Flipped $$\mathbf {g_\mu - 2}$$

We analyze the possible magnitude of the supersymmetric contribution to $$g_\mu - 2$$ g μ - 2 in a flipped SU(5) GUT model. Unlike other GUT models which are severely constrained by universality relations, in flipped SU(5) the U(1) gaugino mass and the soft supersymmetry-breaking masses of right-handed sleptons are unrelated to the other gaugino, slepton and squark masses. Consequently, the lightest neutralino and the right-handed smuon may be light enough to mitigate the discrepancy between the experimental measurement of $$g_\mu - 2$$ g μ - 2 and the Standard Model calculation, in which case they may be detectable at the LHC and/or a 250 GeV $$e^+ e^-$$ e + e - collider, whereas the other gauginos and sfermions are heavy enough to escape detection at the LHC.

Flipped SU(5) GUT phenomenology: proton decay and $$\mathbf {g_\mu - 2}$$

We consider proton decay and $$g_\mu - 2$$ g μ - 2 in flipped SU(5) GUT models. We first study scenarios in which the soft supersymmetry-breaking parameters are constrained to be universal at some high scale $$M_{in}$$ M in above the standard GUT scale where the QCD and electroweak SU(2) couplings unify. In this case the proton lifetime is typically $$ > rsim 10^{36}$$ ≳ 10 36 years, too long to be detected in the foreseeable future, and the supersymmetric contribution to $$g_\mu - 2$$ g μ - 2 is too small to contribute significantly to resolving the discrepancy between the experimental measurement and data-driven calculations within the Standard Model. However, we identify a region of the constrained flipped SU(5) parameter space with large couplings between the 10- and 5-dimensional GUT Higgs representations where $$p \rightarrow e^+ \pi ^0$$ p → e + π 0 decay may be detectable in the Hyper-Kamiokande experiment now under construction, though the contribution to $$g_\mu -2$$ g μ - 2 is still small. A substantial contribution to $$g_\mu - 2$$ g μ - 2 is possible, however, if the universality constraints on the soft supersymmetry-breaking masses are relaxed. We find a ‘quadrifecta’ region where observable proton decay co-exists with a (partial) supersymmetric resolution of the $$g_\mu - 2$$ g μ - 2 discrepancy and acceptable values of $$m_h$$ m h and the relic LSP density.

Weak scale right-handed neutrino as pseudo-Goldstone fermion of spontaneously broken $$ \mathrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} $$

Possibility of a Right-Handed (RH) neutrino being a Goldstone fermion of a spontaneously broken global U(1) symmetry in a supersymmetric theory is considered. This fermion obtains mass from the supergravity effects leading to a RH neutrino at the electroweak scale with a mass similar to the gravitino mass. A prototype model realizing this scenario contains just three gauge singlet superfields needed for the type I seesaw mechanism. Masses of the other two neutrinos are determined by the U(1) breaking scale which too can be around the electroweak scale. Light neutrinos obtain their masses in this scenario through (a) mixing with the RH neutrinos (type I seesaw), (b) mixing with neutralinos (R-parity breaking), (c) indirectly through mixing of the RH neutrinos with neutralinos, and (d) radiative corrections. All these contributions are described by the same set of a small number of underlying parameters and provide a very constrained and predictive framework for the neutrino masses which is investigated in detail for various choices of U(1) symmetries. It is found that flavour independent U(1) symmetries cannot describe neutrino masses if the soft supersymmetry breaking terms are flavour universal and one needs to consider flavour dependent symmetries. Considering a particular example of Lμ− Lτ symmetry, it is shown that viable neutrino masses and mixing can be obtained without introducing any flavour violation in the soft sector. The leptonic couplings of Majoron are worked out in the model and shown to be consistent with various laboratory, astrophysical and cosmological constraints. The neutrino data allows sizeable couplings between the RH neutrinos and Higgsinos which can be used to probe the pseudo-Goldstone fermion at colliders through its displaced decay vertex.

Revisiting the multi-monopole point of SU(N) $$ \mathcal{N} $$ = 2 gauge theory in four dimensions

Motivated by applications to soft supersymmetry breaking, we revisit the expansion of the Seiberg-Witten solution around the multi-monopole point on the Coulomb branch of pure SU(N) $$ \mathcal{N} $$ N = 2 gauge theory in four dimensions. At this point N − 1 mutually local magnetic monopoles become massless simultaneously, and in a suitable duality frame the gauge couplings logarithmically run to zero. We explicitly calculate the leading threshold corrections to this logarithmic running from the Seiberg-Witten solution by adapting a method previously introduced by D’Hoker and Phong. We compare our computation to existing results in the literature; this includes results specific to SU(2) and SU(3) gauge theories, the large-N results of Douglas and Shenker, as well as results obtained by appealing to integrable systems or topological strings. We find broad agreement, while also clarifying some lingering inconsistencies. Finally, we explicitly extend the results of Douglas and Shenker to finite N , finding exact agreement with our first calculation.

Explicit soft supersymmetry breaking in the heterotic M-theory B − L MSSM

The strongly coupled heterotic M-theory vacuum for both the observable and hidden sectors of the B − L MSSM theory is reviewed, including a discussion of the “bundle” constraints that both the observable sector SU(4) vector bundle and the hidden sector bundle induced from a single line bundle must satisfy. Gaugino condensation is then introduced within this context, and the hidden sector bundles that exhibit gaugino condensation are presented. The condensation scale is computed, singling out one line bundle whose associated condensation scale is low enough to be compatible with the energy scales available at the LHC. The corresponding region of Kähler moduli space where all bundle constraints are satisfied is presented. The generic form of the moduli dependent F-terms due to a gaugino superpotential — which spontaneously break N = 1 supersymmetry in this sector — is presented and then given explicitly for the unique line bundle associated with the low condensation scale. The moduli-dependent coefficients for each of the gaugino and scalar field soft supersymmetry breaking terms are computed leading to a low-energy effective Lagrangian for the observable sector matter fields. We then show that at a large number of points in Kähler moduli space that satisfy all “bundle” constraints, these coefficients are initial conditions for the renormalization group equations which, at low energy, lead to completely realistic physics satisfying all phenomenological constraints. Finally, we show that a substantial number of these initial points also satisfy a final constraint arising from the quadratic Higgs-Higgs conjugate soft supersymmetry breaking term.

A minimal supersymmetric SU(5) missing-partner model

We explore a missing-partner model based on the minimal SU(5) gauge group with $$\mathbf{75} $$ 75 , $$\mathbf{50} $$ 50 and $$\overline{\mathbf{50 }}$$ 50 ¯ Higgs representations, assuming a super-GUT CMSSM scenario in which soft supersymmetry-breaking parameters are universal at some high scale $$M_{\mathrm{in}}$$ M in above the GUT scale $$M_{\mathrm{GUT}}$$ M GUT . We identify regions of parameter space that are consistent with the cosmological dark matter density, the measured Higgs mass and the experimental lower limit on $$\tau (p \rightarrow K^+ \nu )$$ τ ( p → K + ν ) . These constraints can be satisfied simultaneously along stop coannihilation strips in the super-GUT CMSSM with $$\tan \beta \sim $$ tan β ∼ 3.5–5 where the input gaugino mass $$m_{1/2} \sim $$ m 1 / 2 ∼ 15–25 TeV, corresponding after strong renormalization by the large GUT Higgs representations between $$M_{\mathrm{in}}$$ M in and $$M_{\mathrm{GUT}}$$ M GUT to $$m_{\mathrm{LSP}}, m_{{\tilde{t}}_1} \sim $$ m LSP , m t ~ 1 ∼ 2.5–5 TeV and $$m_{{\tilde{g}}} \sim $$ m g ~ ∼ 13–20 TeV, with the light-flavor squarks significantly heavier. We find that $$\tau (p \rightarrow K^+ \nu ) \lesssim 3 \times 10^{34}$$ τ ( p → K + ν ) ≲ 3 × 10 34 years throughout the allowed range of parameter space, within the range of the next generation of searches with the JUNO, DUNE and Hyper-Kamiokande experiments.

Low-energy probes of no-scale SU(5) super-GUTs

We explore the possible values of the $$\mu \rightarrow e \gamma $$ μ → e γ branching ratio, $$\text {BR}(\mu \rightarrow e\gamma )$$ BR ( μ → e γ ) , and the electron dipole moment (eEDM), $$d_e$$ d e , in no-scale SU(5) super-GUT models with the boundary conditions that soft supersymmetry-breaking matter scalar masses vanish at some high input scale, $$M_\mathrm{in}$$ M in , above the GUT scale, $$M_{\mathrm{GUT}}$$ M GUT . We take into account the constraints from the cosmological cold dark matter density, $$\Omega _{CDM} h^2$$ Ω CDM h 2 , the Higgs mass, $$M_h$$ M h , and the experimental lower limit on the lifetime for $$p \rightarrow K^+ \bar{\nu }$$ p → K + ν ¯ , the dominant proton decay mode in these super-GUT models. Reconciling this limit with $$\Omega _{CDM} h^2$$ Ω CDM h 2 and $$M_h$$ M h requires the Higgs field responsible for the charge-2/3 quark masses to be twisted, and possibly also that responsible for the charge-1/3 and charged-lepton masses, with model-dependent soft supersymmetry-breaking masses. We consider six possible models for the super-GUT initial conditions, and two possible choices for quark flavor mixing, contrasting their predictions for proton decay with versions of the models in which mixing effects are neglected. We find that $$\tau \left( p\rightarrow K^+ \bar{\nu }\right) $$ τ p → K + ν ¯ may be accessible to the upcoming Hyper-Kamiokande experiment, whereas all the models predict $$\text {BR}(\mu \rightarrow e\gamma )$$ BR ( μ → e γ ) and $$d_e$$ d e below the current and prospective future experimental sensitivities or both flavor choices, when the dark matter density, Higgs mass and current proton decay constraints are taken into account. However, there are limited regions with one of the flavor choices in two of the models where $$\mu \rightarrow e$$ μ → e conversion on a heavy nucleus may be observable in the future. Our results indicate that there is no supersymmetric flavor problem in the class of no-scale models we consider.

Non-supersymmetric string models from anti-D3-/D7-branes in strongly warped throats

This article discusses model-building scenarios including anti-D3-/D7-branes, in which supersymmetry is broken spontaneously, despite having no scale at which sparticles appear and standard supersymmetry is restored. If the branes are placed on singularities at the tip of warped throats in Calabi-Yau orientifold flux compactifications, they may give rise to realistic particle spectra, closed- and open-string moduli stabilisation with a Minkowski/de Sitter uplift, and a geometrical origin for the scale hierarchies. The paper derives the low-energy effective field theory description for such scenarios, i.e. a non-linear supergravity theory for standard and constrained supermultiplets, including soft supersymmetry-breaking matter couplings. The effect of closed-string moduli stabilisation on the open-string matter sector is worked out, incorporating non-perturbative and perturbative effects, and the mass and coupling hierarchies are computed with a view towards phenomenology.

Further Studies of the Supersymmetric NJL-Type Model for a Real Superfield Composite

This is a sequel to our earlier paper presenting a supersymmetric Nambu–Jona–Lasinio (NJL)-type model for a real superfield composite. The model in the simplest version has only a chiral superfield (multiplet), with a strong four-superfield interaction in the Kähler potential that induces a real two-superfield composite with vacuum condensate. The latter can have supersymmetry breaking parts, which we have shown to bear nontrivial solutions under a standard nonperturbative analysis for a Nambu–Jona–Lasinio-type model on a superfield setting. In this article, we generalize our earlier analysis by allowing a supersymmetric mass term for the chiral superfield, as well as possible θ2 components for the soft supersymmetry breaking part of the condensate. We present admissible nontrivial vacuum solutions and an analysis of the resulted low energy effective theory with components of the composite becoming dynamical. The determinant of the fermionic modes is shown to be zero, illustrating the presence of the expected Goldstino.