rev. D, 85(5), 054507–13pp.
Abstract: We present a way to evaluate the scattering of unstable particles quantized in a finite volume with the aim of extracting physical observables for infinite volume from lattice data. We illustrate the method with the pi rho scattering which generates dynamically the axial-vector a(1)(1260) resonance. Energy levels in a finite box are evaluated both considering the rho as a stable and unstable resonance and we find significant differences between both cases. We discuss how to solve the problem to get the physical scattering amplitudes in the infinite volume, and hence phase shifts, from possible lattice results on energy levels quantized inside a finite box.
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Restrepo, D., Taoso, M., Valle, J. W. F., & Zapata, O. (2012). Gravitino dark matter and neutrino masses with bilinear R-parity violation. Phys. Rev. D, 85(2), 023523–7pp.
Abstract: Bilinear R-parity violation provides an attractive origin for neutrino masses and mixings. In such schemes the gravitino is a viable decaying dark matter particle whose R-parity violating decays lead to monochromatic photons with rates accessible to astrophysical observations. We determine the parameter region allowed by gamma-ray line searches, dark matter relic abundance, and neutrino oscillation data, obtaining a limit on the gravitino mass m((G) over tilde) less than or similar to 1-10 GeV corresponding to a relatively low reheat temperature T-R less than or similar to few x 10(7)-10(8) GeV. Neutrino mass and mixing parameters may be reconstructed at accelerator experiments like the Large Hadron Collider.
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