0000000000750644
AUTHOR
M. Malek
Measurement of Coherent π+ Production in Low Energy Neutrino-Carbon Scattering
We report the first measurement of the flux-averaged cross section for charged current coherent π+ production on carbon for neutrino energies less than 1.5 GeV, and with a restriction on the final state phase space volume in the T2K near detector, ND280. Comparisons are made with predictions from the Rein-Sehgal coherent production model and the model by Alvarez-Ruso et al., the latter representing the first implementation of an instance of the new class of microscopic coherent models in a neutrino interaction Monte Carlo event generator. We observe a clear event excess above background, disagreeing with the null results reported by K2K and SciBooNE in a similar neutrino energy region. The …
Search for short baseline nu(e) disappearance with the T2K near detector
8 pages.- 6 figures
T2K neutrino flux prediction
The Tokai-to-Kamioka (T2K) experiment studies neutrino oscillations using an off-axismuon neutrino beam with a peak energy of about 0.6 GeV that originates at the Japan Proton Accelerator Research Complex accelerator facility. Interactions of the neutrinos are observed at near detectors placed at 280 m from the production target and at the far detector-Super-Kamiokande-located 295 km away. The flux prediction is an essential part of the successful prediction of neutrino interaction rates at the T2K detectors and is an important input to T2K neutrino oscillation and cross section measurements. A FLUKA and GEANT3-based simulation models the physical processes involved in the neutrino producti…
Combined Analysis of Neutrino and Antineutrino Oscillations at T2K.
T2K reports its first results in the search for CP violation in neutrino oscillations using appearance and disappearance channels for neutrino- and antineutrino-mode beams. The data include all runs from January 2010 to May 2016 and comprise 7.482 ×10^(20) protons on target in neutrino mode, which yielded in the far detector 32 e-like and 135 μ-like events, and 7.471 × 10^(20) protons on target in antineutrino mode, which yielded 4 e-like and 66 μ-like events. Reactor measurements of sin(2)2θ(13) have been used as an additional constraint. The one-dimensional confidence interval at 90% for the phase δCP spans the range (−3.13, −0.39) for normal mass ordering. The CP conservation hypothesis …
Search for Electron Antineutrino Appearance in a Long-baseline Muon Antineutrino Beam
Electron antineutrino appearance is measured by the T2K experiment in an accelerator-produced antineutrino beam, using additional neutrino beam operation to constrain parameters of the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix. T2K observes 15 candidate electron antineutrino events with a background expectation of 9.3 events. Including information from the kinematic distribution of observed events, the hypothesis of no electron antineutrino appearance is disfavored with a significance of 2.40 σ and no discrepancy between data and PMNS predictions is found. A complementary analysis that introduces an additional free parameter which allows non-PMNS values of electron neutrino and a…
Measurements of ν̅ μ and ν̅ μ + ν μ charged-current cross-sections without detected pions or protons on water and hydrocarbon at a mean anti-neutrino energy of 0.86 GeV
Abstract We report measurements of the flux-integrated ν̅μ and ν̅μ + νμ charged-current cross-sections on water and hydrocarbon targets using the T2K anti-neutrino beam with a mean beam energy of 0.86 GeV. The signal is defined as the (anti-)neutrino charged-current interaction with one induced $\mu^\pm$ and no detected charged pion or proton. These measurements are performed using a new WAGASCI module recently added to the T2K setup in combination with the INGRID Proton Module. The phase space of muons is restricted to the high-detection efficiency region, $p_{\mu}>400~{\rm MeV}/c$ and $\theta_{\mu}<30^{\circ}$, in the laboratory frame. An absence of pions and protons in the …
Measurements of the T2K neutrino beam properties using the INGRID on-axis near detector
Precise measurement of neutrino beam direction and intensity was achieved based on a new concept with modularized neutrino detectors. INGRID (Interactive Neutrino GRID) is an on-axis near detector for the T2K long baseline neutrino oscillation experiment. INGRID consists of 16 identical modules arranged in horizontal and vertical arrays around the beam center. The module has a sandwich structure of iron target plates and scintillator trackers. INGRID directly monitors the muon neutrino beam profile center and intensity using the number of observed neutrino events in each module. The neutrino beam direction is measured with accuracy better than 0.4 mrad from the measured profile center. The …
First T2K measurement of transverse kinematic imbalance in the muon-neutrino charged-current single- π+ production channel containing at least one proton
This paper reports the first T2K measurement of the transverse kinematic imbalance in the single-$\pi^+$ production channel of neutrino interactions. We measure the differential cross sections in the muon-neutrino charged-current interaction on hydrocarbon with a single $\pi^+$ and at least one proton in the final state, at the ND280 off-axis near detector of the T2K experiment. The extracted cross sections are compared to the predictions from different neutrino-nucleus interaction event generators. Overall, the results show a preference for models which have a more realistic treatment of nuclear medium effects including the initial nuclear state and final-state interactions.
Measurement of the muon neutrino inclusive charged-current cross section in the energy range of 1–3 GeV with the T2K INGRID detector
International audience; We report a measurement of the $\nu_{\mu}$-nucleus inclusive charged current cross section (=$\sigma^{cc}$) on iron using data from exposed to the J-PARC neutrino beam. The detector consists of 14 modules in total, which are spread over a range of off-axis angles from 0$^\circ$ to 1.1$^\circ$. The variation in the neutrino energy spectrum as a function of the off-axis angle, combined with event topology information, is used to calculate this cross section as a function of neutrino energy. The cross section is measured to be $\sigma^{cc}(1.1\text{ GeV}) = 1.10 \pm 0.15$ $(10^{-38}\text{cm}^2/\text{nucleon})$, $\sigma^{cc}(2.0\text{ GeV}) = 2.07 \pm 0.27$ $(10^{-38}\te…
Search for heavy neutrinos with the T2K near detector ND280
This paper reports on the search for heavy neutrinos with masses in the range 140<MN<493 MeV/c2 using the off-axis near detector ND280 of the T2K experiment. These particles can be produced from kaon decays in the standard neutrino beam and then subsequently decay in ND280. The decay modes under consideration are N→ℓ±απ∓ and N→ℓ+αℓ−β(−)ν(α,β=e,μ). A search for such events has been made using the Time Projection Chambers of ND280, where the background has been reduced to less than two events in the current dataset in all channels. No excess has been observed in the signal region. A combined Bayesian statistical approach has been applied to extract upper limits on the mixing elements of heav…
Measurement of the $\nu_{\mu}$ charged current quasi-elastic cross-section on carbon with the T2K on-axis neutrino beam
17 pages.- 21 figures
Search for signatures of magnetically-induced alignment in the arrival directions measured by the Pierre Auger Observatory
We present the results of an analysis of data recorded at the Pierre Auger Observatory in which we search for groups of directionally-aligned events (or ‘multiplets’) which exhibit a correlation between arrival direc- tion and the inverse of the energy. These signatures are expected from sets of events coming from the same source after having been deflected by intervening coherent magnetic fields. The observation of several events from the same source would open the possibility to accurately reconstruct the position of the source and also measure the integral of the component of the magnetic field orthogonal to the trajectory of the cos- mic rays. We describe the largest multiplets found an…
Measurement of double-differential muon neutrino charged-current interactions onC8H8without pions in the final state using the T2K off-axis beam
We report the measurement of muon neutrino charged-current interactions on carbon without pions in the final state at the T2K beam energy using 5.734×1020 protons on target. For the first time the measurement is reported as a flux-integrated, double-differential cross section in muon kinematic variables (cosθμ, pμ), without correcting for events where a pion is produced and then absorbed by final state interactions. Two analyses are performed with different selections, background evaluations and cross-section extraction methods to demonstrate the robustness of the results against biases due to model-dependent assumptions. The measurements compare favorably with recent models which include n…
Measurement of the inclusive $\nu_{\mu}$ charged current cross section on iron and hydrocarbon in the T2K on-axis neutrino beam
We report a measurement of the $\nu_\mu$ inclusive charged current cross sections on iron and hydrocarbon in the T2K on-axis neutrino beam. The measured inclusive charged current cross sections on iron and hydrocarbon averaged over the T2K on-axis flux with a mean neutrino energy of 1.51 GeV are $(1.444\pm0.002(stat.)_{-0.157}^{+0.189}(syst.))\times 10^{-38}\mathrm{cm}^2/\mathrm{nucleon}$, and $(1.379\pm0.009(stat.)_{-0.147}^{+0.178}(syst.))\times 10^{-38}\mathrm{cm}^2/\mathrm{nucleon}$, respectively, and their cross section ratio is $1.047\pm0.007(stat.)\pm0.035(syst.)$. These results agree well with the predictions of the neutrino interaction model, and thus we checked the correct treatme…
Observation of Electron Neutrino Appearance in a Muon Neutrino Beam
The T2K experiment has observed electron neutrino appearance in a muon neutrino beam produced 295 km from the Super-Kamiokande detector with a peak energy of 0.6 GeV. A total of 28 electron neutrino events were detected with an energy distribution consistent with an appearance signal, corresponding to a significance of 7.3$\sigma$ when compared to 4.92 $\pm$ 0.55 expected background events. In the PMNS mixing model, the electron neutrino appearance signal depends on several parameters including three mixing angles $\theta_{12}$, $\theta_{23}$, $\theta_{13}$, a mass difference $\Delta m^2_{32}$ and a CP violating phase $\delta_{\mathrm{CP}}$. In this neutrino oscillation scenario, assuming $…
The ALICE experiment at the CERN LHC
Journal of Instrumentation 3(08), S08002 (2008). doi:10.1088/1748-0221/3/08/S08002
Simultaneous measurement of the muon neutrino charged-current cross section on oxygen and carbon without pions in the final state at T2K
Authors: K. Abe,56 N. Akhlaq,45 R. Akutsu,57 A. Ali,32 C. Alt,11 C. Andreopoulos,54,34 L. Anthony,21 M. Antonova,19 S. Aoki,31 A. Ariga,2 T. Arihara,59 Y. Asada,69 Y. Ashida,32 E. T. Atkin,21 Y. Awataguchi,59 S. Ban,32 M. Barbi,46 G. J. Barker,66 G. Barr,42 D. Barrow,42 M. Batkiewicz-Kwasniak,15 A. Beloshapkin,26 F. Bench,34 V. Berardi,22 L. Berns,58 S. Bhadra,70 S. Bienstock,53 S. Bolognesi,6 T. Bonus,68 B. Bourguille,18 S. B. Boyd,66 A. Bravar,13 D. Bravo Berguño,1 C. Bronner,56 S. Bron,13 A. Bubak,51 M. Buizza Avanzini ,10 T. Campbell,7 S. Cao,16 S. L. Cartwright,50 M. G. Catanesi,22 A. Cervera,19 D. Cherdack,17 N. Chikuma,55 G. Christodoulou,12 M. Cicerchia,24,† J. Coleman,34 G. Collazu…
Theia: an advanced optical neutrino detector
The European physical journal. C, Particles and fields 80(5), 416 (2020). doi:10.1140/epjc/s10052-020-7977-8
Indication of electron neutrino appearance from an accelerator-produced off-axis muon neutrino beam
The T2K experiment observes indications of $\nu_\mu\rightarrow \nu_e$ appearance in data accumulated with $1.43\times10^{20}$ protons on target. Six events pass all selection criteria at the far detector. In a three-flavor neutrino oscillation scenario with $|\Delta m_{23}^2|=2.4\times10^{-3}$ eV$^2$, $\sin^2 2\theta_{23}=1$ and $\sin^2 2\theta_{13}=0$, the expected number of such events is 1.5$\pm$0.3(syst.). Under this hypothesis, the probability to observe six or more candidate events is 7$\times10^{-3}$, equivalent to 2.5$\sigma$ significance. At 90% C.L., the data are consistent with 0.03(0.04)$<\sin^2 2\theta_{13}<$ 0.28(0.34) for $\delta_{\rm CP}=0$ and a normal (inverted) hierarchy.
Characterization of nuclear effects in muon-neutrino scattering on hydrocarbon with a measurement of final-state kinematics and correlations in charged-current pionless interactions at T2K
This paper reports measurements of final-state proton multiplicity, muon and proton kinematics, and their correlations in charged-current pionless neutrino interactions, measured by the T2K ND280 near detector in its plastic scintillator (C$_8$H$_8$) target. The data were taken between years 2010 and 2013, corresponding to approximately 6$\times10^{20}$ protons on target. Thanks to their exploration of the proton kinematics and of kinematic imbalances between the proton and muon kinematics, the results offer a novel probe of the nuclear-medium effects most pertinent to the (sub-)GeV neutrino-nucleus interactions that are used in accelerator-based long-baseline neutrino oscillation measureme…
Measurement of theνμcharged-current quasielastic cross section on carbon with the ND280 detector at T2K
We thank the J-PARC staff for superb accelerator performance and the CERN NA61 Collaboration for providing valuable particle production data. We acknowledge the support of MEXT, Japan; NSERC, NRC, and CFI, Canada; CEA and CNRS/IN2P3, France; DFG, Germany; INFN, Italy; National Science Centre (NCN), Poland; RSF, RFBR, and MES, Russia; MINECO and ERDF funds, Spain; SNSF and SER, Switzerland; STFC, UK; and DOE, USA. We also thank CERN for the UA1/NOMAD magnet, DESY for the HERA-B magnet mover system, NII for SINET4, the WestGrid and SciNet consortia in Compute Canada, GridPP, UK. In addition participation of individual researchers and institutions has been further supported by funds from ERC (…
Measurement of thett¯production cross section inpp¯collisions ats=1.96 TeVusing soft electronb-tagging
The authors present a measurement of the t{bar t} production cross section using events with one charged lepton and jets from p{bar p} collisions at a center-of-mass energy of 1.96 TeV. A b-tagging algorithm based on the probability of displaced tracks coming from the event interaction vertex is applied to identify b quarks from top decay. Using 318 pb{sup -1} of data collected with the CDF II detector, they measure the t{bar t} production cross section in events with at least one restrictive (tight) b-tagged jet and obtain 8.9{sub -1.0}{sup +1.0}(stat.){sub -1.0}{sup +1.1}(syst.) pb. The cross section value assumes a top quark mass of m{sub t} is presented in the paper. This result is cons…
Search for First Harmonic Modulation in the Right Ascension Distribution of Cosmic Rays Detected at the Pierre Auger Observatory
We present the results of searches for dipolar-type anisotropies in different energy ranges above 2.5 × 1017 eV with the surface detector array of the Pierre Auger Observatory, reporting on both the phase and the amplitude measurements of the first harmonic modulation in the right-ascension distribution. Upper limits on the amplitudes are obtained, which provide the most stringent bounds at present, being below 2% at 99% C.L. for EeV energies. We also compare our results to those of previous experiments as well as with some theoretical expectations.
First Muon-Neutrino Disappearance Study with an Off-Axis Beam
We report a measurement of muon-neutrino disappearance in the T2K experiment. The 295-km muon-neutrino beam from Tokai to Kamioka is the first implementation of the off-axis technique in a long-baseline neutrino oscillation experiment. With data corresponding to 1.43 × 10(20) protons on target, we observe 31 fully-contained single μ-like ring events in Super-Kamiokande, compared with an expectation of 104 ± 14(syst) events without neutrino oscillations. The best-fit point for two-flavor νμ → ντ oscillations is sin 2(2θ(23)) = 0.98 and |Δm(2)(32)| = 2.65 × 10(−3) eV2. The boundary of the 90% confidence region includes the points (sin2 (2θ(23)), |Δm(2)(32)|) = (1.0, 3.1 × 10(−3) eV2), (0.84, …
Precise measurement of the neutrino mixing parameter θ23 from muon neutrino disappearance in an off-axis beam
New data from the T2K neutrino oscillation experiment produce the most precise measurement of the neutrino mixing parameter theta_{23}. Using an off-axis neutrino beam with a peak energy of 0.6 GeV and a data set corresponding to 6.57 x 10^{20} protons on target, T2K has fit the energy-dependent nu_mu oscillation probability to determine oscillation parameters. Marginalizing over the values of other oscillation parameters yields sin^2 (theta_{23}) = 0.514 +0.055/-0.056 (0.511 +- 0.055), assuming normal (inverted) mass hierarchy. The best-fit mass-squared splitting for normal hierarchy is Delta m^2_{32} = (2.51 +- 0.10) x 10^{-3} eV^2/c^4 (inverted hierarchy: Delta m^2_{13} = (2.48 +- 0.10) …
Search for CP Violation in Neutrino and Antineutrino Oscillations by the T2K Experiment with 2.2×1021 Protons on Target
The T2K experiment measures muon neutrino disappearance and electron neutrino appearance in accelerator-produced neutrino and antineutrino beams. With an exposure of $14.7(7.6)\times 10^{20}$ protons on target in neutrino (antineutrino) mode, 89 $\nu_e$ candidates and 7 anti-$\nu_e$ candidates were observed while 67.5 and 9.0 are expected for $\delta_{CP}=0$ and normal mass ordering. The obtained $2\sigma$ confidence interval for the $CP$ violating phase, $\delta_{CP}$, does not include the $CP$-conserving cases ($\delta_{CP}=0,\pi$). The best-fit values of other parameters are $\sin^2\theta_{23} = 0.526^{+0.032}_{-0.036}$ and $\Delta m^2_{32}=2.463\pm0.065\times10^{-3} \mathrm{eV}^2/c^4$.
Measurement of the neutrino-oxygen neutral-current interaction cross section by observing nuclear deexcitation gamma rays
We report the first measurement of the neutrino-oxygen neutral-current quasielastic (NCQE) cross section. It is obtained by observing nuclear deexcitation $\gamma$-rays which follow neutrino-oxygen interactions at the Super-Kamiokande water Cherenkov detector. We use T2K data corresponding to $3.01 \times 10^{20}$ protons on target. By selecting only events during the T2K beam window and with well-reconstructed vertices in the fiducial volume, the large background rate from natural radioactivity is dramatically reduced. We observe 43 events in the $4-30$ MeV reconstructed energy window, compared with an expectation of 51.0, which includes an estimated 16.2 background events. The background …
First measurement of the charged current ν¯μ double differential cross section on a water target without pions in the final state
We thank the J-PARC staff for superb accelerator performance. We thank the CERN NA61/SHINE Collaboration for providing valuable particle production data. We acknowledge the support of MEXT, Japan; NSERC (Grant No. SAPPJ-2014-00031), the NRC and CFI, Canada; the CEA and CNRS/IN2P3, France; the DFG, Germany; the INFN, Italy; the National Science Centre and Ministry of Science and Higher Education, Poland; the RSF (Grant No. 19-12-00325) and the Ministry of Science and Higher Education, Russia; MINECO and ERDF funds, Spain; the SNSF and SERI, Switzerland; the STFC, UK; and the DOE, USA. We also thank CERN for the UA1/NOMAD magnet, DESY for the HERA-B magnet mover system, NII for SINET4, the We…
The ALICE Collaboration
The production of mesons containing strange quarks (KS, φ) and both singly and doubly strange baryons ( , , and − + +) are measured at mid-rapidity in pp collisions at √ s = 0.9 TeV with the ALICE experiment at the LHC. The results are obtained from the analysis of about 250 k minimum bias events recorded in 2009. Measurements of yields (dN/dy) and transverse momentum spectra at mid-rapidity for inelastic pp collisions are presented. For mesons, we report yields (〈dN/dy〉) of 0.184 ± 0.002(stat.) ± 0.006(syst.) for KS and 0.021 ± 0.004(stat.) ± 0.003(syst.) for φ. For baryons, we find 〈dN/dy〉 = 0.048 ± 0.001(stat.) ± 0.004(syst.) for , 0.047 ± 0.002(stat.) ± 0.005(syst.) for and 0.0101 ± 0.0…
Search for ultrahigh energy neutrinos in highly inclined events at the Pierre Auger Observatory
Erratum: Phys. Rev. D 85, 029902(E) (2012) [http://dx.doi.org/10.1103/PhysRevD.85.029902]
The effect of the geomagnetic field on cosmic ray energy estimates and large scale anisotropy searches on data from the Pierre Auger Observatory
We present a comprehensive study of the influence of the geomagnetic field on the energy estimation of extensive air showers with a zenith angle smaller than $60^\circ$, detected at the Pierre Auger Observatory. The geomagnetic field induces an azimuthal modulation of the estimated energy of cosmic rays up to the ~2% level at large zenith angles. We present a method to account for this modulation of the reconstructed energy. We analyse the effect of the modulation on large scale anisotropy searches in the arrival direction distributions of cosmic rays. At a given energy, the geomagnetic effect is shown to induce a pseudo-dipolar pattern at the percent level in the declination distribution t…
Measurement of the Inclusive NuMu Charged Current Cross Section on Carbon in the Near Detector of the T2K Experiment
T2K has performed the first measurement of nu(mu) inclusive charged current interactions on carbon at neutrino energies of similar to 1 GeV where the measurement is reported as a flux-averaged double differential cross section in muon momentum and angle. The flux is predicted by the beam Monte Carlo and external data, including the results from the NA61/SHINE experiment. The data used for this measurement were taken in 2010 and 2011, with a total of 10.8 x 10(19) protons-on-target. The analysis is performed on 4485 inclusive charged current interaction candidates selected in the most upstream fine-grained scintillator detector of the near detector. The flux-averaged total cross section is (…
Abstracts of papers and posters advanced activities in pharmaceutical care 24th European Symposium on Clinical Pharmacy
First measurement of the muon neutrino charged current single pion production cross section on water with the T2K near detector
The T2K off-axis near detector, ND280, is used to make the first differential cross section measurements of muon neutrino charged current single positive pion production on a water target at energies ∼0.8 GeV. The differential measurements are presented as a function of the muon and pion kinematics, in the restricted phase space defined by pπ+>200 MeV/c, pμ>200 MeV/c, cos(θπ+)>0.3 and cos(θμ)>0.3. The total flux integrated νμ charged current single positive pion production cross section on water in the restricted phase space is measured to be ⟨σ⟩ϕ=4.25±0.48(stat)±1.56(syst)×10-40 cm2/nucleon. The total cross section is consistent with the NEUT prediction (5.03×10-40 cm2/nucleon) and 2σ…
Measurement of the Inclusive Electron Neutrino Charged Current Cross Section on Carbon with the T2K Near Detector
The T2K off-axis near detector, ND280, is used to make the first differential cross-section measurements of electron neutrino charged current interactions at energies ~1 GeV as a function of electron momentum, electron scattering angle and four-momentum transfer of the interaction. The total flux-averaged $\nu_e$ charged current cross-section on carbon is measured to be $1.11\pm0.09~(stat)\pm0.18~(syst)\times10^{-38} cm^2/nucleon$. The differential and total cross-section measurements agree with the predictions of two leading neutrino interaction generators, NEUT and GENIE. The NEUT prediction is $1.23\times10^{-38} cm^2/nucleon$ and the GENIE prediction is $1.08\times10^{-38} cm^2/nucleon$…
The T2K Experiment
The T2K experiment is a long-baseline neutrino oscillation experiment. Its main goal is to measure the last unknown lepton sector mixing angle {\theta}_{13} by observing {\nu}_e appearance in a {\nu}_{\mu} beam. It also aims to make a precision measurement of the known oscillation parameters, {\Delta}m^{2}_{23} and sin^{2} 2{\theta}_{23}, via {\nu}_{\mu} disappearance studies. Other goals of the experiment include various neutrino cross section measurements and sterile neutrino searches. The experiment uses an intense proton beam generated by the J-PARC accelerator in Tokai, Japan, and is composed of a neutrino beamline, a near detector complex (ND280), and a far detector (Super-Kamiokande)…
Evidence of Electron Neutrino Appearance in a Muon Neutrino Beam
The T2K Collaboration reports evidence for electron neutrino appearance at the atmospheric mass splitting, vertical bar Delta m(32)(2)vertical bar approximate to 2.4 X 10(-3) eV(2). An excess of electron neutrino interactions over background is observed from a muon neutrino beam with a peak energy of 0.6 GeV at the Super-Kamiokande (SK) detector 295 km from the beam's origin. Signal and background predictions are constrained by data from near detectors located 280 m from the neutrino production target. We observe 11 electron neutrino candidate events at the SK detector when a background of 3.3 +/- 0.4(syst) events is expected. The background-only hypothesis is rejected with a p value of 0.0…
Measurement of the single π0 production rate in neutral current neutrino interactions on water
The single π0 production rate in neutral current neutrino interactions on water in a neutrino beam with a peak neutrino energy of 0.6 GeV has been measured using the POD, one of the subdetectors of the T2K near detector. The production rate was measured for data taking periods when the POD contained water (2.64×1020 protons-on-target) and also periods without water (3.49×1020 protons-on-target). A measurement of the neutral current single π0 production rate on water is made using appropriate subtraction of the production rate with water in from the rate with water out of the target region. The subtraction analysis yields 106±41±69 signal events where the uncertainties are statistical (stat.…