Showing papers on "Gauge boson published in 2018"

Hunting All the Hidden Photons

Abstract: We explore constraints on gauge bosons of a weakly coupled U(1)B − L, $$ \mathrm{U}{(1)}_{L_{\mu }-{L}_e},\kern0.5em \mathrm{U}{(1)}_{L_e-{L}_{\tau }}\kern0.5em \mathrm{and}\kern0.5em \mathrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} $$ . To do so we apply the full constraining power of experimental bounds derived for a hidden photon of a secluded U(1)X and translate them to the considered gauge groups. In contrast to the secluded hidden photon that acquires universal couplings to charged Standard Model particles through kinetic mixing with the photon, for these gauge groups the couplings to the different Standard Model particles can vary widely. We take finite, computable loop-induced kinetic mixing effects into account, which provide additional sensitivity in a range of experiments. In addition, we collect and extend limits from neutrino experiments as well as astrophysical and cosmological observations and include new constraints from white dwarf cooling. We discuss the reach of future experiments in searching for these gauge bosons.

Neutrino oscillations and Non-Standard Interactions

Abstract: Current neutrino experiments are measuring the neutrino mixing parameters with an unprecedented accuracy. The upcoming generation of neutrino experiments will be sensitive to subdominant oscillation effects that can give information on the yet-unknown neutrino parameters: the Dirac CP-violating phase, the mass ordering and the octant of $\theta_{23}$. Determining the exact values of neutrino mass and mixing parameters is crucial to test neutrino models and flavor symmetries designed to predict these neutrino parameters. In the first part of this review, we summarize the current status of the neutrino oscillation parameter determination. We consider the most recent data from all solar experiments and the atmospheric data from Super-Kamiokande, IceCube and ANTARES. We also implement the data from the reactor neutrino experiments KamLAND, Daya Bay, RENO and Double Chooz as well as the long baseline neutrino data from MINOS, T2K and NOvA. If in addition to the standard interactions, neutrinos have subdominant yet-unknown Non-Standard Interactions (NSI) with matter fields, extracting the values of these parameters will suffer from new degeneracies and ambiguities. We review such effects and formulate the conditions on the NSI parameters under which the precision measurement of neutrino oscillation parameters can be distorted. Like standard weak interactions, the non-standard interaction can be categorized into two groups: Charged Current (CC) NSI and Neutral Current (NC) NSI. Our focus will be mainly on neutral current NSI because it is possible to build a class of models that give rise to sizeable NC NSI with discernible effects on neutrino oscillation. These models are based on new $U(1)$ gauge symmetry with a gauge boson of mass $\lesssim 10$~MeV. The UV complete model should be of course electroweak invariant which in general implies that along with neutrinos, charged fermions also acquire new interactions on which there are strong bounds. We enumerate the bounds that already exist on the electroweak symmetric models and demonstrate that it is possible to build viable models avoiding all these bounds. In the end, we review methods to test these models and suggest approaches to break the degeneracies in deriving neutrino mass parameters caused by NSI.

Search for additional heavy neutral Higgs and gauge bosons in the ditau final state produced in 36 fb−1 of pp collisions at √s=13 TeV with the ATLAS detector

Abstract: A search for heavy neutral Higgs bosons and Z' bosons is performed using a data sample corresponding to an integrated luminosity of 36.1 fb(-1) from proton-proton collisions at root s = 13 TeV reco ...

Severely Constraining Dark-Matter Interpretations of the 21-cm Anomaly

Abstract: The EDGES Collaboration has recently reported the detection of a stronger-than-expected absorption feature in the global 21-cm spectrum, centered at a frequency corresponding to a redshift of z≃17. This observation has been interpreted as evidence that the gas was cooled during this era as a result of scattering with dark matter. In this Letter, we explore this possibility, applying constraints from the cosmic microwave background, light element abundances, Supernova 1987A, and a variety of laboratory experiments. After taking these constraints into account, we find that the vast majority of the parameter space capable of generating the observed 21-cm signal is ruled out. The only viable models are those in which a small fraction, ∼0.3%-2%, of the dark matter consists of particles with a mass of ∼10-80 MeV and which couple to the photon through a small electric charge, roughly 10^{-6}-10^{-4} as large as the electron charge. Furthermore, in order to avoid being overproduced in the early Universe, such models must be supplemented with an additional depletion mechanism, such as annihilations through a L_{μ}-L_{τ} gauge boson or annihilations to a pair of rapidly decaying hidden sector scalars.

Serendipity in dark photon searches

Abstract: Searches for dark photons provide serendipitous discovery potential for other types of vector particles We develop a framework for recasting dark photon searches to obtain constraints on more general theories, which includes a data-driven method for determining hadronic decay rates We demonstrate our approach by deriving constraints on a vector that couples to the B-L current, a leptophobic B boson that couples directly to baryon number and to leptons via B-γ kinetic mixing, and on a vector that mediates a protophobic force Our approach can easily be generalized to any massive gauge boson with vector couplings to the Standard Model fermions, and software to perform any such recasting is provided at https://gitlabcom/philten/darkcast

Search for electroweak production of supersymmetric particles in final states with two or three leptons at √s=13 TeV with the ATLAS detector

Abstract: A search for the electroweak production of charginos, neutralinos and sleptons decaying into final states involving two or three electrons or muons is presented. The analysis is based on 36.1 fb$^{-1}$ of $\sqrt{s}=13$ TeV proton–proton collisions recorded by the ATLAS detector at the Large Hadron Collider. Several scenarios based on simplified models are considered. These include the associated production of the next-to-lightest neutralino and the lightest chargino, followed by their decays into final states with leptons and the lightest neutralino via either sleptons or Standard Model gauge bosons, direct production of chargino pairs, which in turn decay into leptons and the lightest neutralino via intermediate sleptons, and slepton pair production, where each slepton decays directly into the lightest neutralino and a lepton. No significant deviations from the Standard Model expectation are observed and stringent limits at 95% confidence level are placed on the masses of relevant supersymmetric particles in each of these scenarios. For a massless lightest neutralino, masses up to 580 GeV are excluded for the associated production of the next-to-lightest neutralino and the lightest chargino, assuming gauge-boson mediated decays, whereas for slepton-pair production masses up to 500 GeV are excluded assuming three generations of mass-degenerate sleptons.

Testing large non-standard neutrino interactions with arbitrary mediator mass after COHERENT data

Abstract: In the presence of neutrino Non-Standard Interactions (NSI) with matter, the derivation of neutrino parameters from oscillation data must be reconsidered. In particular, along with the standard solution to neutrino oscillation, another solution known as “LMA-Dark” is compatible with global oscillation data and requires both θ12 > π/4 and a certain flavor pattern of NSI with an effective coupling comparable to GF . Contrary to conventional expectations, there is a class of models based on a new U(1)X gauge symmetry with a gauge boson of mass of few MeV to few 10 MeV that can viably give rise to such large NSI. These models can in principle be tested by Coherent Elastic ν-Nucleus Scattering (CEνNS) experiments such as COHERENT and the upcoming reactor neutrino experiment, CONUS. We analyze how the recent results from the COHERENT experiment constrain these models and forecast the discovery potential with future measurements from COHERENT and CONUS. We also derive the constraints from COHERENT on lepton flavor violating NSI.

Dark Neutrino Portal to Explain MiniBooNE Excess

Abstract: We present a novel framework that provides an explanation to the long-standing excess of electronlike events in the MiniBooNE experiment at Fermilab. We suggest a new dark sector containing a dark neutrino and a dark gauge boson, both with masses between a few tens and a few hundreds of MeV. Dark neutrinos are produced via neutrino-nucleus scattering, followed by their decay to the dark gauge boson, which in turn gives rise to electronlike events. This mechanism provides an excellent fit to MiniBooNE energy spectra and angular distributions.

The Weak Gravity Conjecture and Emergence from an Ultraviolet Cutoff

Abstract: We study ultraviolet cutoffs associated with the Weak Gravity Conjecture (WGC) and Sublattice Weak Gravity Conjecture (sLWGC). There is a magnetic WGC cutoff at the energy scale $$e G_N^{-1/2}$$ with an associated sLWGC tower of charged particles. A more fundamental cutoff is the scale at which gravity becomes strong and field theory breaks down entirely. By clarifying the nature of the sLWGC for nonabelian gauge groups we derive a parametric upper bound on this strong gravity scale for arbitrary gauge theories. Intriguingly, we show that in theories approximately saturating the sLWGC, the scales at which loop corrections from the tower of charged particles to the gauge boson and graviton propagators become important are parametrically identical. This suggests a picture in which gauge fields emerge from the quantum gravity scale by integrating out a tower of charged matter fields. We derive a converse statement: if a gauge theory becomes strongly coupled at or below the quantum gravity scale, the WGC follows. We sketch some phenomenological consequences of the UV cutoffs we derive.

Searching for Dark Photon Dark Matter with Gravitational-Wave Detectors.

Abstract: If dark matter stems from the background of a very light gauge boson, this gauge boson could exert forces on test masses in gravitational wave detectors, resulting in displacements with a characteristic frequency set by the gauge boson mass. We outline a novel search strategy for such dark matter, assuming the dark photon is the gauge boson of U(1)_{B} or U(1)_{B-L}. We show that both ground-based and future space-based gravitational wave detectors have the capability to make a 5σ discovery in unexplored parameter regimes.

Symmetry and emergence

Abstract: In a modern understanding of particle physics, global symmetries are approximate and gauge symmetries may be emergent. This view, which has echoes in condensed-matter physics, is supported by a variety of arguments from experiment and theory.

Infinite Set of Soft Theorems in Gauge-Gravity Theories as Ward-Takahashi Identities.

Abstract: We show that the soft photon, gluon, and graviton theorems can be understood as the Ward-Takahashi identities of large gauge transformation, i.e., diffeomorphism that does not fall off at spatial infinity. We found infinitely many new identities which constrain the higher order soft behavior of the gauge bosons and gravitons in scattering amplitudes of gauge and gravity theories. Diagrammatic representations of these soft theorems are presented.

Self-interacting dark matter and muon ( g − 2) in a gauged U 1 L μ − L τ $$ \mathrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} $$ model

Abstract: We construct a self-interacting dark matter model that could simultaneously explain the observed muon anomalous magnetic moment. It is based on a gauged $$ \mathrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} $$ extension of the standard model, where we introduce a vector-like pair of fermions as the dark matter candidate and a new Higgs boson to break the symmetry. The new gauge boson has a sizable contribution to muon (g − 2), while being consistent with other experimental constraints. The $$ \mathrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} $$ Higgs boson acts as a light force carrier, mediating dark matter self-interactions with a velocity-dependent cross section. It is large enough in galaxies to thermalize the inner halo and explain the diverse rotation curves and diminishes towards galaxy clusters. Since the light mediator dominantly decays to the $$ \mathrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} $$ gauge boson and neutrinos, the astrophysical and cosmological constraints are weak. We study the thermal evolution of the model in the early Universe and derive a lower bound on the gauge boson mass.

Radiative bound-state formation in unbroken perturbative non-Abelian theories and implications for dark matter

Abstract: We compute the cross-sections for the radiative capture of non-relativistic particles into bound states, in unbroken perturbative non-Abelian theories. We find that the formation of bound states via emission of a gauge boson can be significant for a variety of dark matter models that feature non-Abelian long-range interactions, including multi-TeV scale WIMPs, dark matter co-annihilating with coloured partners and hidden-sector models. Our results disagree with previous computations, on the relative sign of the Abelian and non-Abelian contributions. In particular, in the case of capture of a particle-antiparticle pair into its tightest bound state, we find that these contributions add up, rather than partially canceling each other. We apply our results to dark matter co-annihilating with particles transforming in the (anti)fundamental of SU(3)c, as is the case in degenerate stop-neutralino scenarios in the MSSM. We show that the radiative formation and decay of particle-antiparticle bound states can deplete the dark matter density by (40 − 240)%, for dark matter heavier than 500 GeV. This implies a larger mass difference between the co-annihilating particles, and allows for the dark matter to be as heavy as 3.3 TeV.

Strong gravitational radiation from a simple dark matter model

Abstract: A rather minimal possibility is that dark matter consists of the gauge bosons of a spontaneously broken symmetry. Here we explore the possibility of detecting the gravitational waves produced by the phase transition associated with such breaking. Concretely, we focus on the scenario based on an $SU(2)_D$ group and argue that it is a case study for the sensitivity of future gravitational wave observatories to phase transitions associated with dark matter. This is because there are few parameters and those fixing the relic density also determine the effective potential establishing the strength of the phase transition. Particularly promising for LISA and even the Einstein Telescope is the super-cool dark matter regime, with DM masses above $\mathcal{O}$(100) TeV, for which we find that the gravitational wave signal is notably strong. In our analysis, we include the effect of astrophysical foregrounds, which are often ignored in the context of phase transitions.

Bubble wall velocities in the Standard Model and beyond

Abstract: We present results for the bubble wall velocity and bubble wall thickness during a cosmological first-order phase transition in a condensed form. Our results are for minimal extensions of the Standard Model but in principle are applicable to a much broader class of settings. Our first assumption about the model is that only the electroweak Higgs is obtaining a vacuum expectation value during the phase transition. The second is that most of the friction is produced by electroweak gauge bosons and top quarks. Under these assumptions the bubble wall velocity and thickness can be deduced as a function of two equilibrium properties of the plasma: the strength of the phase transition and the pressure difference along the bubble wall.

Anomaly-free models for flavour anomalies.

Abstract: We explore the constraints imposed by the cancellation of triangle anomalies on models in which the flavour anomalies reported by LHCb and other experiments are due to an extra U(1) $$^\prime $$ gauge boson Z $$^\prime $$ . We assume universal and rational U(1) $$^\prime $$ charges for the first two generations of left-handed quarks and of right-handed up-type quarks but allow different charges for their third-generation counterparts. If the right-handed charges vanish, cancellation of the triangle anomalies requires all the quark U(1) $$^\prime $$ charges to vanish, if there are either no exotic fermions or there is only one Standard Model singlet dark matter (DM) fermion. There are non-trivial anomaly-free models with more than one such ‘dark’ fermion, or with a single DM fermion if right-handed up-type quarks have non-zero U(1) $$^\prime $$ charges. In some of the latter models the U(1) $$^\prime $$ couplings of the first- and second-generation quarks all vanish, weakening the LHC $$Z^\prime $$ constraint, and in some other models the DM particle has purely axial couplings, weakening the direct DM scattering constraint. We also consider models in which anomalies are cancelled via extra vector-like leptons, showing how the prospective LHC Z $$^\prime $$ constraint may be weakened because the $$Z^\prime \rightarrow \mu ^+ \mu ^-$$ branching ratio is suppressed relative to other decay modes.

Locality and Unitarity of Scattering Amplitudes from Singularities and Gauge Invariance.

Abstract: We conjecture that the leading two-derivative tree-level amplitudes for gluons and gravitons can be derived from gauge invariance together with mild assumptions on their singularity structure. Assuming locality (that the singularities are associated with the poles of cubic graphs), we prove that gauge invariance in just n-1 particles together with minimal power counting uniquely fixes the amplitude. Unitarity in the form of factorization then follows from locality and gauge invariance. We also give evidence for a stronger conjecture: assuming only that singularities occur when the sum of a subset of external momenta go on shell, we show in nontrivial examples that gauge invariance and power counting demand a graph structure for singularities. Thus, both locality and unitarity emerge from singularities and gauge invariance. Similar statements hold for theories of Goldstone bosons like the nonlinear sigma model and Dirac-Born-Infeld by replacing the condition of gauge invariance with an appropriate degree of vanishing in soft limits.

Self-interacting dark matter and muon $g-2$ in a gauged U$(1)_{L_{\mu} - L_{\tau}}$ model

Abstract: We construct a self-interacting dark matter model that could simultaneously explain the observed muon anomalous magnetic moment. It is based on a gauged U$(1)_{L_{\mu} - L_{\tau}}$ extension of the standard model, where we introduce a vector-like pair of fermions as the dark matter candidate and a new Higgs boson to break the symmetry. The new gauge boson has a sizable contribution to muon $(g-2)$, while being consistent with other experimental constraints. The U$(1)_{L_{\mu} - L_{\tau}}$ Higgs boson acts as a light force carrier, mediating dark matter self-interactions with a velocity-dependent cross section. It is large enough in galaxies to thermalize the inner halo and explain the diverse rotation curves and diminishes towards galaxy clusters. Since the light mediator dominantly decays to the U$(1)_{L_{\mu} - L_{\tau}}$ gauge boson and neutrinos, the astrophysical and cosmological constraints are weak. We study the thermal evolution of the model in the early Universe and derive a lower bound on the gauge boson mass.

Common exotic decays of top partners

Abstract: Many standard model extensions that address the hierarchy problem contain Dirac-fermion partners of the top quark, which are typically expected around the TeV scale. Searches for these vector-like quarks mostly focus on their decay into electroweak gauge bosons and Higgs plus a standard model quark. In this article, backed by models of composite Higgs, we propose a set of simplified scenarios, with effective Lagrangians and benchmarks, that include more exotic decay channels, which modify the search strategies and affect the bounds. Analysing several classes of underlying models, we show that exotic decays are the norm and commonly appear with significant rates. All these models contain light new scalars that couple to top partners with charge 5/3, 2/3, and −1/3.

Next-to-Next-to-Leading-Order QCD Corrections to the Transverse Momentum Distribution of Weak Gauge Bosons.

Abstract: The transverse momentum spectra of weak gauge bosons and their ratios probe the underlying dynamics and are crucial in testing our understanding of the standard model. They are an essential ingredient in precision measurements, such as the W boson mass extraction. To fully exploit the potential of the LHC data, we compute the second-order [next-to-next-to-leading-order (NNLO)] QCD corrections to the inclusive-pW T spectrum as well as to the ratios of spectra for W−=Wþ and Z=W. We find that the inclusion of NNLO QCD corrections considerably improves the theoretical description of the experimental CMS data and results in a substantial reduction of the residual scale uncertainties.

Towards ultimate parton distributions at the high-luminosity LHC

Abstract: Since its start of data taking, the LHC has provided an impressive wealth of information on the quark and gluon structure of the proton. Indeed, modern global analyses of parton distribution functions (PDFs) include a wide range of LHC measurements of processes such as the production of jets, electroweak gauge bosons, and top quark pairs. In this work, we assess the ultimate constraining power of LHC data on the PDFs that can be expected from the complete dataset, in particular after the High-Luminosity (HL) phase, starting in around 2025. The huge statistics of the HL-LHC, delivering L=3ab-1 to ATLAS and CMS and L=0.3ab-1 to LHCb, will lead to an extension of the kinematic coverage of PDF-sensitive measurements as well as to an improvement in their statistical and systematic uncertainties. Here we generate HL-LHC pseudo-data for different projections of the experimental uncertainties, and then quantify the resulting constraints on the PDF4LHC15 set by means of the Hessian profiling method. We find that HL-LHC measurements can reduce PDF uncertainties by up to a factor of 2 to 4 in comparison to state-of-the-art fits, leading to few-percent uncertainties for important observables such as the Higgs boson transverse momentum distribution via gluon-fusion. Our results illustrate the significant improvement in the precision of PDF fits achievable from hadron collider data alone, and motivate the continuation of the ongoing successful program of PDF-sensitive measurements by the LHC collaborations.

Dynamics of Relaxed Inflation

Abstract: The cosmological relaxation of the electroweak scale has been proposed as a mechanism to address the hierarchy problem of the Standard Model. A field, the relaxion, rolls down its potential and, in doing so, scans the squared mass parameter of the Higgs, relaxing it to a parametrically small value. In this work, we promote the relaxion to an inflaton. We couple it to Abelian gauge bosons, thereby introducing the necessary dissipation mechanism which slows down the field in the last stages. We describe a novel reheating mechanism, which relies on the gauge-boson production leading to strong electro-magnetic fields, and proceeds via the vacuum production of electron-positron pairs through the Schwinger effect. We refer to this mechanism as Schwinger reheating. We discuss the cosmological dynamics of the model and the phenomenological constraints from CMB and other experiments. We find that a cutoff close to the Planck scale may be achieved. In its minimal form, the model does not generate sufficient curvature perturbations and additional ingredients, such as a curvaton field, are needed.

Audible Axions.

Abstract: Conventional approaches to probing axions and axion-like particles (ALPs) typically rely on a coupling to photons. However, if this coupling is extremely weak, ALPs become invisible and are effectively decoupled from the Standard Model. Here we show that such invisible axions, which are viable candidates for dark matter, can produce a stochastic gravitational wave background in the early universe. This signal is generated in models where the invisible axion couples to a dark gauge boson that experiences a tachyonic instability when the axion begins to oscillate. Incidentally, the same mechanism also widens the viable parameter space for axion dark matter. Quantum fluctuations amplified by the exponentially growing gauge boson modes source chiral gravitational waves. For axion decay constants $f \gtrsim 10^{17}$ GeV, this signal is detectable by either pulsar timing arrays or space/ground-based gravitational wave detectors for a broad range of axion masses, thus providing a new window to probe invisible axion models.

Heavy Majorana neutrino pair productions at the LHC in minimal U(1) extended Standard Model

Abstract: In our recent paper (Das et al. in Phys Rev D 97:115023, 2018) we explored a prospect of discovering the heavy Majorana right-handed neutrinos (RHNs) at the future LHC in the context of the minimal non-exotic U(1) extended Standard Model (SM), where a pair of RHNs are created via decay of resonantly produced massive U(1) gauge boson ( $$Z^{\prime }$$ ). We have pointed out that this model can yield a significant enhancement of the branching ratio of the $$Z^\prime $$ boson to a pair of RHNs, which is crucial for discovering the RHNs under the very severe LHC Run-2 constraint from the search for the $$Z^\prime $$ boson with dilepton final states. In this paper, we perform a general parameter scan to evaluate the maximum production rate of the same-sign dilepton final states (smoking gun signature of Majorana RHNs production) at the LHC, while reproducing the neutrino oscillation data. We also consider the minimal non-exotic U(1) model with an alternative charge assignment. In this case, we find a further enhancement of the branching ratio of the $$Z^\prime $$ boson to a pair of RHNs compared to the conventional case, which opens up a possibility of discovering the RHNs even before the $$Z^\prime $$ boson at the future LHC experiment.

Light dark Higgs boson in minimal sub-GeV dark matter scenarios

Abstract: Minimal scenarios with light (sub-GeV) dark matter whose relic density is obtained from thermal freeze-out must include new light mediators. In particular, a very well-motivated case is that of a new “dark” massive vector gauge boson mediator. The mass term for such mediator is most naturally obtained by a “dark Higgs mechanism” which leads to the presence of an often long-lived dark Higgs boson whose mass scale is the same as that of the mediator. We study the phenomenology and experimental constraints on two minimal, self-consistent dark sectors that include such a light dark Higgs boson. In one the dark matter is a pseudo-Dirac fermion, in the other a complex scalar. We find that the constraints from BBN and CMB are considerably relaxed in the framework of such minimal dark sectors. We present detection prospects for the dark Higgs boson in existing and projected proton beam-dump experiments. We show that future searches at experiments like Xenon1T or LDMX can probe all the relevant parameter space, complementing the various upcoming indirect constraints from astrophysical observations.

Decays of the neutral Higgs bosons into SM fermions and gauge bosons in the $$\mathcal{CP}$$ CP -violating NMSSM

Abstract: The Next-to-Minimal Supersymmetric Standard Model (NMSSM) offers a rich framework embedding physics beyond the Standard Model as well as consistent interpretations of the results about the Higgs signal detected at the LHC. We investigate the decays of neutral Higgs states into Standard Model (SM) fermions and gauge bosons. We perform full one-loop calculations of the decay widths and include leading higher-order QCD corrections. We first discuss the technical aspects of our approach, before confronting our predictions to those of existing public tools, performing a numerical analysis and discussing the remaining theoretical uncertainties. In particular, we find that the decay widths of doublet-dominated heavy Higgs bosons into electroweak gauge bosons are dominated by the radiative corrections, so that the tree-level approximations that are often employed in phenomenological analyses fail. Finally, we focus on the phenomenological properties of a mostly singlet-like state with a mass below the one at 125 GeV, a scenario that appears commonly within the NMSSM. In fact, the possible existence of a singlet-dominated state in the mass range around or just below 100 GeV would have interesting phenomenological implications. Such a scenario could provide an interpretation for both the $$2.3\,\sigma $$ local excess observed at LEP in the $$e^+e^-\rightarrow Z(H\rightarrow b\bar{b})$$ searches at $$\mathord {\sim }\,98$$ GeV and for the local excess in the diphoton searches recently reported by CMS in this mass range, while at the same time it would reduce the “Little Hierarchy” problem.