Erratum: Search for Cosmic-Ray Boosted Sub-GeV Dark Matter Using Recoil Protons at Super-Kamiokande [Phys. Rev. Lett. 130, 031802 (2023)]

This corrects the article DOI: 10.1103/PhysRevLett.130.031802.

Measurements of neutrino oscillation parameters from the T2K experiment using 3.6×1021 protons on target

The T2K experiment presents new measurements of neutrino oscillation parameters using 19.7 ( 16.3 ) × 10 20 protons on target (POT) in (anti-)neutrino mode at the far detector (FD). Compared to the previous analysis, an additional 4.7 × 10 20 POT neutrino data was collected at the FD. Significant improvements were made to the analysis methodology, with the near-detector analysis introducing new selections and using more than double the data. Additionally, this is the first T2K oscillation analysis to use NA61/SHINE data on a replica of the T2K target to tune the neutrino flux model, and the neutrino interaction model was improved to include new nuclear effects and calculations. Frequentist and Bayesian analyses are presented, including results on sin 2 θ 13 and the impact of priors on the δ CP measurement. Both analyses prefer the normal mass ordering and upper octant of sin 2 θ 23 with a nearly maximally CP-violating phase. Assuming the normal ordering and using the constraint on sin 2 θ 13 from reactors, sin 2 θ 23 = 0 . 561 - 0.032 + 0.021 using Feldman-Cousins corrected intervals, and Δ m 32 2 = 2 . 494 - 0.058 + 0.041 × 10 - 3 eV 2 using constant Δ χ 2 intervals. The CP-violating phase is constrained to δ CP = - 1 . 97 - 0.70 + 0.97 using Feldman-Cousins corrected intervals, and δ CP = 0 , π is excluded at more than 90% confidence level. A Jarlskog invariant of zero is excluded at more than 2 σ credible level using a flat prior in δ CP , and just below 2 σ using a flat prior in sin δ CP . When the external constraint on sin 2 θ 13 is removed, sin 2 θ 13 = 28 . 0 - 6.5 + 2.8 × 10 - 3 , in agreement with measurements from reactor experiments. These results are consistent with previous T2K analyses.

Search for Cosmic-Ray Boosted Sub-GeV Dark Matter Using Recoil Protons at Super-Kamiokande

We report a search for cosmic-ray boosted dark matter with protons using the 0.37  megaton×years data collected at Super-Kamiokande experiment during the 1996-2018 period (SKI-IV phase). We searched for an excess of proton recoils above the atmospheric neutrino background from the vicinity of the Galactic Center. No such excess is observed, and limits are calculated for two reference models of dark matter with either a constant interaction cross section or through a scalar mediator. This is the first experimental search for boosted dark matter with hadrons using directional information. The results present the most stringent limits on cosmic-ray boosted dark matter and exclude the dark matter-nucleon elastic scattering cross section between 10^{-33}cm^{2} and 10^{-27}cm^{2} for dark matter mass from 1  MeV/c^{2} to 300  MeV/c^{2}.

Constraints on Cosmic Strings Using Data from the Third Advanced LIGO-Virgo Observing Run

We search for gravitational-wave signals produced by cosmic strings in the Advanced LIGO and Virgo full O3 dataset. Search results are presented for gravitational waves produced by cosmic string loop features such as cusps, kinks, and, for the first time, kink-kink collisions. A template-based search for short-duration transient signals does not yield a detection. We also use the stochastic gravitational-wave background energy density upper limits derived from the O3 data to constrain the cosmic string tension Gμ as a function of the number of kinks, or the number of cusps, for two cosmic string loop distribution models. Additionally, we develop and test a third model that interpolates between these two models. Our results improve upon the previous LIGO-Virgo constraints on Gμ by 1 to 2 orders of magnitude depending on the model that is tested. In particular, for the one-loop distribution model, we set the most competitive constraints to date: Gμ≲4×10^{-15}. In the case of cosmic strings formed at the end of inflation in the context of grand unified theories, these results challenge simple inflationary models.

Constraints on Cosmic Strings Using Data from the Third Advanced LIGO-Virgo Observing Run

We search for gravitational-wave signals produced by cosmic strings in the Advanced LIGO and Virgo full O3 dataset. Search results are presented for gravitational waves produced by cosmic string loop features such as cusps, kinks, and, for the first time, kink-kink collisions. A template-based search for short-duration transient signals does not yield a detection. We also use the stochastic gravitational-wave background energy density upper limits derived from the O3 data to constrain the cosmic string tension Gμ as a function of the number of kinks, or the number of cusps, for two cosmic string loop distribution models. Additionally, we develop and test a third model that interpolates between these two models. Our results improve upon the previous LIGO-Virgo constraints on Gμ by 1 to 2 orders of magnitude depending on the model that is tested. In particular, for the one-loop distribution model, we set the most competitive constraints to date: Gμ≲4×10^{-15}. In the case of cosmic strings formed at the end of inflation in the context of grand unified theories, these results challenge simple inflationary models.

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 2.40σ 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 antineutrino appearance also finds no discrepancy between data and PMNS predictions.

Prospects for observing and localizing gravitational-wave transients with Advanced LIGO, Advanced Virgo and KAGRA

We present our current best estimate of the plausible observing scenarios for the Advanced LIGO, Advanced Virgo and KAGRA gravitational-wave detectors over the next several years, with the intention of providing information to facilitate planning for multi-messenger astronomy with gravitational waves. We estimate the sensitivity of the network to transient gravitational-wave signals for the third (O3), fourth (O4) and fifth observing (O5) runs, including the planned upgrades of the Advanced LIGO and Advanced Virgo detectors. We study the capability of the network to determine the sky location of the source for gravitational-wave signals from the inspiral of binary systems of compact objects, that is binary neutron star, neutron star-black hole, and binary black hole systems. The ability to localize the sources is given as a sky-area probability, luminosity distance, and comoving volume. The median sky localization area (90% credible region) is expected to be a few hundreds of square degrees for all types of binary systems during O3 with the Advanced LIGO and Virgo (HLV) network. The median sky localization area will improve to a few tens of square degrees during O4 with the Advanced LIGO, Virgo, and KAGRA (HLVK) network. During O3, the median localization volume (90% credible region) is expected to be on the order of 10 5 , 10 6 , 10 7 Mpc 3 for binary neutron star, neutron star-black hole, and binary black hole systems, respectively. The localization volume in O4 is expected to be about a factor two smaller than in O3. We predict a detection count of 1 - 1 + 12 ( 10 - 10 + 52 ) for binary neutron star mergers, of 0 - 0 + 19 ( 1 - 1 + 91 ) for neutron star-black hole mergers, and 17 - 11 + 22 ( 79 - 44 + 89 ) for binary black hole mergers in a one-calendar-year observing run of the HLV network during O3 (HLVK network during O4). We evaluate sensitivity and localization expectations for unmodeled signal searches, including the search for intermediate mass black hole binary mergers.

The geomorphology, color, and thermal properties of Ryugu: Implications for parent-body processes

The near-Earth carbonaceous asteroid 162173 Ryugu is thought to have been produced from a parent body that contained water ice and organic molecules. The Hayabusa2 spacecraft has obtained global multicolor images of Ryugu. Geomorphological features present include a circum-equatorial ridge, east-west dichotomy, high boulder abundances across the entire surface, and impact craters. Age estimates from the craters indicate a resurfacing age of [Formula: see text] years for the top 1-meter layer. Ryugu is among the darkest known bodies in the Solar System. The high abundance and spectral properties of boulders are consistent with moderately dehydrated materials, analogous to thermally metamorphosed meteorites found on Earth. The general uniformity in color across Ryugu's surface supports partial dehydration due to internal heating of the asteroid's parent body.

Search for CP Violation in Neutrino and Antineutrino Oscillations by the T2K Experiment with 2.2×10^{21} 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)×10^{20} protons on target in the neutrino (antineutrino) mode, 89 ν_{e} candidates and seven anti-ν_{e} candidates are observed, while 67.5 and 9.0 are expected for δ_{CP}=0 and normal mass ordering. The obtained 2σ confidence interval for the CP-violating phase, δ_{CP}, does not include the CP-conserving cases (δ_{CP}=0, π). The best-fit values of other parameters are sin^{2}θ_{23}=0.526_{-0.036}^{+0.032} and Δm_{32}^{2}=2.463_{-0.070}^{+0.071}×10^{-3}  eV^{2}/c^{4}.

Search for Boosted Dark Matter Interacting with Electrons in Super-Kamiokande

A search for boosted dark matter using 161.9 kt yr of Super-Kamiokande IV data is presented. We search for an excess of elastically scattered electrons above the atmospheric neutrino background, with a visible energy between 100 MeV and 1 TeV, pointing back to the Galactic center or the Sun. No such excess is observed. Limits on boosted dark matter event rates in multiple angular cones around the Galactic center and Sun are calculated. Limits are also calculated for a baseline model of boosted dark matter produced from cold dark matter annihilation or decay. This is the first experimental search for boosted dark matter from the Galactic center or the Sun interacting in a terrestrial detector.

Prospects for observing and localizing gravitational-wave transients with Advanced LIGO, Advanced Virgo and KAGRA

We present possible observing scenarios for the Advanced LIGO, Advanced Virgo and KAGRA gravitational-wave detectors over the next decade, with the intention of providing information to the astronomy community to facilitate planning for multi-messenger astronomy with gravitational waves. We estimate the sensitivity of the network to transient gravitational-wave signals, and study the capability of the network to determine the sky location of the source. We report our findings for gravitational-wave transients, with particular focus on gravitational-wave signals from the inspiral of binary neutron star systems, which are the most promising targets for multi-messenger astronomy. The ability to localize the sources of the detected signals depends on the geographical distribution of the detectors and their relative sensitivity, and [Formula: see text] credible regions can be as large as thousands of square degrees when only two sensitive detectors are operational. Determining the sky position of a significant fraction of detected signals to areas of 5-[Formula: see text] requires at least three detectors of sensitivity within a factor of [Formula: see text] of each other and with a broad frequency bandwidth. When all detectors, including KAGRA and the third LIGO detector in India, reach design sensitivity, a significant fraction of gravitational-wave signals will be localized to a few square degrees by gravitational-wave observations alone.

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 δ_{CP} spans the range (-3.13, -0.39) for normal mass ordering. The CP conservation hypothesis (δ_{CP}=0, π) is excluded at 90% C.L.

Simple microfluidic formation of highly heterogeneous microfibers using a combination of sheath units

This paper presents the formation of complex cross-sectional microfibers using three-dimensional microfluidic devices. The compartments and shapes of core and shell layers in the microfibers were independently controlled via three-dimensional fluidic channels fabricated by the combination of sheath units. The number of layers is easily expanded by the stacking of these units. Therefore, the highly heterogeneous microfibers of alginate hydrogel are obtained in polydimethylsiloxane structures. This widely expandable method has great potential for the development of functional and complex fiber-shaped materials.

A high-resolution passive droplet-phase sample sorter using multi-stage droplet transfer

A fully passive volume-dependent droplet sorter using repeated and multiple on-rail transfer of microdroplets in a cascade channel is presented in this research.

Quadrupole shift of nuclear magnetic resonance of donors in silicon at low magnetic field

Shifts from the expected nuclear magnetic resonance frequencies of antimony and bismuth donors in silicon of greater than a megahertz are observed in electrically detected magnetic resonance spectra. Defects created by ion implantation of the donors are discussed as the source of effective electric field gradients generating these shifts via quadrupole interaction with the nuclear spins. The experimental results are modeled quantitatively by molecular orbital theory for a coupled pair consisting of a donor and a spin-dependent recombination readout center.

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 measured flux-averaged cross sections are below those predicted by both the Rein-Sehgal and Alvarez-Ruso et al.

Measurement of Muon Antineutrino Oscillations with an Accelerator-Produced Off-Axis Beam

T2K reports its first measurements of the parameters governing the disappearance of ν[over ¯]_{μ} in an off-axis beam due to flavor change induced by neutrino oscillations. The quasimonochromatic ν[over ¯]_{μ} beam, produced with a peak energy of 0.6 GeV at J-PARC, is observed at the far detector Super-Kamiokande, 295 km away, where the ν[over ¯]_{μ} survival probability is expected to be minimal. Using a data set corresponding to 4.01×10^{20} protons on target, 34 fully contained μ-like events were observed. The best-fit oscillation parameters are sin^{2}(θ[over ¯]_{23})=0.45 and |Δm[over ¯]_{32}^{2}|=2.51×10^{-3}  eV^{2} with 68% confidence intervals of 0.38-0.64 and 2.26-2.80×10^{-3}  eV^{2}, respectively. These results are in agreement with existing antineutrino parameter measurements and also with the ν_{μ} disappearance parameters measured by T2K.

Search for Nucleon and Dinucleon Decays with an Invisible Particle and a Charged Lepton in the Final State at the Super-Kamiokande Experiment

Search results for nucleon decays p→e^{+}X, p→μ^{+}X, n→νγ (where X is an invisible, massless particle) as well as dinucleon decays np→e^{+}ν, np→μ^{+}ν, and np→τ^{+}ν in the Super-Kamiokande experiment are presented. Using single-ring data from an exposure of  273.4  kton·yr, a search for these decays yields a result consistent with no signal. Accordingly, lower limits on the partial lifetimes of τ_{p→e^{+}X}>7.9×10^{32} yr, τ_{p→μ^{+}X}>4.1×10^{32} yr, τ_{n→νγ}>5.5×10^{32} yr, τ_{np→e^{+}ν}>2.6×10^{32}  yr, τ_{np→μ^{+}ν}>2.2×10^{32} yr, and τ_{np→τ^{+}ν}>2.9×10^{31} yr at a 90% confidence level are obtained. Some of these searches are novel.

Phonon Engineering in Isotopically Disordered Silicon Nanowires

The introduction of stable isotopes in the fabrication of semiconductor nanowires provides an additional degree of freedom to manipulate their basic properties, design an entirely new class of devices, and highlight subtle but important nanoscale and quantum phenomena. With this perspective, we report on phonon engineering in metal-catalyzed silicon nanowires with tailor-made isotopic compositions grown using isotopically enriched silane precursors (28)SiH4, (29)SiH4, and (30)SiH4 with purity better than 99.9%. More specifically, isotopically mixed nanowires (28)Si(x)(30)Si(1-x) with a composition close to the highest mass disorder (x ∼ 0.5) were investigated. The effect of mass disorder on the phonon behavior was elucidated and compared to that in isotopically pure (29)Si nanowires having a similar reduced mass. We found that the disorder-induced enhancement in phonon scattering in isotopically mixed nanowires is unexpectedly much more significant than in bulk crystals of close isotopic compositions. This effect is explained by a nonuniform distribution of (28)Si and (30)Si isotopes in the grown isotopically mixed nanowires with local compositions ranging from x = ∼0.25 to 0.70. Moreover, we also observed that upon heating, phonons in (28)Si(x)(30)Si(1-x) nanowires behave remarkably differently from those in (29)Si nanowires suggesting a reduced thermal conductivity induced by mass disorder. Using Raman nanothermometry, we found that the thermal conductivity of isotopically mixed (28)Si(x)(30)Si(1-x) nanowires is ∼30% lower than that of isotopically pure (29)Si nanowires in agreement with theoretical predictions.

Search for neutrinos from annihilation of captured low-mass dark matter particles in the sun by super-kamiokande

Super-Kamiokande (SK) can search for weakly interacting massive particles (WIMPs) by detecting neutrinos produced from WIMP annihilations occurring inside the Sun. In this analysis, we include neutrino events with interaction vertices in the detector in addition to upward-going muons produced in the surrounding rock. Compared to the previous result, which used the upward-going muons only, the signal acceptances for light (few-GeV/c^{2}-200-GeV/c^{2}) WIMPs are significantly increased. We fit 3903 days of SK data to search for the contribution of neutrinos from WIMP annihilation in the Sun. We found no significant excess over expected atmospheric-neutrino background and the result is interpreted in terms of upper limits on WIMP-nucleon elastic scattering cross sections under different assumptions about the annihilation channel. We set the current best limits on the spin-dependent WIMP-proton cross section for WIMP masses below 200  GeV/c^{2} (at 10  GeV/c^{2}, 1.49×10^{-39}  cm^{2} for χχ→bb[over ¯] and 1.31×10^{-40}  cm^{2} for χχ→τ^{+}τ^{-} annihilation channels), also ruling out some fraction of WIMP candidates with spin-independent coupling in the few-GeV/c^{2} mass range.

A fluorescence XAFS measurement instrument in the soft X-ray region toward observation under operando conditions

X-ray absorption fine structure (XAFS) measurements are widely used for the analysis of electronic structure. Generally, XAFS in the soft X-ray region is measured under vacuum, but chemical structures under vacuum are typically different from those under operando conditions, where chemical species exhibit their function. Here, we developed an XAFS measurement instrument, as a step toward operando fluorescent, which yields XAFS measurement using synchrotron radiation in the soft X-ray region. We applied this method to analyze the local electronic structure of the sulfur atoms in L-cysteine in different pH solutions. In water at pH 7, the hydrogen atom does not dissociate from the thiol (-SH) group in L-cysteine, which forms a structure surrounded by and interacting with water molecules. The XAFS spectrum of L-cysteine in solution was altered by changing the pH. At pH 9, the hydrogen atom dissociated and a thiolate anion was formed. Although the -SH group was oxidized to SO4 (2-) when L-cysteine was adsorbed on a metal surface and dried, no oxidation was observed in solution. This may be because the water molecules were densely packed and protected the -SH group from oxidation. Our results show that this instrument aimed toward operando fluorescence XAFS measurements in the soft X-ray region is useful for structural analysis of sulfur atoms in organic molecules in air and in solution. The instrument will be applied to the structural analysis of materials containing elements that have absorption edges in soft X-ray region, such as phosphorus and alkali metals (potassium and cesium). It will be also particularly useful for the analysis of samples that are difficult to handle under vacuum and materials that have specific functions in solution.

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 ν(e) charged current cross section on carbon is measured to be ⟨σ⟩(ϕ)=1.11±0.10(stat)±0.18(syst)×10⁻³⁸ cm²/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 1.23×10⁻³⁸ cm²/nucleon and the GENIE prediction is 1.08×10⁻³⁸ cm²/nucleon. The total ν(e) charged current cross-section result is also in agreement with data from the Gargamelle experiment.

Local defect-induced red-shift of cathodoluminescence in individual ZnS nanobelts

The luminescence of semiconductor nanostructures is strongly dependent on their size, dimensions, morphology, composition, or defects, and their band emissions can be properly and selectively tailored through the rational manipulation of these parameters during material growth. Using spatially-resolved cathodoluminescence spectroscopy, monochromatic contrast maps and high-resolution transmission electron microscopy, an obvious red-shift of the near-band-edge emission of wurtzite ZnS nanobelts, resulting from a strip of stacking faults or a zinc-blende phase with tens of atomic layers in width, has been observed and its related mechanism has been discussed. This finding is not specific to the defect-dependent optical properties tailoring of ZnS nanostructures and represents a general validity for clarifying the mechanism of peak-shift (band-gap expansion or shrinking) of a wide range of semiconductor nanostructures with various defects. In addition, the general formation mechanism of the belt-like nanostructure was proposed based on precise microstructure analyses on a ZnS nanobelt with atomic terrace growth fronts.

Search for nucleon decay via n→ν[over ¯]π0 and p→ν[over ¯]π+ in Super-Kamiokande

We present the results of searches for nucleon decay via n→ν[over ¯]π0 and p→ν[over ¯]π+ using data from a combined 172.8  kt·yr exposure of Super-Kamiokande-I,-II, and-III. We set lower limits on the partial lifetime for each of these modes: τn→ν[over ¯]π0>1.1×10(33) years and τp→ν[over ¯]π+>3.9×10(32) years at a 90% confidence level.

Search for trilepton nucleon decay via p→e+νν and p→μ+νν in the Super-Kamiokande experiment

The trilepton nucleon decay modes p→e+νν and p→μ+νν violate |Δ(B-L)| by two units. Using data from a 273.4 kt yr exposure of Super-Kamiokande a search for these decays yields a fit consistent with no signal. Accordingly, lower limits on the partial lifetimes of τp→e+νν>1.7×10(32) years and τp→μ+νν>2.2×10(32) years at a 90% confidence level are obtained. These limits can constrain Grand Unified Theories which allow for such processes.

Zn vacancy induced green luminescence on non-polar surfaces in ZnO nanostructures

Although generally ascribed to the presence of defects, an ultimate assignment of the different contributions to the emission spectrum in terms of surface states and deep levels in ZnO nanostructures is still lacking. In this work we unambiguously give first evidence that zinc vacancies at the (1010) nonpolar surfaces are responsible for the green luminescence of ZnO nanostructures. The result is obtained by performing an exhaustive comparison between spatially resolved cathodoluminescence spectroscopy and imaging and ab initio simulations. Our findings are crucial to control undesired recombinations in nanostructured devices.

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 θ23. Using an off-axis neutrino beam with a peak energy of 0.6 GeV and a data set corresponding to 6.57×10(20) protons on target, T2K has fit the energy-dependent νμ oscillation probability to determine oscillation parameters. The 68% confidence limit on sin(2)(θ23) is 0.514(-0.056)(+0.055) (0.511±0.055), assuming normal (inverted) mass hierarchy. The best-fit mass-squared splitting for normal hierarchy is Δm32(2)=(2.51±0.10)×10(-3)  eV(2)/c(4) (inverted hierarchy: Δm13(2)=(2.48±0.10)×10(-3)  eV(2)/c(4)). Adding a model of multinucleon interactions that affect neutrino energy reconstruction is found to produce only small biases in neutrino oscillation parameter extraction at current levels of statistical uncertainty.

Search for dinucleon decay into kaons in Super-Kamiokande

A search for the dinucleon decay pp → K+ K+ has been performed using 91.6  kton·yr data from Super-Kamiokande-I. This decay provides a sensitive probe of the R-parity-violating parameter λ112''. A boosted decision tree analysis found no signal candidates in the data. The expected background was 0.28±0.19 atmospheric neutrino induced events and the estimated signal detection efficiency was 12.6%±3.2%. A lower limit of 1.7×10(32)  years has been placed on the partial lifetime of the decay O16 → C14K+ K+ at 90% C.L. A corresponding upper limit of 7.8×10(-9) has been placed on the parameter λ112''.