Fine-tuning Measure Research Articles

Quiet islands in a world of fear: Wolves seek core zones of protected areas to escape human disturbance

The Anthropocene continuously escalates the challenges and threats faced by large carnivores in human-dominated landscapes. Given their unique conservation and management requirements, detailed insights into their behaviour in relation to human-induced risks are crucial to designing landscapes of coexistence for people and predators, containing key features such as nature conservation areas. Adaptations like selection or avoidance of areas at certain times reveal the dynamic perception of large carnivores to risk-landscapes and the trade-offs with potential resources. This study investigates these ideas by applying a habitat-selection approach to GPS collared wolves in Belovezhskaya Pushcha National Park (Belarus) to quantify fine-scale avoidance of human disturbance. Our results indicate that wolves selected strongly for areas of higher nature protection within the national park. They also avoided human disturbance from settlements and roads, but mediated their behaviour depending on the shifting risk throughout the day and night. They selected for more open areas during darkness. Seasonal and sex-based differences shifted avoidance, such as females being more avoidant of settlements. This suggests evidence of a successful anti-predator strategy against humans. Our study offers some of the most detailed and novel insights into wolf spatio-temporal avoidance of disturbance in the context of protected areas, which is imperative for fine-tuning management measures for continued coexistence and effective conservation of this functionally important species.

Energy poverty in pandemic times: Fine-tuning emergency measures for better future responses to extreme events in Spain

Energy poverty has been exacerbated by the COVID-19 pandemic and the economic crisis it triggered. Spain, one of the first countries affected by the outbreak, introduced several measures to protect energy consumers during the initial lockdown and to provide them with economic relief (including a disconnection ban and the introduction of new categories of beneficiaries for its energy assistance programmes). This article presents a critical assessment of these interventions, based on the regulatory theory and a review of international experiences. It shows how emergency measures should rely on a robust but flexible targeting strategy and be supported by appropriate financing; it also sheds light on the importance of information campaigns that allow the aid to reach more households, improving the effectiveness of the intervention. The reflections and recommendations presented in this article may help improve the design of emergency measures during future health crises or extreme weather events.

Spontaneous CP violation and horizontal symmetry in the MSSM: toward lepton flavor naturalness

We study the contributions of supersymmetric models with a U(1) horizontal symmetry and only spontaneous CP breaking to various lepton flavor observables, such as μ → eγ and the electron electric dipole moment. We show that both a horizontal symmetry and a lack of explicit CP violation can alleviate the existing bounds from such observables. The undetermined mathcal{O} (1) coefficients in such mass matrix models muddle the interpretation of the bounds from various flavor observables. To overcome this, we define a new fine-tuning measure for different observables in such setups. This allows us to study how naturally the observed IR flavor observables can emerge from a given mass matrix model. We use our flavor-naturalness measure in study of our supersymmetric models and quantify the degree of fine tuning required by the bounds from various lepton flavor observables at each mass scale of sleptons, neutralinos, and charginos.

The current status of fine-tuning in supersymmetry

In this paper, we minimize and compare two different fine-tuning measures in four high-scale supersymmetric models that are embedded in the MSSM. In addition, we determine the impact of current and future dark matter direct detection and collider experiments on the fine-tuning. We then compare the low-scale electroweak measure with the high-scale Barbieri-Giudice measure. We find that they reduce to the same value when the higgsino parameter drives the degree of fine-tuning. We also find spectra where the high-scale measure turns out to be lower than the low-scale measure. Depending on the high-scale model and fine-tuning definition, we find a minimal fine-tuning of 3–38 (corresponding to O(10–1)%) for the low-scale measure, and 63–571 (corresponding to O(1–0.1)%) for the high-scale measure. We stress that it is too early to conclude on the fate of supersymmetry, based only on the fine-tuning paradigm.

Supersymmetric naturalness beyond MSSM

The experiments at the Large Hadron Collider (LHC) have pushed the limits on masses of supersymmetric particles beyond the ∼TeV scale. This compromises naturalness of the simplest supersymmetric extension of the Standard Model, the minimal supersymmetric Standard Model (MSSM). In this paper we advocate that perhaps the current experimental data are actually hinting towards the physics beyond MSSM. To illustrate this, we treat the MSSM as a low-energy limit of a more fundamental yet unspecified theory at a scale Λ, and compute the fine-tuning measure Δ for generic boundary conditions with soft SUSY breaking parameters and various cut-off scales. As a general trend we observe reduction in fine-tuning together with lowering Λ. In particular, perfectly natural [Δ ≲ mathcal{O} (10)] theories with a multi-TeV spectrum of supersymmetric particles that are consistent with all current observations can be obtained for Λ ∼ mathcal{O} (100)TeV. The lowering of the fine-tuning for large cut-off scales can also be observed in theories exhibiting special quasi-fixed point behaviour for certain parameters. Our observations call for a more thorough exploration of possible alternative ultraviolet completions of MSSM.

Analysis of fine-tuning measures in models with extended Higgs sectors

In the literature measures of fine-tuning have been discussed as one of the tools to assess the feasibility of beyond the Standard Model theories. In this paper we focus on two specific measures and investigate what kind of fine-tuning they actually quantify. First we apply both measures to the two Higgs doublet model, for which one can analyze the numerical results in terms of available analytic expressions. After drawing various conclusions about the fine-tuning measures, we investigate a particular left-right symmetric model for which it has been claimed that already at tree-level it suffers from a high amount of fine-tuning. We will reach a different conclusion, although left-right symmetric models may require a modest amount of fine-tuning if phenomenological constraints are imposed. Our analysis shows that the two considered measures can probe different aspects of fine-tuning and are both useful if applied and interpreted in the appropriate way.

NMSSM with generalized deflected mirage mediation

We propose to generate a realistic soft SUSY breaking spectrum for Next-to-Minimal Supersymmetric Standard Model (NMSSM) with a generalized deflected mirage mediation scenario, in which additional Yukawa and gauge mediation contributions are included to deflect the renormalization group equation trajectory. Based on the Wilsonian effective action obtained by integrating out the messengers, the NMSSM soft SUSY breaking spectrum can be given analytically at the messenger scale. We find that additional contributions to m_S^2 can possibly ameliorate the stringent constraints from the electroweak symmetry breaking and 125 GeV Higgs mass. Constraints from dark matter and fine-tuning are also discussed. The Barbieri–Giudice fine-tuning measure and electroweak fine-tuning measure in our scenario can be as low as {mathcal O}(1), which possibly indicates that our scenario is natural.

Exploring fine-tuning of the Next-to-Minimal Composite Higgs Model

We perform a detailed study of the fine-tuning of the two-site, 4D, Next-to-Minimal Composite Higgs Model (NMCHM), based on the global symmetry breaking pattern SO(6) → SO(5). Using our previously-defined fine-tuning measure that correctly combines the effect of multiple sources of fine-tuning, we quantify the fine-tuning that is expected to result from future collider measurements of the Standard Model-like Higgs branching ratios, in addition to null searches for the new resonances in the model. We also perform a detailed comparison with the Minimal Composite Higgs Model, finding that there is in general little difference between the fine-tuning expected in the two scenarios, even after measurements at a high-luminosity, 1 TeV linear collider. Finally, we briefly consider the relationship between fine-tuning and the ability of the extra scalar in the NMCHM model to act as a dark matter candidate, finding that the realisation of a Z2 symmetry that stabilises the scalar is amongst the most natural solutions in the parameter space, regardless of future collider measurements.

LHC luminosity and energy upgrades confront natural supersymmetry models

The electroweak fine-tuning measure ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{EW}}$ allows for correlated supersymmetry (SUSY) soft terms as are expected in any ultraviolet complete theory. Requiring no less than 3% electroweak fine-tuning implies upper bounds of about 360 GeV on all Higgsinos, while top squarks are lighter than $\ensuremath{\sim}3\text{ }\text{ }\mathrm{TeV}$ and gluinos are bounded by $\ensuremath{\sim}6--9\text{ }\text{ }\mathrm{TeV}$. We examine the reach for SUSY of the planned high luminosity (HL: $3\text{ }\text{ }{\mathrm{ab}}^{\ensuremath{-}1}$ at 14 TeV) and the proposed high energy (HE: $15\text{ }\text{ }{\mathrm{ab}}^{\ensuremath{-}1}$ at 27 TeV) upgrades of the LHC via four LHC collider search channels relevant for natural SUSY: 1. gluino pair production followed by gluino decay to third generation (s)quarks, 2. top squark pair production followed by decay to third generation quarks and light Higgsinos, 3. neutral Higgsino pair production with QCD jet radiation (resulting in monojet events with soft dileptons), and 4. wino pair production followed by decay to light Higgsinos leading to same-sign diboson production. We confront our reach results with upper limits on superpartner masses in four natural SUSY models: natural gravity mediation via the 1. two- and 2. three-extra-parameter nonuniversal Higgs models, 3. natural minilandscape models with generalized mirage mediation and 4. natural anomaly mediation We find that while the HL-LHC can probe considerable portions of natural SUSY parameter space in all these models, the HE-LHC will decisively cover the entire natural SUSY parameter space with better than 3% fine-tuning.

Focus point gauge mediation without a severe fine-tuning

We consider focus point gauge mediation within the framework of the next-to-minimal supersymmetric standard model, which substantially reduces the degree of finetuning for the electroweak symmetry breaking. The milder fine-tuning is realized by a messenger field in the adjoint representation of SU(5) gauge group with SU(3)c octet being heavy. Our model has a simple ultraviolet completion. The fine-tuning measure Δ can be as small as 40-50 without any contradiction with LHC constraints.

Status of natural supersymmetry from the generalized minimal supergravity in light of the current LHC run-2 and LUX data

We study natural supersymmetry in the Generalized Minimal Supergravity (GmSUGRA). For the parameter space with low energy electroweak fine-tuning measures less than 50, we are left with only the $Z$-pole, Higgs-pole and Higgsino LSP scenarios for dark matter (DM). We perform the focused scans for such parameter space and find that it satisfies various phenomenological constraints and is compatible with the current direct detection bound on neutralino DM reported by the LUX experiment. Such parameter space also has solutions with correct DM relic density besides the solutions with DM relic density smaller or larger than 5$\sigma$ WMAP9 bounds. We present five benchmark points as examples. In these benchmark points, gluino and the first two generations of squarks are heavier than 2 TeV, stop $\tilde t_{1,2}$ are in the mass range $[1,2]$ TeV, while sleptons are lighter than 1 TeV. Some part of the parameter space can explain the muon anomalous magnetic moment within 3$\sigma$ as well. We also perform the collider study of such solutions by implementing and comparing with relevant studies done by the ATLAS and CMS Collaborations. We find that the points with Higgsino dominant $\tilde{\chi}_2^0/\tilde{\chi_1}^\pm$ mass up to $300$ GeV are excluded in $Z$-pole scenario while for Higgs-pole scenario, the points with $\tilde{\chi}_2^0$ mass up to $460$ GeV are excluded. We also notice that the Higgsino LSP points in our present scans are beyond the reach of present LHC searches. Next, we show that for both the $Z$-pole and Higgs-pole scenarios, the points with electroweak fine-tuning measure around 20 do still survive.

Least fine-tuned U(1) extended SSM

We consider the Higgs boson mass in a class of the UMSSM models in which the MSSM gauge group is extended by an additional U(1)′ group. Implementing the universal boundary condition at the GUT scale we target phenomenologically interesting regions of UMSSM where the necessary radiative contributions to the lightest CP-even Higgs boson mass are significantly small and LSP is always the lightest neutralino. We find that the smallest amount of radiative contributions to the Higgs boson mass is about 50 GeV in UMSSM, this result is much lower than that obtained in the MSSM framework, which is around 90 GeV. Additionally, we examine the Higgs boson properties in these models in order to check whether if it can behave similar to the SM Higgs boson under the current experimental constraints. We find that enforcement of smaller radiative contribution mostly restricts the U(1)′ breaking scale as vS≲10 TeV. Besides, such low contributions demand hS∼0.2–0.45. Because of the model dependency in realizing these radiative contributions θE6<0 are more favored, if one seeks for the solutions consistent with the current dark matter constraints. As to the mass spectrum, we find that stop and stau can be degenerated with the LSP neutralino in the range from 300 GeV to 700 GeV; however, the dark matter constraints restrict this scale as mt˜,mτ˜≳500 GeV. Such degenerate solutions also predict stop-neutralino and stau-neutralino co-annihilation channels, which are effective to reduce the relic abundance of neutralino down to the ranges consistent with the current dark matter observations. Finally, we discuss the effects of heavy MZ′ in the fine-tuning. Even though the radiative contributions are significantly low, the required fine-tuning can still be large. We comment about reinterpretation of the fine-tuning measure in the UMSSM framework, which can yield efficiently low results for the fine-tuning the electroweak scale.

Status and prospects of light bino\u2013higgsino dark matter in natural SUSY

Given the recent progress in dark matter direction detection experiments, we examine a light bino–higgsino dark matter (DM) scenario (M_1<100 GeV and mu <300 GeV) in natural supersymmetry with the electroweak fine tuning measure Delta _mathrm{EW}<30. By imposing various constraints, we note that: (i) For mathrm{sign}(mu /M_1)=+1, the parameter space allowed by the DM relic density and collider bounds can almost be excluded by the very recent spin-independent (SI) scattering cross-section limits from the XENON1T (2017) experiment. (ii) For mathrm{sign}(mu /M_1)=-1, the SI limits can be evaded due to the cancelation effects in the htilde{chi }^0_1tilde{chi }^0_1 coupling, while rather stringent constraints come from the PandaX-II (2016) spin-dependent (SD) scattering cross-section limits, which can exclude the higgsino mass |mu | and the LSP mass m_{tilde{chi }^0_1} up to about 230 and 37 GeV, respectively. Furthermore, the surviving parameter space will be fully covered by the projected XENON1T experiment or the future trilepton searches at the HL-LHC.

Naturalness, dark matter, and the muon anomalous magnetic moment in supersymmetric extensions of the standard model with a pseudo-Dirac gluino

We study the naturalness, dark matter, and muon anomalous magnetic moment in the Supersymmetric Standard Models (SSMs) with a pseudo-Dirac gluino (PDGSSMs) from hybrid F- and D-term supersymmetry (SUSY) breakings. To obtain the observed dark matter relic density and explain the muon anomalous magnetic moment, we find that the low energy fine-tuning measures are larger than about 30 due to strong constraints from the LUX and PANDAX experiments. Thus, to study the natural PDGSSMs, we consider multi-component dark matter and then the relic density of the lightest supersymmetric particle (LSP) neutralino is smaller than the correct value. We classify our models into six kinds: (i) Case A is a general case, which has small low energy fine-tuning measure and can explain the anomalous magnetic moment of the muon; (ii) Case B with the LSP neutralino and light stau coannihilation; (iii) Case C with Higgs funnel; (iv) Case D with Higgsino LSP; (v) Case E with light stau coannihilation and Higgsino LSP; (vi) Case F with Higgs funnel and Higgsino LSP. We study these Cases in details, and show that our models can be natural and consistent with the LUX and PANDAX experiments, as well as explain the muon anomalous magnetic moment. In particular, all these cases except the stau coannihilation can even have low energy fine-tuning measures around 10.

Bayesian analysis and naturalness of (Next-to-)Minimal Supersymmetric Models

The Higgs boson discovery stirred interest in next-to-minimal supersymmetric models, due to the apparent fine-tuning required to accommodate it in minimal theories. To assess their naturalness, we compare fine-tuning in a ℤ3 conserving semi-constrained Next-to-Minimal Supersymmetric Standard Model (NMSSM) to the constrained MSSM (CMSSM). We contrast popular fine-tuning measures with naturalness priors, which automatically appear in statistical measures of the plausibility that a given model reproduces the weak scale. Our comparison shows that naturalness priors provide valuable insight into the hierarchy problem and rigorously ground naturalness in Bayesian statistics. For the CMSSM and semi-constrained NMSSM we demonstrate qualitative agreement between naturalness priors and popular fine tuning measures. Thus, we give a clear plausibility argument that favours relatively light superpartners.

Naturalness and dark matter in the supersymmetric B−L extension of the standard model

We study the naturalness properties of the $B-L$ Supersymmetric Standard Model (BLSSM) and compare them to those of the Minimal Supersymmetric Standard Model (MSSM) at both low (i.e., Large Hadron Collider) energies and high (i.e., unification) scales. By adopting standard measures of naturalness, we assess that, in presence of full unification of the additional gauge couplings and scalar/fermionic masses of the BLSSM, such a scenario reveals a somewhat higher degree of Fine-Tuning (FT) than the MSSM, when the latter is computed at the unification scale and all available theoretical and experimental constraints, but the Dark Matter (DM) ones, are taken into account. Yet, such a difference, driven primarily by the collider limits requiring a high mass for the gauge boson associated to the breaking of the additional $U(1)_{B-L}$ gauge group of the BLSSM in addition to the $SU(3)_C\times SU(2)_L \times U(1)_Y$ of the MSSM, should be regarded as a modest price to pay for the former in relation to the latter, if one notices that the non-minimal scenario offers a significant volume of parameter space where numerous DM solutions of different compositions can be found to the relic density constraints, unlike the case of the minimal structure, wherein only one type of solution is accessible over an ever diminishing parameter space. In fact, this different level of tension within the two SUSY models in complying with current data is well revealed when the FT measure is recomputed in terms of the low energy spectra of the two models, over their allowed regions of parameter space now in presence of all DM bounds, as it is shown that the tendency is now opposite, the BLSSM appearing more natural than the MSSM.

Constraining fine tuning in composite Higgs models with partially composite leptons

Minimal Composite Higgs Models (MCHM) have long provided a solution to the hierarchy problem of the Standard Model, yet suffer from various sources of fine tuning that are becoming increasingly problematic with the lack of new physics observations at the LHC. We develop a new fine tuning measure that accurately counts each contribution to fine tuning (single, double, triple, etc) that can occur in a theory with np parameters, that must reproduce no observables. We then use a novel scanning procedure to perform a comprehensive study of three different two-site, 4D, SO(5) → SO(4) MCHMs with all third generation fermions included, distinguished by the choice of the lepton embeddings. These are the MCHM5 − 5 − 55 − 5 − 5, MCHM14 − 14 − 105 − 5 − 5 and MCHM14 − 1 − 105 − 5 − 5, where MCHMl − τ − νq − t − b has the lepton doublet partner in representation l, tau partner in representation τ, and so on. We find that embedding at least one massive lepton in the symmetric 14 of SO(5) moderately reduces the tuning for the case of low top partner masses (in line with previous results), but that this is balanced against the increased complexity of the model when one properly accounts for all sources of fine tuning. We study both the current relative fine-tuning of each scenario, and the future prospects. Noting that the different scenarios behave differently with respect to future improvements in collider measurements, we find that the MCHM14 − 1 − 105 − 5 − 5 enjoys a relatively low increase in fine tuning even for a future lower bound on the top partner masses of 3.4 TeV (or equivalently a maximum Higgs-fermion or Higgs-gluon coupling deviation of 2%).

Higgs-strahlung production of the lightest CP-even Higgs boson at ILC in natural NMSSM

Considering various experimental constraints, we scan over the parameter space of the NMSSM by requiring the fine tuning measures ΔZ and Δh are less than 50. Then in the allowed parameter space we investigate the Higgs-strahlung production of the lightest CP-even Higgs boson h1 at ILC assuming the next-to-lightest CP-even Higgs boson acts as SM-like. we calculate the cross section of the process e+e−→Zh1 at ILC with center-of-mass energy of 250 GeV, and also discuss the decay patterns of h1. We find that the cross section of the process e+e−→Zh1 can reach about 84 fb. Moreover, the cross section increases with the mass of h1 and strongly depends on the Higgs doublet-component of h1. For most of the surviving samples, h1 mainly decays to bb¯. However, for certain regions of the surviving samples, the branching ratio of h1 → γγ can maximally reach 2%, which can be used to discriminate the NMSSM from MSSM.

Naturalness made easy: two-loop naturalness bounds on minimal SM extensions

The main result of this paper is a collection of conservative naturalness bounds on minimal extensions of the Standard Model by (vector-like) fermionic or scalar gauge multiplets. Within, we advocate for an intuitive and physical concept of naturalness built upon the renormalisation group equations. In the effective field theory of the Standard Model plus a gauge multiplet with mass M , the low scale Higgs mass parameter is a calculable function of overline{mathrm{MS}} input parameters defined at some high scale Λh> M . If the Higgs mass is very sensitive to these input parameters, then this signifies a naturalness problem. To sensibly capture the sensitivity, it is shown how a sensitivity measure can be rigorously derived as a Bayesian model comparison, which reduces in a relevant limit to a Barbieri-Giudice-like fine-tuning measure. This measure is fully generalisable to any perturbative EFT. The interesting results of our two-loop renormalisation group study are as follows: for Λh = ΛPl we find “10% fine-tuning” bounds on the masses of various gauge multiplets of M<mathcal{O}left(1-10right) TeV, with bounds on fermionic gauge multiplets significantly weaker than for scalars; these bounds remain finite in the limit Λh → M+, weakening to M<mathcal{O}left(1-100right) TeV; and bounds on coloured multiplets are no more severe than for electroweak multiplets, since they only directly correct the Higgs mass at three-loop.

Where to look for natural supersymmetry

Why is natural supersymmetry neither detected nor ruled-out to date? To answer this question we use the Bayesian approach where the emphasis on finding prior-independent features within broader and minimally biased frames is taken as the guiding principle. The 20-parameter minimal supersymmetric standard model (MSSM) fits to subjective naturalness indicate the existence of a prior-independent upper bound on the pseudoscalar Higgs boson mass $m_A$ as a function of $\tan \beta$, the ratio of the vacuum expectation values of the MSSM Higgs doublets. For a 30-parameter MSSM this implies that $m_A \lesssim 3$ TeV and $\tan \beta \lesssim 25$ at 95\% Bayesian confidence. Removing the contradictory subjectiveness within the electroweak fine-tuning measure leads to finding the naturalness line, $m_A \sim \frac{1}{\sqrt{2}} \, m_Z \, \tan \beta,$ that reduces by one the number of MSSM Higgs sector free parameters.