Gravitino Mass Research Articles

Dark matter via baryogenesis: Affleck–Dine mechanism in the minimal supersymmetric standard model

We conducted an investigation into Affleck–Dine baryogenesis within the context of polynomial inflation, specifically focusing on its relationship with a recent reheating formalism. It was found that by considering a specific reheating temperature, the observed baryon asymmetry can be accounted through Affleck–Dine baryogenesis. Additionally, the majority of gravitinos are inferred to be generated from the decay of the next-to-lightest supersymmetric particle, with Q-balls potentially serving as a source of gravitinos via the NSP decay. The temperature at which decay occurs depends on the charge of the Q-balls, which is determined by the fragmentation of the Affleck–Dine condensate. Remarkably, the gravitino mass required for dark matter aligns naturally with the theoretical gravitino mass.

Natural anomaly mediation from the landscape with implications for LHC SUSY searches

Supersymmetric models with the anomaly-mediated supersymmetry (SUSY) breaking (AMSB) form for soft SUSY breaking terms arise in two different settings: (1) extra-dimensional models where SUSY breaking occurs in a sequestered sector, and (2) 4−d models with dynamical SUSY breaking in a hidden sector where scalars gain masses of order the gravitino mass m3/2, but gaugino masses and trilinear soft terms are assumed to be of the AMSB form. Both models run into serious conflicts with (1) LHC sparticle and Higgs mass constraints, (2) constraints from winolike weakly interacting massive particle dark matter searches, and (3) bounds from naturalness. These conflicts may be avoided by introducing minor changes to the underlying phenomenological models consisting of nonuniversal bulk scalar Higgs masses and A terms, providing a setting for natural anomaly mediation (nAMSB). In nAMSB, the wino is still expected to be the lightest of the gauginos, but the Higgsinos are expected to be the lightest electroweakinos (EWinos) in accord with naturalness. We examine what sorts of spectra are expected to emerge when nAMSB arises from a string landscape setting: While model 2 can only be natural for a Higgs mass mh≲123 GeV, model 1 can accommodate naturalness along with mh∼125 GeV while still respecting LHC bounds on sparticle masses. We explore the LHC phenomenology of nAMSB models where we find that for Higgsino pair production, typically larger dilepton mass gaps arise from the soft dilepton-plus-jets signature than in models with gaugino mass unification. For wino-pair production, the higher m3/2 portion of nAMSB parameter space is excluded by recent LHC bounds from gaugino pair production searches. We characterize the dominant LHC signatures arising from the remaining lower m3/2∼90–200 TeV range of parameter space, which should be fully testable at high-luminosity LHC via EWino pair production searches. Published by the American Physical Society 2024

Gravitational Waves and gravitino mass in No-Scale Supergravity inflation with Polonyi term

We study a No-Scale supergravity inflation model which has a non-minimal deformation of the Kähler potential and a Wess-Zumino superpotential extended by the inclusion of a Polonyi mass term. The non-minimal structure of the Kähler potential is responsible for an inflexion point that can lead to the production of gravitational waves at late stages of inflation, while the Polonyi term breaks supersymmetry at the end of inflation, generating a non-vanishing gravitino mass. After a thorough parameter space scan, we identify promising points for gravitational wave production. We then study the resulting gravitational wave energy density for this set of points, and we observe that the gravitational waves should be observable in the next generation of both space-based and ground-based interferometers. Finally, we show how the presence of the Polonyi term can be used to further boost the gravitational wave energy density, which is correlated with the gravitino mass. The code used for the scan and the numerical analysis is provided at https://gitlab.com/miguel.romao/gw-and-m32-no-scale-inflation-polonyi.

Sequestered string models imply split supersymmetry

Sequestering is a promising mechanism in 4D string models to reconcile high-scale inflation with low-energy supersymmetry. In this scenario the MSSM lives on branes at singularities and it is sequestered from the sources of supersymmetry breaking in the bulk. The soft-terms are suppressed with respect to the gravitino mass so that all moduli are heavy enough to avoid any cosmological moduli problem. In this paper we study stability bounds and flavour constraints on sequestered string models, finding that they can be satisfied if the soft-terms give rise to a mass spectrum typical of split supersymmetry with TeV-scale gauginos and sfermions around 107 GeV. When instead scalar and gaugino masses are of the same order of magnitude, large flavour changing neutral currents can be avoided only by pushing the soft-terms above 106 GeV. However this scenario is in tension with stability bounds due to the presence of charge and colour breaking vacua which could be populated in the early universe, and the possible emergence of directions along which the potential is unbounded from below.

How effective is N eff at discovering dark radiation in a cosmology with heavy particle decay?

Any light relic which was in thermal equilibrium with the Standard Model before it freezes out results in a shift in the effective number of neutrino species, N eff. This quantity is being measured with increasing precision, and planned experiments would seemingly rule out light particles beyond the Standard Model, even for rather high temperature light particle freeze out. Here we explore how these bounds are loosened if the energy density of the light particles is diluted with respect to that of Standard Model radiation. This can happen if a heavy particle that is decoupled from the Standard Model decays into the Standard Model bath after the light particle freezes out. After calculating how heavy state decays alter N eff for light particles beyond the Standard Model, we focus in particular on the case that the heavy decaying particle is a gravitino, and use current bounds on N eff to place constraints on the gravitino mass and the branching ratio into light particles for different values of the reheating temperature of the Universe.

New non-supersymmetric flux vacua in string theory

In this note we construct large ensembles of supersymmetry breaking solutions arising in the context of flux compactifications of type IIB string theory. This class of solutions was previously proposed in [1] for which we provide the first explicit examples in Calabi-Yau orientifold compactifications with discrete fluxes below their respective tadpole constraint. As a proof of concept, we study the degree 18 hypersurface in weighted projective space CP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathbbm{CP} $$\\end{document}1,1,1,6,9. Furthermore, we look at 10 additional orientifolds with h1,2 = 2, 3. We find several flux vacua with hierarchical suppression of the vacuum energy with respect to the gravitino mass. These solutions provide a crucial stepping stone for the construction of explicit de Sitter vacua in string theory. Lastly, we also report the difference in the distribution of W0 between supersymmetric and non-supersymmetric minima.

Bounds on tower mass scales in the presence of throats of different warping

In Type IIB flux compactification realizing the metastable de Sitter (dS) vacuum, the uplift potential can be generated by D3‾-branes at the tip of Klebanov-Strassler throat. Then the uplift potential obeys the scaling law with respect to the tower mass scale msc, which can be the Kaluza-Klein (KK) mass scale associated with the throat containing D3‾-branes or the bulk tower mass scales, depending on the warping of the throat. On the other hand, in the presence of another throat of stronger warping, the KK mass scale associated with this throat is lower than msc. Nevertheless, the Higuchi bound and the condition that the tower mass scale is higher than the gravitino mass provide the upper bound on msc determined by the lowest tower mass scale (or gravitino mass). This bound also can be interpreted as the lower bound on the lowest tower mass scale determined by msc. We investigate this bound in detail when the throat containing D3‾-branes is strongly and weakly warped, respectively.

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.

Fayet–Iliopoulos D-term in non-supersymmetric heterotic string orbifolds

The Fayet–Iliopoulos D-term is a common feature in N=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {N}}=1$$\\end{document} string vacua that contain an anomalous U(1) gauge symmetry, and arises from a one-loop diagram in string perturbation theory. The same diagram is generated in string vacua in which supersymmetry is broken directly at the string scale, either via spontaneous Scherk–Schwarz breaking, in which case the gravitino mass is determined by the radius of the circle used in the Scherk–Schwarz mechanism, or via explicit supersymmetry breaking by the GSO projections. We analyse the resulting would-be Fayet–Illiopoulos D-term in the non-supersymmetric string vacua and its contribution to the vacuum energy. A numerical estimate in an explicit tachyon-free string-derived model suggests that the would-be D-term contribution may uplift the vacuum energy to a positive value.

A Note on Modular Invariant Species Scale and Potentials

AbstractThe species scale provides an upper bound for the ultraviolet cutoff of effective theories of gravity coupled to a number of light particle species. Modular invariant (super‐)potentials provide a simple and computable expression of the species scale as a function of the moduli in toroidal orbifold compactifications of type II and heterotic string are pointed out. Due t o modular symmetry, these functions are valid over all moduli space and not only in asymptotic regions. Additive logarithmic corrections to the species scale arise from the requirement that the latter be modular invariant are observed. The moduli‐dependent expression of the species scale in terms of the gravitino mass or the scalar potential of these models are recasted and swampland conjectures such as the anti‐de Sitter distance conjecture and the gravitino conjecture are connected.

Quantum gravity constraints on scale separation and de Sitter in five dimensions

We give evidence that supersymmetric anti-de Sitter vacua of five-dimensional supergravity cannot be scale separated as a consequence of quantum gravity constraints, such as the weak gravity conjecture or the species scale. We show this in a model-independent way for the minimal and the maximal theory and we believe that the argument can be extended to any amount of preserved supercharges in the between. If combined with previous works stating that non-supersymmetric anti-de Sitter vacua must be unstable, our results suggest that five-dimensional effective field theories in anti-de Sitter belong to the swampland. At the cost of introducing an additional assumption on the gravitino mass, we can extend our analysis to de Sitter vacua as well. However, the few known stable de Sitter vacua of minimal five-dimensional supergravity do not satisfy such an assumption and thus evade our constraints. This suggest that they are on a somehow different footing than their four-dimensional counterparts and therefore deserve further investigation.

The Scale of Supersymmetry Breaking and the Dark Dimension

We argue for a relation between the supersymmetry breaking scale and the measured value of the dark energy density Λ. We derive it by combining two quantum gravity consistency swampland constraints, which tie the dark energy density Λ and the gravitino mass M3/2, respectively, to the mass scale of a light Kaluza-Klein tower and, therefore, to the UV cut-off of the effective theory. Whereas the constraint on Λ has recently led to the Dark Dimension scenario, with a prediction of a single mesoscopic extra dimension of the micron size, we use the constraint on M3/2 to infer the implications of such a scenario for the scale of supersymmetry breaking. We find that a natural scale for supersymmetry signatures isM=OΛ18=OTeV.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ M=\\mathcal{O}\\left({\\Lambda}^{\\frac{1}{8}}\\right)=\\mathcal{O}\\left(\ extrm{TeV}\\right). $$\\end{document}This mass scale is within reach of LHC and of the next generation of hadron colliders. Finally, we discuss possible string theory and effective supergravity realizations of the Dark Dimension scenario with broken supersymmetry.

More on massive gravitino scattering amplitudes and the unitarity cutoff of the new Fayet-Iliopoulos terms

We extend the 2 → 2 gravitino scattering amplitude computed in [1] to an arbitrary mathcal{N} = 1 supergravity model of one chiral and one vector multiplet, in a Minkowski background with supersymmetry breaking driven by both F- and D-terms. We find that the cancellation of the leading term in mathcal{O} (κ2E4/|m3/2|2), that would lead to a breakdown of perturbative unitarity at a scale Λ ~ MSUSY, is a consequence of the vanishing of the scalar potential at its minimum, which is implied by the flat background. We then analyse the inclusion of the new Fayet-Iliopoulos (FI) terms. We find that, since they modify the scalar potential without contributing to the amplitudes, they generically lead to uncanceled leading terms in the latter and a perturbative cutoff at the supersymmetry breaking scale, except for particular cases where the new FI term does not modify the potential at its minimum and the cutoff is pushed up to the Planck scale.

A novel solution to the gravitino problem

In a general phenomenological model with local supersymmetry, the amount of massive gravitinos produced in early universe tends to violate the known dark matter density bound by many orders of magnitude. In the brane world scenario in Type IIB string theory, we propose a novel way to evade this problem. There, the standard model of strong and electroweak interactions live inside the anti-D3-branes ( overline{textrm{D}3} -branes) that span the 3 large spatial dimensions. Here, the “potential” Goldstino to be absorbed by the gravitino (to become massive) is the fermion component of the open string nilpotent superfield X (i.e., X2 = 0) which is present only inside the overline{textrm{D}3} -branes. This non-linear supergravity scenario offers 2 ways to solve the gravitino problem, with very different particle physics phenomenologies: (1) To satisfy the necessary condition for a naturally small cosmological constant Λ, the supersymmetry breaking overline{textrm{D}3} -branes tension is precisely cancelled by the Higgs spontaneous symmetry breaking effect, so the gravitino is ultra-light and its contribution to the dark matter density is negligible. If exist, the super-particles should have already been detected in experiments. To avoid contradiction with their non-observation, X is applied to project out all the “R-parity odd” fields. Consequently, this non-linear supergravity model is almost identical to the standard model. (2) As an alternative, one can have a massive gravitino (e.g., {hat{m}}_{3/2} > 100 GeV) due to the supersymmetry breaking tension of the overline{textrm{D}3} -branes. Here, the super-particles can be heavy enough to have avoided detection so far. Since the open string Goldstino exists only inside the overline{textrm{D}3} -branes, the gravitino is heavy only inside the overline{textrm{D}3} -branes, but massless or ultra-light outside the overline{textrm{D}3} -branes. This means that the gravitinos will be pushed out of the overline{textrm{D}3} -branes to the extra dimensions in the bulk, a phenomenon analogous to the Meissner effect for the massive photons inside super-conductors but massless outside. As a result, the massive gravitinos will be depleted so the gravitino problem is absent. In this case, a fine-tuning is necessary to obtain the very small observed Λobs.

Massive gravitino scattering amplitudes and the unitarity cutoff of the new Fayet-Iliopoulos terms

We compute the 2 → 2 gravitino scattering amplitudes at tree level in supergravity theories where supersymmetry is spontaneously broken. In the unitary gauge, the gravitino becomes massive (of mass m3/2) by absorbing the Goldstino, and the scattering amplitudes of its longitudinal polarisations grow with energy as {kappa}^2{E}^4/{m}_{3/2}^2 , signaling a potential breakdown of unitarity at a scale {Lambda}^2sim {m}_{3/2}/kappa sim {M}_{textrm{SUSY}}^2 . As we show explicitly in the Polonyi model, this leading term is cancelled by the contributions coming from the scalar partner of the Goldstino (sgoldstino), restoring perturbative unitarity up to the Planck scale. This is expected since supersymmetry is spontaneously broken, in analogy with the situation occuring in the Standard Model, where massive gauge bosons scattering preserves unitarity at high energy once we consider the contributions from the Higgs boson. However, when supersymmetry is broken by the new Fayet-Iliopoulos D-term, with ungauged R-symmetry, the above cancellation does not occur. In this case, the unbroken phase is singular and there is no contribution able to cancel the quartic divergences of the amplitudes, leading to a cutoff Λ ~ MSUSY where the effective theory breaks down. The same behaviour is obtained when supersymmetry is non-linearly realised.

Joint statistics of cosmological constant and SUSY breaking in flux vacua with nilpotent Goldstino

We obtain the joint distribution of the gravitino mass and the cosmological constant in KKLT and LVS models with anti-D3 brane uplifting described via the nilpotent goldstino formalism. Moduli stabilisation (of both complex structure and Kähler moduli) is incorporated so that we sample only over points corresponding to vacua. Our key inputs are the distributions of the flux superpotential, the string coupling and the hierarchies of warped throats. In the limit of zero cosmological constant, we find that both in KKLT and LVS the distributions are tilted favourably towards lower scales of supersymmetry breaking.

High quality axion in supersymmetric models

In this work, we discuss how the use of the symmetries well motivated in physics beyond the Standard model (BSM) can guarantee the high quality axions. We avoid to introduce symmetries only useful for addressing the axion quality problem. Rather, we rely on symmetries well motivated by other issues in BSM: supersymmetry, U(1)B−L and the discrete R-symmetry ZNR. We show that the interplay among these guarantees the high quality of the axion even for the gravitino mass and axion decay constant as large as m3/2 = mathcal{O} (10)TeV and Fa = mathcal{O} (1015)GeV respectively. The key point of this work relies on the observation that the MSSM contribution to the mixed anomalies ZNR − [SU(2)L]2 and ZNR − [SU(3)c]2 is not enough for gauging ZNR for N ≠ 6, which necessitates the introduction of new matter fields. We make the introduction to achieve zero mixed anomalies, which logically supports a desired large enough N for ZNR. This mechanism effectively makes ZNR equal to U(1)R and thus offers a logically complete solution to the axion quality problem.

Higgsino dark matter in pure gravity mediated supersymmetry

We consider the prospects for the direct detection of dark matter in pure gravity meditation (PGM) models of supersymmetry breaking. Minimal PGM models require only two parameters, the gravitino mass, $m_{3/2}$, which sets the UV mass for all scalar masses, and $\tan\beta$. Gaugino masses are generated through anomaly mediation. Typically the lightest supersymmetric state (the dark matter candidate) is a wino. Here, we consider a one-parameter extension of the minimal model by allowing the Higgs soft masses to deviate from universality. For simplicity, we take these to be equal and use the $\mu$-term as a surrogate. We also consider non-universal stop masses. When $|\mu| \sim 1$ TeV, the Higgsino is a viable dark matter candidate when the gravitino mass is of order $\sim 1$ PeV and $\tan\beta \simeq 2$. We calculate the spin-dependent and spin-independent cross sections for dark matter scattering on protons. For spin-independent scattering, existing experimental limits place constraints on the PGM parameter space. Much of the currently allowed parameter space lies above the irreducible neutrino background. Thus, future direct detection experiments will be able to probe much of the remaining PGM parameter space.

Inflation, SUSY breaking, and primordial black holes in modified supergravity coupled to chiral matter

We propose a novel model of the modified (Starobinsky-like) old-minimal-type supergravity coupled to a chiral matter superfield, that can simultaneously describe multi-field inflation, primordial black hole (PBH) formation, dark matter (DM), and spontaneous supersymmetry (SUSY) breaking after inflation in a Minkowski vacuum. The PBH masses in our supergravity model of double slow-roll inflation, with a short phase of “ultra-slow-roll” between two slow-roll phases, are close to 10^{18} g. We find that a significant PBH fraction in the allowed mass window can be supplemented by spontaneous SUSY breaking in the vacuum with the gravitino mass close to the scalaron (inflaton) mass M of the order 10^{13} GeV. Our supergravity model favors the composite nature of DM as a mixture of PBH and heavy gravitinos as the lightest SUSY particles. The composite DM significantly relaxes fine-tuning needed for the whole PBH-DM. The PBH-DM fraction is derived, and the second-order gravitational wave background induced by the enhanced scalar perturbations is calculated. Those gravitational waves may be accessible by the future space-based gravitational interferometers.

Gravitational waves in metastable supersymmetry breaking

If supersymmetry is broken in metastable vacua, it is not clear why we are now in there rather than supersymmetric vacua. Moreover, it is natural to expect that we were in supersymmetric vacua, which have higher symmetry than metastable vacua, in the early universe. In this paper, we reexamine and improve the previous analysis on the cosmological evolution of the vacuum structure in the ISS model of metastable supersymmetry breaking by taking into account constraints on the reheating temperature, which is needed to avoid the overproduction of gravitinos. It turns out that the desired phase transition from a supersymmetric vacuum to a metastable vacuum is allowed only in the light gravitino mass region $m_{3/2} < 4.7$ eV. This is achieved by either rolling down potential or tunneling processes depending on the reheating temperature. We show that when the tunneling processes are realized, abundant gravitational waves could be produced from collisions of runaway bubbles. The resulting gravitational waves are detectable with the future gravitational wave interferometers like LISA and DECIGO.