Abstract: In this paper we discuss SU(5)3 with cyclic symmetry as a possible grand unified theory (GUT). The basic idea of such a tri-unification is that there is a separate SU(5) for each fermion family, with the light Higgs doublet(s) arising from the third family SU(5), providing a basis for charged fermion mass hierarchies. SU(5)3 tri-unification reconciles the idea of gauge non-universality with the idea of gauge coupling unification, opening the possibility to build consistent non-universal descriptions of Nature that are valid all the way up to the scale of grand unification. As a concrete example, we propose a grand unified embedding of the tri-hypercharge model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{U}}{\left(1\right)}_{Y}<^>{3}$$\end{document} based on an SU(5)3 framework with cyclic symmetry. We discuss a minimal tri-hypercharge example which can account for all the quark and lepton (including neutrino) masses and mixing parameters. We show that it is possible to unify the many gauge couplings into a single gauge coupling associated with the cyclic SU(5)3 gauge group, by assuming minimal multiplet splitting, together with a set of relatively light colour octet scalars. We also study proton decay in this example, and present the predictions for the proton lifetime in the dominant e+pi 0 channel.

Abstract: Treatment planning systems at proton-therapy centres entirely use X-ray computed tomography (CT) as primary imaging technique to infer the proton treatment doses to tumour and healthy tissues. However, proton stopping powers in the body, as derived from X-ray images, suffer from important proton-range uncertainties. In order to reduce this uncertainty in range, one could use proton-CT images instead. The main goal of this work is to test the capabilities of a newly-developed proton-CT scanner, based on the use of a set of tracking detectors and a high energy resolution scintillator for the residual energy of the protons. Different custom-made phantoms were positioned at the field of view of the scanner and were irradiated with protons at the CCB proton-therapy center in Krakow. We measured with the phantoms at different angles and produced sinograms that were used to obtain reconstructed images by Filtered Back-Projection. The obtained images were used to determine the capabilities of our scanner in terms of spatial resolution and proton Relative Stopping Power (RSP) mapping and validate its use as proton-CT scanner. The results show that the scanner can produce medium-high quality images, with spatial resolution better than 2 mm in radiography, below 3 mm in tomography and resolving power in the RSP comparable to other state-of-the-art pCT scanners.