Bodenstein, S., Bordes, J., Dominguez, C. A., Peñarrocha, J., & Schilcher, K. (2010). Charm-quark mass from weighted finite energy QCD sum rules. Phys. Rev. D, 82(11), 114013–5pp.
Abstract: The running charm-quark mass in the scheme is determined from weighted finite energy QCD sum rules involving the vector current correlator. Only the short distance expansion of this correlator is used, together with integration kernels (weights) involving positive powers of s, the squared energy. The optimal kernels are found to be a simple pinched kernel and polynomials of the Legendre type. The former kernel reduces potential duality violations near the real axis in the complex s plane, and the latter allows us to extend the analysis to energy regions beyond the end point of the data. These kernels, together with the high energy expansion of the correlator, weigh the experimental and theoretical information differently from e. g. inverse moments finite energy sum rules. Current, state of the art results for the vector correlator up to four-loop order in perturbative QCD are used in the finite energy sum rules, together with the latest experimental data. The integration in the complex s plane is performed using three different methods: fixed order perturbation theory, contour improved perturbation theory, and a fixed renormalization scale mu. The final result is (m) over bar (c)(3 GeV) = 1008 +/- 26 MeV, in a wide region of stability against changes in the integration radius s(0) in the complex s plane.
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Bordes, J., Chan, H. M., & Tsun, S. S. (2018). A closer study of the framed standard model yielding testable new physics plus a hidden sector with dark matter candidates. Int. J. Mod. Phys. A, 33(33), 1850195–75pp.
Abstract: This closer study of the FSM (1) retains the earlier results of Ref. 1 in offering explanation for the existence of three fermion generations, as well as the hierarchical mass and mixing patterns of leptons and quarks; (II) predicts a vector boson G with mass of order TeV which mixes gamma with and Z of the standard model. The subsequent deviations from the standard mixing scheme are calculable in terms of the G mass. While these deviations for (i) mz – mw, (ii) Gamma(Z -> l (+)l( -)), and (iii) F(Z -> hadrons) are all within present experimental errors so long as mG > 1 TeV, they should soon be detectable if the G mass is not too much bigger; (III) suggests that in parallel to the standard sector familiar to us, there is another where the roles of flavour and colour are interchanged. Though quite as copiously populated and as vibrant in self-interactions as our own, it communicates but little with the standard sector except via mixing through a couple of known portals, one of which is the gamma – Z – G complex noted in (II), and the other is a scalar complex which includes the standard model Higgs. As a result, the new sectors paper. appears hidden to us as we appear hidden to them, and so its lowest members with masses of order 10 MeV, being electrically neutral and seemingly stable, but abundant, may make eligible candidates as constituents of dark matter. A more detailed summary of these results together with some remarks on the model's special theoretical features can be found in the last section of this paper.
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Bordes, J., Hong-Mo, C., & Tsun, T. S. (2022). Resolving an ambiguity of Higgs couplings in the FSM, greatly improving thereby the model's predictive range and prospects. Int. J. Mod. Phys. A, 37(27), 2250167–10pp.
Abstract: We show that, after resolving what was thought to be an ambiguity in the Higgs coupling, the FSM gives, apart from two extra terms (i) and (ii) to be specified below, an effective action in the standard sector which has the same form as the SM action, the two differing only in the values of the mass and mixing parameters of quarks and leptons which the SM takes as Finputs from experiment while the FSM obtains as a result of a fit with a few parameters. Hence, to the accuracy that these two sets of parameters agree in value, and they do to a good extent as shown in earlier work,' the FSM should give the same result as the SM in all the circumstances where the latter has been successfully applied, except for the noted modifications due to (i) and (ii). If so, it would be a big step forward for the FSM. The correction terms are: (i) a mixing between the SM's gamma – Z with a new vector boson in the hidden sector, (ii) a mixing between the standard Higgs with a new scalar boson also in the hidden sector. And these have been shown a few years back to lead to (i') an enhancement of the W mass over the SM value,(2) – and (ii') effects consistent with the g – 2 and some other anomalies,(3) precisely the two deviations from the SM reported by experiments(4,5) recently much in the news.
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