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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Baker, M. J., Bordes, J., Hong-Mo, C., & Tsun, T. S. (2012). Developing the Framed Standard Model. Int. J. Mod. Phys. A, 27(17), 1250087–45pp.
Abstract: The framed standard model (FSM) suggested earlier, which incorporates the Higgs field and three fermion generations as part of the framed gauge theory (FGT) structure, is here developed further to show that it gives both quarks and leptons hierarchical masses and mixing matrices akin to what is experimentally observed. Among its many distinguishing features which lead to the above results are (i) the vacuum is degenerate under a global su(3) symmetry which plays the role of fermion generations, (ii) the fermion mass matrix is “universal,” rank-one and rotates (changes its orientation in generation space) with changing scale mu, (iii) the metric in generation space is scale-dependent too, and in general nonflat, (iv) the theta-angle term in the quantum chromodynamics (QCD) action of topological origin gets transformed into the CP-violating phase of the Cabibbo-Kobayashi-Maskawa (CKM) matrix for quarks, thus offering at the same time a solution to the strong CP problem.
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ATLAS Collaboration(Aad, G. et al), Amoros, G., Cabrera Urban, S., Castillo Gimenez, V., Costa, M. J., Escobar, C., et al. (2012). Measurements of the electron and muon inclusive cross-sections in proton-proton collisions at root s=7 TeV with the ATLAS detector. Phys. Lett. B, 707(5), 438–458.
Abstract: This Letter presents measurements of the differential cross-sections for inclusive electron and muon production in proton-proton collisions at a centre-of-mass energy of root s = 7 TeV, using data collected by the ATLAS detector at the LHC. The muon cross-section is measured as a function of p(T) in the range 4 < p(T) < 100 GeV and within pseudorapidity vertical bar eta vertical bar < 2.5. In addition the electron and muon cross-sections are measured in the range 7 < p(T) < 26 GeV and within vertical bar eta vertical bar < 2.0, excluding 1.37 < vertical bar eta vertical bar < 1.52. Integrated luminosities of 1.3 pb(-1) and 1.4 pb(-1) are used for the electron and muon measurements, respectively. After subtraction of the W/Z/gamma* contribution, the differential cross-sections are found to be in good agreement with theoretical predictions for heavy-flavour production obtained from Fixed Order NLO calculations with NLL high-p(T) resummation, and to be sensitive to the effects of NLL resummation.
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ATLAS Collaboration(Aad, G. et al), Cabrera Urban, S., Castillo Gimenez, V., Costa, M. J., Ferrer, A., Fiorini, L., et al. (2012). Measurement of the b-hadron production cross section using decays to D*(+)mu X- final states in pp collisions at root s=7 TeV with the ATLAS detector. Nucl. Phys. B, 864(3), 341–381.
Abstract: The b-hadron production cross section is measured with the ATLAS detector in pp collisions at root s = 7 TeV, using 3.3 pb(-1) of integrated luminosity, collected during the 2010 LHC run. The b-hadrons are selected by partially reconstructing D*(+)mu X- final states. Differential cross sections are measured as functions of the transverse momentum and pseudorapidity. The measured production cross section for a b-hadron with p(T) > 9 GeV and vertical bar eta vertical bar < 2.5 is 32.7 +/- 0.8(stat.)(-6.8)(+4.5)(syst.) μb, higher than the next-to-leading-order QCD predictions but consistent within the experimental and theoretical uncertainties.
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Kleiss, R. H. P., Malamos, I., Papadopoulos, C. G., & Verheyen, R. (2012). Counting to one: reducibility of one- and two-loop amplitudes at the integrand level. J. High Energy Phys., 12(12), 038–24pp.
Abstract: Calculation of amplitudes in perturbative quantum field theory involve large loop integrals. The complexity of those integrals, in combination with the large number of Feynman diagrams, make the calculations very difficult. Reduction methods proved to be very helpful, lowering the number of integrals that need to be actually calculated. Especially reduction at the integrand level improves the speed and set-up of these calculations. In this article we demonstrate, by counting the numbers of tensor structures and independent coefficients, how to write such relations at the integrand level for one-and two-loop amplitudes. We clarify their connection to the so-called spurious terms at one loop and discuss their structure in the two-loop case. This method is also applicable to higher loops, and the results obtained apply to both planar and non-planar diagrams.
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