Soft Supersymmetry Breaking Terms Research Articles

A minimal modular invariant neutrino model

We present a neutrino mass model based on modular symmetry with the fewest input parameters to date, which successfully accounts for the 12 lepton masses and mixing parameters through 6 real free parameters including the modulus. The neutrino masses are predicted to be normal ordering, the atmospheric angle θ23 is quite close to maximal value and the Dirac CP phase δCP is about 1.34π. We also study the soft supersymmetry breaking terms due to the modulus F-term in this minimal model, which are constrained to be the non-holomorphic modular forms. The radiative lepton flavor violation process μ → eγ is discussed.

Radiative symmetry breaking, cosmic strings and observable gravity waves in \U0001d5b4(1)\U0001d5b1 symmetric \U0001d5b2\U0001d5b4(5) × \U0001d5b4(1)χ

We implement shifted hybrid inflation in the framework of supersymmetric SU(5) × U(1)χ GUT model which provides a natural solution to the monopole problem appearing in the spontaneous symmetry breaking of SU(5). The U(1)χ symmetry is radiatevely broken after the end of inflation at an intermediate scale, yielding topologically stable cosmic strings. The Planck's bound on the gravitational interaction strength of these strings, characterized by GNμs are easily satisfied with the U(1)χ symmetry breaking scale which depends on the initial boundary conditions at the GUT scale. The dimension-5 proton lifetime for the decay p → K + ν̅, mediated by color-triplet Higgsinos is found to satisfy current Super-Kamiokande bounds for SUSY breaking scale M SUSY ≳ 12.5 TeV. We show that with minimal Kähler potential, the soft supersymmetry breaking terms play a vital role in bringing the scalar spectral index n_s within the Planck's latest bounds, although with small tensor modes r ≲ 2.5 × 10-6 and SU(5) gauge symmetry breaking scale in the range (2 × 1015≲ Mα ≲ 2 × 1016) GeV. By employing non-minimal terms in the Kähler potential, the tensor-to-scalar ratio approaches observable values (r ≲ 10-3) with the SU(5) symmetry breaking scale Mα ≃ 2 × 1016 GeV.

Modular symmetry of soft supersymmetry breaking terms

Abstract We study the modular symmetry of soft supersymmetry breaking terms. Soft scalar masses and A-term coefficients are invariant under the modular symmetry when we regard the F-term as a spurion with the modular weight −2. Their flavor structure is determined by the same symmetry as Yukawa couplings, i.e., fermion masses. The modular symmetric behavior of the μ-term and B-term depends on how the μ-term is generated.

Smooth hybrid inflation with low reheat temperature and observable gravity waves in SU(5) × U(1)χ super-GUT

We realize smooth hybrid inflation in the framework of supersymmetric SU(5) × U(1)χ ⊂ SO(10) model which provides a natural solution to the monopole problem appearing in the spontaneous symmetry breaking of SU(5). The breaking of U(1)χ symmetry leaves a residual discrete Z 2 symmetry, that serves as the MSSM matter parity, realizing the possibility of the lightest supersymmetric particle as a cold dark matter candidate. The d = 5 proton lifetime for the decay p ⟶ K +ν̅, mediated by color-triplet Higgsinos is found to satisfy current experimental bounds if split-high scale SUSY scenario is employed. We show that with minimal Kähler potential, the soft supersymmetry breaking terms play a vital rôle in bringing the scalar spectral index ns within the Planck's latest bounds. In a minimal Kähler potential setup, small values of tensor-to-scalar ratio r ≲ 3.5 × 10-7 are obtained, whereas the gravitino mass turns out to be in the range that favors PeV scale SUSY but is not sufficiently high to avoid the d = 5 proton decay. A non-minimal Kähler potential including higher order corrections is required to realize successful inflation with central value of scalar spectral index ns = 0.9655, large tensor modes r ≲ 0.056 and a low reheat temperature (3 × 106 ≲ Tr ≲ 6.5 × 107) GeV consistent with leptogenesis and baryogenesis.

μ -hybrid inflation, gravitino dark matter, and stochastic gravitational wave background from cosmic strings

We present a successful realization of supersymmetric $\mu$-hybrid inflation model based on a gauged $U(1)_{B-L}$ extension of the minimal supersymmetric standard model, with the soft supersymmetry breaking terms are playing an important role. Successful non-thermal leptogenesis with gravitino dark matter yields a reheat temperature in the range $2 \times 10^{7} \lesssim T_R \lesssim 5 \times 10^{9}$ GeV. This corresponds to the predictions $2 \times 10^{-18} \lesssim r\lesssim 4 \times 10^{-13}$ for the tensor to scalar ratio, and $-2 \times 10^{-6} \lesssim dn_s/d\ln k \lesssim -5 \times 10^{-11}$ for the running of the scalar spectral index. The $B-L$ breaking scale is estimated as $ 6 \times 10^{14}\lesssim M/ \text{GeV}\lesssim 10^{16}$, calculated at the central value of the scalar spectral index, $n_s =0.9655$, reported by Planck 2018. Finally, in a grand unified theory setup the dimensionless string tension parameter associated with the metastable strings is in the range $ 10^{-9} \lesssim G\mu_\text{cs} \lesssim 10^{-6}$ corresponding to a stochastic gravitational wave background lying within the 2$\sigma$ bound of the recent NANOGrav 12.5-yr data.

The supersymmetry breaking soft terms, and fermion masses and mixings in the supersymmetric Pati-Salam model from intersecting D6-branes

A supersymmetric Pati-Salam model with wrapping number equal to 5 has been constructed in Type IIA orientifolds on T6/(ℤ2× ℤ2) with intersecting D6-branes recently. In particular, the string-scale gauge coupling unification can be achieved due to the intermediate-scale vector-like particles from mathcal{N} = 2 sector. We calculate the supersymmetry breaking soft terms, and study the Standard Model (SM) fermion masses and mixings. There are nine pairs of Higgs doublets from mathcal{N} = 2 sector. Interestingly, we can explain the SM quark masses and mixings, as well as the charged leptons masses from three point and four-point Yukawa interactions. Moreover, we calculate the supersymmetry breaking soft terms in a previous model with gauge coupling unification since we find a typo in the previous study.

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.

Explicit soft supersymmetry breaking in the heterotic M-theory B \u2212 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.

Soft supersymmetry breaking terms and lepton flavor violations in modular flavor models

We study the soft supersymmetry (SUSY) breaking terms due to the modulus F-term in the modular flavor models of leptons. It is found that the soft SUSY breaking terms are constrained by the modular forms, and specific patterns are derived. Those phenomenological implications are discussed in such as the lepton flavor violation μ→e+γ and μ→3e decays and μ→e conversion in nuclei. In order to examine numerically, two modular flavor A4 models are taken. The SUSY breaking scale is significantly constrained by inputting the observed upper bound of the μ→e+γ decay. The SUSY mass scale is larger than around 8TeV and 5TeV for the two A4 models, respectively. Therefore, the current experimental upper bound for the μ→e+γ decay corresponds to the new physics of the SUSY particle at the 5–10TeV scale in the modular flavor models. The SUSY scale will be explored by future experiments of lepton flavor violation up to 8–17 TeV. The predicted branching ratio depends on a modulus τ significantly. It decreases of one order at the large Im τ. We also calculate the branching ratios of tauon decays to e+γ and μ+γ. Predicted ones are at most O(10−15), which are much below the current experimental bounds.

Confronting grand unification with lepton flavour violation, dark matter and LHC data

We explore possible signatures for charged lepton flavour violation (LFV), sparticle discovery at the LHC and dark matter (DM) searches in grand unified theories (GUTs) based on SU(5), flipped SU(5) (FSU(5)) and SU(4)c×SU(2)L×SU(2)R (4-2-2). We assume that soft supersymmetry-breaking terms preserve the group symmetry at some high input scale, and focus on the non-universal effects on different matter representations generated by gauge interactions at lower scales, as well as the charged LFV induced in Type-1 see-saw models of neutrino masses. We identify the different mechanisms that control the relic DM density in the various GUT models, and contrast their LFV and LHC signatures. The SU(5) and 4-2-2 models offer good detection prospects both at the LHC and in LFV searches, though with different LSP compositions, and the SU(5) and FSU(5) models offer LFV within the current reach. The 4-2-2 model allows chargino and gluino coannihilations with neutralinos, and the former offer good detection prospects for both the LHC and LFV, while gluino coannihilations lead to lower LFV rates. Our results indicate that LFV is a powerful tool that complements LHC and DM searches, providing significant insights into the sparticle spectra and neutrino mass parameters in different models.

Phenomenology and cosmology of no-scale attractor models of inflation

We have recently proposed attractor models for modulus fixing, inflation, supersymmetry breaking and dark energy based on no-scale supergravity. In this paper we develop phenomenological and cosmological aspects of these no-scale attractor models that underpin their physical applications. We consider models in which inflation is driven by a modulus field (T-type) with supersymmetry broken by a Polonyi field, or a matter field (ϕ-type) with supersymmetry broken by the modulus field. We derive the possible patterns of soft supersymmetry-breaking terms, which depend in T-type models whether the Polonyi and/or matter fields are twisted or not, and in ϕ-type models on whether the inflaton and/or other matter fields are twisted or not. In ϕ-type models, we are able to directly relate the scale of supersymmetry breaking to the inflaton mass. We also discuss cosmological constraints from entropy considerations and the density of dark matter on the mechanism for stabilizing the modulus field via higher-order terms in the no-scale Kähler potential.

Radiatively generated source of flavor universal scalar soft masses

We report that models of electroweak supersymmetry with gaugino mass unification and sequestered scalar masses can still produce viable spectra, as long as we include a set of non-standard supersymmetry breaking terms, which are trilinear in scalars like the A-terms, but are non-holomorphic in visible sector fields unlike the A- terms. These terms impart a subtle feature to one loop renormalisation group equations of soft supersymmetry breaking terms, indirectly sourcing flavor universal contributions to all scalar masses. These new contributions can even dominate over radiative corrections form bino, and help raise right handed sleptons above bino, while leaving a tell-tale signature in the spectrum.

Inspiration from intersecting D-branes: general supersymmetry breaking soft terms in no-scale mathcal{F}-SU(5)

Motivated by D-brane model building, we evaluate the mathcal {F}-SU(5) model with additional vector-like particle multiplets, referred to as flippons, within the framework of No-Scale Supergravity with non-vanishing general supersymmetry breaking soft terms at the string scale. The viable phenomenology is uncovered by applying all current experimental constraints, including but not limited to the correct light Higgs boson mass, WMAP and Planck relic density measurements, and several LHC constraints on supersymmetric particle spectra. Four interesting regions of the parameter space arise, as well as mixed scenarios, given by: (1) light stop coannihilation; (2) pure Higgsino dark matter; (3) Higgs funnel; and (4) light stau coannihilation. All regions can generate the observed value of the relic density commensurate with a 125 GeV light Higgs boson mass, with the exception of the relatively small relic density value for the pure Higgsino lightest supersymmetric particle. This work is concluded by gauging the model against present LHC search constraints and derivation of the final states observable at the LHC for each of these scenarios.

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 $Q<{M}_{E}$, where ${M}_{E}<{M}_{\text{Planck}}$ 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.

Flavored gauge mediation with discrete non-Abelian symmetries

We explore the model-building and phenomenology of flavored gauge mediation models of supersymmetry breaking in which the electroweak Higgs doublets and the SU(2) messenger doublets are connected by a discrete non-Abelian symmetry. The embedding of the Higgs and messenger fields into representations of this non-Abelian Higgs-messenger symmetry results in specific relations between the Standard Model Yukawa couplings and the messenger-matter Yukawa interactions. Taking the concrete example of an S(3) Higgs-messenger symmetry, we demonstrate that while the minimal implementation of this scenario suffers from a severe mu/B_mu problem that is well-known from ordinary gauge mediation, expanding the Higgs-messenger field content allows for the possibility that mu and B_mu can be separately tuned, allowing for the possibility of phenomenologically viable models of the soft supersymmetry breaking terms. We construct toy examples of this type that are consistent with the observed 125 GeV Higgs boson mass.

Quadratic contributions of softly broken supersymmetry in the light of loop regularization

Loop regularization (LORE) is a novel regularization scheme in modern quantum field theories. It makes no change to the spacetime structure and respects both gauge symmetries and supersymmetry. As a result, LORE should be useful in calculating loop corrections in supersymmetry phenomenology. To further demonstrate its power, in this article we revisit in the light of LORE the old issue of the absence of quadratic contributions (quadratic divergences) in softly broken supersymmetric field theories. It is shown explicitly by Feynman diagrammatic calculations that up to two loops the Wess–Zumino model with soft supersymmetry breaking terms (WZ’ model), one of the simplest models with the explicit supersymmetry breaking, is free of quadratic contributions. All the quadratic contributions cancel with each other perfectly, which is consistent with results dictated by the supergraph techniques.

Radiative corrections to Higgs boson masses for the MSSM Higgs potential with dimension-six operators

In the framework of the effective field theory approach to heavy supersymmetry radiative corrections in the Higgs sector of the Minimal Supersymmetric Standard Model (MSSM) for the effective potential decomposition up to the dimension-six operators are calculated. Symbolic expressions for the threshold corrections induced by $F$- and $D$- soft supersymmetry breaking terms are derived and the Higgs boson mass spectrum respecting the condition $m_h=$125 GeV for the lightest $CP$-even scalar is evaluated.

Loop suppressed electroweak symmetry breaking and naturally heavy superpartners

A model is presented in which O(10 TeV) stop masses, typically required by the Higgs boson mass in supersymmetric models, do not originate from soft supersymmetry breaking terms that would drive the Higgs mass squared parameter to large negative values but rather from the mixing with vectorlike partners. Their contribution to the Higgs mass squared parameter is reduced to threshold corrections and, thus, it is one loop suppressed compared to usual scenarios. New fermion and scalar partners of the top quark with O(10 TeV) masses are predicted.

MSSM without free parameters

It is often argued that the minimal supersymmetric standard model has O(100) free parameters and the generic parameter region is already excluded by the null observation of the flavor and CP violating processes as well as the constraints from the LHC experiments. This situation naturally leads us to consider the case where all the dangerous soft supersymmetry breaking terms such as the scalar masses and scalar couplings are absent, while only the unified gaugino mass term and the mu term are non-vanishing at the grand unification scale. We revisit this simple situation taking into account the observed Higgs boson mass, 125 GeV. Since the gaugino mass and the mu term are fixed in order to explain the Higgs boson and the Z boson masses, there is no free parameter left in this scenario. We find that there are three independent parameter sets exist including ones which have not been discussed in the literature. We also find that the abundance of the dark matter can be explained by relic gravitinos which are non-thermally produced as decay products of the SUSY particles while satisfying constraints from Big Bang Nucleosynthesis. We discuss the effects of the gravity mediation which generically give contribution to the soft terms of the order of the gravitino mass. It turns out that newly found parameter set is preferable to explain the Higgs boson mass as well as the gravitino dark matter while satisfying the constraints from the electric dipole moments of the electron and the nucleon.

A Model of Bulk Supersymmetry in Warped Spacetime

The Randall-Sundrum solution to the hierarchy problem in the brane-world scenario has made a significant impact on the development of model building.We investigate in this paper a model of supersymmetry in a 5D spacetime with the Randal-Sundrum warped metric.The minimal supersymmetric extension of the standard model (MSSM) superfields propagate in the bulk between the UV and IR branes at separated orbifold fixed points, while the hidden sector in charge of supersymmetry breaking is confined on the UV brane.We derive the 4D effective action from the original 5D action of the underlying theory.The effective 4D Yukawa couplings and all the soft supersymmetry breaking terms are calculated in terms of the 5D theory's coefficients. We comment on the important role of the bulk mass parameter in the relation with the geometrical properties of particles.