arXiv subjects

Vasja Susič

Publications and source records attributed to Vasja Susič.

14 recordsLinked to original sources

arXiv2026

Reality-constrained Minimal Yukawa Structure in SO(10) GUT

We investigate the minimal Yukawa sector of $\mathrm{SO}(10)$ grand unified theories with Higgs representations $\mathbf{10}_{\mathbb{R}}\oplus\mathbf{120}_{\mathbb{R}}\oplus\mathbf{126}$. Taking $\mathbf{10}_{\mathbb{R}}$ and $\mathbf{120}_{\mathbb{R}}$ to be real scalars, we derive the corresponding reality conditions for their weak-doublet components and revisit previously reported fermion mass relations. We find a relative sign difference between the reality constraints on the two weak doublets in $\mathbf{120}_{\mathbb{R}}$, introducing a new magnitude parameter in the mass relations. We establish this result through four complementary approaches: an explicit $\mathrm{SO}(10)$ tensorial calculation of invariants, a Pati-Salam embedding map, an algorithm transporting reality structures from parent to daughter irreps, and an $\mathrm{SU}(5)$ calculation using the $\mathrm{SO}(10)$ oscillator method, all yielding consistent results. The methods for determining reality conditions can be applied to any parent-daughter representation pair of $\mathrm{SO}(10)$ and its Pati-Salam subgroup, while the transport algorithm generalizes to arbitrary groups $H\subset G$. Incorporating the correct mass relations, we perform an extensive numerical scan and find that the model successfully reproduces SM fermion masses and mixings, including recent precision measurements of solar oscillation parameters by JUNO. It accommodates both octants of $θ_{23}$ while mildly disfavoring $δ_\mathrm{PMNS} \sim (140^\circ - 220^\circ)$. The model predicts a strongly hierarchical right-handed neutrino spectrum $(10^{5},10^{12},10^{15})$ GeV and a neutrinoless double beta decay parameter $m_{ββ}\sim 3$-$4$ meV, just below future experimental sensitivity. Proton decay is dominated by $p\toπ^+\overlineν$ and $p\toπ^0 e^+$, making these channels testable in upcoming experiments.

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arXiv2025

High-quality Peccei-Quinn symmetry from the interplay of vertical and horizontal gauge symmetries

We explore a class of axion models where an accidental $\mathrm{U}(1)$ Peccei-Quinn (PQ) symmetry automatically emerges from the interplay of vertical (grand-unified) and horizontal (flavor) gauge symmetries. We study a specific Pati-Salam realization in detail, and aim to generalize the conclusions. We show that our specific model offers protection from PQ-violating operators to high dimension, and demonstrate that the model can reproduce the Standard Model flavor structure. A distinctive feature of the vertical-horizontal setup is the presence of parametrically light fermions, known as anomalons, which are introduced to cancel the gauge anomalies of the flavor symmetry. We also identify a major challenge to building a fully realistic model, most notably that of Landau poles in gauge couplings before the Planck scale. For the specific model investigated, the pre-inflationary PQ-breaking scenario predicts the axion mass window to be $m_a \in [2 \times 10^{-8}, 10^{-3}]\,\mathrm{eV}$. Conversely, a high-quality axion may be obtained instead in the post-inflationary scenario, with axion mass $m_a \gtrsim 0.01\,\mathrm{eV}$, and anomalon masses predicted below the $\mathrm{eV}$ scale. We elaborate on anomalons' cosmological production in the early universe, highlighting how measurements of $ΔN_{\rm eff}$ could serve as a low-energy probe of the ultraviolet dynamics addressing the PQ quality problem.

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arXiv2025

A new perspective on the CMSSM: Yukawa Unification, DM and the SUSY scale

What does third family ($t$-$b$-$τ$) Yukawa unification, a typical prediction from embedding the Standard Model (SM) fermions in 16-plets of a $\mathrm{SO}(10)$ GUT, imply for the scale of the supersymmetric (SUSY) partners? Which neutralino dark matter (DM) candidate can be realized, and how large is the DM relic density? In this work, we address these questions in a simplified SUSY-breaking framework: the Constrained Minimal Supersymmetric Standard Model (CMSSM). To this end, we recast the parameter space of the CMSSM in a way that for all parameter points the SM-like Higgs mass is correctly reproduced. Considering fixed $\tanβ$ and $\mathrm{sgn}(μ)$, for every point in the $(x:=\frac{M_{1/2}}{m_0},y:=\frac{A_0}{m_0})$ parameter plane ranges for all observables are predicted. This provides a new perspective on where in parameter space different types of DM are realized, and which value of the SUSY scale is required in order to explain the observed mass of the SM Higgs boson. In our analysis we consider and compare two strategies: grid scans over the $(x,y,\tanβ)$ parameter region and MCMC sampling. We find both techniques yield similar results. For $t$-$b$-$τ$ unification within $5\,\%$ or $10\,\%$, we find $μ<0$, the SUSY spectrum showing a characteristic pattern, and the SUSY scale around $\mathcal{O}(10)\,\mathrm{TeV}$. The extra MSSM Higgses are the lowest lying new states at $\sim 2÷3\,\mathrm{TeV}$ (with discovery potential at the HL-LHC), the $\mathcal{O}(10)\,\mathrm{TeV}$ stops and gluino are in reach of a possible FCC-hh, while bino DM has a mass above $2.5\,\mathrm{TeV}$, is overabundant, and effectively unobservable in planned direct and indirect detection experiments. The DM relic density requires a dilution factor of $10<\mathcal{D}<1000$, implying non-standard cosmology that could leave its imprints in the stochastic gravitational wave background.

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arXiv2024

A realistic theory of $\mathrm{E_{6}}$ unification through novel intermediate symmetries

We propose a non-supersymmetric $\mathrm{E}_{6}$ GUT with the scalar sector consisting of $\mathbf{650}\oplus \mathbf{351'} \oplus \mathbf{27}$. Making use of the first representation for the initial symmetry breaking to an intermediate stage, and the latter two representations for second-stage breaking to the Standard Model and a realistic Yukawa sector, this theory represents the minimal $\mathrm{E}_{6}$ GUT that proceeds through one of the intermediate stages that are novel compared to $\mathrm{SU(5)}$ or $\mathrm{SO}(10)$ GUT: trinification $\mathrm{SU}(3)_C\times \mathrm{SU}(3)_L\times \mathrm{SU}(3)_R$, $\mathrm{SU}(6)\times \mathrm{SU}(2)$ and flipped $\mathrm{SO}(10)\times\mathrm{U}(1)$. We analyze these possibilities under the choice of vacuum that preserves a $\mathbb{Z}_{2}$ ``spinorial parity'', which disentangles the chiral and vector-like fermions of $\mathrm{E}_{6}$ and provides a dark matter candidate in the form of a (scalar) inert doublet. Three cases are shown to consistently unify under the extended survival hypothesis (with minimal fine-tuning): trinification symmetry $\mathrm{SU}(3)_C\times \mathrm{SU}(3)_L\times \mathrm{SU}(3)_R$ with either $LR$ or $CR$ parity, and $\mathrm{SU}(6)_{CR}\times\mathrm{SU}(2)_L$. Although the successful cases give a large range for proton lifetime estimates, all of them include regions consistent with current experimental bounds and within reach of forthcoming experiments. The scenario investigated in this paper essentially represents the unique (potentially) viable choice in the class of $\mathrm{E}_{6}$ GUTs proceeding through a novel-symmetry intermediate stage, since non-minimal alternatives seem to be intrinsically non-perturbative.

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arXiv2023

Trinification from $\mathrm{E}_{6}$ symmetry breaking

In the context of $\mathrm{E}_{6}$ Grand Unified Theories (GUTs), an intriguing possibility for symmetry breaking to the Standard Model (SM) group involves an intermediate stage characterized by either $\mathrm{SU}(3)\times\mathrm{SU}(3)\times\mathrm{SU}(3)$ (trinification) or $\mathrm{SU}(6)\times\mathrm{SU}(2)$. The more common choices of $\mathrm{SU(5)}$ and $\mathrm{SO}(10)$ GUT symmetry groups do not offer such breaking chains. We argue that the presence of a real (rank $2$ tensor) representation $\mathbf{650}$ of $\mathrm{E}_{6}$ in the scalar sector is the minimal and likely only reasonable possibility to obtain one of the novel intermediate stages. We analyze the renormalizable scalar potential of a single copy of the $\mathbf{650}$ and find vacuum solutions that support regularly embedded subgroups $\mathrm{SU}(3)\times\mathrm{SU}(3)\times\mathrm{SU}(3)$, $\mathrm{SU}(6)\times\mathrm{SU}(2)$, and $\mathrm{SO}(10)\times\mathrm{U}(1)$, as well as specially embedded subgroups $\mathrm{F}_{4}$ and $\mathrm{SU}(3)\times\mathrm{G}_{2}$ that do not contain the SM gauge symmetry. We show that for a suitable choice of parameters, each of the regular cases can be obtained as the lowest among the analyzed minima in the potential.

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arXiv2023

The trouble with the minimal renormalizable SO(10) GUT

We scrutinize the physical viability of the minimal non-supersymmetric $\mathrm{SO}(10)$ GUT with the scalar sector $\mathbf{45}\oplus\mathbf{126}\oplus\mathbf{10}_{\mathbb{C}}$, in which the unified symmetry is broken by the former two representations, and a realistic Yukawa sector is supported by the last two. Alongside the known issue of a relatively low GUT scale (and thus overly fast proton decay) encountered in minimally fine-tuned scenarios, we identify a very general problem of the model: the inability to properly accommodate a Standard-Model-like low-energy Higgs doublet in the perturbative regime.

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arXiv2022

Quantum nature of the minimal potentially realistic $\mathrm{SO}(10)$ Higgs model

We study several aspects of the quantum structure of the minimal potentially realistic renormalizable $\mathrm{SO}(10)$ Higgs model in which the $\mathbf{45}\oplus \mathbf{126}$ scalars spontaneously break the symmetry down to the Standard Model group $\mathrm{SU}(3)_{c}\times \mathrm{SU}(2)_{L}\times \mathrm{U}(1)_{Y}$. With a complete information about the one-loop corrections to the masses of all scalars in the theory and the one-loop beta functions governing the running of all dimensionless scalar self-couplings, the domains of the parameter space where the model can be treated perturbatively are established, along with improved bounds from the requirements of the SM vacuum stability and gauge coupling unification. We demonstrate that the model is fully consistent and potentially realistic only in very narrow regions of the parameter space corresponding to the breaking chains with well pronounced $\mathrm{SU}(4)_{C}\times \mathrm{SU}(2)_L\times \mathrm{U}(1)_R$ and $\mathrm{SU}(3)_{c}\times \mathrm{SU}(2)_L\times \mathrm{SU}(2)_R\times \mathrm{U}(1)_{B-L}$ intermediate symmetries, with a clear preference for the former case. Barring accidental fine-tunings in the scalar sector, this makes it possible to provide a very sharp prediction for the position of the unification scale and the value of the associated gauge coupling, with clear implications for the phenomenology of grand unified models based on this structure.

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arXiv2020

Employing nucleon decay as a fingerprint of SUSY GUT models using \texttt{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 \texttt{SusyTCProton}, which is an extension of the module \texttt{SusyTC} to be used with the \texttt{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 \texttt{SusyTCProton} we also make the additional module \texttt{ProtonDecay} public. It can be used independently from \texttt{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.

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arXiv2019

Yukawa ratio predictions in non-renormalizable $\mathrm{SO}(10)$ GUT models

Since $\mathrm{SO}(10)$ GUTs unify all fermions of the Standard Model plus a right-chiral neutrino in a representation $\mathbf{16}$ per family, they have the potential to be maximally predictive regarding the ratios between the masses (or Yukawa couplings) of different fermion types, i.e.~the up-type quarks, down-type quarks, charged leptons and neutrinos. We analyze the predictivity of classes of $\mathrm{SO}(10)$ (SUSY) GUT models for the fermion mass ratios, where the Yukawa couplings for each family are dominated by a single effective GUT operator of the schematic form $\mathbf{16}^2\cdot\mathbf{45}^n\cdot\mathbf{210}^{m}\cdot\mathbf{H}$, for $\mathbf{H}\in\{\mathbf{10},\mathbf{120},\mathbf{\overline{126}}\}$. This extends previous works to general vacuum expectation value directions for GUT-scale VEVs and to larger Higgs representations. In addition, we show that the location of the MSSM Higgses in the space of all doublets is a crucial aspect to consider. We discuss highly predictive cases and illustrate the predictive power in toy models consisting of masses for the 3rd and 2nd fermion family.

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arXiv2016

One-loop pseudo-Goldstone masses in the minimal $SO(10)$ Higgs model

We calculate the prominent perturbative contributions shaping the one-loop scalar spectrum of the minimal non-supersymmetric renormalizable $SO(10)$ Higgs model whose unified gauge symmetry is spontaneously broken by an adjoint scalar. Focusing on its potentially realistic $45\oplus 126$ variant in which the rank is reduced by a VEV of the 5-index self-dual antisymmetric tensor, we provide a thorough analysis of the corresponding one-loop Coleman-Weinberg potential, paying particular attention to the masses of the potentially tachyonic pseudo-Goldstone bosons (PGBs) transforming as $(8,1,0)$ and $(1,3,0)$ under the Standard Model gauge group. The results confirm the assumed existence of extended regions in the parameter space supporting a locally stable SM-like quantum vacuum inaccessible at the tree-level. The effective potential (EP) tedium is compared to that encountered in the previously studied $45\oplus 16$ $SO(10)$ Higgs model where the polynomial corrections to the relevant pseudo-Goldstone masses turn out to be easily calculable within a very simplified purely diagrammatic approach.

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arXiv2015

A Minimal Supersymmetric $\mathrm{E}_6$ Unified Theory

We show explicitly that supersymmetric $E_6$ Grand Unified Theory with a Higgs sector consisting of $\{27+\bar{27}+351'+\bar{351'}+78\}$ fields provides a realistic scenario for symmetry breaking and fermion mass generation. While gauge symmetry breaking can be achieved without the $78$ field, its presence is critical for a successful doublet-triplet mass splitting. The Yukawa sector of the model consists of only two symmetric matrices describing all of quark, lepton and neutrino masses and mixings. The fermion mass matrices are computed at low energy and a fit to the second and third generation masses and mixings is performed. We find a good numerical fit to the low-energy data. Thus, this model, having $11$ superpotential parameters, alongside the two symmetric Yukawa matrices, seems to be the best realistic candidate for a minimal renormalizable supersymmetric $E_6$ unified theory.

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arXiv2014

Model building for flavor changing Higgs couplings

If $t\rightarrow hq$ ($q=c,u$) or $h\rightarrowτ\ell$ ($\ell=μ,e$) decays are observed, it will be a clear signal of new physics. We investigate whether natural and viable flavor models can saturate the present direct upper bounds without violating the indirect constraints from low energy loop processes. We carry out our analysis in two theoretical frameworks: minimal flavor violation (MFV) and Froggatt-Nielsen symmetry (FN). The simplest models in either framework predict flavor changing couplings that are too small to be directly observed. Yet, in the MFV framework, it is possible to have lepton flavor changing Higgs couplings close to the bound if spurions related to heavy singlet neutrinos play a role. In the FN framework, it is possible to have large flavor changing couplings in both the up and the charged lepton sectors if supersymmetry plays a role.

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arXiv2014

Towards the minimal renormalizable supersymmetric $E_6$ model

We find an explicit renormalizable supersymmetric $E_6$ model with all the ingredients for being realistic. It consists of the Higgs sector $351'+\overline{351'}+27+\overline{27}$, which breaks $E_6$ directly to the Standard Model gauge group. Three copies of $27$ dimensional representations then describe the matter sector, while an extra $27+\overline{27}$ pair is needed to successfully split the Standard Model Higgs doublet from the heavy Higgs triplet. We perform the analysis of the vacuum structure and the Yukawa sector of this model, as well as compute contributions to proton decay. Also, we show why some other simpler $E_6$ models fail to be realistic at the renormalizable level.

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arXiv2013

A realistic renormalizable supersymmetric E6 model

A complete realistic model based on the supersymmetric version of $E_6$ is presented. It consists of three copies of matter 27, and a Higgs sector made of $2\times(27+\bar{27})+351'+\bar{351'}$ representations. An analytic solution to the equations of motion is found which spontaneously breaks the gauge group into the Standard Model. The light fermion mass matrices are written down explicitly as non-linear functions of three Yukawa matrices. This contribution is based on Ref. [1].

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