Gravitino Mass Research Articles

SUSY’s Ladder: reframing sequestering at Large Volume

Theories with approximate no-scale structure, such as the Large Volume Scenario, have a distinctive hierarchy of multiple mass scales in between TeV gaugino masses and the Planck scale, which we call SUSY's Ladder. This is a particular realization of Split Supersymmetry in which the same small parameter suppresses gaugino masses relative to scalar soft masses, scalar soft masses relative to the gravitino mass, and the UV cutoff or string scale relative to the Planck scale. This scenario has many phenomenologically interesting properties, and can avoid dangers including the gravitino problem, flavor problems, and the moduli-induced LSP problem that plague other supersymmetric theories. We study SUSY's Ladder using a superspace formalism that makes the mysterious cancelations in previous computations manifest. This opens the possibility of a consistent effective field theory understanding of the phenomenology of these scenarios, based on power-counting in the small ratio of string to Planck scales. We also show that four-dimensional theories with approximate no-scale structure enforced by a single volume modulus arise only from two special higher-dimensional theories: five-dimensional supergravity and ten-dimensional type IIB supergravity. This gives a phenomenological argument in favor of ten dimensional ultraviolet physics which is different from standard arguments based on the consistency of superstring theory.

Low-scale gauge mediation with a 100 TeV gravitino

We propose a new framework of low-scale gauge-mediated supersymmetry (SUSY) breaking with a gravitino mass of O(100) TeV. The usual 4D gauge mediation models predict a light gravitino and suffer from cosmological problems. In our framework, a heavy gravitino in gauge mediation is realized with a flat extra-dimension, whose compactification scale is around the grand unified theory scale. Superparticle masses of the visible sector from gravity/anomaly mediation are suppressed, and they are purely generated by usual gauge mediation on the visible brane. Importantly, the Higgs Bmu-term vanishes at the leading order, which enables us to obtain the suitable mu-Bmu relation for the electroweak symmetry breaking. We discuss such models considering two possibilities of the SUSY breaking source: 1) Scherk-Schwarz SUSY breaking which we call Scherk-Schwarz Gauge Mediation and 2) gravitational SUSY breaking localized on a hidden brane. In the case 2), the cosmological moduli problem may be relaxed as well.

High-scale SUSY from anR-invariant new inflation in the landscape

We provide an anthropic reason that the supersymmetry breaking scale is much higher than the electroweak scale as indicated by the null result of collider experiments and observed 125 GeV Higgs boson. We focus on a new inflation model as a typical low-scale inflation model that may be expected in the string landscape. In this model, the R-symmetry is broken at the minimum of the inflaton potential and its breaking scale is related to the reheating temperature. Once we admit that the anthropic principle requires thermal leptogenesis, we obtain a lower bound on gravitino mass, which is related to R-symmetry breaking scale. This scenario and resulting gravitino mass predict the consistent amplitude of density perturbations. We also find that string axions and saxions are consistently implemented in this scenario.

Stop decay with LSP gravitino in the final state: $$\tilde{t}_1\rightarrow \,\widetilde{G}\,W\,b$$ t ~ 1 → G ~ W b

In MSSM scenarios where the gravitino is the lightest supersymmetric particle (LSP), and therefore a viable dark matter candidate, the stop $\tilde{t}_1$ could be the next-to-lightest superpartner (NLSP). For a mass spectrum satisfying: $m_{\widetilde{G}}+m_t>m_{\tilde{t}_1}>m_{\widetilde{G}}+m_b+m_W$, the stop decay is dominated by the 3-body mode $\tilde{t}_1\rightarrow b\,W\,\tilde{G}$. We calculate the stop life-time, including the full contributions from top, sbottom and chargino as intermediate states. We also evaluate the stop lifetime for the case when the gravitino can be approximated by the goldstino state. Our analytical results are conveniently expressed using an expansion in terms of the intermediate state mass, which helps to identify the massless limit. In the region of low gravitino mass ($m_{\widetilde{G}}\ll m_{\tilde{t}_1}$) the results obtained using the gravitino and goldstino cases turns out to be similar, as expected. However for higher gravitino masses $m_{\widetilde{G}} \lesssim m_{\tilde{t}_1}$ the results for the lifetime could show a difference of O(100)\%.

Cosmology with orthogonal nilpotent superfields

We study the application of a supersymmetric model with two constrained supermultiplets to inflationary cosmology. The first superfield S is a stabilizer chiral superfield satisfying a nilpotency condition of degree 2, S^2=0. The second superfield Phi is the inflaton chiral superfield, which can be combined into a real superfield B=(Phi-Phi*)/2i. The real superfield B is orthogonal to S, S B=0, and satisfies a nilpotency condition of degree 3, B^3=0. We show that these constraints remove from the spectrum the complex scalar sgoldstino, the real scalar inflaton partner (i.e. the "sinflaton"), and the fermionic inflatino. The corresponding supergravity model with de Sitter vacua describes a graviton, a massive gravitino, and one real scalar inflaton, with both the goldstino and inflatino being absent in unitary gauge. We also discuss relaxed superfield constraints where S^2=0 and S Phi* is chiral, which removes the sgoldstino and inflatino, but leaves the sinflaton in the spectrum. The cosmological model building in both of these inflatino-less models offers some advantages over existing constructions.

Pure gravity mediation and spontaneous B–L breaking from strong dynamics

In pure gravity mediation (PGM), the most minimal scheme for the mediation of supersymmetry (SUSY) breaking to the visible sector, soft masses for the standard model gauginos are generated at one loop rather than via direct couplings to the SUSY-breaking field. In any concrete implementation of PGM, the SUSY-breaking field is therefore required to carry nonzero charge under some global or local symmetry. As we point out in this note, a prime candidate for such a symmetry might be B–L, the Abelian gauge symmetry associated with the difference between baryon number B and lepton number L. The F-term of the SUSY-breaking field then not only breaks SUSY, but also B–L, which relates the respective spontaneous breaking of SUSY and B–L at a fundamental level. As a particularly interesting consequence, we find that the heavy Majorana neutrino mass scale ends up being tied to the gravitino mass, ΛN∼m3/2. Assuming nonthermal leptogenesis to be responsible for the generation of the baryon asymmetry of the universe, this connection may then explain why SUSY necessarily needs to be broken at a rather high energy scale, so that m3/2≳1000 TeV in accord with the concept of PGM. We illustrate our idea by means of a minimal model of dynamical SUSY breaking, in which B–L is identified as a weakly gauged flavor symmetry. We also discuss the effect of the B–L gauge dynamics on the superparticle mass spectrum as well as the resulting constraints on the parameter space of our model. In particular, we comment on the role of the B–L D-term.

LHC constraints on gravitino dark matter

Gravitino dark matter (DM) represents a compelling scenario in supersymmetry (SUSY), which brings together a variety of data from cosmology and collider physics. We discuss the constraints obtained from the LHC on supersymmetric models with gravitino dark matter and the neutralino next-to-lightest SUSY particle, which is the case most difficult to disentangle at colliders from a neutralino lightest SUSY particle forming DM. The phenomenological SUSY model with $19+1$ free parameters is adopted. Results are obtained from broad scans of the phase space of these uncorrelated parameters. The relation between gravitino mass, gluino mass and reheating temperature as well as the derived constraints on these parameters are discussed in detail. This relation offers a unique opportunity to place stringent bounds on the cosmological model, within the gravitino dark matter scenario, from the results of the LHC searches in run-2 and the planned high-luminosity upgrade.

Gravitino dark matter and low-scale baryogenesis

A very simple way to obtain comparable baryon and DM densities in the early Universe is through their contemporary production from the out-of-equilibrium decay of a mother particle, if both populations are suppressed by comparably small numbers, i.e. the CP violation in the decay and the branching fraction respectively. We present a detailed study of this kind of scenario in the context of a R-parity violating realization of the MSSM in which the baryon asymmetry and the gravitino Dark Matter are produced by the decay of a Bino. The implementation of this simple picture in a realistic particle framework results, however, quite involving, due to the non trivial determination of the abundance of the decaying Bino, as well as due to the impact of wash-out processes and of additional sources both for the baryon asymmetry and the DM relic density. In order to achieve a quantitative determination of the baryon and Dark Matter abundances, we have implemented and solved a system of coupled Boltzmann equations for the particle species involved in their generation, including all the relevant processes. In the most simple, but still general, limit, in which the processes determining the abundance and the decay rate of the Bino are mediated by degenerate right-handed squarks, the correct values of the DM and baryon relic densities are achieved for a Bino mass between 50 and 100 TeV, Gluino NLSP mass in the range 15-60 TeV and a gravitino mass between 100 GeV and few TeV. These high masses are unfortunately beyond the kinematical reach of LHC. On the contrary, an antiproton signal from the decays of the gravitino LSP might be within the sensitivity of AMS-02 and gamma-ray telescopes.

Microscopic origin of volume modulus inflation

High-scale string inflationary models are in well-known tension with low-energy supersymmetry. A promising solution involves models where the inflaton is the volume of the extra dimensions so that the gravitino mass relaxes from large values during inflation to smaller values today. We describe a possible microscopic origin of the scalar potential of volume modulus inflation by exploiting non-perturbative effects, string loop and higher derivative perturbative corrections to the supergravity effective action together with contributions from anti-branes and charged hidden matter fields. We also analyse the relation between the size of the flux superpotential and the position of the late-time minimum and the inflection point around which inflation takes place. We perform a detailed study of the inflationary dynamics for a single modulus and a two moduli case where we also analyse the sensitivity of the cosmological observables on the choice of initial conditions.

De Sitter vacuum fromR2supergravity

We propose a supergravity model with a constrained curvature multiplet, which realizes the Starobinsky inflation and the de Sitter vacuum in the present universe simultaneously. Surprisingly, at the vacuum, the soft supersymmetry breaking scale for minimal supersymmetric standard model sector becomes the TeV scale, however, the gravitino mass scale becomes much higher than that of soft supersymmetry breaking. Such a hierarchical structure, which naturally avoids the gravitino problem, appears without introducing a new scale other than inflation scale.

Confronting recent AMS-02 positron fraction and Fermi-LAT extragalactic γ-ray background measurements with gravitino dark matter

Recent positron flux fraction measurements in cosmic-rays (CR) made by the AMS-02 satellite confirm and extends the evidence on the existence of a new (yet unknown) source of high energy positrons. To explain this excess, we use the gravitino of bilinear R-parity violating SUSY models as a decaying Dark Matter candidate, as the source of those high energy particles. Being a long lived weak-interacting and spin 3/2 particle, it offers several particularities which makes it an attractive candidate. We compute the electron, positron and $\gamma$-ray\ fluxes produced by each gravitino decay channel at the Earth. Combining the flux from the different decay modes we can fit AMS-02 measurements of the positron fraction, as well as the electron and positron fluxes, with a gravitino mass in the range $1-2$ TeV and lifetimes of $\sim 1.0-0.8\times 10^{26}$ s. . Then, we study the viability of these scenarios through their implications in $\gamma$-ray observations. We set limits on the gravitino lifetime using the Extragalactic $\gamma$-ray Background recently reported by the {\it Fermi}-LAT Collaboration and a state-of-the-art model of its known contributors. These limits exclude the gravitino parameter space which provides an acceptable explanation of the AMS-02 data. Therefore, we conclude that the gravitino of bilinear R-parity violating models is ruled out as the unique primary source of electrons and positrons needed to explain the rise in the positron fraction.

Peccei-Quinn symmetry from dynamical supersymmetry breaking

The proximity of the Peccei-Quinn scale to the scale of supersymmetry breaking in models of pure gravity mediation hints at a common dynamical origin of these two scales. To demonstrate how to make such a connection manifest, we embed the Peccei-Quinn mechanism into the vector-like model of dynamical supersymmetry breaking a la IYIT. Here, we rely on the anomaly-free discrete Z4R symmetry required in models of pure gravity mediation to solve the mu problem to protect the Peccei-Quinn symmetry from the dangerous effect of higher-dimensional operators. This results in a rich phenomenology featuring a QCD axion with a decay constant of O(10^10) GeV and mixed WIMP/axion dark matter. In addition, exactly five pairs of extra 5 and 5* matter multiplets, directly coupled to the supersymmetry breaking sector and with masses close to the gravitino mass, m3/2 ~ 100 TeV, are needed to cancel the Z4R anomalies.

α-attractors: Planck, LHC and dark energy

We develop four-parameter supergravity models of inflation and dark energy, constrained so that $$ \frac{\delta \rho }{\rho } $$ , n s and the cosmological constant Λ take their known observable values, but where the mass of gravitino m 3/2 and the tensor-to-scalar ratio r are free parameters. We focus on generalized cosmological α-attractor models, with logarithmic Kahler potentials, a nilpotent goldstino and spontaneously broken supersymmetry at the de Sitter minimum. The future data on B-modes will specify the parameter α, measuring the geometry of the Kahler manifold. The string landscape idea for dark energy is supported in these models via an incomplete cancellation of the universal positive goldstino and negative gravitino contribution. The scale of SUSY breaking M related to the mass of gravitino in our models is a controllable parameter, independent on the scale of inflation, it will be constrained by LHC data and future collider Energy-frontier experiments.

The goldstone and goldstino of supersymmetric inflation

We construct the minimal effective field theory (EFT) of supersymmetric inflation, whose field content is a real scalar, the goldstone for time-translation breaking, and a Weyl fermion, the goldstino for supersymmetry (SUSY) breaking. The inflating background can be viewed as a single SUSY-breaking sector, and the degrees of freedom can be efficiently parameterized using constrained superfields. Our EFT is comprised of a chiral superfield X_NL containing the goldstino and satisfying X_NL^2 = 0, and a real superfield B_NL containing both the goldstino and the goldstone, satisfying X_NL B_NL = B_NL^3 = 0. We match results from our EFT formalism to existing results for SUSY broken by a fluid background, showing that the goldstino propagates with subluminal velocities. The same effect can also be derived from the unitary gauge gravitino action after embedding our EFT in supergravity. If the gravitino mass is comparable to the Hubble scale during inflation, we identify a new parameter in the EFT related to a time-dependent phase of the gravitino mass parameter. We briefly comment on the leading contributions of goldstino loops to inflationary observables.

Moduli backreaction and supersymmetry breaking in string-inspired inflation models

We emphasize the importance of effects from heavy fields on supergravity models of inflation. We study, in particular, the backreaction of stabilizer fields and geometric moduli in the presence of supersymmetry breaking. Many effects do not decouple even if those fields are much heavier than the inflaton field. We apply our results to successful models of Starobinsky-like inflation and natural inflation. In most scenarios producing a plateau potential it proves difficult to retain the flatness of the potential after backreactions are taken into account. Some of them are incompatible with non-perturbative moduli stabilization. In natural inflation there exist a number of models which are not constrained by backreactions at all. In those cases the correction terms from heavy fields have the same inflaton-dependence as the uncorrected potential, so that inflation may be possible even for very large gravitino masses.

Seminatural SUSY from theE7nonlinear sigma model

We present a new focus point supersymemtry breaking scenario based on the supersymmetric $E_7$ non-linear sigma model. In this non-linear sigma model, squarks and sleptons are identified with (pseudo) Nambu-Goldstone bosons. Their masses are generated only radiatively through gauge and yukawa interactions, and they are much smaller than the gravitino and gaugino masses at a high energy scale. On the other hand, Higgs doublets belong to matter multiplets and hence may have unsuppressed supersymmetry-breaking soft masses. We consider their masses to be equal to the gravitino mass at the high energy scale, assuming the minimal Kahler potential for Higgs doublets. We show that the fine-tuning measure of the electroweak symmetry breaking scale is reduced significantly to $\Delta=30-70$, if the ratio of the gravitino mass to the gaugino mass is around $5/4$. Also, the prospects of the discovery/exclusion of supersymmetric particles at the Large Hadron Collider and dark matter direct detection experiments are discussed.

Strongly Coupled Cosmologies

Models including an energy transfer from CDM to DE were widely considered in the literature, namely to allow DE a significant high-z density. Strongly Coupled cosmologies assume a much larger coupling between DE and CDM, together with an uncoupled warm DM component, the role of Cbeing mostly restricted to radiative eras. This allows us to preserve small scale fluctuations even if the warm particle is quite light, O(100 eV). Linear theory shows full agreement between these cosmologies and ΛCDM on supergalactic scales; e.g., CMB spectra are identical. Simultaneously, simulations show that they ease problems related to the properties of MW satellites and cores in dwarfs. While opening new perspectives on early black hole formation and possibly leading towards unificating DE and inflationary fields, the critical prediction of SC cosmologies is a sterile neutrino or gravitino of mass ∼ 100 eV.

The early universe with high-scale supersymmetry

A small tensor-to-scalar ratio $r$ may lead to distinctive phenomenology of high-scale supersymmetry. Assuming the same origin of SUSY breaking between the inflation and visible sector, we show model independent features. The simplest hybrid inflation, together with a new linear term for the inflaton field which is induced by large gravitino mass, is shown to be consistent with all experimental data for $r$ of order $10^{-5}$. For superpartner masses far above the weak scale we find that the reheating temperature after inflation might be beneath the value required by thermal leptogenesis if the inflaton decays to its products perturbatively, but above it if non-perturbatively instead. Remarkably, the gravitino overproduction can be evaded in such high-scale supersymmetry because of the kinematically blocking effect.

Three-body calculation of exotic molecules with negatively charged massive particle

SynopsisIf the gravitino mass is in the region from a few GeV to a few 10’s GeV, the scalar lepton X− such as stau is most likely the next lightest supersymmetry particle. The negatively charged and long-lived X− can form a Coulombic bound state, an exotic atom, with a nucleus. Energy levels and structures of exotic molecules consisting of two nuclei and X− are precisely calculated. We discuss stabilities of the exotic molecule and intramolecular nuclear reactions.

Low-energy supersymmetry breaking without the gravitino problem

In models of low-energy gauge mediation, the observed Higgs mass is in tension with the cosmological limit on the gravitino mass $m_{3/2} \lesssim 16$ eV. We present an alternative mediation mechanism of supersymmetry breaking via a $U(1)$ $D$-term with an $E_6$-inspired particle content, which we call "vector mediation". The gravitino mass can be in the eV range. The sfermion masses are at the 10 TeV scale, while gauginos around a TeV. This mechanism also greatly ameliorates the $\mu$-problem.