Lightest Neutralino Research Articles

Higgsino dark matter in the MSSM

A comologically stable neutral component from a nearly pure $SU(2)$ doublet, with a mass $\sim$1.1 TeV, is one appealing candidate for dark matter (DM) consistent with all direct dark matter searches. We have explored this possibility in the context of the Minimal Supersymmetric extension of the Standard Model (MSSM), with the Higgsino playing the role of DM, in theories where supersymmetry breaking is transmitted by gravitational interactions at the unification scale $M\simeq 2\times 10^{16}$ GeV. We have focussed our work in the search of "light" supersymmetric spectra, which could be at reach of present and/or future colliders, in models with universal and non-universal Higgs and gaugino Majorana masses. The lightest supersymmetric particles of the spectrum are, by construction, two neutralinos and one chargino, almost degenerate, with a mass $\sim $1.1 TeV, and a mass splitting of a few GeV. Depending on the particular scenario the gluino can be at its experimental mass lower bound $\sim$ 2.2 TeV; in the squark sector, the lightest stop can be as light as $\sim$ 1.3 TeV, and the lightest slepton, the right-handed stau, can have a mass as light as $1.2$ TeV. The lightest neutralino can be found at the next generation of direct dark matter experimental searches. In the most favorable situation, the gluino, with some specific decay channels, could be found at the next run of the Large Hadron Collider (LHC), and the lightest stop at the High-Luminosity LHC run.

Search for top squark pair production using dilepton final states in {text {p}}{text {p}} collision data collected at sqrt{s}=13,text {TeV}

A search is presented for supersymmetric partners of the top quark (top squarks) in final states with two oppositely charged leptons (electrons or muons), jets identified as originating from {text {b}}quarks, and missing transverse momentum. The search uses data from proton-proton collisions at sqrt{s}=13,text {TeV} collected with the CMS detector, corresponding to an integrated luminosity of 137,{text {fb}}^{-1}. Hypothetical signal events are efficiently separated from the dominant top quark pair production background with requirements on the significance of the missing transverse momentum and on transverse mass variables. No significant deviation is observed from the expected background. Exclusion limits are set in the context of simplified supersymmetric models with pair-produced lightest top squarks. For top squarks decaying exclusively to a top quark and a lightest neutralino, lower limits are placed at 95% confidence level on the masses of the top squark and the neutralino up to 925 and 450,text {GeV}, respectively. If the decay proceeds via an intermediate chargino, the corresponding lower limits on the mass of the lightest top squark are set up to 850,text {GeV} for neutralino masses below 420,text {GeV}. For top squarks undergoing a cascade decay through charginos and sleptons, the mass limits reach up to 1.4,text {TeV} and 900,text {GeV} respectively for the top squark and the lightest neutralino.

Implementation of the ATLAS-SUSY-2018-31 analysis in the MadAnalysis 5 framework (sbottoms with multi-bottoms and missing transverse energy; 139 fb−1)

We present the implementation, in the MadAnalysis 5 framework, of the ATLAS-SUSY-2018-31 search for new physics, and document the validation of this implementation. This analysis targets, with 139 fb[Formula: see text] of proton–proton collisions at a center-of-mass energy of 13 TeV recorded by the ATLAS detector between 2015 and 2018, the production of a pair of supersymmetric bottom squarks when they further decay through a cascade decay involving the second lightest neutralino and a Standard Model Higgs boson. The validation of our work is based on three benchmark scenarios targeting different kinematic configurations. The first of them considers a new physics spectrum leading to the presence of high-[Formula: see text] [Formula: see text]-jets originating from sbottom decays, whereas the last two, that differ by the neutralino mass spectrum, are dedicated to the compressed regime and thus yield the presence of soft [Formula: see text]-jets in the final state. We obtain an agreement between the MadAnalysis 5 predictions and the official ATLAS results at the level of 20–30%, the largest discrepancies being related to cases exhibiting a poor Monte Carlo numerical precision at the level of the official ATLAS results.

Leptophobic Z′ bosons in the secluded UMSSM

We perform a comprehensive analysis of the secluded UMSSM model, consistent with present experimental constraints. We find that in this model the additional $Z^\prime$ gauge boson can be leptophobic without resorting to gauge kinetic mixing and, consequently, also $d$-quark-phobic, thus lowering the LHC bounds on its mass. The model can accommodate very light singlinos as DM candidates, consistent with present day cosmological and collider constraints. Light charginos and neutralinos are responsible for muon anomalous magnetic predictions within 1$\sigma$ of the measured experimental value. Finally, we look at the possibility that a lighter $Z^\prime$, expected to decay mainly into chargino pairs and followed by the decay into lepton pairs, could be observed at 27 TeV.

Status of low mass LSP in SUSY

In this article we review the case for a light ($< m_{h_{125}}/2$) neutralino and sneutrino being a viable Dark Matter (DM) candidate in Supersymmetry(SUSY). To that end we recapitulate, very briefly, three issues related to the DM which impact the discussions : calculation of DM relic density, detection of the DM in Direct and Indirect experiments and creation /detection at the Colliders. In case of SUSY, the results from Higgs and SUSY searches at the colliders also have implications for the DM mass and couplings. In view of the constraints coming from all these sources, the possibility of a light neutralino is all but ruled out for the constrained MSSM : cMSSM. The pMSSM, where the gaugino masses are not related at high scale, is also quite constrained and under tension in case of thermal DM and will be put to very stern test in the near future in Direct Detection (DD) experiments as well as by the LHC analyses. However in the pMSSM with modified cosmology and hence non-thermal DM or in the NMSSM, a light neutralino is much more easily accommodated. A light RH sneutrino is also still a viable DM candidate although it requires extending the MSSM with additional singlet neutrino superfields. All of these possibilities can be indeed tested jointly in the upcoming SUSY-electroweakino and Higgs searches at the HL/HE luminosity LHC, the upcoming experiments for the Direct Detection (DD) and indirect detection for the DM as well as the high precision electron-positron colliders under planning.

Light singlino dark matter at the LHC

The light singlino-like neutralino is expected to be a promising candidate for DM in the allowed parameter space of the NMSSM. The DM annihilation process takes place via the light Higgs bosons which are natural in this model. Identifying the allowed region of parameter space including various constraints, the detection prospect of such light DM candidate and Higgs bosons are explored at the LHC with its high luminosity options. Light Higgs bosons and the DM candidate, the lightest singlino-like neutralino are indirectly produced at the LHC via the SM Higgs production and its subsequent decays. Jet substructure techniques are used to tag boosted Higgs. It is found that the favourable range of masses of Higgs bosons and neutralino, compatible with a low mass DM solution, can be discovered with a reasonable signal significance ($\sim 5 \sigma$) at the LHC, with the center of mass energy $\sqrt{s}=14$ TeV and integrated luminosity options $\rm{\cal L}=300~fb^{-1}$ and 3000 $\rm fb^{-1}$.

Improved (g-2)_mu measurements and supersymmetry

The electroweak (EW) sector of the Minimal Supersymmetric Standard Model (MSSM) can account for variety of experimental data. The lighest supersymmetric particle (LSP), which we take as the lightest neutralino, {tilde{chi }}_{1}^0, can account for the observed Dark Matter (DM) content of the universe via coannihilation with the next-to-LSP (NLSP), while being in agreement with negative results from Direct Detection (DD) experiments. Owing to relatively small production cross-sections a comparably light EW sector of the MSSM is also in agreement with the unsuccessful searches at the LHC. Most importantly, the EW sector of the MSSM can account for the persistent 3-4,sigma discrepancy between the experimental result for the anomalous magnetic moment of the muon, (g-2)_mu , and its Standard Model (SM) prediction. Under the assumption that the {tilde{chi }}_{1}^0 provides the full DM relic abundance we first analyze which mass ranges of neutralinos, charginos and scalar leptons are in agreement with all experimental data, including relevant LHC searches. We find an upper limit of sim 600 ,, mathrm {GeV} for the LSP and NLSP masses. In a second step we assume that the new result of the Run 1 of the “MUON G-2” collaboration at Fermilab yields a precision comparable to the existing experimental result with the same central value. We analyze the potential impact of the combination of the Run 1 data with the existing (g-2)_mu data on the allowed MSSM parameter space. We find that in this case the upper limits on the LSP and NLSP masses are substantially reduced by roughly 100 ,, mathrm {GeV}. This would yield improved upper limits on these masses of sim 500 ,, mathrm {GeV}. In this way, a clear target could be set for future LHC EW searches, as well as for future high-energy e^+e^- colliders, such as the ILC or CLIC.

Search for new phenomena in final states with large jet multiplicities and missing transverse momentum using sqrt{s} = 13 TeV proton-proton collisions recorded by ATLAS in Run 2 of the LHC

Results of a search for new particles decaying into eight or more jets and moderate missing transverse momentum are presented. The analysis uses 139 fb−1 of proton-proton collision data at sqrt{s} = 13 TeV collected by the ATLAS experiment at the Large Hadron Collider between 2015 and 2018. The selection rejects events containing isolated electrons or muons, and makes requirements according to the number of b-tagged jets and the scalar sum of masses of large-radius jets. The search extends previous analyses both in using a larger dataset and by employing improved jet and missing transverse momentum reconstruction methods which more cleanly separate signal from background processes. No evidence for physics beyond the Standard Model is found. The results are interpreted in the context of supersymmetry-inspired simplified models, significantly extending the limits on the gluino mass in those models. In particular, limits on the gluino mass are set at 2 TeV when the lightest neutralino is nearly massless in a model assuming a two-step cascade decay via the lightest chargino and second-lightest neutralino.

Searching for the Higgsino-Bino sector at the LHC

We study the search for electroweakinos at the 13 TeV LHC in the case of heavy scalar superpartners. We consider both the direct production mode and the one associated with the decay of heavy Higgs bosons, and concentrate on the case of light Higgsinos and Binos. In this case, the direct production searches becomes more challenging than in the light Wino scenario. In the direct production mode, we use the current experimental searches to set the reach for these particles at larger luminosities, and we emphasize the relevance of considering both the neutral gauge boson and the neutral Higgs decay modes of the second and third lightest neutralino. We show the complementarity of these searches with the ones induced by the decay of the heavy Higgs bosons, which are dominated by the associated production of the lightest neutralino with the second and third lightest ones, with the latter decaying into gauge bosons. We show that, depending on the value of tan β, the Higgs boson decay channel remains competitive with the direct production channel up to heavy Higgs boson masses of about 1 TeV. Moreover, this search is not limited by the same kinematic considerations as the ones in the direct production mode and can cover masses up to the kinematic threshold for the decay of the heavier electroweakinos into the lightest neutralino. This decay mode provides also an alternative way of looking for heavy Higgs bosons in this range of masses and hence should be a high priority for future LHC analyses.

Measurements of top-quark pair spin correlations in the emu channel at sqrt{s} = 13 TeV using pp collisions in the ATLAS detector

A measurement of observables sensitive to spin correlations in tbar{t} production is presented, using 36.1 hbox {fb}^{-1} of pp collision data at sqrt{s} = 13 TeV recorded with the ATLAS detector at the Large Hadron Collider. Differential cross-sections are measured in events with exactly one electron and one muon with opposite-sign electric charge as a function of the azimuthal opening angle and the absolute difference in pseudorapidity between the electron and muon candidates in the laboratory frame. The azimuthal opening angle is also measured as a function of the invariant mass of the tbar{t} system. The measured differential cross-sections are compared to predictions by several NLO Monte Carlo generators and fixed-order calculations. The observed degree of spin correlation is somewhat higher than predicted by the generators used. The data are consistent with the prediction of one of the fixed-order calculations at NLO, but agree less well with higher-order predictions. Using these leptonic observables, a search is performed for pair production of supersymmetric top squarks decaying into Standard Model top quarks and light neutralinos. Top squark masses between 170 and 230 GeV are largely excluded at the 95% confidence level for kinematically allowed values of the neutralino mass.

Search for a scalar partner of the top quark in the all-hadronic t{bar{t}} plus missing transverse momentum final state at sqrt{s}=13\xa0TeV with the ATLAS detector

A search for direct pair production of scalar partners of the top quark (top squarks or scalar third-generation up-type leptoquarks) in the all-hadronic t{bar{t}} plus missing transverse momentum final state is presented. The analysis of 139 hbox {fb}^{-1} of {sqrt{s}=13} TeV proton–proton collision data collected using the ATLAS detector at the LHC yields no significant excess over the Standard Model background expectation. To interpret the results, a supersymmetric model is used where the top squark decays via {tilde{t}} rightarrow t^{(*)} {tilde{chi }}^0_1, with t^{(*)} denoting an on-shell (off-shell) top quark and {tilde{chi }}^0_1 the lightest neutralino. Three specific event selections are optimised for the following scenarios. In the scenario where m_{{tilde{t}}}> m_t+m_{{tilde{chi }}^0_1}, top squark masses are excluded in the range 400–1250 GeV for {tilde{chi }}^0_1 masses below 200 GeV at 95% confidence level. In the situation where m_{{tilde{t}}}sim m_t+m_{{tilde{chi }}^0_1}, top squark masses in the range 300–630 GeV are excluded, while in the case where m_{{tilde{t}}}< m_W+m_b+m_{{tilde{chi }}^0_1} (with m_{{tilde{t}}}-m_{{tilde{chi }}^0_1}ge 5 GeV), considered for the first time in an ATLAS all-hadronic search, top squark masses in the range 300–660 GeV are excluded. Limits are also set for scalar third-generation up-type leptoquarks, excluding leptoquarks with masses below 1240 GeV when considering only leptoquark decays into a top quark and a neutrino.

Search for direct production of electroweakinos in final states with one lepton, missing transverse momentum and a Higgs boson decaying into two b-jets in pp collisions at sqrt{s}=13\xa0TeV with the ATLAS detector

The results of a search for electroweakino pair production pp rightarrow tilde{chi }^pm _1 tilde{chi }^0_2 in which the chargino (tilde{chi }^pm _1) decays into a W boson and the lightest neutralino (tilde{chi }^0_1), while the heavier neutralino (tilde{chi }^0_2) decays into the Standard Model 125 GeV Higgs boson and a second tilde{chi }^0_1 are presented. The signal selection requires a pair of b-tagged jets consistent with those from a Higgs boson decay, and either an electron or a muon from the W boson decay, together with missing transverse momentum from the corresponding neutrino and the stable neutralinos. The analysis is based on data corresponding to 139 mathrm {fb}^{-1} of sqrt{s}=13 TeV pp collisions provided by the Large Hadron Collider and recorded by the ATLAS detector. No statistically significant evidence of an excess of events above the Standard Model expectation is found. Limits are set on the direct production of the electroweakinos in simplified models, assuming pure wino cross-sections. Masses of tilde{chi }^{pm }_{1}/tilde{chi }^{0}_{2} up to 740 GeV are excluded at 95% confidence level for a massless tilde{chi }^{0}_{1}.

A novel scenario in the semi-constrained NMSSM

In this work, we develop a novel efficient scan method, combining the Heuristically Search (HS) and the Generative Adversarial Network (GAN), where the HS can shift marginal samples to perfect samples, and the GAN can generate a huge amount of recommended samples from noise in a short time. With this efficient method, we find a new scenario in the semi-constrained Next-to Minimal Supersymmetric Standard Model (scNMSSM), or NMSSM with non-universal Higgs masses. In this scenario, (i) Both muon g-2 and right relic density can be satisfied, along with the high mass bound of gluino, etc. As far as we know, that had not been realized in the scNMSSM before this work. (ii) With the right relic density, the lightest neutralinos are singlino-dominated, and can be as light as 0-12 GeV. (iii) The future direct detections XENONnT and LUX-ZEPLIN (LZ-7 2T) can give strong constraints to this scenario. (iv) The current indirect constraints to Higgs invisible decay {h}_2to {tilde{chi}}_1^0{tilde{chi}}_1^0 are weak, but the direct detection of Higgs invisible decay at the future HL-LHC may cover half of the samples, and that of the CEPC may cover most. (v) The branching ratio of Higgs exotic decay h2→ h1h1, a1a1 can be over 20 percent, while their contributions left({h}_2to 4{tilde{chi}}_1^0right) to the invisible decay are very small.

Physics with far detectors at future lepton colliders

At the Large Hadron Collider (LHC), several far detectors such as FASER and MATHUSLA have been proposed to target the long-lived particles (LLPs) featured with displaced vertices. Naturally one question arises as to the feasibility of installing similar far detectors at future lepton colliders like the CEPC and FCC-ee. Because of the different kinematics of final state particles and the freedom to locate both the experiment hall and the detectors, the future lepton collider with an additional far detector may play a unique role in searching for LLPs. In this study, we consider various locations and designs of far detectors at future $e^- e^+$ colliders and investigate their potentials for discovering LLPs in the physics scenarios including exotic Higgs decays, heavy neutral leptons, and the lightest neutralinos. Our analyses show that the kinematical distinctions between the lepton and hadron colliders render the optimal positions of far detectors lying at the direction perpendicular to the collider beams at future $e^- e^+$ colliders, in contrast to the LHC where a boost in the forward direction can be exploited. We also find that when searching for LLPs, such new experiments with far detectors at future lepton colliders may extend and complement the sensitivity reaches of the experiments at the future lepton colliders with usual near detectors, and the present and future experiments at the LHC. In particular, we find that, for the theory models considered in this study, a MATHUSLA-sized far detector would give a modest improvement compared to the case with a near detector only at future lepton colliders.

Expanding the parameter space of natural supersymmetry

SUSY/SUGRA models with naturalness defined via small μ are constrained due to experiment on the relic density and the experimental limits on the WIMP-proton cross-section and WIMP annihilation cross-section from indirect detection experiments. Specifically models with small μ where the neutralino is higgsino-like lead to dark matter relic density below the observed value. In several works this problem is overcome by assuming dark matter to be constituted of more than one component and the neutralino relic density deficit is made up from contributions from other components. In this work we propose that the dark matter consists of just one component, i.e., the lightest neutralino and the relic density of the higgsino-like neutralino receives contributions from the usual freeze-out mechanism along with contributions arising from the decay of hidden sector neutralinos. The model we propose is an extended MSSM model where the hidden sector is constituted of a U(1)X gauge sector along with matter charged under U(1)X which produce two neutralinos in the hidden sector. The U(1)X and the hypercharge U(1)Y of the MSSM have kinetic and Stueckelberg mass mixing where the mixings are ultraweak. In this case the hidden sector neutralinos have ultraweak interactions with the visible sector. Because of their ultraweak interactions the hidden sector neutralinos are not thermally produced and we assume their initial relic density to be negligible. However, they can be produced via interactions of MSSM particles in the early universe, and once produced they decay to the neutralino. For a range of mixings the decays occur before the BBN producing additional relic density for the neutralino. Models of this type are testable in dark matter direct and indirect detection experiments and at the high luminosity and high energy LHC.

Search for Supersymmetry with a Compressed Mass Spectrum in Events with a Soft τ Lepton, a Highly Energetic Jet, and Large Missing Transverse Momentum in Proton-Proton Collisions at sqrt[s]=13 TeV.

The first search for supersymmetry in events with an experimental signature of one soft, hadronically decaying τ lepton, one energetic jet from initial-state radiation, and large transverse momentum imbalance is presented. These event signatures are consistent with direct or indirect production of scalar τ leptons (τ[over ˜]) in supersymmetric models that exhibit coannihilation between the τ[over ˜] and the lightest neutralino (χ[over ˜]_{1}^{0}), and that could generate the observed relic density of dark matter. The data correspond to an integrated luminosity of 77.2 fb^{-1} of proton-proton collisions at sqrt[s]=13 TeV collected with the CMS detector at the LHC in 2016 and 2017. The results are interpreted in a supersymmetric scenario with a small mass difference (Δm) between the chargino (χ[over ˜]_{1}^{±}) or next-to-lightest neutralino (χ[over ˜]_{2}^{0}), and the χ[over ˜]_{1}^{0}. The mass of the τ[over ˜] is assumed to be the average of the χ[over ˜]_{1}^{±} and χ[over ˜]_{1}^{0} masses. The data are consistent with standard model background predictions. Upper limits at 95%confidence level are set on the sum of the χ[over ˜]_{1}^{±}, χ[over ˜]_{2}^{0}, and τ[over ˜] production cross sections for Δm(χ[over ˜]_{1}^{±},χ[over ˜]_{1}^{0})=50 GeV, resulting in a lower limit of 290GeV on the mass of the χ[over ˜]_{1}^{±}, which is the most stringent to date and surpasses the bounds from the LEP experiments.

Superstring-inspired particle cosmology: inflation, neutrino masses, leptogenesis, dark matter & the SUSY scale

We develop a string-inspired model for particle cosmology, based on a flipped SU(5)×U(1) gauge group formulated in a no-scale supergravity framework. The model realizes Starobinsky-like inflation, which we assume to be followed by strong reheating, with the GUT symmetry being broken subsequently by a light `flaton' field whose decay generates a second stage of reheating. We discuss the production of gravitinos and the non-thermal contribution made by their decays to the density of cold dark matter, which is assumed to be provided by the lightest neutralino. We also discuss the masses of light and heavy neutrinos and leptogenesis. As discussed previously [1], a key rôle is played by a superpotential coupling between the inflaton, matter and GUT Higgs fields, called λ6. We scan over possible values of λ6, exploring the correlations between the possible values of observables. We emphasize that the release of entropy during the GUT transition allows large regions of supersymmetry-breaking parameter space that would otherwise lead to severe overdensity of dark matter. Furthermore, we find that the Big Bang nucleosynthesis lower limit on the reheating temperature of ∼ 1 MeV restricts the supersymmetry-breaking scale to a range \U0001d4aa(10) TeV that is consistent with the absence of supersymmetric particles at the LHC.

Search for bottom-squark pair production with the ATLAS detector in final states containing Higgs bosons, b-jets and missing transverse momentum

The result of a search for the pair production of the lightest supersymmetric partner of the bottom quark left({tilde{b}}_1right) using 139 fb−1 of proton-proton data collected at sqrt{s} = 13 TeV by the ATLAS detector is reported. In the supersymmetric scenarios considered both of the bottom-squarks decay into a b-quark and the second-lightest neutralino, {tilde{b}}_1to b+{tilde{chi}}_2^0 . Each {tilde{chi}}_2^0 is assumed to subsequently decay with 100% branching ratio into a Higgs boson (h) like the one in the Standard Model and the lightest neutralino: {tilde{chi}}_2^0to h+{tilde{chi}}_1^0 . The {tilde{chi}}_1^0 is assumed to be the lightest supersymmetric particle (LSP) and is stable. Two signal mass configurations are targeted: the first has a constant LSP mass of 60 GeV; and the second has a constant mass difference between the {tilde{chi}}_2^0 and {tilde{chi}}_1^0 of 130 GeV. The final states considered contain no charged leptons, three or more b-jets, and large missing transverse momentum. No significant excess of events over the Standard Model background expectation is observed in any of the signal regions considered. Limits at the 95% confidence level are placed in the supersymmetric models considered, and bottom-squarks with mass up to 1.5 TeV are excluded.

Search for displaced vertices of oppositely charged leptons from decays of long-lived particles in pp collisions at [formula omitted] TeV with the ATLAS detector

A search for long-lived particles decaying into an oppositely charged lepton pair, μμ, ee, or eμ, is presented using 32.8fb−1 of pp collision data collected at s=13 TeV by the ATLAS detector at the LHC. Candidate leptons are required to form a vertex, within the inner tracking volume of ATLAS, displaced from the primary pp interaction region. No lepton pairs with an invariant mass greater than 12 GeV are observed, consistent with the background expectations derived from data. The detection efficiencies for generic resonances with lifetimes (cτ) of 100–1000 mm decaying into a dilepton pair with masses between 0.1–1.0 TeV are presented as a function of pT and decay radius of the resonances to allow the extraction of upper limits on the cross sections for theoretical models. The result is also interpreted in a supersymmetric model in which the lightest neutralino, produced via squark–antisquark production, decays into ℓ+ℓ′−ν (ℓ,ℓ′=e, μ) with a finite lifetime due to the presence of R-parity violating couplings. Cross-section limits are presented for specific squark and neutralino masses. For a 700 GeV squark, neutralinos with masses of 50–500 GeV and mean proper lifetimes corresponding to cτ values between 1 mm to 6 m are excluded. For a 1.6 TeV squark, cτ values between 3 mm to 1 m are excluded for 1.3 TeV neutralinos.

Alleviating the B̄ → Dτντ and B̄ → D∗τντ puzzle in the MSSM

We show that Supersymmetric effects driven by penguin contributions to the [Formula: see text] transition are able to account simultaneously for a sizeable increase of both branching ratios of [Formula: see text] and [Formula: see text] with respect to the Standard Model predictions, thereby approaching their experimentally measured values. We emphasize that a light chargino and neutralino, with masses less than 300 GeV, in addition to a large stau/sneutrino mass and a large [Formula: see text], are essential for enhancing the effect of the lepton penguin [Formula: see text], which is responsible for the improved theoretical predictions with respect to current data.