dataesr/scientific-paragraphs-categorization huggingface dataset:
org/10. 1016/j. physletb. 2020. 135769. Fig. 1. Correlation between the ratios R(B → h s ν ν) (h s = K , K * , X s ) and R(K L → π 0 ν ν) in the linear MFV limit. Due to the correlation mentioned in (5), all three curves described in the text collapse to a single straight line spanning over the whole plane. The horizontal bands correspond to the 90 % CL limits on the observables for R(B → K * ν ν) (dark orange) and R(B → K ν ν) (blue) obtained by the Belle Collaboration  [2] , while the vertical bands correspond to the 90 % CL limits on the observables for B(K L → π 0 ν ν) obtained by the KOTO Collaboration with the 2015  [3]  and the 2016-18  [4]  datasets. The right side of the canvas is shown on a logarithmic scale in order to display the results in Refs. [3, 4]. Fig. 2. Correlation between the ratios R(K + → π + ν ν) and R(K L → π 0 ν ν) in the GMFV limit.
Additionally to the curves described in the text, we include the dashed green curve corresponding to the Grossman-Nir bound  [5]. The vertical bands correspond to the 90 % CL limits on the observables for B(K L → π 0 ν ν) obtained by the KOTO Collaboration with the 2015  [3]  and the 2016-18  [4]  datasets, while the horizontal blue band indicates the recent B(K + → π + ν ν) measurement by the NA62 Collaboration  [6]. B(B → h s ν ν) B(B → h s ν ν) SM = 1 3 ν α 2 ν α = 1 3 ν α 1 - s 2 W X t C ν α , N P L 2 (3) = 1 3 ν α 1 + π s 2 W α em X t λ q 33 λ αα (C S -C T ) θ q e -iφ q V tb 2 (4) where θ q = 1 and φ q = 0 in (linear) MFV but they take arbitrary values in Generalised MFV (GMFV), as discussed in Ref. [1]. This means that in the MFV limit these modes are fully correlated, up to small corrections of order O(1 -V tb ) B(K L → π 0 ν ν) B(B → h s ν ν) MFV = B(K L → π 0 ν ν) SM B(B → h s ν ν) SM ( 5 ) This relation is violated completely in any more general scenario (already in GMFV), for instance, by the inclusion of a non-zero phase (φ q ), the variation of θ q from 1 (where φ q and θ q are the GMFV parameters introduced in Eq.
DUSTGRAIN-pathfinder simulations The DUSTGRAIN-pathfinder suite consists of N-body simulations of volume (750 h -1 Mpc) 3 filled with N p = 768 3 particles, corresponding to a particle mass resolution m p of approximately 8×10 10 h -1 M  (Giocoli et al. 2018a ). The standard reference CPs have been set to values consistent with the results of the Planck-2015 (Planck Collaboration I 2016) cosmological data analysis, namely a matter density Ω m of 0. 31345, a baryon density Ω b of 0. 0491, Hubble constant H 0 of 67. 31 km s -1 Mpc -1 , a scalar spectral index n s of 0. 9658, and mean amplitude σ 8 of the linear density fluctuations on the 8 h -1 Mpc scale of 0. 842. Since the DUSTGRAIN-pathfinder simulations are part of a cosmological data set that also accounts for modified gravity models, the simula-tions (including those assuming standard general relativity) were carried out with the MG-Gadget code  (Puchwein et al.
This distinction lowers the risk of any impact of the n(z) difference between the two sets of data on the cosmological inference. After the magnitude cut, the COSMOS2015 n(z) is smoothed by fitting the parametrization from  Fu et al. (2008)  as it was shown in  Martinet et al. (2021b)  to capture the high-redshift tail better than the standard  Smail et al. (1994)  fit. The redshift distributions of the   2016 ) COSMOS2015 catalog after removing galaxies with magnitudes I E ≥ 24. 5 and i ≥ 24. 5 for DUSTGRAINpathfinder and SLICS, respectively (red and blue histograms). Bottom: Fractional difference between the DUSTGRAIN-pathfinder and SLICS redshift distributions. The difference is always below 5% except for redshifts lower than 0. 2. n(z) = A z a + z ab z b + c , (1) and the parameters listed in Table  2.
Conversely, the positions and ellipticities are fully random for any realization used in the covariance matrix computation, either with the DUSTGRAIN-pathfinder or SLICS simulations. This ensures the shape noise contribution to the error budget is faithfully captured. This process of fixing shape noise in the model and leaving it free in the covariance has become standard A120, page 5 of 32 Table  3. Statistics that have been applied to the HOWLS data set, with their abbreviation in the present article, the filter and smoothing scale employed, the number of independent teams for each statistic and links to the corresponding subsections. Notes. Numbers in parentheses refer to additional teams who participated in former HOWLS data sets. When multiple teams exist, we retained only one implementation after coordinating the independent team results.
In this article, the γ-2PCF has been computed with the ATHENA software  (Kilbinger et al. 2014)  using 10 logarithmic bins between 0. 1 and 300. The κ-2PCF has been measured using the public code TreeCorr  (Jarvis et al. 2004 ). The minimum separation considered is 0. 59 (corresponding to the pixel scale) and the maximum separation is approximately 424 (corresponding to the DUSTGRAIN-pathfinder map diagonal), with 25 bins. As discussed in Sect. 4 several bins are later removed to pass our quality criteria, with the final scale range described in Table  3. We also show these DVs as well as their standard Fisher derivatives with respect to Ω m , σ 8 , and w in Figs. 4  and 5 for γ-2PCF and κ-2PCF respectively. Finally, we note some difference in the chosen binning by the different teams computing the 2PCFs which leads to some artificial difference between ξ + and ξ κ , for example.
Fisher analysis The aim of this paper is to estimate the constraints on (a subset of) CPs for each of the HOS probes described in Sect. 3. To this end, one could perform a Monte Carlo Markov chain (MCMC) analysis fitting the data as measured on, for example, the SLICS simulated maps. For this approach to be feasible, a mandatory ingredient would be a way to estimate the expected HOS value for any given set of CPs -in other words, a theoretical model and/or an emulator-like method. For most of the probes of interest here, these are not available, and so we need to look for an A120, page 15 of 32 alternative approach that can be implemented for all the statistics. This is the Fisher matrix method, which is routinely used to forecast the accuracy that a probe can achieve on constraining CPs given the specifics of the survey at hand.
Covariance matrices The covariance matrix for each HOS probe can be estimated using the SLICS ellipticity mocks and convergence maps. To this end, we simply measure each probe on all realizations, take the mean as our fiducial DV, and use the definition (39) to compute the data covariance matrix C d. We also use this simple method when investigating the joint use of second and HOS, or of more HOS probes at the same time. We then just concatenate the individual DVs into a single DV, which we then measure on the different mock realizations for the estimate of the covariance matrix. Unless otherwise stated, however, we focus first on A120, page 17 of 32   45 )) is given in the top left quadrant of each panel. S ≤ 0. 15 indicates compatibility with the Gaussian hypothesis, which is verified for all statistics but the three bottom panels with gray shaded background.
Acknowledgements. NM acknowledges support from a fellowship of the  Centre National d'Etudes Spatiales (CNES). CG acknowledges the support from the grant  PRIN-MIUR 2017 WSCC32 ZOOMING , from the grant  ASI n. 2018-23-HH. 0 ,from the  Italian National Institute of Astrophysics  under the grant " Bando PrIN 2019 ", PI:  Viola Allevato , from the  HPC-Europa3 Transnational Access programme   HPC17VDILO , from  INAF  theory Grant 2022: Illuminating Dark Matter using Weak Lensing by  Cluster Satellites , PI:  Carlo Giocoli. IT acknowledges support from the  Fundacao para a Ciencia e a Tecnologia (FCT)  through the projects  UIDB/04434/2020 ,  UIDP/04434/2020  and the  Investigador FCT  Contract No. IF/01518/2014  and  POCH/FSE (EC). The Euclid Consortium acknowledges the  European Space Agency  and a number of agencies and institutes that have supported the development of Euclid, in particular the  Academy of Finland , the  Agenzia Spaziale Italiana , the  Belgian Science Policy , the  Canadian Euclid Consortium , the  French Centre National d'Etudes Spatiales , the  Deutsches Zentrum für Luft-und Raumfahrt , the  Danish Space Research Institute , the  Fundação para a Ciência e a Tecnologia , the  Ministerio de Ciencia e Innovación , the  National Aeronautics and Space Administration , the  National Astronomical Observatory of Japan , the  Netherlandse Onderzoekschool Voor Astronomie , the  Norwegian Space Agency , the  Romanian Space Agency , the  State Secretariat for Education, Research and Innovation (SERI)  at the Swiss Space Office (SSO), and the  United Kingdom Space Agency.
A simultaneous analysis of the B þ → K þ l þ l -and B 0 → K Ã0 l þ l -decays is performed to test muonelectron universality in two ranges of the square of the dilepton invariant mass, q 2. The measurement uses a sample of beauty meson decays produced in proton-proton collisions collected with the LHCb detector between 2011 and 2018, corresponding to an integrated luminosity of 9 fb -1. A sequence of multivariate selections and strict particle identification requirements produce a higher signal purity and a better statistical sensitivity per unit luminosity than previous LHCb lepton universality tests using the same decay modes. Residual backgrounds due to misidentified hadronic decays are studied using data and included in the fit model. Each of the four lepton universality measurements reported is either the first in the given q 2 interval or supersedes previous LHCb measurements.
1 < q 2 < 1. 1 GeV 2 =c 4 (low-q 2 ); 1. 1 < q 2 < 6. 0 GeV 2 =c 4 (central-q 2 ). All proton-proton collision data recorded by the LHCb detector between 2011 and 2018 are used, corresponding to integrated luminosities of 1. 0, 2. 0, and 6. 0 fb -1 at center-of-mass energies of 7, 8, and 13 TeV, respectively. While the B 0 → K Ã0 μ þ μ -and B þ → K þ μ þ μ - muonmode signal decays are experimentally independent of one another, this is not the case for the electron-mode signal decays due to their poorer mass resolution: partially reconstructed B 0 → K Ã0 e þ e -decays represent a significant background to the B þ → K þ e þ e -decay. The simultaneous measurement introduced here allows this background to be determined directly from the observed yields of the signal B 0 → K Ã0 e þ e -decay. The processes B 0 → K Ã0 J=ψ and B þ → K þ J=ψ ("resonant modes"), with J=ψ → l þ l -, share the same final state as the signal modes and therefore dominate in q 2 regions corresponding to the square of the J=ψ meson mass.
The large resonant mode samples serve as a normalization channel for the signal decays and allow determination of correction factors, which account for imperfect modeling of the LHCb detector. The corrections obtained from the B þ (B 0 ) channel are applied to the B 0 → K Ã0 l þ l - (B þ → K þ l þ l -) decay and the two sets are shown to be interchangeable. This analysis is performed at a higher purity level than previous LHCb tests of LU, due to both stricter particle identification (PID) criteria and dedicated multivariate selections to reject misidentified and partially reconstructed backgrounds. The trigger strategy is also optimized to improve the signal purity and to minimize the differences in trigger efficiency between electrons and muons. Finally, data are used to estimate residual backgrounds that survive all these criteria and allow them to be modeled in the analysis.
The definition of the low-q 2 region is changed from that used in the previous LHCb measurement of R K Ã  [21] , where it extended down to the dimuon mass threshold of 0. 045 GeV 2 =c 4 to increase the signal yield, leading to substantial contamination from the photon pole in the electron mode. This lepton mass effect induces significant LU breaking also within the SM, with an expected R K Ã value of ∼0. 9. The current analysis defines FIG. 2. Examples of Feynman diagrams for b → sl þ l -decays beyond the SM. Potential contributions from new heavy Z 0 gauge bosons are shown on the left, contributions from leptoquarks (LQ) on the right. FIG. 3. Variation of (left) R K and (right) R K Ã as a function of q 2 within the SM obtained using the FLAVIO software package  [71] , taking into account potential heavy BSM contributions to the Wilson coefficients.
A. Combinatorial and partially reconstructed backgrounds A multivariate classifier  [75, 76]  is trained to distinguish between B ðþ;0Þ → K ðþ;Ã0Þ l þ l -decays and combinatorial background. The training uses simulated signal events, and data with reconstructed B meson invariant masses above 5400 ð5600Þ MeV=c 2 as a proxy for the muon (electron) combinatorial background. Background events are combined for the low-and central-q 2 regions to increase the size of the training samples. The full set of preselection and PID requirements are applied to the data before training, for which the same number of signal and background events are used. Separate classifiers are trained for the RUN 1, RUN 2P1, and RUN 2P2 data-taking periods. Ten different classifiers are trained for each period, using a k-fold crossvalidation approach to avoid biases  [77]  in which each of the ten classifiers is trained leaving out a different 10% of the data sample.
Here N S is obtained from simulated samples of resonant J=ψ decays, normalized to the measured yields in data with no selections applied on the classifiers. It is scaled by the SM expectation for the ratios of nonresonant and resonant branching fractions, computed using FLAVIO package  [71] , as well as the ratio of efficiencies between the nonresonant and resonant modes at the respective working points of the classifiers. The expected number of combinatorial background events in the signal window, N B , is obtained from simplified fits to samples of data candidates passing the preselection and PID requirements. A one-dimensional optimization of the combinatorial classifier response is performed for muon signals, while a two-dimensional optimization of the combinatorial and partially reconstructed classifier response is performed for the electron signals.
This example is similar to the backgrounds discussed in Ref. [78] , with a misidentified hadron substituted for one of the electrons. More generally, however, any decay of the type B þ → K þ π -ðπ 0 ; γÞX or B 0 → K Ã0 π -ðπ 0 ; γÞX, where X is any number of other final state particles, can contribute. Not all particles from such processes are used to reconstruct the signal, therefore such backgrounds are characterized by low invariant masses. Compared to previous LU measurements at LHCb, the tighter PID requirements used for electrons reduces the expected rates for pions and kaons to be misidentified as electrons. Table III compares the misidentification rates at the working point used in this analysis to those from Ref. [24] , for each of the three data taking periods considered. The misidentification rates are determined from data using  1  a similar pion-to-electron misidentification rate is found from this data-driven method, while a factor two suppression is achieved for kaon-to-electron misidentification.
This task is complicated by the fact that there is a very large number of such backgrounds, many of which are poorly known. Even where the branching fractions of individual B þ → K þ π -ðπ 0 ; γÞX or B 0 → K Ã0 π -ðπ 0 ; γÞX decays have been measured, their Dalitz structure is often unknown. A representative subset of these backgrounds is studied using simulation, and the expected contribution of each individual background found to be negligible. However, even if the contribution of any given background is small, the contribution of all these TABLE III. Single-particle misidentification rates obtained on data averaging over the kinematics of prompt D Ãþ → D 0 ð→K -π þ Þπ þ decays. The misidentification rates are evaluated for the PID criteria used in this analysis given the acceptance and kinematic requirements applied in the track final state.
This strategy consists of inverting the stringent lepton identification requirements in the selection, while maintaining the preselection requirements. The resulting dataset (referred to as the control region in the following) predominantly contains misidentified background rather than signal candidates and can be used, together with standard PID calibration samples, to estimate the residual misidentified backgrounds. The most straightforward backgrounds to address are the fully reconstructed misidentified decays: they are limited in number, relatively well understood experimentally, and can be reconstructed under their own mass hypothesis leading to clear signals in the invariant mass distribution. The background yield is estimated in this dataset by fitting to the invariant mass of K þ e þ e -(K Ã0 e þ e -) candidates where electrons are assigned the pion or kaon mass hypothesis and the bremsstrahlung correction is ignored.
The rate for misidentifying two hadrons as electrons in the nominal dataset is found to be about 2% of that in the control dataset. This procedure is repeated for each trigger category and data-taking period, separately for low-and central-q 2 regions. For the dielectron final states, it is found to be nonzero. The residual contribution is found to be higher in the low-q 2 region, and this difference is due to contributions from low mass hadronic resonances. It is found that this expected contamination is compatible with zero for the dimuon final states. In contrast to fully reconstructed backgrounds, backgrounds of the type B þ → K þ π -ðπ 0 ; γÞX or B 0 → K Ã0 π -ðπ 0 ; γÞX do not have distinctive invariant-mass distributions, even with inverted PID criteria. Figure  9  shows the invariant mass shape in the control region with inverted lepton identification criteria, as defined above.
VI. CALIBRATION OF SIMULATION AND DETERMINATION OF EFFICIENCIES Simulated events must be calibrated to reproduce fully all aspects of the LHC production environment and LHCb detector performance. The calibration consists of a set of weights, the product of which is applied to the simulation to ensure both reliable modeling of the different components that enter the invariant mass fits, described in the next section, and the accurate determination of detector efficiencies used to calculate R K and R K Ã. For each data-taking year the simulation is calibrated using abundant, highpurity, control samples from data. As no single data control sample can calibrate all aspects of the simulated detector performance, a multistep sequential procedure is followed, each with its own weight, w, as summarized below.
The nonfactorization of electron efficiencies is sufficiently different in the signal and control regions that a dedicated treatment is required. This is most significant for those candidates having d ECAL < 100 mm. As only a few percent of signal candidates fall into this region they are excluded from the analysis in order to avoid having to model the effect of the overlap when computing efficiencies. Electron efficiencies are evaluated from truth-level information to account for nonfactorization, but must be corrected for imperfections in modeling by simulation. Therefore, electron PID efficiencies are evaluated in both data and simulation using identically selected control samples. These efficiencies are computed in bins of p T , η, and n Tracks and are further determined in separate categories depending on whether the electron has an associated bremsstrahlung photon or not.
The kinematics are calibrated in three dimensions: the momentum, transverse momentum, and pseudorapidity of the B hadron. A dedicated boosted decision tree from the hep_ml library  [81]  is trained to align the simulation with data in the three kinematic observables and the occupancy proxy observable. The outputs of this decision tree are w Mult&Kin weights which encode the relative statistical importance that the final efficiency determination should assign to each simulated event. The calibration is performed using simulated and data samples of B ðþ;0Þ → K ðþ;Ã0Þ J=ψð→μ þ μ -Þ decays selected by the L0 muon trigger. This is both the most abundant and the highest-purity sample available; since multiplicity and kinematic corrections are by construction independent of the B hadron decay it is appropriate to use the muonic decay as a proxy for the electron modes.
The bins are, from top left to right: R K low-q 2 , R K central-q 2 , R K Ã low-q 2 and R K Ã central-q 2. The quoted relative uncertainties are statistical only. the statistical component. The result agrees perfectly with the SM prediction which has been evaluated multiplying the known world best average branching ratio of B 0 → K Ã0 γ  [51]  to the ratio of decay rates of B 0 → K Ã0 e þ e -in the very low-q 2 and B 0 → K Ã0 γ. The latter has been evaluated using the FLAVIO package  [71]. Moreover no significant trends in the efficiency corrected yields are observed when varying the PID requirements.
994 on the branching fractions, with the exception of the effect induced by the normalization channel; this is taken to be uncorrelated. The correlations between the statistical uncertainties of the LU observables and the branching fractions are evaluated based on the overlap between B þ → K þ μ þ μ - and B 0 → K Ã0 μ þ μ -datasets used in either measurements. It is found that 61% of the B þ → K þ μ þ μ -RUN 1 sample was used in the corresponding branching-fraction measurement, whereas for B 0 → K Ã0 μ þ μ -this overlap is 69%. Combined with the RUN 2 yields, this leads to a correlation of 0. 13 between the statistical uncertainties of the B þ → K þ μ þ μ -branching fraction measurement and this LU measurement. We similarly find a correlation of 0. 14 between the B 0 → K Ã0 μ þ μ -statistical uncertainties.
XI. CONCLUSION We present the first simultaneous test of LU in B þ → K þ l þ l -and B 0 → K Ã0 l þ l -decays using all pp collision data collected with the LHCb detector between 2011 and 2018, corresponding to an integrated luminosity of 9 fb -1. The ratios of the branching fractions of muon and electron modes are measured in both channels and in two ranges of the square of the dilepton invariant mass. Each of these four measurements is either the first (R K low-q 2 ) or the most precise (R K Ã low-q 2 , R K central-q 2 and R K Ã central-q 2 ) such measurement to date. The measured values are low-q 2 R K ¼ 0. 994 þ0. 090 -0. 082 ðstatÞ þ0. 029 -0. 027 ðsystÞ; R K Ã ¼ 0. 927 þ0. 093 -0. 087 ðstatÞ þ0. 036 -0. 035 ðsystÞ; central-q 2 R K ¼ 0. 949 þ0. 042 -0. 041 ðstatÞ þ0. 022 -0. 022 ðsystÞ; R K Ã ¼ 1.
027 þ0. 072 -0. 068 ðstatÞ þ0. 027 -0. 026 ðsystÞ; where the first uncertainty in each row is statistical and the second systematic. The central values of the SM prediction, as calculated by the FLAVIO software package  [71] , are given in Table  XI. An additional uncertainty of 1% is assigned to take into account uncertainties in the modeling of QED effects in B þ → K þ l þ l -and B 0 → K Ã0 l þ l -decays, following Ref. [14]. This uncertainty is assumed to be uncorrelated between the LU observables and dominates the covariance matrix of the SM predictions. Each of these four measured relative decay rates is compatible with SM predictions  [14, 15, 71, [101] [102] [103] [104] [105] [106] [107] [108] , with the maximum difference between measurement and prediction being around 1 standard deviation.