Yukawa Unification Research Articles

Non-supersymmetric SO(10) models with Gauge and Yukawa coupling unification

We study a non-supersymmetric SO(10) Grand Unification Theory with a very high energy intermediate symmetry breaking scale in which not only gauge but also Yukawa coupling unification are enforced via suitable threshold corrections and matching conditions. For gauge unification, we focus on a few symmetry breaking patterns with the intermediate gauge groups text {SU}(4)_{textrm{C}} times text {SU}(2)_{textrm{L}} times text {SU}(2)_{textrm{R}} (Pati–Salam) and text {SU}(3)_{textrm{C}} times text {SU}(2)_{textrm{L}} times text {SU}(2)_{textrm{R}}times text {U}(1)_{{textrm{B}}-{textrm{L}}} (minimal left-right symmetry) assuming an additional global U(1) Peccei–Quinn symmetry, and having the Standard Model supplemented by a second Higgs doublet field at the electroweak scale. We derive the conditions as well as the approximate analytical solutions for the unification of the gauge coupling constants at the two-loop level and discuss the constraints from proton decay on the resulting high scale. Specializing to the case of the Pati–Salam intermediate breaking pattern, we then impose also the unification of the Yukawa couplings of third generation fermions at the high scale, again at the two-loop level. In the considered context, Yukawa unification implies a relation between the fermion couplings to the 10- and 126-dimensional scalar representations of the SO(10) group. We consider one such possible relation which is obtainable in an text {E}_6 model where the previous two scalar fields are part of a single multiplet. Taking into account some phenomenological features such as the absence of flavor changing neutral currents at tree-level, we derive constraints on the parameters of the low energy model, in particular on the ratio of the two Higgs doublets vacuum expectation values tan beta .

T \u2212 b \u2212 \u03c4 Yukawa unification in non-holomorphic MSSM

We show that in the CMSSM with the non-holomorphic soft SUSY breaking terms, the Yukawa coupling unification of the third family fermions at the GUT scale, called t − b − τ Yukawa unification (YU), is possible under the recent collider and Dark Matter results. The YU parameter can also be found Rtbτ≈ 1, called perfect unification. We find that the squark masses exceed 3 TeV while the stau can be considerably lighter. In the case of YU, the tan β is in the interval [46,55]. We obtain bino-like dark matter (DM) of mass in the range of 0.6 TeV ≲ {m}_{upchi_1^0} ≲ 1.3 TeV where the recent Dark Matter direct detection limits are also satisfied. We also identify A-resonance solutions which reduce the relic abundance of LSP neutralino down to the ranges compatible with the current Planck measurements.

Testing Yukawa unification at LHC Run-3 and HL-LHC

We explore t-b-τ Yukawa unification (YU) in a supersymmetric SU(4)c× SU(2)L× SU(2)R model without imposing a discrete left-right (L-R) symmetry. A number of interesting solutions that are compatible with t-b-τ YU, LSP neutralino dark matter (DM), and LHC and other experimental constraints are identified. In particular, they include gluino-neutralino and stau-neutralino coannihilation scenarios, where the NLSP gluino mass can range from 1–3 TeV. Higgsino-like dark matter solutions are also identified for which gluino masses can approach 5 TeV or so. This scenario will be tested at LHC Run-3 and its future upgrades.

Comparatively light extra Higgs states as signature of SUSY SO(10) GUTs with 3rd family Yukawa unification

We study 3rd family Yukawa unification in the context of supersymmetric (SUSY) SO (10) GUTs and SO(10)-motivated boundary conditions for the SUSY-breaking soft terms. We consider μ < 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 TeV, which could be tested e.g. by future LHC searches for ditau decays H0/A0→ ττ . Finding the extra MSSM Higges before the other new MSSM particles could thus be a smoking gun for a Yukawa unified SO(10) GUT.

Supersymmetric SU(5)×U(1)χ and the weak gravity conjecture

The gauge symmetry $SU(5) \times U(1)_\chi$ is the unique maximal subgroup of SO(10) which retains manifest unification at $M_{GUT}$ of the Standard Model gauge couplings, especially if low scale supersymmetry is present. The spontaneous breaking of $U(1)_\chi$ at some intermediate scale leaves unbroken a $Z_2$ symmetry which is precisely `matter' parity. This yields a stable supersymmetric dark matter particle as well as topologically stable cosmic strings. Motivated by the weak gravity conjecture we impose unification of $SU(5)$ and $U(1)_\chi$ at an ultraviolet cutoff $\Lambda \sim \alpha_\Lambda ^{1/2} M_{P} \approx 5 \times 10^{17}$ GeV, where $\alpha_\Lambda$ denotes the $SU(5)$ gauge coupling at $\Lambda$ and $M_P \approx 2.4 \times 10^{18}$ GeV is the reduced Planck Scale. The impact of dimension five operators suppressed by $\Lambda$ on gauge coupling unification, proton lifetime estimates and $b-\tau$ Yukawa unification is discussed. In particular, the gauge boson mediated proton decay into $e^+\pi^0$ can lie within the $2-\sigma$ sensitivity of HyperKamiokande. We also discuss how the intermediate scale strings may survive inflation while the $SU(5)$ monopoles are inflated away. The unbroken $Z_2$ symmetry provides an intriguing link between dark matter, black holes carrying `quantum hair' and cosmic strings.

B \u2212 \u03c4 Yukawa unification in SUSY SU(5) with mirage mediation: LHC and dark matter implications

We consider a class of b − τ Yukawa unified Supersymmetric (SUSY) SU(5) GUTs, in which the asymptotic gaugino M1,2,3 masses are generated through the mirage mediated supersymmetry breaking, which is a combination of the gravity and anomaly mediation. Due to the contributions from the anomaly contribution, M3 is always lighter than M1 and M2, and consequently for the range of asymptotic masses considered, the gluino mass {m}_{tilde{g}} at low scale is bounded from above at about 4 TeV. We realize two different regions, in one of which the MSSM μ−term is less than about 3 TeV. This region yields a stop mass up to 5 TeV, and the stop mass is nearly degenerate with the LSP neutralino for mass around 0.8 to 1.7 TeV. A stau mass can be realized up to about 5 TeV, and the stau mass is approximately degenerate with the LSP neutralino for mass around 2 to 3 TeV. In addition, an A-funnel solution with {m}_Aapprox 2{m}_{{tilde{chi}}_1^0} and {m}_{{tilde{chi}}_1^0}sim 700-900 GeV is realized. These three cases yield LSP dark matter abundance in accordance with observations. A second region, on the other hand, arises for {m}_{tilde{g}}lesssim 1.1{m}_{{tilde{chi}}_1^0} . The μ−term is rather large (≳20 TeV), and the LSP neutralino is a bino-wino mixture. The gluino mass (∼ 0.8−1.2 TeV) is nearly degenerate with the LSP neutralino mass and hence, the gluino-neutralino coannihilation processes play a role in reducing the relic abundance of LSP neutralino down to ranges allowed by the current WMAP measurements. The two regions above can be distinguished through the direct detection experiments. The first region with relatively low μ values yields Higgsino-like DM, whose scattering on the nucleus typically has a large cross-section. We find that such solutions are still allowed by the current results from the LUX experiment, and they will be severely tested by the LUX-Zeplin (LZ) experiment. The second region contains bino-wino DM whose scattering cross-section is relatively low. These solutions are harder to rule out in the foreseeable future.

Yukawa unification with light supersymmetric particles consistent with LHC constraints

We investigate supersymmetric models with left-right symmetry based on the group SU(4)c×SU(2)L×SU(2)R (4-2-2) with negative sign of bilinear Higgs potential parameter μ in the context of the latest experimental results. In the backdrop of experimental results from the Large Hadron Collider, we investigate the possibility of Yukawa unification in 4-2-2 and find out the same is still not ruled out. Furthermore, this scenario also provides a satisfactory dark matter candidate. The current experimental bounds on sparticle masses, mass bounds on Higgs particle, updated phenomenological constraints from the rare decays of B meson and the anomalous magnetic moment of muon with the requirement of a Yukawa unified theory having 10% or better third family Yukawa unification are utilized to bound the parametric space of these models.

Yukawa unification with four Higgs doublets in supersymmetric GUT

We discuss the Yukawa coupling unification, which can emerge in the grand unified theory, in the context of scenarios with more than one pair of Higgs doublet since the current LHC constraint has become a problem for the Yukawa unification scenarios with just one pair of Higgs doublet. More than one pair of Higgs doublets can easily arise in missing partner mechanism which solves the doublet-triplet splitting problem. In such a scenario, the Yukawa unification occurs at a medium tan⁡β value, e.g., ∼ 30, which corresponds to much smaller threshold corrections compared to usual large tan⁡β scenario for t−b−τ unification in the context of SO(10) and b−τ unification in the context of SU(5) models. Further, we show that an additional Higgs doublet pair lowers the sensitivity of the radiative symmetry breaking of the electroweak vacuum.

R -parity violating solutions to the RD(*) anomaly and their GUT-scale unifications

Recently, several $B$-physics experiments report interesting anomalies in the semi-leptonic decays of $B$-mesons, such as the excess in the $R_{D^{(\ast)}}$ measurements. These anomalies seem to suggest intriguing hints of lepton flavor non-universality, and the R-parity violating (RPV) interactions are candidates for explaining this non-universality. In this paper, we discuss the RPV interactions for resolving the $R_{D^{(\ast)}}$ anomaly with the Grand Unified Theory (GUT) assumption. To solve the $R_{D^{(\ast)}}$ anomaly, it is known that large RPV couplings and around $1~{\rm TeV}$ sfermion masses are required. At the same time, large RPV couplings are conducive to realize the bottom-tau Yukawa unification which appears in the GUT models. On the other hand, there are problems for realizing favorable sfermion masses in the constrained minimal supersymetric standard model. To resolve these problems, we show that two non-universalities, the non-universal sfermion masses and the non-universal gaugino masses, are favorable.

New minimal supersymmetric GUT emergence and sub-Planckian renormalization group flow

Consistency of trans-unification renormalization group (RG) evolution is used to discuss the domain of definition of the New Minimal Supersymmetric SO(10)GUT (NMSGUT). We define the 1-loop RGE $\ensuremath{\beta}$ functions, simplifying generic formulae using constraints of gauge invariance and superpotential structure. We also calculate the 2 loop contributions to the gauge coupling and gaugino mass and indicate how to get full 2 loop results for all couplings. Our method overcomes combinatorial barriers that frustrate computer algebra based attempts to calculate SO(10) $\ensuremath{\beta}$ functions involving large irreps. Use of the RGEs identifies a perturbative domain $Q&lt;{M}_{E}$, where ${M}_{E}&lt;{M}_{\text{Planck}}$ is the scale of emergence where the NMSGUT, with GUT compatible soft supersymmetry breaking terms emerges from the strong UV dynamics associated with the Landau poles in gauge and Yukawa couplings. Due to the strength of the RG flows the Landau poles for gauge and Yukawa couplings lie near a cutoff scale ${\mathrm{\ensuremath{\Lambda}}}_{E}$ for the perturbative dynamics of the NMSGUT which just above ${M}_{E}$. SO(10) RG flows into the IR are shown to facilitate small gaugino masses and generation of negative Non Universal Higgs masses squared needed by realistic NMSGUT fits of low energy data. Running the simple canonical theory emergent at ${M}_{E}$ through ${M}_{X}$ down to the electroweak scale enables tests of candidate scenarios such as supergravity based NMSGUT with canonical kinetic terms and NMSGUT based dynamical Yukawa unification.

Effective field theory approach to trans-TeV supersymmetry: covariant matching, Yukawa unification and Higgs couplings

Dismissing traditional naturalness concerns while embracing the Higgs boson mass measurement and unification motivates careful analysis of trans-TeV supersymmetric theories. We take an effective field theory (EFT) approach, matching the Minimal Supersymmetric Standard Model (MSSM) onto the Standard Model (SM) EFT by integrating out heavy superpartners, and evolving MSSM and SMEFT parameters according to renormalization group equations in each regime. Our matching calculation is facilitated by the recent covariant diagrams formulation of functional matching techniques, with the full one-loop SUSY threshold corrections encoded in just 30 diagrams. Requiring consistent matching onto the SMEFT with its parameters (those in the Higgs potential in particular) measured at low energies, and in addition requiring unification of bottom and tau Yukawa couplings at the scale of gauge coupling unification, we detail the solution space of superpartner masses from the TeV scale to well above. We also provide detailed views of parameter space where Higgs coupling measurements have probing capability at future colliders beyond the reach of direct superpartner searches at the LHC.

Vectorlike particles, Z′ and Yukawa unification in F-theory inspired E6

We explore the low energy implications of an F-theory inspired E6 model whose breaking yields, in addition to the MSSM gauge symmetry, a Z′ gauge boson associated with a U(1) symmetry broken at the TeV scale. The zero mode spectrum of the effective low energy theory is derived from the decomposition of the 27 and 27‾ representations of E6 and we parametrise their multiplicities in terms of a minimum number of flux parameters. We perform a two-loop renormalisation group analysis of the gauge and Yukawa couplings of the effective theory model and estimate lower bounds on the new vectorlike particles predicted in the model. We compute the third generation Yukawa couplings in an F-theory context assuming an E8 point of enhancement and express our results in terms of the local flux densities associated with the gauge symmetry breaking. We find that their values are compatible with the ones computed by the renormalisation group equations, and we identify points in the parameter space of the flux densities where the t−b−τ Yukawa couplings unify.

Pati-Salam SUSY GUT with Yukawa unification

Previous studies of a three family Yukawa unified supersymmetric grand unified theory (SUSY GUT) with SO(10) or Pati-Salam (PS) gauge symmetry proposed by Raby and students show that this model is able to fit low energy and inflation observables. However, the fit to low energy observables is not great especially for $\sin2\beta$, and up and down quark masses. In this paper, we show that by choosing PS as the gauge group and modifying the Yukawa sector, the low energy fit improves significantly while other qualities of the model are maintained. In particular, the lightest SUSY particle is the neutralino with mass of order 300 - 500 GeV, the lightest stop and sbottom have mass of order 3 - 5 TeV and the CP odd Higgs mass is of order 5 - 6 TeV, so we are in the decoupling limit for the light Higgs. In addition, we reinterpret gluino simplified model analyses by the ATLAS and CMS collaborations and find that the most stringent gluino mass bound for our model is $M_{\tilde{g}}\sim1.9\,\text{TeV}$. The current best fit point, consistent with this bound, with gluino mass $M_{\tilde{g}}=1.9\,\text{TeV}$ has $\chi^2/\text{dof}\approx1.12$, compared to the best fit point of the previous model with $\chi^2/\text{dof}=1.90$. We find that predictions for the electric dipole moment of the electron, the branching ratio $BR(\mu \rightarrow e \gamma)$ and the CP violating angle in the lepton sector, $\sin\delta$, are affected significantly as compared to previous results. In summary, we are unable to rule out this model or place an upper bound on gluino mass accessible by this run of the LHC because the $\chi^2/\text{dof}$ of this model is well below $2\sigma$ even for a gluino mass as high as 2.7 TeV. On the bright side, this means that this model is still viable and we might find low energy SUSY particles in the near future.

Analysis of the right-handed Majorana neutrino mass in an SU(4)×SU(2)L×SU(2)R Pati-Salam model with democratic texture

In this paper, we attempt to build an unified model with democratic texture, that have some unification between $Y_{\nu}$ and $Y_{u}$. Since the $S_{3L} \times S_{3R}$ flavor symmetry is chiral, the unified gauge group is assumed to be Pati-Salam type $SU(4)_{c} \times SU(2)_{L} \times SU(2)_{R}$. The flavor symmetry breaking scheme is considered to be $S_{3L} \times S_{3R} \to S_{2L} \times S_{2R} \to 0$. In this picture, the four-zero texture is desirable for realistic mass and mixings. This texture is realized by a specific representation for the second breaking of the $S_{3L} \times S_{3R}$ flavor symmetry. Assuming only renormalizable Yukawa interactions, type-I seesaw mechanism, and neglecting $CP$ phases for simplicity, the right-handed neutrino mass matrix $M_{R}$ can be reconstructed from low energy input values. Numerical analysis shows that the texture of $M_{R}$ basically behaves like the "waterfall texture". Since $M_{R}$ tends to be the "cascade texture" in the democratic texture approach, a model with type-I seesaw and up-type Yukawa unification $Y_{\nu} \simeq Y_{u}$ basically requires fine-tunings between parameters. Therefore, it seems to be more realistic to consider universal waterfall textures for both $Y_{f}$ and $M_{R}$, e.g., by the radiative mass generation or the Froggatt--Nielsen mechanism. Moreover, analysis of eigenvalues shows that the lightest mass eigenvalue $M_{R1}$ is too light to achieve successful thermal leptogenesis. Although the resonant leptogenesis might be possible, it also requires fine-tunings of parameters.

Quasi-Yukawa unification and fine-tuning in U(1) extended SSM

We consider the low scale implications in the U(1)' extended MSSM (UMSSM). We restrict the parameter space such that the lightest supersymmetric particle (LSP) is always the lightest neutralino. In addition, we impose quasi Yukawa unification (QYU) at the grand unification scale (M_GUT). QYU strictly requires the ratios among the yukawa couplings as y_t/y_b ~ 1.2, y_tau/y_b ~ 1.4, and y_t/y_tau ~ 0.8. We find that the need of fine-tuning over the fundamental parameter space of QYU is in the acceptable range (Delta_EW <= 10^3), even if the universal boundary conditions are imposed at M_ GUT, in contrast to CMSSM and NUHM. UMSSM with the universal boundary conditions yields heavy stops (m_{stop} >~ 2.5 TeV), gluinos (m_gluino >~ 2 TeV), and squarks from the first two families (m_squarks >~ 4 TeV). Similarly the stau mass is bounded from below at about 1.5 TeV. Despite this heavy spectrum, we find Delta_EW >~ 300, which is much lower than that needed for the minimal supersymmetric models. In addition, UMSSM yield relatively small mu-term, and the LSP neutralio is mostly form by the Higgsinos of mass >~ 700 GeV. We obtain also bino-like dark matter (DM) of mass about 400 GeV. Wino is usually found to be heavier than Higgsinos and binos, but there is a small region where mu ~ M_1 ~ M_2 ~ 1 TeV. We also identify chargino-neutralino coannihilation channel and A-resonance solutions which reduce the relic abundance of LSP neutralino down to the ranges compatible with the current WMAP measurements.

Bottom-tau unification in a supersymmetric model with anomaly-mediation

We study the Yukawa unification, in particular, the unification of the Yukawa coupling constants of $b$ and $\tau$, in the framework of supersymmetric (SUSY) model. We concentrate on the model in which the SUSY breaking scalar masses are of the order of the gravitino mass while the gaugino masses originate from the effect of anomaly mediation and hence are one-loop suppressed relative to the gravitino mass. We perform an accurate calculation of the Yukawa coupling constants of $b$ and $\tau$ at the grand unified theory (GUT) scale, including relevant renormalization group effects and threshold corrections. In particular, we study the renormalization group effects, taking into account the mass splittings among sfermions, gauginos, and the standard model particles. We found that the Yukawa coupling constant of $b$ at the GUT scale is about $70\ \%$ of that of $\tau$ if there is no hierarchy between the sfermion masses and the gravitino mass. Our results suggest sizable threshold corrections to the Yukawa coupling constants at the GUT scale or significant suppressions of the sfermion masses relative to the gravitino mass.

Yukawa unification in heterotic string theory

We analyze Yukawa unification in the the context of $E_8\times E_8$ heterotic Calabi-Yau models which rely on breaking to a GUT theory via a non-flat gauge bundle and subsequent Wilson line breaking to the standard model. Our focus is on underlying GUT theories with gauge group $SU(5)$ or $SO(10)$. We provide a detailed analysis of the fact that, in contrast to traditional field theory GUTs, the underlying GUT symmetry of these models does not enforce Yukawa unification. Using this formalism, we present various scenarios where Yukawa unification can occur as a consequence of additional symmetries. These additional symmetries arise naturally in some heterotic constructions and we present an explicit heterotic line bundle model which realizes one of these scenarios.

Neutralino dark matter and other LHC predictions from quasi Yukawa unification

We explore the dark matter and LHC implications of t−b−τ quasi Yukawa unification in the framework of supersymmetric models based on the gauge symmetry G=SU(4)c×SU(2)L×SU(2)R. The deviation from exact Yukawa unification is quantified by a dimensionless parameter C (|C|≲0.2), such that the Yukawa couplings at MGUT are related by yt:yb:yτ=|1+C|:|1−C|:|1+3C|. In contrast to earlier studies which focused on universal gaugino masses, we consider non-universal gaugino masses at MGUT that are compatible with the gauge symmetry G. Our results reveal a variety of neutralino dark matter scenarios consistent with the observations. These include stau and chargino coannihilation scenarios, the A-resonance scenario, as well as Higgsino dark matter solutions which are more readily probed by direct detection searches. The gluino mass is found to be ≲4 TeV, the stop mass is ≳2 TeV, while the first two family squarks and sleptons are of order 4–5 TeV and 3 TeV respectively.

NLSP gluino and NLSP stop scenarios fromb−τYukawa unification

We present a study of b-tau Yukawa unified supersymmetric SU(4)_c x SU(2)_L x SU(2)_R model (with mu > 0), which predicts the existence of gluino - neutralino and stop - neutralino coannihilation scenarios compatible with the desired relic LSP neutralino dark matter abundance and other collider constraints. The NLSP gluino or NLSP stop masses vary between 400 GeV to ~ 1 TeV. The NLSP gluinos will be accessible at the 14 TeV LHC, while we hope that the NSLP stop solutions will be probed in future LHC searches. We also identify regions of the parameter space in which the gluino and the lighter stop are closely degenerate in mass, interchangeably playing the role of NLSP and NNLSP. We also update a previous study of t-b-tau Yukawa unification and show that NLSP gluino of mass ~ 1 TeV, with a mass difference between the gluino and neutralino of less than 80 GeV, can be realized consistent with the current collider and astrophysical constraints. We present benchmark points for b-tau and t-b-tau Yukawa unification that can be accessible at the LHC.

Yukawa unification in an SO(10) SUSY GUT: SUSY on the edge

In this paper we analyze Yukawa unification in a three family SO(10) SUSY GUT. We perform a global $\chi^2$ analysis and show that SUSY effects do not decouple even though the universal scalar mass parameter at the GUT scale, $m_{16}$, is found to lie between 15 and 30 TeV with the best fit given for $m_{16} \approx 25$ TeV. Note, SUSY effects don't decouple since stops and bottoms have mass of order 5 TeV, due to RG running from $M_{GUT}$. The model has many testable predictions. Gauginos are the lightest sparticles and the light Higgs boson is very much Standard Model-like. The model is consistent with flavor and CP observables with the $BR(\mu \to e\gamma)$ close to the experimental upper bound. With such a large value of $m_{16}$ we clearly cannot be considered "natural" SUSY nor are we "Split" SUSY. We are thus in the region in between or "SUSY on the Edge."