Predictions from a flavour GUT model combined with a SUSY breaking sector

We discuss how flavour GUT models in the context of supergravity can be completed with a simple SUSY breaking sector, such that the flavour-dependent (non-universal) soft breaking terms can be calculated. As an example, we discuss a model based on an SU(5) GUT symmetry and $A_4$ family symmetry, plus additional discrete "shaping symmetries" and a $\mathbb{Z}_4^\mathrm{R}$ symmetry. We calculate the soft terms and identify the relevant high scale input parameters, and investigate the resulting predictions for the low scale observables, such as flavour violating processes, the sparticle spectrum and the dark matter relic density.Comment: 24 pages, 3 figure

Non-universal Z' from SO(10) GUTs with vector-like family and the origin of neutrino masses

A $Z'$ gauge boson with mass around the (few) TeV scale is a popular example of physics beyond the Standard Model (SM) and can be a fascinating remnant of a Grand Unified Theory (GUT). Recently, $Z'$ models with non-universal couplings to the SM fermions due to extra vector-like states have received attention as potential explanations of the present $R_K$, $R_{K^{\ast}}$ anomalies; this includes GUT model proposals based on the $\mathrm{SO}(10)$ group. In this paper we further develop GUT models with a flavour non-universal low scale $Z'$ and clarify several outstanding issues within them. First, we successfully incorporate a realistic neutrino sector (with linear and/or inverse low scale seesaw mechanism), which was so far a missing ingredient. Second, we investigate in detail their compatibility with the $R_K$, $R_{K^{\ast}}$ anomalies; we find that the anomalies do not have a consistent explanation within such models. Third, we demonstrate that these models have other compelling phenomenological features; we study the correlations between the flavour violating processes of $\mu\to 3e$ and $\mu$-$e$ conversion in a muonic atom, showing how a GUT imprint could manifest itself in experiments.Comment: Revised version, published in NPB. New material, general conclusions unchanged. 30 pages, 4 figures, 2 table

Flavour model building in the framework of Grand Unification and supergravity

In this thesis, we study new aspects of flavour model building in the context of supersymmetric Grand Unified Theories, where the focus lies on models with an SU(5) or SO(10) gauge group. In the framework of supergravity, we discuss how a typical flavon sector of a flavour model with spontaneously broken family symmetry can be combined with a SUSY breaking sector in a consistent manner. To demonstrate the predictive power of such an implementation, an example calculation for a flavour GUT model, which is based on an SU(5) gauge group, an A_4 family symmetry and a Z^R_4 R-symmetry, is performed. Assuming hidden sector SUSY breaking, we determine the structure of the soft SUSY breaking terms at the GUT scale and investigate the predictions for observables at low energy scales, such as the sparticle spectrum, the dark matter relic density and flavour violating processes. Next, we carry out a systematic analysis of a class of predictive SU(5) flavour GUT models with the CSD2 setup in the neutrino sector, and where the ratios of the Yukawa couplings in the down-quark and charged lepton sector are fixed by Clebsch-Gordan coefficients at the GUT scale, following the principle of single operator dominance. Alongside the identification of viable model candidates by performing a fit to experimental data for different combinations of CG coefficients, we calculate, among others, the predictions for the 2-3 mixing angle theta^PMNS_23 and the CP violating phase delta^PMNS in the lepton sector. In the context of SO(10) Grand Unification, a class of non-renormalizable Yukawa operators of the schematic form 16_I 16_J H 45^n 210^m is investigated, where H in {10,120,126bar} contains SU(2)_L doublet and antidoublet states, and 16_I,J the SM fermions. Moreover, the representations 45 and 210 acquire SM singlet vevs at the GUT scale. We provide general formulas to compute the resulting Yukawa couplings in the different fermion sectors of the MSSM, and discuss the construction of such operators from renormalizable interactions by using heavy mediators. In addition, we show that the alignment of the MSSM Higgs (anti)doublets H_u and H_d in the space of all SU(2)_L (anti)doublets of a concrete model is a central aspect for the prediction of Yukawa ratios at the GUT scale. Finally, we specify the numerical procedure to quantitatively calculate nucleon decay from dimension 5 operators in SUSY models, and apply the analysis to an example model with an SU(5) GUT symmetry

Comparatively Light Extra Higgs States as Signature of SUSY SO(10)\mathrm{SO}(10) GUTs with 3rd Family Yukawa Unification

We study $3$rd family Yukawa unification in the context of supersymmetric (SUSY) $\mathrm{SO}(10)$ GUTs and $\mathrm{SO}(10)$-motivated boundary conditions for the SUSY-breaking soft terms. We consider $\mu<0$ such that the SUSY loop-threshold effects enable a good fit to all third family masses of the charged Standard Model (SM) fermions. We find that fitting the third family masses together with the mass of the SM-like Higgs particle, the scenario predicts the masses of the superpartner particles and of the extra Higgs states of the MSSM: while the sparticles are predicted to be comparatively heavy (above the present LHC bound but within reach of future colliders), the spectrum has the characteristic feature that the lightest new particles are the extra MSSM Higgses. We show that this effect is rather robust with respect to many deformations of the GUT boundary conditions, but turns out to be sensitive to the exactness of top-bottom Yukawa unification. Nevertheless, with moderate deviations of a few percent from exact top-bottom Yukawa unification (stemming e.g.\ from GUT-threshold corrections or higher-dimensional operators), the scenario still predicts extra MSSM Higgs particles with masses not much above $1.5\,\mathrm{TeV}$, which could be tested e.g.\ by future LHC searches for ditau decays $H^0/A^{0}\to\tau\tau$. Finding the extra MSSM Higges before the other new MSSM particles could thus be a smoking gun for a Yukawa unified $\mathrm{SO}(10)$ GUT.Comment: 39 pages, 13 figures, 1 table, 2 appendice

Employing nucleon decay as a fingerprint of SUSY GUT models using SusyTCProton

While the observation of nucleon decay would be a smoking gun of Grand Unified Theories (GUTs) in general, the ratios between the decay rates of the various channels carry rich information about the specific GUT model realization. To investigate this fingerprint of GUT models in the context of supersymmetric (SUSY) GUTs, we present the software tool SusyTCProton, which is an extension of the module SusyTC to be used with the REAP package. It allows to calculate nucleon decay rates from the relevant dimension five GUT operators specified at the GUT scale, including the full loop-dressing at the SUSY scale. As an application, we investigate the fingerprints of two example GUT toy models with different flavor structures, performing an MCMC analysis to include the experimental uncertainties for the charged fermion masses and CKM mixing parameters. While both toy models provide equally good fits to the low energy data, we show how they could be distinguished via their predictions of ratios for nucleon decay rates. Together with SusyTCProton we also make the additional module ProtonDecay public. It can be used independently from REAP and allows to calculate nucleon decay rates from given D = 5 and D = 6 operator coefficients (accepting the required SUSY input for the D = 5 case in SLHA format). The D = 6 functionality can also be used to calculate nucleon decay in non-SUSY GUTs

Predicting δPMNS\delta^\text{PMNS}, θ23PMNS\theta_{23}^\text{PMNS} and fermion mass ratios from flavour GUTs with CSD2

Constrained Sequential neutrino Dominance of type 2 (referred to as CSD2) is an attractive building block for flavour Grand Unified Theories (GUTs) because it predicts a non-zero leptonic mixing angle $\theta_{13}^\text{PMNS}$, a deviation of $\theta_{23}^\text{PMNS}$ from $\pi /4$, as well as a leptonic Dirac CP phase $\delta^\text{PMNS}$ which is directly linked to the CP violation relevant for generating the baryon asymmetry via the leptogenesis mechanism. When embedded into GUT flavour models, these predictions are modified in a specific way, depending on which GUT operators are responsible for generating the entries of fermion Yukawa matrices. In this paper, we systematically investigate and classify the resulting predictions from supersymmetric $\mathrm{SU}(5)$ based flavour models by fitting the known fermion mass and mixing data, in order to provide a roadmap for future model building. Interestingly, the promising models predict the lepton Dirac CP phase $\delta^\mathrm{PMNS}$ between $230^\circ$ and $290^\circ$, and the quark CP phase $\delta^\mathrm{CKM}$ in accordance with a right-angled unitarity triangle ($\alpha_\mathrm{UT}=90^\circ$). Also, our model setup predicts the quantities $\theta_{23}^\mathrm{PMNS}$ and $m_d/m_s$ with less uncertainty than current experimental precision, and allowing with future sensitivity to discriminate between them.Comment: 46 pages, 6 figures, 3 tables; we provide neutrino RGE data tables at https://particlesandcosmology.unibas.ch/fileadmin/user_upload/particlesandcosmology-unibas-ch/files/RGrunning.zi