Grand Unified Models Research Articles

Application of grand unified model and ring model in understanding the isomeric structures of Au28(SR)20 nanoclusters

We present the application of grand unified model (GUM) and ring model in understanding the isomeric structures of six Au28(SR)20 nanoclusters. In light of GUM, three Au14 cores could be attributed to the different packing modes of four tetrahedral Au4 units. The binding of the protection ligands with three Au14 cores can be guided by the ring model, in which the protection ligands and some gold core atoms can form the rings with different radii. Therefore the structural isomerism of six isomers can be understood by different types of ring structures packing, fusing, or interlocking together.

What the Fermilab muon g−2 experiment tells us about discovering supersymmetry at high luminosity and high energy upgrades to the LHC

Using an artificial neutral network we explore the parameter space of supergravity grand unified models consistent with the combined Fermilab E989 and Brookhaven E821 data on $(g-2)_\mu$. The analysis indicates that the region favored by the data is the one generated by gluino-driven radiative breaking of the electroweak symmetry. This region naturally leads to a split sparticle spectrum with light sleptons and weakinos but heavy squarks, with the stau and the chargino as the lightest charged particles. We show that if the entire deviation from the standard model $(g-2)_{\mu}$ arises from supersymmetry, then supersymmetry is discoverable at HL-LHC and HE-LHC via production and decay of sleptons within the optimal integrated luminosity of HL-LHC and with a smaller integrated luminosity at HE-LHC.

Elucidating the stabilities and properties of the thiolate-protected Au nanoclusters with detaching the staple motifs.

Thiolate-protected Au nanoclusters (AuNCs) have been widely studied in areas of catalysis, biosensors, and bioengineering. In real applications, e.g., catalytic reactions, the thiolate groups are normally partially detached. However, which of the thiolate groups are easily detached and how the detachment of the ligands affects the geometries and electronic structures of the Au nanoclusters have been rarely studied. In this work, we employed the density functional theory calculations as well as the molecular orbital analysis to explore the detachment effect of the ligands using nine thiolate-protected AuNCs as examples. Our results showed that there existed a nearly linear relationship between the averaged detachment energies and the numbers of Au atoms in the motifs. Detaching longer motifs normally required more energies owing to the stronger aurophilic effects. For detaching a full motif, based on the structure decomposition via the grand unified model, analysis on the inner Au core indicated that the change in Au-Au bond length was more sensitive for the inter-block compared to the intra-block. The detachment of the -SH fragment generally needs less energy and brings less structural deformations when compared to the removal of a full motif. Molecular orbital analysis showed that the relative energies of the HOMO orbitals were elevated, which led to the narrow down of the HOMO-LUMO gap. This work provides a primary description of the correlation of the ligands' detachment with the relative stabilities and structures of the AuNCs, which would be beneficial for establishing the structure-property relationship of AuNCs in real applications.

R parity from string compactification

The strategy for assigning ${\mathbf{Z}}_{4R}$ parity in the string compactification is presented. For the visible sector, an anti-SU(5) [flipped-SU(5)] grand unification (GUT) model with three families is used to reduce the number of representations compared to the number in the minimal supersymmetric standard models. The SO(32) heterotic string is used to allow a large non-Abelian gauge group $\mathrm{SU}(N)$, $N\ensuremath{\ge}9$, for the hidden sector such that the number of extra U(1) factors is small. A discrete subgroup of the gauge U(1)'s is defined as the ${\mathbf{Z}}_{4R}$ parity. Spontaneous symmetry breaking of anti-SU(5) GUT is achieved by the vacuum expectation values of two index antisymmetric tensor Higgs fields ${\mathbf{10}}_{+1}$ and ${\overline{\mathbf{10}}}_{\ensuremath{-}1}$ that led to our word ``anti-SU(5).'' In the illustrated example, the multiplicity 3 in one twisted sector allows the permutation symmetry ${S}_{3}$ that leads us to select the third family members and one MSSM pair of the Higgs quintets.

Yukawa coupling unification in an SO(10) model consistent with Fermilab (g \u2212 2)\u03bc result

We investigate the Yukawa coupling unification for the third generation in a class of SO(10) unified models which are consistent with the 4.2 σ deviation from the standard model of the muon g − 2 seen by the Fermilab experiment E989. A recent analysis in supergravity grand unified models shows that such an effect can arise from supersymmetric loops correction. Using a neural network, we further analyze regions of the parameter space where Yukawa coupling unification consistent with the Fermilab result can appear. In the analysis we take into account the contributions to Yukawas from the cubic and the quartic interactions. We test the model at the high luminosity and high energy LHC and estimate the integrated luminosities needed to discover sparticles predicted by the model.

Unraveling the Atomic Structures of 10-Electron (10e) Thiolate-Protected Gold Nanoclusters: Three Au32(SR)22 Isomers, One Au28(SR)18, and One Au33(SR)23.

The atomic structures of 10-electron (10e) thiolate-protected gold nanoclusters have not received extensive attention both experimentally and theoretically. In this paper, five new atomic structures of 10e thiolate-protected gold nanoclusters, including three Au32(SR)22 isomers, one Au28(SR)18, and one Au33(SR)23, are theoretically predicted. Based on grand unified model (GUM), four Au17 cores with different morphologies can be obtained via three different packing modes of five tetrahedral Au4 units. Then, five complete structures of three Au32(SR)22 isomers, one Au28(SR)18, and one Au33(SR)23 isomers can be formed by adding the thiolate ligands to three Au17 cores based on the interfacial interaction between thiolate ligands and gold core in known gold nanoclusters. Density functional theory calculations show that the relative energies of three newly predicted Au32(SR)22 isomers are quite close to two previously reported isomers. In addition, five new 10e gold nanoclusters have large highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gaps and all-positive harmonic vibration frequencies, indicating their high stabilities.

Updated constraints on Z′ and W′ bosons decaying into bosonic and leptonic final states using the run 2 ATLAS data

The full ATLAS Run 2 data set with time-integrated luminosity of 139 fb$^{-1}$ in the diboson and dilepton channels is used to probe benchmark models with extended gauge sectors: the $E_6$-motivated Grand Unification models, the left-right symmetric $LR$ and the sequential standard model (EGM). These all predict neutral $Z'$ vector bosons, decaying into lepton pairs, $\ell\ell$, or into electroweak gauge boson pairs $WW$, where one $W$ in turn decays semileptonically. 95% C.L. exclusion limits on the $Z'$ resonance production cross section times branching ratio to electroweak gauge boson pairs and to lepton pairs in the mass range of $\sim$ 1 - 6 TeV are converted to constraints on the $Z$-$Z'$ mixing parameter and the heavy resonance mass. We present exclusion regions on the parameter space of the $Z'$ which are significantly extended compared to those obtained from the previous analyses performed with LHC data collected at 7 and 8 TeV in Run 1 as well as at 13 TeV in Run 2 at time-integrated luminosity of 36.1 fb$^{-1}$ and are the most stringent bounds to date. Also presented, from a similar analysis of electrically charged $W'$ bosons arising in the EGM, which can decay through $W'\to WZ$ and $W'\to \ell\nu$, are limits on the $W$-$W'$ mixing parameter and the charged $W'$ vector boson mass.

Ring Model for Understanding How Interfacial Interaction Dictates the Structures of Protection Motifs and Gold Cores in Thiolate-Protected Gold Nanoclusters.

Understanding the effect of interfacial interactions between the protection motifs and gold cores on the stabilities of thiolate-protected gold nanoclusters is still a challenging task. Based on analyses of 95 experimentally crystallized and theoretically predicted thiolate-protected gold nanoclusters, we present a ring model to offer a deeper insight into the interfacial interactions for this class of nanoclusters. In the ring model, all the gold nanoclusters can be generically viewed as a fusion or interlocking of several [Aum(SR)n] (m = 4-8, 10, and 12 and 0 ≤ n ≤ m) rings. Guided by the ring model and the grand unified model, a new Au42(SR)26 isomer is predicted, whose total energy is lower than those of two previously crystallized isomers. The ring model offers a mechanistic understanding of the interactions between the protection ligands and gold cores and practical guidance on predicting new gold nanoclusters for future experimental synthesis and confirmation.

Primordial nucleosynthesis with varying fundamental constants

The success of primordial nucleosynthesis as a cornerstone of the hot Big Bang model has been limited by the long-standing lithium problem. Recent work presented a self-consistent perturbative analysis of the effects of variations in nature’s fundamental constants on primordial nucleosynthesis for a broad class of grand unified theory models, showing that such models provide a possible solution to the lithium problem, provided the value of the fine-structure constant α at the nucleosynthesis epoch is larger than the current laboratory one by a few parts per million of relative variation. Here we extend the earlier analysis, focusing on how this preferred value of α is affected if relevant cosmological parameters are also allowed to vary–specifically focusing on the baryon-to-photon ratio, the number of neutrinos, and the neutron lifetime. We rephrase the lithium problem in terms of the values of these parameters that would be needed to solve it within this class of grand unified theories, thus obtaining values that would disagree with the results of other experiments by several standard deviations. Using these experimental results as priors in the analysis, we find that a larger value of α is still preferred, confirming our previous results. By excluding lithium from the analysis, we also obtain upper limits on possible variations of α at the primordial nucleosynthesis epoch. At the two-sigma level, these are |Δα/α|< 50 ppm without nuclear physics, cosmology, or atomic clocks priors, or alternatively |Δα/α|< 5 ppm if these priors are used. While the simplest solution to the lithium problem is likely to be found within observational astrophysics, our work shows that varying fundamental constants remain a viable alternative.

Primordial monopoles and strings, inflation, and gravity waves

We consider magnetic monopoles and strings that appear in non-supersymmetric SO(10) and E6 grand unified models paying attention to gauge coupling unification and proton decay in a variety of symmetry breaking schemes. The dimensionless string tension parameter Gμ spans the range 10−6− 10−30, where G is Newton’s constant and μ is the string tension. We show how intermediate scale monopoles with mass ∼ 1013− 1014 GeV and flux ≲ 2.8 × 10−16 cm−2s−1sr−1, and cosmic strings with Gμ ∼ 10−11− 10−10 survive inflation and are present in the universe at an observable level. We estimate the gravity wave spectrum emitted from cosmic strings taking into account inflation driven by a Coleman-Weinberg potential. The tensor-to-scalar ratio r lies between 0.06 and 0.003 depending on the details of the inflationary scenario.

Gravitational waves from breaking of an extra U(1) in SO(10) grand unification

Abstract In a class of gauged $U(1)$ extended Standard Models (SMs), the breaking of the $U(1)$ symmetry is not only a source for Majorana masses of right-handed (RH) neutrinos crucial for the seesaw mechanism, but also a source of stochastic gravitational wave (GW) background. Such $U(1)$ extended models are well-motivated from the viewpoint of grand unification. In this paper, we discuss a successful ultraviolet completion of a $U(1)$ extended SM by an $SO(10)$ grand unified model through an intermediate step of $SU(5) \times U(1)$ unification. With a parameter set that is compatible with the $SO(10)$ grand unification, we find that a first-order phase transition associated with the $U(1)$ symmetry breaking can be strong enough to generate GWs with a detectable size of amplitude. We also find that the resultant GW amplitude reduces and its peak frequency becomes higher as the RH neutrino masses increase.

Renormalizable SO (10) grand unified theory with suppressed dimension-5 proton decays

Abstract We study a renormalizable supersymmetric (SUSY) $SO(10)$ grand unified theory model where the Yukawa couplings of single ${\bf 10}$, single ${\bf \overline{126}}$, and single ${\bf 120}$ fields ($Y_{10}$, $Y_{126}$, and $Y_{120}$) account for the quark and lepton Yukawa couplings and the neutrino mass. We pursue the possibility that $Y_{10}$, $Y_{126}$, and $Y_{120}$ reproduce the correct quark and lepton masses, Cabibbo–Kobayashi–Maskawa and Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrices and neutrino mass differences, and at the same time suppress dimension-5 proton decays (proton decays via colored Higgsino exchange) through their texture, so that the soft SUSY-breaking scale can be reduced as much as possible without conflicting the current experimental bound on proton decays. We perform a numerical search for such a texture, and investigate implications of that texture on unknown neutrino parameters, the Dirac CP phase of the PMNS matrix, the lightest neutrino mass, and the $(1,1)$-component of the neutrino mass matrix in the charged lepton basis. Here we concentrate on the case when the active neutrino mass is generated mostly by the Type-2 seesaw mechanism, in which case we can obtain predictions for the neutrino parameters from the condition that dimension-5 proton decays be suppressed as much as possible.

Simplified leptoquark models for precision li→lfγ experiments: Two-loop structure of O(αSY2) corrections

We put forward the framework of simplified leptoquark models: simple extensions of the Standard Model that serve as benchmarks to test the interactions of leptons with new colored degrees of freedom considered, for instance, in leptoquark or grand unification models. As a first application of the scheme, we analyze the power of precision lepton observables by computing gauge invariant two-loop radiative corrections to the lepton-photon vertex, generated here by Yukawa interactions between the lepton and new colored degrees of freedom. The result, detailed in explicit expressions for the involved form factors, improves on the literature for the higher loop order considered and highlights the existence of regions in the parameter space of the model where two-loop corrections cannot be neglected.

Grand unification models from SO(32) heterotic string

Grand unification groups (GUTs) are constructed from SO(32) heterotic string via [Formula: see text] orbifold compactification. So far, most phenomenological studies from string compactification relied on [Formula: see text] heterotic string, and this invites the SO(32) heterotic string very useful for future phenomenological studies. Here, spontaneous symmetry breaking is achieved by Higgsing of the antisymmetric tensor representations of SU[Formula: see text]. The anti-SU[Formula: see text] presented in this paper is a completely different class from the flipped-SU[Formula: see text]’s from the spinor representations of SO[Formula: see text]. Here, we realize chiral representations: [Formula: see text] for a SU(9) GUT and [Formula: see text] for a SU(5)[Formula: see text] GUT. In particular, we confirm that the non-Abelian anomalies of SU(9) gauge group vanish and hence our compactification scheme achieves the key requirement. We also present the Yukawa couplings, in particular for the heaviest fermion, [Formula: see text], and lightest fermions, neutrinos. In the supersymmetric version, we present a scenario how supersymmetry can be broken dynamically via the confining gauge group SU(9). Three families in the visible sector are interpreted as the chiral spectra of SU[Formula: see text] GUT.

R-symmetric flipped SU(5)

We construct a supersymmetric flipped SU(5) grand unified model that possesses an R symmetry. This R symmetry forbids dangerous non-renormalizable operators suppressed by a cut-off scale up to sufficiently large mass dimensions so that the SU(5)-breaking Higgs field develops a vacuum expectation value of the order of the unification scale along the F- and D-flat directions, with the help of the supersymmetry-breaking effect. The mass terms of the Higgs fields are also forbidden by the R symmetry, with which the doublet-triplet splitting problem is solved with the missing partner mechanism. The masses of right-handed neutrinos are generated by non-renormalizable operators, which then yield a light neutrino mass spectrum and mixing through the seesaw mechanism that are consistent with neutrino oscillation data. This model predicts one of the color-triplet Higgs multiplets to lie at an intermediate scale, and its mass is found to be constrained by proton decay experiments to be ≳ 5 × 1011 GeV. If it is ≲ 1012 GeV, future proton decay experiments at Hyper-Kamiokande can test our model in the p → π0μ+ and p → K0μ+ decay modes, in contrast to ordinary grand unified models where p → π0e+ or p → {K}^{+}overline{nu} is the dominant decay mode. This characteristic prediction for the proton decay branches enables us to distinguish our model from other scenarios.

Realizing unification in two different SO(10) models with one intermediate breaking scale

We derive the threshold corrections in text {SO}(10) grand unified models with the intermediate symmetry being flipped ,text {SU}(5)times text {U}(1) or ,text {SU}(3)times ,text {SU}(2)times text {U}(1)times text {U}(1), with the masses of the scalar fields set by the survival hypothesis. These models do not achieve gauge coupling unification if the matching conditions do not take threshold corrections into account. We present results showing the required size of threshold corrections for any value of the intermediate and unification scales. In particular, our results demonstrate that both of these models are disfavored since they require large threshold corrections to allow for unification with a predicted proton lifetime above current experimental bounds.

Predictive power of grand unification from quantum gravity

If a grand-unified extension of the asymptotically safe Reuter fixed-point for quantum gravity exists, it determines free parameters of the grand-unified scalar potential. All quartic couplings take their fixed-point values in the trans-Planckian regime. They are irrelevant parameters that are, in principle, computable for a given particle content of the grand unified model. In turn, the direction of spontaneous breaking of the grand-unified gauge symmetry becomes predictable. For the flow of the couplings below the Planck mass, gauge and Yukawa interactions compete for the determination of the minimum of the effective potential.

Lμ−Lτ effects to quarks and leptons from flavor unification

In the family grand unification models (fGUTs), we propose that gauge U(1)'s beyond the minimal GUT gauge group are family gauge symmetries. For the symmetry $L_\mu-L_\tau$, i.e. $Q_{2}-Q_{3}$ in our case, to be useful for the LHC anomaly, we discuss an SU(9) fGUT and also present an example in Georgi's SU(11) fGUT.

Generalized Uncertainty Principle in Astrophysics from Fermi Statistical Physics Arguments

The Heisenberg’s uncertainty principle is one of the most important concepts in quantum mechanics. One of its important outcomes is that enormously high momentum is required to look at extremely small length-scales. Nevertheless, quantum gravity and Grand Unified models taught us that a minimal observable length cutoff which is of the order of the Planck length is required. Such an important feature suggests that the conventional uncertainty principle must be generalized and accordingly the Heisenberg’s uncertainty principle is replaced by a generalized uncertainty relation. Although the effects of the generalized uncertainty relation can only be found in the context of extremely high energies/short distances and not at any scale currently probed in the laboratory, we discuss in this study its impacts on white dwarfs using the quantum mechanical statistical properties of a degenerate Fermi gas in D-spatial dimensions. Both the non-relativistic and extreme relativistic cases were discussed. It was observed that the effect of the generalized uncertainty relation is to shrink the radius of proton, a phenomenon which was observed recently using high precision laser spectroscopy of atomic hydrogen. Several points were discussed and a number of quantum statistical properties were derived.

New ultraviolet operators in supersymmetric SO(10) GUT and consistent cosmology

We consider the minimal supersymmetric grand unified model (MSGUT) based on the group $\mathrm{SO}(10)$, and study conditions leading to possible domain wall (DW) formation. It has been shown earlier that the supersymmetry preserving vacuum expectation values (vev's) get mapped to distinct but degenerate set of vev's under action of $D$ parity, leading to formation of domain walls as topological pseudo-defects. The metastability of such walls can make them relatively long lived and contradict standard cosmology. Thus we are led to consider adding a nonrenormalisable Planck scale suppressed operator, that breaks $\mathrm{SO}(10)$ symmetry but preserves Standard Model symmetry. For a large range of right handed breaking scales $M_R$, this is shown to give rise to the required pressure difference to remove the domain walls without conflicting with consistent big bang nucleosynthesis (BBN) while avoiding gravitino overproduction. However, if the walls persist till the onset of weak (thermal) inflation, then a low $\sim 10 - 100$ TeV $M_R$ becomes problematic.