dataesr/scientific-paragraphs-categorization huggingface dataset:
The most studied  [12, 87]  scenario is the dilepton scenario in Eq. 4. 19. Reinterpretation of the ATLAS and CMS 8 TeV data concerning searches of charginos, neutralinos and sleptons, to the case of the IDM was conducted in Ref. [33]. They are essentially based on the dilepton signature of the IDM, Eq. 4. 19, with the important caveat that dileptons from the Z-boson decay are vetoed by the CMS/ATLAS cut (|m -M Z | > 10 GeV). Combined with the LEP data, one learns  [32, 33, 37 ] that one should impose 3 M X > 45GeV. (4. 22) Simulations for all process 4. 18-4. 21 were studied for some benchmark points in  [86]  while a full simulation was performed for 4. 19 in Ref. [37]. The caveat, |m -M Z | > 10 GeV, we alluded to earlier, has a crucial impact on the searches, existing and forthcoming. This cut is meant to reduce the large SM background in events containing a (on-shell) Z-boson.
Yet, for a large part of the IDM parameter space, ∆M AX > M Z , where A → XZ proceeds with an on-shell Z. Therefore, large values of M A not only give smaller cross-sections but also a very large fraction of the yield of leptons are cut. Thus, the prospects for future discovery are slim. Very recently, ATLAS has also given limits on the masses of the supersymmetric charginos and neutralinos in the pure (simplified) wino and (non-degenerate) higgsino limits of the MSSM (minimal supersymmetric model)  [88]  based on data from the LHC at √ s = 13 TeV. In these special manifestations of the MSSM (heavy mass sfermions), the production mechanisms and the signatures at the LHC are the same as those of the IDM. The only (notable) difference is the spin of the produced particles in these models. Therefore, we also take into account the ATLAS exclusion zones observing that the corresponding limits on the IDM are more relaxed because of the scalar nature of the IDM particles resulting in much smaller cross-sections.
7  [70] [71] [72] [73] 104]  for computing the relic densities. Some considerations beyond tree-level are taken into account in micrOMEGAs; in particular the Higgs couplings to the SM particles. The code also uses a running for the electromagnetic coupling with an effective coupling estimated at α(M Z ) ∼ 1/128. 907 instead of the OS coupling in the Thomson limit, i. e. , α = /137. 036. For many annihilation cross-sections, this change of α amounts to an overall rescaling that brings a correction of about 13% in 2 → 2 annihilation processes. However, in many scenarios and models beyond the SM, this rescaling does not account for the full one-loop correction  [5, 52, 54, 60, 61]. It is therefore wise when we select benchmarks points, using micrOMEGAs for the relic density constraint, to allow for a theoretical uncertainty of 20%.
We will therefore keep points that satisfy 0. 096 < Ωh 2 < 0. 144. (4. 27) Moreover, we quote the value of the relic density using micrOMEGAs with both an effective α(M Z ) and α. Once we compute the full one-loop corrections, we comment on the use of the effective electromagnetic coupling for each of the benchmark points that we study at one-loop. When running micrOMEGAs, we also let the code check explicitly for the direct detection and possible indirect detection constraints. Table  2 : Benchmarks points that pass the constraints discussed in Section 4. All masses are in GeV. The benchmarks are divided into three classes: 1) the Higgs resonance region, 2) the small coannihilation region with ∆M = M A -M X allowed by LEPII and 3) the less tuned annihilation class for masses of a DM around M X = 70 GeV.
We have conducted a very thorough investigation on the allowed parameter space of the model which includes new LHC and direct detection data to delimit the range of the low mass IDM scenarios and the DM annihilation mechanisms that are involved. A set of representative IDM points covering these mechanisms was presented. It will serve as a starting point to conduct full one-loop calculations in these three scenarios. XX → W f f (a 2 → 3 process) at one-loop which has never been attended before, will figure in all three scenarios but with varying degree of importance. Salient features of this process are contained in the 2 → 2 processes XX → W + W -and ZZ which we have studied in this paper. Crucial technical process specific issues, beyond the general renormalisation procedure presented at some length here, are presented in the accompanying papers that cover each of the three scenarios.
Acknowledgments We are grateful to  Guillaume Chalons  who contributed to the early stages of this work. We thank  Jack Y. Araz  for assistance regarding aspects of MadAnalysis 5. HS is supported by the  National Natural Science Foundation of China  (Grant No. 12075043 , No. 11675033 ). He warmly thanks the  CPTGA and LAPTh  for support during his visit to France in 2019 when this work was initiated. SB is grateful for the support received from  IPPP, Durham, UK , where most of this work was performed. SB also thanks  LAPTh  for the support provided during his visit, when this work started. NC is financially supported by  IISc (Indian Institute of Science, Bangalore, India)  through the C. V. Raman postdoctoral fellowship. NC also acknowledges support from  DST, India , under grant number  IFA19-PH237  ( INSPIRE Faculty Award ).
Scientific Objectives of the Multidisciplinary Investigations The MESSENGER and BepiColombo missions were conceived to address key scientific questions regarding Mercury's origin and evolution, and its surrounding environment  (Solomon et al. 2007; Benkhoff et al. 2010). The measurements acquired by the MES-SENGER spacecraft enabled the accomplishment of the NASA mission goals, but raised also fundamental questions  (Solomon et al. 2018 ), which will be investigated by the Bepi-Colombo mission. Table  1  shows the BepiColombo GGWG science themes, questions, and objectives. The MPO will provide extremely highly accurate measurements with the onboard science instruments, and a uniform planet coverage through the MPO lower eccentric orbit than MESSENGER. A global view of Mercury and the improved MPO data qualities will help answer the fundamental questions that are still open.
The gravity and topography investigations will yield Mercury's global crustal thickness and bulk density. The Mercury Imaging X-ray Spectrometer (MIXS) and Mercury Gamma-ray and Neutron Spectrometer (MGNS) will determine the elemental composition of Mercury's crust  (Fraser et al. 2010; Mitrofanov et al. 2010). Multispectral imaging and spectroscopic data collected by the Spectrometer and Imagers for MPO BepiColombo Integrated Observatory System (SIMBIO-SYS) will reveal crustal differentiation, space weathering, and rock minerals abundances  (Flamini et al. 2010). The synergetic analysis of these complementary datasets will enhance our knowledge of the physical parameters of the outer layers, including particle size, strength, and porosity. High-resolution gravity and topographic global maps will provide crucial information on Mercury's geological history.
2013). The distribution and orientation of the gravity gradient anomalies indicate the stress state induced by the radius contraction. Magnetic field measurements may provide further constraints on Mercury's evolution. MESSENGER data showed that the crust is strongly magnetized  (Johnson et al. 2015) , which suggests that Mercury once may have had a stronger magnetic field than Earth. These measurements were obtained during the XM2 low-altitude campaign of the mission when the spacecraft was closer than ∼ 130 km to the surface. Measuring crustal magnetization will be more challenging for the MPO spacecraft because of its high initial pericenter. This will decline over the course of the mission-how fast depends on the gravity field which has to be further explored as described here. Also, it remains to be seen how long MPO will survive in the Hermean harsh thermal environment.
Furthermore, gravity and altimetry data will allow us to measure Mercury's gravitational (i. e. , Love number k 2 ) and radial surface (i. e. , Love number h 2 ) tidal responses, respectively. An accurate estimation of both Love numbers k 2 and h 2 will provide a strong constraint on the size of the outer liquid core  (Padovan et al. 2014 ) and of the solid inner core  (Steinbrügge et al. 2018). The retrieval of the gravitational phase lag, which informs on the level of internal dissipation, will also enhance our knowledge of the rheology (i. e. , viscosity and rigidity) of the mantle, which plays a major role in Mercury's thermochemical evolution  (Tosi et al. 2013). Therefore, the GGWG joint analysis of altimetry, gravity, and magnetic results will be crucial to precisely recover the thermal state and configuration of Mercury's internal structure.
Mercury's orbit around the Sun and its 3:2 spin-orbit resonance help understand how the planet formed and evolved  (Correia and Laskar 2004; Wieczorek et al. 2012). Refinements of Mercury's ephemeris will indicate possible departures from this minimum-energy condition. The MORE radio science instrument will enable a precise determination of Mercury's orbit by using extremely accurate range measurements. A thorough investigation of Mercury's ephemeris also represents a great opportunity to conduct fundamental physics and heliophysics experiments. Because of the planet's proximity to the Sun, Einstein's theory of General Relativity (GR)  (Einstein 2019 ) must be accounted for to accurately model its orbital evolution (i. e. , perihelion precession). The sub-meter precision of the MORE range data will be well-suited to estimate the parameterized post-Newtonian (PPN) parameters β, γ , α 1 , and α 2 to test possible GR violations.
SQ3. 4 How and when did Mercury get captured in the 3:2 spin-orbit resonance? SO3. 4. 1 Mercury rotation from altimetry and orbital period from radio science. The estimate of this upper bound altitude is based on instrument specifications providing global surface coverage. It will be refined in orbit around Mercury since it depends on several unknown parameters (e. g. , short-scale surface roughness of Mercury). BELA will provide a global surface coverage, including first altimetric observations of the southern hemisphere. The range data is computed by accurately measuring the time-of-flight of a short (∼5 ns) laser pulse emitted from the instrument to the planetary surface and back-scattered to the receiver. The start time is recorded by transferring a small fraction of the emitted pulse directly to the receiver through fiber optics.
From a precise two-way time-of-flight measurement between the transmitted and received wave-package, which is ∼3. 2 ms and ∼7 ms for altitudes of 480 km and 1055 km, respectively, topographic data can be retrieved when combined with spacecraft position and attitude data. Topographic models of the planetary surface at global, regional, and local scales will be derived from several hundred million laser shots collected during the BepiColombo nominal mission. The onboard software of BELA is capable of analyzing the return pulse by using polynomial fits to approximate the pulse shapes. If requested, the fully digitized pulse can be returned to Earth. Furthermore, the shape of the return pulse provides information on the surface albedo at the laser wavelength and on the roughness of the surface on the scale of the laser footprint (∼16 to 53 m diameter, depending on spacecraft altitudes).
1 m at 200-m baseline and 6. 4 m at 50-m baseline, and a mean albedo of 0. 19  (Steinbrugge et al. 2018). By analyzing the energy of the transmitted and returned pulses BELA will also be sensitive to Mercury's surface albedo at the laser wavelength of 1064 nm. After the successful launch of the BepiColombo mission, three BELA instrument checkouts have been performed (Near-Earth Commissioning Phase and the first two cruise checkouts). Since BELA is facing the Mercury Transfer Module (MTM), firing the laser is not possible due to the enhanced risk of harmful back-reflections into the instrument. Therefore, functional check-outs focused on the receiver chain and general housekeeping data. Dark noise levels of the detector were recorded and the first data for calibrating the long-term drift of the RFM clock with respect to the on-board clock were obtained.
Mercury Orbiter Radio Science Experiment (MORE) The MPO radio science experiment, MORE, will enable the precise orbit determination of the spacecraft to accurately estimate the physical quantities responsible for the dynamical evolution of both the MPO and Mercury's trajectories. The radio science data are acquired by Earth's ground stations during dedicated radio tracking passages. The spacecraft receives a signal from one of the ESA's Deep Space Antennas (DSA) and sends it back to the same DSA (i. e. , two-way link) or another ground station (i. e. , three-way link) to establish telecommunication operations. The radio tracking measurements that are acquired by the DSA station are range and range-rate observables. The time delay and the Doppler shift of the received signal measure the spacecraft relative distance and velocity in the line-of-sight between the spacecraft and the ground station, respectively.
This configuration was significantly affected by fluctuations of the solar plasma in proximity of superior solar conjunctions  (Iess et al. 2014). MESSENGER radio data acquired at Sun-probe-Earth (SPE) angles larger than 30 • showed accuracies of ∼1-2 m and ∼50 µm s -1 at 60-s integration time for range and rangerate, respectively  (Genova et al. 2018 (Genova et al. , 2019)). This level of noise was mainly due to thermal effects induced by the telecommunication system. At lower SPE angles, the plasma noise caused larger errors in both range and range-rate data. The high quality of the MORE radio tracking data will guarantee significantly enhanced accuracies of orbit and gravity determination compared to the MESSENGER spacecraft. To compensate undesired effects due to mismodeling of perturbing forces, the MPO hosts the ISA instrument  (Iafolla et al.
2021). Due to the low amplitude of the planetary magnetic field, the expected signals are very weak. Therefore, an enhanced understanding of the spacecraft generated disturbances and the magnetosphere, which will be investigated by the MMO/MGF instrument onboard the Mio spacecraft  (Baumjohann et al. 2010) , is required. The two MPO magnetometers are mounted on a boom, which was deployed in the Near-Earth Commissioning Phase. Since then, the MPO-MAG instrument has been fully operational and has collected data continuously in order to characterize the spacecraft magnetically. Table  2  gives an overview of the experiment characteristics and the spacecraft effects on the instrument as verified in space so far. During cruise, the offsets can be corrected on a routine basis, using the approach established by  Hedgecock (1975).
Given the predicted trajectory of the MPO spacecraft and the instrument performance in Table  2 , we can estimate the accuracies of the internal planetary magnetic field inversion. The resulting uncertainties mainly depend on the MPO orbit configuration, offset determination (i. e. , instrument readings in zero ambient field), and orientation knowledge. A conservative inversion estimate yields a solution of the internal magnetic field in spherical harmonics to degree and order 6 as it is described in detail by  Heyner et al. in  this issue. The predicted error in the Gauss coefficients becomes as large as the field coefficients beyond degree 6. More robust inversion techniques and data cleaning algorithms could enhance the model resolution.
The maximum degree, l max , of the estimated spherical harmonic coefficients constrains the spatial resolution of the gravity field. Higher degrees provide crucial information on the finer spatial scales of the gravity field. A better understanding of the gravity anomalies at different spatial scales enables a more comprehensive geophysical investigation of Mercury's internal structure from the outer silicate layers to the core. The radio science team of the MESSENGER mission provided very accurate models of Mercury's gravity field, named HgM008, and orientation  (Genova et al. 2019). These geophysical results were retrieved by processing the entire MESSENGER radio science dataset, which includes the measurements collected during the low-altitude campaign of the extended mission. The HgM008 gravity model reports the global field with the associated uncertainties in spherical harmonics to degree and order 100 (Fig.
(1974)  already concluded that a weak axial dipole dominates the internal magnetic field, but its center is shifted northwards. Ness (1978)  discuss several other analysis attempts by assuming different internal field geometries and structures of the external field. The internal axial dipole coefficient was estimated to range from 170 to 350 nT. Strong axial quadrupole contributions were also identified, demonstrating the non-uniqueness of the inversion caused by a limited spatial measurement coverage before the arrival of the MESSENGER mission. After the first two Mercury flybys of the MESSENGER spacecraft,  Alexeev et al. (2010)  employed a relatively simple magnetospheric model to prevent high correlations among the coefficients of internal and external fields. The combination of the Mariner 10 measurements with the MESSENGER two-flyby dataset yielded an axial dipole moment of -196 nT R 3 and a northward dipole offset of 0.
(2015)  adapted a crustal field modeling technique (i. e. , equivalent source dipoles) to model the core field of Mercury during the first six months of the MESSENGER mission. Thébault et al. (2017)  considered another localized approach (i. e. , revised spherical cap analysis) to model the field in the northern hemisphere by processing the entire MESSENGER mission dataset. Both analyses used MESSENGER measurements acquired at spacecraft altitudes < 1000 km. The Gauss coefficients of the model by  Oliveira et al. (2015)  yield a g 0 2 /g 0 1 = 0. 212 that is equivalent to d = 0. 106R. The local model by  Thébault et al. (2017)  was converted into a global field in spherical harmonics to degree and order = 5, and the resulting quadrupole-to-dipole ratio is 0. 27, which also results in a less important equivalent dipole offset of d = 0.
2019 ) determined a higher mean rotation rate than that of the exact 3:2 resonant rotation, an offset that could be caused by a long-period libration. Identification of the period and the amplitude is needed to infer properties of the core and requires observations over several years. This might be possible with BepiColombo, which will significantly extend the time series of libration observations. The combination of MESSENGER and BepiColombo datasets will then be fundamental to retrieve long-term variations of Mercury's rotational state.
e. , equal to half a solar day on Mercury) and half that value. The sectorial wave at the orbital period is about 3 times larger than the zonal wave at the same period, which is the third-largest tide  (Van Hoolst and Jacobs 2003). The effect of tides on the external gravitational field of Mercury has already been determined with an accuracy of about 5% by analyzing radio science data of the MESSENGER mission. Early estimates based on data before the extended mission lowaltitude campaign suggested k 2 = 0. 451 ± 0. 014  (Mazarico et al. 2014)  and k 2 = 0. 46 ± 0. 02  (Verma and Margot 2016). The analyses of the entire MESSENGER dataset including data at orbital altitudes lower than 100 km, led to larger independent estimates k 2 = 0. 57 ± 0. 03  (Genova et al. 2019)  and k 2 = 0. 53 ± 0. 03  (Konopliv et al.
From a global perspective, even the largest impacts such as the one that formed the Caloris basin have only short-lived effects on the evolution of the mantle and core  (Roberts and Barnouin 2012). Such impacts locally modify the planform of mantle convection inducing the formation of hot upwellings beneath the impact site and in turn the production of partial melt, which ultimately erupts forming basin-filling melt sheets  (Ghods and Arkani-Hamed 2007; Padovan et al. 2017). The volume and time of emplacement of the melt sheets within Mercury's large basins such as Caloris or Rembrandt can be estimated from dedicated stratigraphic analyses  (Ernst et al. 2015)  and by dating of the corresponding surface units  (Fassett 2016). Padovan et al. (2017)  showed that the possibility to match these observations with numerical models crucially depends on the global thermal state of the mantle at the time of the impact, which indicates that regional-scale datasets related to specific impact sites can provide important additional constraints on the global evolution of Mercury.
2002; Imperi et al. 2018 ). These results were initially yielded through a method that is based on the recovery of Mercury and Earth initial states only  (Milani et al. 2002). This estimation strategy relies on a priori assumptions on Earth's initial conditions (i. e. , rotation) and Sun's position with respect to the SSB (i. e. , rescaling) to solve the degeneracy in the inversion of the ephemeris solution  (Milani et al. 2002; De Marchi et al. 2016; Schettino et al. 2018). Recent results of Einstein's GR and solar system expansion through the analysis of the MESSENGER data indicated that discrepancies in the planetary ephemerides affect significantly the estimation of relativistic and heliophysics parameters  (Genova et al. 2018). Therefore, BepiColombo data will be processed in a global solution of the Solar System planetary ephemerides with complementary datasets of spacecraft in orbit about other celestial bodies  (Fienga et al.
The former uncertainties were obtained by assuming rotation and rescaling constraints, whereas De  Marchi and Cascioli (2020)   (Nordtvedt 1970). This assumption helps especially to disentangle β and J 2 contributions, yielding the accuracies shown in Table  4. The combination of MORE and other radio science datasets will enable the estimation of Ġ M /GM. The time-varying solar gravitational parameter will be measured with an unprecedented accuracy, which is fundamental for monitoring the solar mass loss rate and testing possible time variations of the gravitational constant G. The comparison between the measured Ġ M /GM and the theoretical computations of the Sun's mass loss rate  (Pinto et al. 2011; Pitjeva and Pitjev 2012)  will significantly constrain the universal constant time variation.
Conclusions Improved measurements of the rotation, tides and the magnetic field of Mercury by the BepiColombo mission will enable independent constraints on Mercury's core. However, the main progress is expected from a combined analysis of those datasets. Only interior models that satisfy all constraints can be a candidate for describing Mercury. Accurate rotational data as will be acquired by the MPO science instruments are required to better constrain the density profiles in the core and silicate envelope. This places essential bounds on the composition of the core and silicate envelope in addition to surface compositional data. The bulk composition of the core is intimately linked to the size and composition of the inner core. An indirect knowledge of the composition of the core can, therefore, be obtained by investigating the inner core, whose presence and properties will be studied by measuring the libration amplitude at 88 days, the orientation of the planet (i.
MPO-MAG instrument characteristics. The instrument noise stated here is for a temperature of T = 180 • C, which has not been reached so far. The values for static and dynamic fields related to internal spacecraft sources are derived from the limited dataset collected so far. These measurements enable a first assessment only, since few instruments are already operative. The magnetic disturbance levels, furthermore, exclude solar electric propulsion where disturbances up to 160 nT are expected. The sensor alignment has also been checked during the Earth flyby of the BepiColombo composite by using the well-known terrestrial magnetic field.