SUSY Grand Unified Theories Research Articles

Data-driven analysis of a SUSY GUT of flavour

We present a data-driven analysis of a concrete Supersymmetric (SUSY) Grand Unified Theory (GUT) of flavour, based on SU(5) × S4, which predicts charged fermion and neutrino mass and mixing, and where the mass matrices of both the Standard Model and the Supersymmetric particles are controlled by a common symmetry at the GUT scale. This framework also predicts non-vanishing non-minimal flavour violating effects, motivating a sophisticated data-driven parameter analysis to uncover the signatures and viability of the model. This computer-intensive Markov-Chain-Monte-Carlo (MCMC) based analysis includes a large range of flavour as well as dark matter and SUSY observables, predicts distributions for a range of physical quantities which may be used to test the model. The predictions include maximally mixed sfermions, μ → eγ close to its experimental limit and successful bino-like dark matter with nearby winos (making direct detection unlikely), implying good prospects for discovering winos and gluinos at forthcoming collider runs. The results also demonstrate that the Georgi-Jarlskog mechanism does not provide a good description of the splitting of down type quark masses and charged leptons, while neutrinoless double beta decay is predicted at observable rates.

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.

Enhanced $\Gamma(p\to K^0\mu^+)/\Gamma(p\to K^+\bar{\nu}_\mu)$ as a signature of minimal renormalizable SUSY SO (10) GUT

Abstract The ratio of the partial widths of some dimension-5 proton decay modes can be predicted without detailed knowledge of supersymmetric (SUSY) particle masses, and this allows us to experimentally test various SUSY grand unified theory (GUT) models without discovering SUSY particles. In this paper, we study the ratio of the partial widths of the $p\to K^0\mu^+$ and $p\to K^+\bar{\nu}_\mu$ decays in the minimal renormalizable SUSY $SO(10)$ GUT, under only a plausible assumption that the 1st- and 2nd-generation left-handed squarks are mass-degenerate. In the model, we expect that the Wilson coefficients of dimension-5 operators responsible for these modes are on the same order and that the ratio of $p\to K^0\mu^+$ and $p\to K^+\bar{\nu}_\mu$ partial widths is $O(0.1)$. Hence, we may be able to detect both $p\to K^0\mu^+$ and $p\to K^+\bar{\nu}_\mu$ decays at Hyper-Kamiokande, thereby gaining a hint for the minimal renormalizable SUSY $SO(10)$ GUT. Moreover, since this partial width ratio is quite suppressed in the minimal $SU(5)$ GUT, it allows us to distinguish the minimal renormalizable SUSY $SO(10)$ GUT from the minimal $SU(5)$ GUT. In the main body of the paper, we perform a fitting of the quark and lepton masses and flavor mixings with the Yukawa couplings of the minimal renormalizable $SO(10)$ GUT, and derive a concrete prediction for the partial width ratio based on the fitting results. We find that the partial width ratio generally varies in the range $0.05$–$0.6$, confirming the above expectation.

Non-minimal flavour violation in A4 \xd7 SU(5) SUSY GUTs with smuon assisted dark matter

We study CP-conserving non-minimal flavour violation in A4 × SU(5) inspired Supersymmetric Grand Unified Theories (GUTs), focussing on the regions of parameter space where dark matter is successfully accommodated due to a light right-handed smuon a few GeV heavier than the lightest neutralino. In this region of parameter space we find that some of the flavour-violating parameters are constrained by the requirement of the dark matter relic density, due to the delicate interplay between the smuon and neutralino masses. By scanning over GUT scale flavour violating parameters, constrained by low-energy quark and lepton flavour violating observables, we find a striking difference in the results in which individual parameters are varied to those where multiple parameters are varied simultaneously, where the latter relaxes the constraints on flavour violating parameters due to cancellations and/or correlations. Since charged lepton-flavour violation provides the strongest constraints within a GUT framework, due to relations between quark and lepton flavour violation, we examine in detail a prominent correlation between some of the flavour violating parameters at the GUT scale consistent with the stringent lepton flavour violating process μ → eγ. We also examine the relation between GUT scale and low scale flavour violating parameters, for both quarks and leptons, and show how the usual expectations may be violated due to the correlations when multiple parameters are varied simultaneously.

No-go theorem for fully supersymmetric GUTs with metastable supersymmetry breaking

We introduce fully SGUTs, SUSY grand unified theories that, upon symmetry breaking through the Higgs mechanism, decompose into a visible sector and an extra sector where the dynamics of the extra sector gauge group is responsible for SUSY breaking. Fully SGUTs thus have the important feature that all gauge groups of the visible sector and the extra sector unify into a simple gauge group at the SGUT scale, therefore generalizing the successful MSSM gauge coupling unification to all the gauge couplings of the theory. By focusing on the ISS SUSY-breaking mechanism in the extra sector, we show that it is impossible to reproduce the MSSM matter content when there exists a metastable ISS SUSY-breaking state.

Predicting the sparticle spectrum from GUTs via SUSY threshold corrections with SusyTC

Grand Unified Theories (GUTs) can feature predictions for the ratios of quark and lepton Yukawa couplings at high energy, which can be tested with the increasingly precise results for the fermion masses, given at low energies. To perform such tests, the renormalization group (RG) running has to be performed with sufficient accuracy. In supersymmetric (SUSY) theories, the one-loop threshold corrections (TC) are of particular importance and, since they affect the quark-lepton mass relations, link a given GUT flavour model to the sparticle spectrum. To accurately study such predictions, we extend and generalize various formulas in the literature which are needed for a precision analysis of SUSY flavour GUT models. We introduce the new software tool SusyTC, a major extension to the Mathematica package REAP, where these formulas are implemented. SusyTC extends the functionality of REAP by a full inclusion of the (complex) MSSM SUSY sector and a careful calculation of the one-loop SUSY threshold corrections for the full down-type quark, up-type quark and charged lepton Yukawa coupling matrices in the electroweak-unbroken phase. Among other useful features, SusyTC calculates the one-loop corrected pole mass of the charged (or the CP-odd) Higgs boson as well as provides output in SLHA conventions, i.e. the necessary input for external software, e.g. for performing a two-loop Higgs mass calculation. We apply SusyTC to study the predictions for the parameters of the CMSSM (mSUGRA) SUSY scenario from the set of GUT scale Yukawa relations $y_e / y_d = - 1/2$, $y_\mu / y_s = 6$, and $y_\tau / y_b = - 3/2$, which has been proposed recently in the context of SUSY GUT flavour models.

Nucleon decay via dimension-6 operators in the E6 x SU(2)F x U(1)A SUSY GUT model

In the previous paper, we have shown that $R_1\equiv\frac{\Gamma_{n \rightarrow \pi^0 + \nu^c}}{\Gamma_{p \rightarrow \pi^0 + e^c}}$ and $R_2\equiv\frac{\Gamma_{p \rightarrow K^0 + \mu^c}}{\Gamma_{p \rightarrow \pi^0 + e^c}}$ can identify the grand unification group $SU(5)$, $SO(10)$, or $E_6$ in typical anomalous $U(1)_A$ supersymmetric (SUSY) grand unified theory (GUT) in which nucleon decay via dimension-6 operators becomes dominant. When $R_1 > 0.4$ the grand unification group is not $SU(5)$, while when $R_1 > 1$ the grand unification group is $E_6$. Moreover, when $R_2 > 0.3$, $E_6$ is implied. Main ambiguities come from the diagonalizing matrices for quark and lepton mass matrices in this calculation once we fix the vacuum expectation values of GUT Higgs bosons. In this paper, we calculate $R_1$ and $R_2$ in $E_6\times SU(2)_F$ SUSY GUT with anomalous $U(1)_A$ gauge symmetry, in which realistic quark and lepton masses and mixings can be obtained though the flavor symmetry $SU(2)_F$ constrains Yukawa couplings at the GUT scale. The ambiguities of Yukawa couplings are expected to be reduced. We show that the predicted region for $R_1$ and $R_2$ is more restricted than in the $E_6$ model without $SU(2)_F$ as expected. Moreover, we re-examine the previous claim for the identification of grand unification group with $100$ times more model points ($10^6$ model points), including $E_6 \times SU(2)_F$ model.

SO(10) GUT IN FOUR AND FIVE DIMENSIONS: A REVIEW

We review SO(10) grand unified theories (GUTs) in four and five dimensions (4D and 5D). The renormalizable minimal SO(10) SUSY GUT is the central theme of this paper. It is very predictive and makes it possible to construct all mass matrices including those of the Dirac and heavy right-handed Majorana neutrinos. Its predictions covers all ranges of particle phenomena. The explicit construction of the Higgs superpotential and the explicit display of a symmetry breaking pattern from GUT to the SM show that the naive desert from the SM to GUT in the minimal supersymmetric standard model (MSSM) is a too simplified concept and we have many definitely determined intermediate energy scales in general. This situation destroys the naive gauge coupling unification in the MSSM scheme. Also the precise measurements of neutrino oscillation data have revealed several small but manifest mismatches with our predictions. Also there are arguments that it is impossible to construct a GUT theory in 4D with a finite number of multiplets that leads to the MSSM with a residual R symmetry. If we try to solve all these pathologies comprehensively, it is very attractive for us to go into extra dimensions. Extra dimension may be either warped or flat. The fifth dimension, for simplicity, is compactified on the S1/(Z2) (warped) or on the S1/(Z2×Z′2) (flat) orbifold with two inequivalent branes at the orbifold fixed points. In the former warped case, intermediate energy scales are translated with the positions of Higgs fields in the bulk and the fundamental scheme of the MSSM is recovered. On the other hand, in the latter flat scenario, all matter and Higgs multiplets reside on the Pati–Salam (PS) brane where the PS symmetry is manifest. There the original renormalizability in Yukawa coupling is broken but its essential structures of mass matrices in minimal SO(10) GUT in 4D is promoted to the PS invariant action in 4D. In the gaugino mediation mechanism, the SO(10) gauge multiplet is transmitted to the PS brane through the gaugino mediation with bulk gauge multiplet. Further breaking of the PS gauge group to the SM group is realized by VEVs of the Higgs multiplets [Formula: see text]. We show that this model not only cures all pathologies in SO(10) GUT in 4D but also provides the consistent inflation scenario and dark matter candidate and leptogenesis. The gauge coupling unification is successfully realized after incorporating the threshold corrections of the Kaluza–Klein modes. Finally we add some comments on the impacts of the discovery of a Higgs-like particle by the Large Hadronic Collider at CERN (LHC) on SUSY GUTs.

A4 × SU(5) SUSY GUT of flavour with trimaximal neutrino mixing

Recent T2K, MINOS and Double CHOOZ results, together with global fits of mixing parameters, indicate a sizeable reactor angle theta13 ~ 8 deg which, if confirmed, would rule out tri-bimaximal (TB) lepton mixing. Recently two of us studied the vacuum alignment of the Altarelli-Feruglio A4 family symmetry model including additional flavons in the 1' and 1" representations, leading to so-called "trimaximal" neutrino mixing and allowing a potentially large reactor angle. Here we show how such a model may arise from a Supersymmetric (SUSY) Grand Unified Theory (GUT) based on SU(5), leading to sum rule bounds |s| < thetaC/3, |a| < (r + thetaC/3)|cos delta|/2, where s,a,r parameterise the solar, atmospheric and reactor angle deviations from their TB mixing values, delta is the CP violating oscillation phase, and thetaC is the Cabibbo angle.

Footprints of SUSY GUTs in flavour physics

Supersymmetric (SUSY) Grand Unified theories (GUTs) generally predict FCNC and CP violating processes to occur both in the leptonic and hadronic sectors. Assuming an underlying SU(5) group plus right-handed neutrinos (RN), we perform an extensive study of FCNC and CP violation, analyzing the correlations between leptonic and hadronic processes like μ → eγ and \( {K^0} - {\bar{K}^0} \) mixing, τ → μγ and b → s transitions such as B d → ϕK s and \( B_s^0 - \bar{B}_s^0 \) mixing. Moreover, we examine the impact of the considered scenario on the UT analyses, monitoring the low energy consequences implied by possible solutions to the various tensions in the present UT analyses. We compare the phenomenological implications of this NP scenario with the ones of supersymmetric flavour models finding a few striking differences that could allow to distinguish these different NP models.

A SUSY GUT of flavour with S 4 × SU(5) to NLO

We construct a Supersymmetric (SUSY) Grand Unified Theory (GUT) of Flavour based on S4 x SU(5), together with an additional (global or local) Abelian symmetry, and study it to next-to-leading order (NLO) accuracy. The model includes a successful description of quark and lepton masses and mixing angles at leading order (LO) incorporating the Gatto-Sartori-Tonin (GST) relation and the Georgi-Jarlskog (GJ) relations. We study the vacuum alignment arising from F-terms to NLO and such corrections are shown to have a negligible effect on the results for fermion masses and mixings achieved at LO. Tri-bimaximal (TB) mixing in the neutrino sector is predicted very accurately up to NLO corrections of order 0.1%. Including charged lepton mixing corrections implies small deviations from TB mixing described by a precise sum rule, accurately maximal atmospheric mixing and a reactor mixing angle close to three degrees.

Waiting for μ →eγ from the MEG experiment

The Standard Model (SM) predictions for the lepton flavor-violating (LFV) processes like μ → eγ are well far from any realistic experimental resolution, thus, the appearance of μ → eγ at the running MEG experiment would unambiguously point towards a New Physics (NP) signal. In this article, we discuss the phenomenological implications in case of observation/improved upper bound on μ → eγ at the running MEG experiment for supersymmetric (SUSY) scenarios with a see-saw mechanism accounting for the neutrino masses. We outline the role of related observables to μ → eγ in shedding light on the nature of the SUSY LFV sources providing useful tools i) to reconstruct some fundamental parameters of the neutrino physics and ii) to test whether an underlying SUSY Grand Unified Theory (GUT) is at work. The perspectives for the detection of LFV signals in τ decays are also discussed.

Threshold and flavor effects in the renormalization group equations of the MSSM. II. Dimensionful couplings

We reexamine the one-loop renormalization group equations (RGEs) for the dimensionful parameters of the minimal supersymmetric standard model (MSSM) with broken supersymmetry, allowing for arbitrary flavor structure of the soft SUSY-breaking parameters. We include threshold effects by evaluating the $\ensuremath{\beta}$-functions in a sequence of (nonsupersymmetric) effective theories with heavy particles decoupled at the scale of their mass. We present the most general form for high-scale, soft SUSY-breaking parameters that obtains if we assume that the supersymmetry-breaking mechanism does not introduce new intergenerational couplings. This form, possibly amended to allow additional sources of flavor-violation, serves as a boundary condition for solving the RGEs for the dimensionful MSSM parameters. We then present illustrative examples of numerical solutions to the RGEs. We find that in a SUSY grand unified theory with the scale of SUSY scalars split from that of gauginos and higgsinos, the gaugino mass unification condition may be violated by $\mathcal{O}(10%)$. As another illustration, we show that in mSUGRA, the rate for the flavor-violating ${\stackrel{\texttildelow{}}{t}}_{1}\ensuremath{\rightarrow}c{\stackrel{\texttildelow{}}{Z}}_{1}$ decay obtained using the complete RGE solution is smaller than that obtained using the commonly used ``single-step'' integration of the RGEs by a factor 10--25, and so may qualitatively change expectations for topologies from top-squark pair production at colliders. Together with the RGEs for dimensionless couplings presented in a companion paper, the RGEs in Appendix B of this paper form a complete set of one-loop MSSM RGEs that include threshold and flavor-effects necessary for two-loop accuracy.

Soft SUSY breaking grand unification: Leptons vs quarks on the flavor playground

We systematically analyze the correlations between the various leptonic and hadronic flavor violating processes arising in SUSY Grand Unified Theories. Using the GUT-symmetric relations between the soft SUSY breaking parameters, we assess the impact of hadronic and leptonic flavor observables on the SUSY sources of flavor violation.

Flavor Physics in SUSY Grand Unified Theories

Within Supersymmetric Grand Unified theories with soft breaking terms arising at the Planck scale, it is generally possible to link Flavor Changing Neutral Current (FCNC) and CP violating processes occurring in the leptonic and hadronic sectors. So, a correlated analysis of low-energy observables in the leptonic and hadronic sectors, can provide indications of the existence of a Grand Unified theory at high energies. We show how bounds on leptonic FCNC involving the third generation translate into constraints on FCNC B decays. Moreover, we show that, besides FCNC transitions, also lepton-flavor (LF) universality tests in M ℓ 2 decays (with M = π , K , B ), offer a unique opportunity to study the flavour structure of physics beyond the SM.

Hadronic EDM constraints on orbifold GUTs

We point out that the null results of the hadronic electric dipole moment (EDM) searches constrain orbifold grand unified theories (GUTs), where the GUT symmetry and supersymmetry (SUSY) are both broken by boundary conditions in extra dimensions and it leads to rich fermion and sfermion flavor structures. A marginal chromoelectric dipole moment (CEDM) of the up quark is induced by the misalignment between the CP violating left- and right-handed up-type squark mixings, in contrast to the conventional four-dimensional SUSY GUTs. The up quark CEDM constraint is found to be as strong as those from charged lepton flavor violation (LFV) searches. The interplay between future EDM and LFV experiments will probe the structures of the GUTs and the SUSY breaking mediation mechanism.

SO(10) group theory for the unified model building

The complete tables of Clebsch–Gordan (CG) coefficients for a wide class of SO(10) SUSY grand unified theories (GUTs) are given. Explicit expressions of states of all corresponding multiplets under standard model gauge group G321=SU(3)C×SU(2)L×U(1)Y, necessary for evaluation of the CG coefficients are presented. The SUSY SO(10) GUT model considered here includes most of the Higgs irreducible representations usually used in the literature, 10, 45, 54, 120, 126, 126¯, and 210. Mass matrices of all G321 multiplets are found for the most general superpotential. These results are indispensable for the precision calculations of the gauge couplings unification and proton decay, etc.

Baryogenesis and gravitino dark matter in gauge-mediated supersymmetry-breaking models

We discuss two cosmological issues in a generic gauge-mediated supersymmetry (SUSY)-breaking model, namely the Universe's baryon asymmetry and the gravitino dark-matter density. We show that both problems can be simultaneously solved if there exist extra matter multiplets of a SUSY-invariant mass of the order of the ``$\mu$-term'', as suggested in several realistic SUSY grand-unified theories. We propose an attractive scenario in which the observed baryon asymmetry is produced in a way totally independent of the reheating temperature of inflation without causing any cosmological gravitino problem. Furthermore, in a relatively wide parameter space, we can also explain the present mass density of cold dark matter by the thermal relics of the gravitinos without an adjustment of the reheating temperature of inflation. We point out that there is an interesting relation between the baryon asymmetry and the dark-matter density.

Bottom-tau unification in a supersymmetric SU(5) grand unified theory and constraints fromb→sγand muong−2

An analysis is made on bottom-tau Yukawa unification in supersymmetric (SUSY) SU(5) grand unified theory (GUT) in the framework of minimal supergravity, in which the parameter space is restricted by some experimental constraints including $\mathrm{Br}(\stackrel{\ensuremath{\rightarrow}}{b}s\ensuremath{\gamma})$ and muon $g\ensuremath{-}2.$ The bottom-tau unification can be accommodated to the measured branching ratio $\mathrm{Br}(\stackrel{\ensuremath{\rightarrow}}{b}s\ensuremath{\gamma})$ if superparticle masses are relatively heavy and the Higgsino mass parameter $\ensuremath{\mu}$ is negative. On the other hand, if we take the latest muon $g\ensuremath{-}2$ data to require positive SUSY contributions, then wrong-sign threshold corrections at the SUSY scale upset the Yukawa unification with more than $20%$ discrepancy. It has to be compensated by superheavy threshold corrections around the GUT scale, which constrains models of flavor in SUSY GUT. A pattern of the superparticle masses preferred by the three requirements is also commented upon.

CP violation in Bd→ φKS in SUSY GUT with right-handed neutrinos

CP violation in the B d system is discussed in the supersymmetric grand unified theory (GUT) with the right-handed neutrinos. Above the GUT scale, the right-handed down-type squarks couple to the right-handed neutrinos. Due to the renormalization group effect, flavor violations in the lepton sector may be transferred to the right-handed down-type squark mass matrix, which affects the CP violation in the B decay. Taking into account this effect, we compare the CP violation in B d → ψK S and B d → φK S processes. We will find that a significant difference is possible between the CP violating phases in two decay processes.