54,252 research outputs found

    Energy dependence of the quark masses and mixings

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    The one loop Renormalization Group Equations for the Yukawa couplings of quarks are solved. From the solution we find the explicit energy dependence on t=lnE/μt=\ln E/\mu of the evolution of the {\em down} quark masses q=d,s,bq=d,s,b from the grand unification scale down to the top quark mass mtm_{t}. These results together with the earlier published evolution of the {\em up} quark masses completes the pattern of the evolution of the quark masses. We also find the energy dependence of the absolute values of the Cabibbo-Kobayashi-Maskawa (CKM) matrix Vij|V_{ij}|. The interesting property of the evolution of the CKM matrix and the ratios of the quark masses: mu,c/mtm_{u,c}/m_{t} and md,s/mbm_{d,s}/m_{b} is that they all depend on tt through only one function of energy h(t)h(t).Comment: Talk presented at the IX Mexican School on Particles and Fields, August 9-19, Metepec, Pue., Mexico. To be published in the AIP Conference Proceedings. 5 pages and 1 eps figure included in the tex

    Grand unification through gravitational effects

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    We systematically study the unification of gauge couplings in the presence of (one or more) effective dimension-5 operators cHGG/4MPl, induced into the grand unified theory by gravitational interactions at the Planck scale MPl. These operators alter the usual condition for gauge coupling unification, which can, depending on the Higgs content H and vacuum expectation value, result in unification at scales MX significantly different than naively expected. We find non-supersymmetric models of SU(5) and SO(10) unification, with natural Wilson coefficients c, that easily satisfy the constraints from proton decay. Furthermore, gauge coupling unification at scales as high as the Planck scale seems feasible, possibly hinting at simultaneous unification of gauge and gravitational interactions. In the Appendix we work out the group theoretical aspects of this scenario for SU(5) and SO(10) unified groups in detail; this material is also relevant in the analysis of non-universal gaugino masses obtained from supergravity.Comment: 27 pages, 5 figures, 8 tables, 1 appendix, revtex; v2: introduction and conclusion expanded, references added, minor changes, version published in PR
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