Supersymmetric Model Research Articles

SKdV, SmKdV flows and their supersymmetric gauge-Miura transformations

The construction of Integrable Hierarchies in terms of zero curvature representation provides a systematic construction for a series of integrable non-linear evolution equations (flows) which shares a common affine Lie algebraic structure. The integrable hierarchies are then classified in terms of a decomposition of the underlying affine Lie algebra $\hat {\cal{G}} $ into graded subspaces defined by a grading operator $Q$. In this paper we shall discuss explicitly the simplest case of the affine $\hat {sl}(2)$ Kac-Moody algebra within the principal gradation given rise to the KdV and mKdV hierarchies and extend to supersymmetric models. It is known that the positive mKdV sub-hierachy is associated to some positive odd graded abelian subalgebra with elements denoted by $E^{(2n+1)}$. Each of these elements in turn, defines a time evolution equation according to time $t=t_{2n+1}$. An interesting observation is that for negative grades, the zero curvature representation allows both, even or odd sub-hierarchies. In both cases, the flows are non-local leading to integro-differential equations. Whilst positive and negative odd sub-hierarchies admit zero vacuum solutions, the negative even admits strictly non-zero vacuum solutions. Soliton solutions can be constructed by gauge transforming the zero curvature from the vacuum into a non trivial configuration (dressing method). Inspired by the dressing transformation method, we have constructed a gauge-Miura transformation mapping mKdV into KdV flows. Interesting new results concerns the negative grade sector of the mKdV hierarchy in which a double degeneracy of flows (odd and its consecutive even) of mKdV are mapped into a single odd KdV flow. These results are extended to supersymmetric hierarchies based upon the affine $\hat {sl}(2,1)$ super-algebra.

On the possibility of mixed axion/neutralino dark matter in specific SUSY DFSZ axion models

We introduce four supersymmetric (SUSY) axion models in which the strong CP problem and the μ problem are solved with the help of the Peccei–Quinn mechanism and the Kim-Nilles mechanism, respectively. The axion physics enriches the SUSY model by introducing axion as a dark matter candidate and, therefore, the lightest supersymmetric particle (LSP) could just be a part of the total dark matter. For this reason, axion relieves the tensions between SUSY models and numerous experimental measurements, such as the dark matter direct detection experiments and the precise measurements of anomalous magnetic moment of the muon a μ . In the present paper, we investigate the constraints imposed by the latest a μ measurements and LUX-ZEPLIN (LZ) experiment on the relic density of the Higgsino-like LSP. Additionally, we consider the constraints arising from the cosmology of saxions and axinos, and their impacts on the parameter space of our models are carefully examined. For the axion constituting the remaining portion of dark matter, we find that the conventional misalignment mechanism can successfully account for the correct dark matter relic density observed by the Planck satellite.

Pauli–Villars Regularization of Kaluza–Klein Casimir Energy with Lorentz Symmetry

Abstract The Pauli–Villars regularization is appropriate to discuss the UV sensitivity of low-energy observables because it mimics how the contributions of new particles at high energies cancel large quantum corrections from the light particles in the effective field theory. We discuss the UV sensitivity of the Casimir energy density and pressure in an extra-dimensional model in this regularization scheme, and clarify the condition on the regulator fields to preserve the Lorentz symmetry of the vacuum state. Some of the conditions are automatically satisfied in spontaneously broken supersymmetric models, but supersymmetry is not enough to ensure the Lorentz symmetry. We show that the necessary regulators can be introduced as bulk fields. We also evaluate the Casimir energy density with such regulators, and its deviation from the result obtained in the analytic regularization.

Weak Scale Supersymmetry Emergent from the String Landscape.

Superstring flux compactifications can stabilize all moduli while leading to an enormous number of vacua solutions, each leading to different 4-d laws of physics. While the string landscape provides at present the only plausible explanation for the size of the cosmological constant, it may also predict the form of weak scale supersymmetry which is expected to emerge. Rather general arguments suggest a power-law draw to large soft terms, but these are subject to an anthropic selection of a not-too-large value for the weak scale. The combined selection allows one to compute relative probabilities for the emergence of supersymmetric models from the landscape. Models with weak scale naturalness appear most likely to emerge since they have the largest parameter space on the landscape. For finetuned models such as high-scale SUSY or split SUSY, the required weak scale finetuning shrinks their parameter space to tiny volumes, making them much less likely to appear compared to natural models. Probability distributions for sparticle and Higgs masses from natural models show a preference for Higgs mass mh∼125 GeV, with sparticles typically beyond the present LHC limits, in accord with data. From these considerations, we briefly describe how natural SUSY is expected to be revealed at future LHC upgrades. This article is a contribution to the Special Edition of the journal Entropy, honoring Paul Frampton on his 80th birthday.

Search for pair production of squarks or gluinos decaying via sleptons or weak bosons in final states with two same-sign or three leptons with the ATLAS detector

A search for pair production of squarks or gluinos decaying via sleptons or weak bosons is reported. The search targets a final state with exactly two leptons with same-sign electric charge or at least three leptons without any charge requirement. The analysed data set corresponds to an integrated luminosity of 139 fb−1 of proton-proton collisions collected at a centre-of-mass energy of 13 TeV with the ATLAS detector at the LHC. Multiple signal regions are defined, targeting several SUSY simplified models yielding the desired final states. A single control region is used to constrain the normalisation of the WZ + jets background. No significant excess of events over the Standard Model expectation is observed. The results are interpreted in the context of several supersymmetric models featuring R-parity conservation or R-parity violation, yielding exclusion limits surpassing those from previous searches. In models considering gluino (squark) pair production, gluino (squark) masses up to 2.2 (1.7) TeV are excluded at 95% confidence level.

Aspects of 4d supersymmetric dynamics and geometry

In this set of five Lectures we present a basic toolbox to discuss the dynamics of four dimensional supersymmetric quantum field theories. In particular we overview the program of geometrically engineering the four dimensional supersymmetric models as compactifications of six dimensional SCFTs. We discuss how strong coupling phenomena in four dimensions, such as duality and emergence of symmetry, can be naturally imbedded in the geometric constructions. The Lectures mostly review results which previously appeared in the literature but also contain some unpublished derivations.

Probing new physics with charge asymmetries in 2 same-sign leptons plus jets final states at the LHC

We study the impact of new physics models in the charge asymmetry defined for LHC final states consisting of two same-sign leptons (2SSl, with l = e, μ) plus jets (Njets ≥ 2), with a center-of-mass energy of s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV, where the main SM contribution is tt¯W\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ t\\overline{t}W $$\\end{document} production. Concretely, we consider three different new physics sources for the charge asymmetries: a heavy neutral scalar/pseudoscalar arising from the general two Higgs doublet model, an effective theory with dimension-6 four-quark operators, and a simplified R-parity-violating supersymmetric model with electroweakino production (higgsino-like or wino-like). We propose measuring the charge asymmetries differentially with respect to several kinematic observables, and inclusively/exclusively with the number of b-tagged jets in the final state (Nb ≥ {1, 2, 3}). Results are compared with the SM prediction using the χ2 criteria, expressing sensitivity in terms of the normal Gaussian significance. We show that some of the proposed new physics scenarios can be probed at the LHC even for the already recorded integrated luminosity of 139 fb−1. Finally, we also estimate the prospects for the potential LHC sensitivity to the considered new physics models in its high-luminosity phase.

Winos from natural SUSY at the high luminosity LHC

In natural supersymmetric models defined by no worse than a part in thirty electroweak fine-tuning, winos and binos are generically expected to be much heavier than Higgsinos. Moreover, the splitting between the Higgsinos is expected to be small, so that the visible decay products of the heavier Higgsinos are soft, rendering the Higgsinos quasi-invisible at the LHC. Within the natural supersymmetry (SUSY) framework, heavy electroweak gauginos decay to W, Z or h bosons plus Higgsinos in the ratio ∼2∶1∶1, respectively. This is in sharp contrast to models with a binolike lightest superpartner and very heavy Higgsinos, where the charged (neutral) wino essentially always decays to a W (h) boson and an invisible bino. Wino pair production at the LHC, in natural SUSY, thus leads to VV, Vh and hh+ET final states (V=W, Z) where, for TeV scale winos, the vector bosons and h daughters are considerably boosted. We identify eight different channels arising from the leptonic and hadronic decays of the vector bosons and the decay h→bb¯, each of which offers an avenue for wino discovery at the high luminosity LHC (HL-LHC). By combining the signal in all eight channels we find, assuming s=14 TeV and an integrated luminosity of 3000 fb−1, that the discovery reach for winos extends to m(wino)∼1.1 TeV, while the 95% CL exclusion range extends to a wino mass of almost 1.4 TeV. We also identify “Higgsino specific channels” which could serve to provide 3σ evidence that winos lighter than 1.2 TeV decay to light Higgsinos rather than to a binolike lightest supersymmetric particle, should a wino signal appear at the HL-LHC. Published by the American Physical Society 2024

Nilpotent local fermionic symmetry with generalized self-duality in D = n + n dimensions embedding supersymmetric integrable models

We present local nilpotent fermionic symmetry with a vector-spinor as its gauge field in D=2+2 space-time dimensions. Our field-content is (AμI,ψμI,χI), where I=1,2,⋯,g≡dim G is the adjoint-index of a gauge group G, while ψμI and χI are Majorana spinors. The field strengths FμνI of AμI and RμνI of ψμI satisfy the self-duality conditions FμνI=+(1/2)ϵμνρσFρσI and RμνI=+(1/2)ϵμνρσRρσI. The lowest flow of super-KdV equations and super-KP equations are embedded into this system in ways more natural than the conventional supersymmetric self-dual theories in D=2+2. This indicates that our theory even without supersymmetry in D=2+2 can serve as the “Master Theory” of all supersymmetric integrable systems in lower dimensions. Our D=2+2 result is further generalized to D=n+n(n=3,4,⋯) with the field content (AμI,ψμI,χI,Bμ1⋯μn−3), with the (n−3)-rank auxiliary Abelian tensor Bμ1⋯μn−3. The generalized self-dual conditions are ▪ and ▪. We conjecture that our theory in D=n+n is the “Grand-Master Theory” of all supersymmetric integrable systems in lower dimensions.

Modified supersymmetric indices in AdS3/CFT2

We consider the \U0001d4a9 = (2, 2) AdS3/CFT2 dualities proposed by Eberhardt, where the bulk geometry is AdS3 × (S3 × T4)/ℤk, and the CFT is a deformation of the symmetric orbifold of the supersymmetric sigma model T4/ℤk (with k = 2, 3, 4, 6). The elliptic genera of the two sides vanish due to fermionic zero modes, so for microstate counting applications one must consider modified supersymmetric indices. In an analysis similar to that of Maldacena, Moore, and Strominger for the standard \U0001d4a9 = (4, 4) case of T4, we study the appropriate helicity-trace index of the boundary CFTs. We encounter a strange phenomenon where a saddle-point analysis of our indices reproduces only a fraction (respectively 12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{2} $$\\end{document}, 23\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{2}{3} $$\\end{document}, 34\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{3}{4} $$\\end{document}, 56\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{5}{6} $$\\end{document}) of the Bekenstein-Hawking entropy of the associated macroscopic black branes.

Search for electroweakinos in R-parity violating SUSY with long-lived particles at HL-LHC

We investigate the R-parity violating (RPV) supersymmetric (SUSY) model at the High-Luminosity Large Hadron Collider (HL-LHC) in the context of compact muon solenoid (CMS) experiment assuming a total integrated luminosity of L\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{L} $$\\end{document} = 3000 fb−1 at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 14 TeV. We focus on the pair production of electroweakinos, specifically, χ20\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\chi}_2^0 $$\\end{document} and χ1±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\chi}_1^{\\pm } $$\\end{document} in wino and higgsino states in a particular scenario where χ20\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\chi}_2^0 $$\\end{document} and χ1±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\chi}_1^{\\pm } $$\\end{document} decay into a Higgs boson and W boson, respectively, along the long-lived lightest supersymmetric particle (LSP), χ10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\chi}_1^0 $$\\end{document}, which decays to three quarks via λ′′ RPV couplings leading to the prompt as well as displaced signatures in the final state. To select events at the level-1 (L1) trigger system, we employ dedicated and standard triggers followed by an offline analysis integrating information from the tracker, electromagnetic calorimeter (ECAL) and minimum ionising particle (MIP) timing detector (MTD). We observe that wino-like χ20/χ1±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\chi}_2^0/{\\chi}_1^{\\pm } $$\\end{document} with a mass of 1900 GeV and χ10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\chi}_1^0 $$\\end{document} with a mass greater than 800 GeV can be probed across a decay length ranging from 1 cm to 200 cm. In the case of higgsino-like pair production of χ20/χ1±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\chi}_2^0/{\\chi}_1^{\\pm } $$\\end{document}, we can probe χ20/χ1±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\chi}_2^0/{\\chi}_1^{\\pm } $$\\end{document} with a mass of 1600 GeV, and χ10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\chi}_1^0 $$\\end{document} with a mass greater than 700 GeV, across a decay length range of 1 cm to 200 cm.

Invisible dark matter decays of a non-Standard Model like CP-even scalar boson

We investigate two extensions of the standard model that include particle dark matter candidates: the Next-to-Two Higgs Doublet Model and the Next-to-minimal Supersymmetric Standard Model. These models feature a non-Standard Model like CP-even scalar with a sub-TeV mass, denoted by H2, among other particles. At a 13 TeV proton–proton collider, the primary production channel for such scalars is via the fusion of a pair of gluons. Subsequently, these scalars can decay invisibly into a pair of dark matter candidates, which can be dominant. In the supersymmetric model, it is possible for the Lightest Supersymmetric Particle (LSP) and Next-to Lightest Supersymmetric Particle (NLSP) to be mass degenerate, leading to quasi-invisible H2 decays to LSP+NLSP and NLSP+NLSP. We present the predictions of both models for this challenging scenario while ensuring compatibility with recent experimental constraints.

ℤ2 × ℤ2-graded Lie algebras and supseralgebras and related physical models

In this paper we construct physical systems with ℤ2×ℤ2-graded symmetries. There are two different structures:ℤ2×ℤ2-graded Lie algebras andℤ2×ℤ2-graded Lie superalgebras. Physical models with the latter symmetries can be seen as generalizations of supersymmetric models. The systems described by ℤ2 × ℤ2-graded Lie algebras have not been investigated yet (up to our knowledge). We present examples of physical models invariant under each one of both kinds of graded structures.

Search for direct production of winos and higgsinos in events with two same-charge leptons or three leptons in pp collision data at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV with the ATLAS detector

A search for supersymmetry targeting the direct production of winos and higgsinos is conducted in final states with either two leptons (e or μ) with the same electric charge, or three leptons. The analysis uses 139 fb−1 of pp collision data at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV collected with the ATLAS detector during Run 2 of the Large Hadron Collider. No significant excess over the Standard Model expectation is observed. Simplified and complete models with and without R-parity conservation are considered. In topologies with intermediate states including either Wh or WZ pairs, wino masses up to 525 GeV and 250 GeV are excluded, respectively, for a bino of vanishing mass. Higgsino masses smaller than 440 GeV are excluded in a natural R-parity-violating model with bilinear terms. Upper limits on the production cross section of generic events beyond the Standard Model as low as 40 ab are obtained in signal regions optimised for these models and also for an R-parity-violating scenario with baryon-number-violating higgsino decays into top quarks and jets. The analysis significantly improves sensitivity to supersymmetric models and other processes beyond the Standard Model that may contribute to the considered final states.

Search for Evidence of Baryogenesis and Dark Matter in B^{+}→ψ_{D}+p Decays at BABAR.

A new dark sector antibaryon, denoted ψ_{D}, could be produced in decays of B mesons. This Letter presents a search for B^{+}→ψ_{D}+p (and the charge conjugate) decays in e^{+}e^{-} annihilations at 10.58GeV, using data collected in the BABAR experiment. Data corresponding to an integrated luminosity of 398 fb^{-1} are analyzed. No evidence for a signal is observed. Branching fraction upper limits in the range from 10^{-7}-10^{-5} are obtained at 90% confidence level for masses of 1.0<m_{ψ_{D}}<4.3 GeV/c^{2}. The result is also reinterpreted to provide the first limits on a supersymmetric model with R-parity violation and a light neutralino.

A hybrid type I + III inverse seesaw mechanism in U(1)R−L-symmetric MSSM

We show that, in a U(1)R−L-symmetric supersymmetric model, the pseudo-Dirac bino and wino can give rise to three light neutrino masses through effective operators, generated at the messenger scale between a SUSY breaking hidden sector and the visible sector. The neutrino-bino/wino mixing follows a hybrid type I+III inverse seesaw pattern. The light neutrino masses are governed by the ratio of the U(1)R−L-breaking gravitino mass, m3/2, and the messenger scale ΛM. The charged component of the SU(2)L-triplet, here the lightest charginos, mix with the charged leptons and generate flavor-changing neutral currents at tree level. We find that resulting lepton flavor violating observables yield a lower bound on the messenger scale, ΛM ≳ (500 − 1000) TeV for a simplified hybrid mixing scenario. We identify interesting mixing structures for certain U(1)R−L-breaking singlino/tripletino Majorana masses. For example, in some parameter regimes, bino or wino has no mixing with the electron neutrino. We also describe the rich collider phenomenology expected in this neutrino-mass generation mechanism.

Monopole harmonics on $\mathbb{CP}^{n-1}$

We find the spectra and eigenfunctions of both ordinary and supersymmetric quantum-mechanical models describing the motion of a charged particle over the \mathbb{CP}^{n-1}ℂℙn−1 manifold in the presence of a background monopole-like gauge field. The states form degenerate SU(n)SU(n) multiplets and their wave functions acquire a very simple form being expressed via homogeneous coordinates. Their relationship to multidimensional orthogonal polynomials of a special kind is discussed. By the well-known isomorphism between the twisted Dolbeault and Dirac complexes, our construction also gives the eigenfunctions and eigenvalues of the Dirac operator on complex projective spaces in a monopole background.

Spontaneous supersymmetry breaking in inhomogeneous supersymmetric field theories and BPS vacua

We study spontaneous supersymmetry breaking in inhomogeneous extensions of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 supersymmetric field theory models in 4-dimensions. The N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 Abelian Higgs model with the inhomogeneous mass parameter and the FI coefficient that are dependent on spatial coordinates, as well as the O’Raifeartaigh model with all its parameters being dependent on spatial coordinates, are studied in detail. In the presence of inhomogeneous parameters, half supersymmetry can be preserved by adding appropriate inhomogeneous deformations to the original Lagrangians. The inhomogeneous deformations often break the R-symmetry explicitly. In cases where the inhomogeneous deformations do not break the R-symmetry explicitly, we demonstrate that spontaneous breaking of the R-symmetry is infeasible. We argue that those models can not be spontaneous supersymmetry breaking models, according to the Nelson-Seiberg argument. We comment on this issue in the context of a generic N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 supersymmetric model as well.

Neutrino Masses in Supersymmetric Models with R-Symmetry

In this article, we give a brief review of the origin of the neutrino mass in some interesting non-linear supersymmetric models with R-symmetry. These models are able to address and solve the most important problems of particle physics and provide mechanisms for neutrino mass generation and their mixing parameters in agreement with the current experimental data. Their prediction could be experimentally tested in the near future by collider experiments.

Supersymmetric higher-derivative models in quantum cosmology

We study the quantum cosmology of supersymmetric, homogeneous and isotropic, higher derivative models. We recall superfield actions obtained in previous works and give classically equivalent actions leading to second order equations for the bosons, and first order for the fermions. Upon quantization, the algebra of fermions leads to a multi-component state, which is annihilated by the Hamiltonian and supersymmetric constraint operators. We obtain asymptotic wave functions of the oscillatory type, whose classical limit corresponds to inflationary evolution, and exact exponential wave functions. We use the latter to derive probability distributions of the initial curvature that are compatible with those obtained using the non-supersymmetric model.