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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Bordes, J., Chan, H. M., & Tsun, T. S. (2010). A solution to the strong CP problem transforming the theta angle to the KM CP-violating phase. Int. J. Mod. Phys. A, 25(32), 5897–5911.
Abstract: It is shown that in the scheme with a rotating fermion mass matrix (i.e. one with a scale-dependent orientation in generation space) suggested earlier for explaining fermion mixing and mass hierarchy, the theta angle term in the QCD action of topological origin can be eliminated by chiral transformations, while giving still nonzero masses to all quarks. Instead, the effects of such transformations get transmitted by the rotation to the CKM matrix as the KM phase giving, for theta of order unity, a Jarlskog invariant typically of order 10(-5), as experimentally observed. Strong and weak CP violations appear then as just two facets of the same phenomenon.
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Baker, M. J., Bordes, J., Hong-Mo, C., & Tsun, T. S. (2013). A comprehensive mechanism reproducing the mass and mixing parameters of quarks and leptons. Int. J. Mod. Phys. A, 28(16), 1350070–29pp.
Abstract: It is shown that if, from the starting point of a universal rank-one mass matrix long favored by phenomenologists, one adds the assumption that it rotates (changes its orientation in generation space) with changing scale, one can reproduce, in terms of only six real parameters, all the 16 mass ratios and mixing parameters of quarks and leptons. Of these 16 quantities so reproduced, 10 for which data exist for direct comparison (i.e. the CKM elements including the CP-violating phase, the angles theta(12), theta(13), theta(23) in nu-oscillation, and the masses m(c), m(mu), m(e)) agree well with experiment, mostly to within experimental errors; four others (m(s), m(u), m(d), m(nu 2)), the experimental values for which can only be inferred, agree reasonably well; while two others (m(nu 1), delta(CP) for leptons), not yet measured experimentally, remain as predictions. In addition, one gets as bonuses, estimates for (i) the right-handed neutrino mass m(nu R) and (ii) the strong CP angle theta inherent in QCD. One notes in particular that the output value for sin(2) 2 theta(13) from the fit agrees very well with recent experiments. By inputting the current experimental value with its error, one obtains further from the fit two new testable constraints: (i) that theta(23) must depart from its “maximal” value: sin(2) 2 theta(23) similar to 0.935 +/- 0.021, (ii) that the CP-violating (Dirac) phase in the PMNS would be smaller than in the CKM matrix: of order only vertical bar sin delta(CP)vertical bar <= 0.31 if not vanishing altogether.
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Mavromatos, N. E., & Mitsou, V. A. (2020). Magnetic monopoles revisited: Models and searches at colliders and in the Cosmos. Int. J. Mod. Phys. A, 35(23), 2030012–81pp.
Abstract: In this review, we discuss recent developments in both the theory and the experimental searches of magnetic monopoles in past, current and future colliders and in the Cosmos. The theoretical models include, apart from the standard Grand Unified Theories, extensions of the Standard Model that admit magnetic monopole solutions with finite energy and masses that can be as light as a few TeV. Specifically, we discuss, among other scenarios, modified Cho-Maison monopoles and magnetic monopoles in (string-inspired, higher derivative) Born-Infeld extensions of the hypercharge sector of the Standard Model. We also outline the conditions for which effective field theories describing the interaction of monopoles with photons are valid and can be used for result interpretation in monopole production at colliders. The experimental part of the review focuses on, past and present, cosmic and collider searches, including the latest bounds on monopole masses and magnetic charges by the ATLAS and MoEDAL experiments at the LHC, as well as prospects for future searches.
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Mitsou, V. A. (2013). Shedding light on dark matter at colliders. Int. J. Mod. Phys. A, 28(31), 1330052–34pp.
Abstract: Dark matter remains one of the most puzzling mysteries in Fundamental Physics of our times. Experiments at high-energy physics colliders are expected to shed light to its nature and determine its properties. This review focuses on recent searches for dark matter signatures at the Large Hadron Collider, also discussing related prospects in future e(+)e(-) colliders.
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