Mixing Angle Sin Research Articles

Measurement of the τ lepton polarization in Z boson decays in proton-proton collisions at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV

The polarization of τ leptons is measured using leptonic and hadronic τ lepton decays in Z → τ+τ− events in proton-proton collisions at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV recorded by CMS at the CERN LHC with an integrated luminosity of 36.3 fb−1. The measured τ− lepton polarization at the Z boson mass pole is PτZ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{P}}_{\ au}\\left(\ extrm{Z}\\right) $$\\end{document} = −0.144 ± 0.006 (stat) ± 0.014 (syst) = −0.144 ± 0.015, in good agreement with the measurement of the τ lepton asymmetry parameter of Aτ = 0.1439 ± 0.0043 = −PτZ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ -{\\mathcal{P}}_{\ au}\\left(\ extrm{Z}\\right) $$\\end{document} at LEP. The τ lepton polarization depends on the ratio of the vector to axial-vector couplings of the τ leptons in the neutral current expression, and thus on the effective weak mixing angle sin2θWeff\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\ heta}_{\ extrm{W}}^{\ extrm{eff}} $$\\end{document}, independently of the Z boson production mechanism. The obtained value sin2θWeff\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\ heta}_{\ extrm{W}}^{\ extrm{eff}} $$\\end{document} = 0.2319 ± 0.0008(stat) ± 0.0018(syst) = 0.2319 ± 0.0019 is in good agreement with measurements at e+e− colliders.

Search for direct production of GeV-scale resonances decaying to a pair of muons in proton-proton collisions at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV

A search for direct production of low-mass dimuon resonances is performed using s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV proton-proton collision data collected by the CMS experiment during the 2017–2018 operation of the CERN LHC with an integrated luminosity of 96.6 fb−1. The search exploits a dedicated high-rate trigger stream that records events with two muons with transverse momenta as low as 3 GeV but does not include the full event information. The search is performed by looking for narrow peaks in the dimuon mass spectrum in the ranges of 1.1–2.6 GeV and 4.2–7.9 GeV. No significant excess of events above the expectation from the standard model background is observed. Model-independent limits on production rates of dimuon resonances within the experimental fiducial acceptance are set. Competitive or world’s best limits are set at 90% confidence level for a minimal dark photon model and for a scenario with two Higgs doublets and an extra complex scalar singlet (2HDM+S). Values of the squared kinetic mixing coefficient ε2 in the dark photon model above 10−6 are excluded over most of the mass range of the search. In the 2HDM+S, values of the mixing angle sin(θH) above 0.08 are excluded over most of the mass range of the search with a fixed ratio of the Higgs doublets vacuum expectation tan β = 0.5.

Revisiting Majorana neutrino textures in the light of dark LMA

We study the possibility of texture zeros in Majorana light neutrino mass matrix in the light of dark large mixing angle (DLMA) solution to solar neutrino problem where solar mixing angle (sin2 θ 12 ≃ 0.7) lies in the second octant instead of first octant in standard large mixing angle (LMA) scenario (sin2 θ 12 ≃ 0.3). In three neutrino scenario, we find that LMA and DLMA solutions lead to different set of allowed and disallowed textures with one and two zeros. While being consistent with existing bounds from neutrino oscillation data, neutrinoless double beta decay and cosmology these allowed textures also lead to interesting correlations among light neutrino parameters which can distinguish LMA from DLMA solution. We also check the implications for texture zeros in 3 + 1 neutrino scenario using both LMA and DLMA solutions. While LMA and DLMA solutions do not play decisive role in ruling out texture zeros in this case, they do give rise to distinct predictions and correlations between light neutrino parameters.

RGE-induced mu -tau symmetry breaking: an analysis of the latest T2K results

The T2K collaboration has recently reported their results, which gives the best-fit values of the atmospheric mixing angle sin ^2 theta _{23} = 0.53 and the Dirac CP-violating phase delta = -1.89 for normal neutrino mass ordering. We give a possible theoretical origin of such values based on the mu -tau reflection symmetry. It has been found that the breaking of such symmetry using one-loop renormalization-group equations (RGEs) in the framework of minimal supersymmetric standard model can fit well with the latest T2K results and the recent global fits. To make a quantitative analysis, we have included for the first time the complete dataset of oscillation, beta decay, neutrinoless double-beta decay and cosmological observations in comparing the theory to experiments. We also further examine the importance of such breaking patterns for neutrinoless double-beta decay experiments.

Measurement of the weak mixing angle using the forward\u2013backward asymmetry of Drell\u2013Yan events in mathrm {p}mathrm {p} collisions at 8,text {TeV}

A measurement is presented of the effective leptonic weak mixing angle (sin ^2theta ^{ell }_{text {eff}}) using the forward–backward asymmetry of Drell–Yan lepton pairs (mu mu and mathrm {e}mathrm {e}) produced in proton–proton collisions at sqrt{s}=8,text {TeV} at the CMS experiment of the LHC. The data correspond to integrated luminosities of 18.8 and 19.6{{,text {fb}^{-1}}} in the dimuon and dielectron channels, respectively, containing 8.2 million dimuon and 4.9 million dielectron events. With more events and new analysis techniques, including constraints obtained on the parton distribution functions from the measured forward–backward asymmetry, the statistical and systematic uncertainties are significantly reduced relative to previous CMS measurements. The extracted value of sin ^2theta ^{ell }_{text {eff}} from the combined dilepton data is sin ^2theta ^{ell }_{text {eff}} =0.23101pm 0.00036,text {(stat)} pm 0.00018,text {(syst)} pm 0.00016,text {(theo)} pm 0.00031,text {(parton distributions in proton)}=0.23101 pm 0.00053.

Searching for the 3.5 keV Line in the Deep Fields with Chandra: The 10 Ms Observations

Abstract We report a systematic search for an emission line around 3.5 keV in the spectrum of the cosmic X-ray background using a total of ∼10 Ms Chandra observations toward the COSMOS Legacy and Extended Chandra Deep Field South survey fields. We find marginal evidence of a feature at an energy of ∼3.51 keV with a significance of 2.5–3σ, depending on the choice of statistical treatment. The line intensity is best fit at (8.8 ± 2.9) × 10−7 ph cm−2 s−1 when using a simple Δχ 2 or ph cm−2 s−1 when Markov chain Monte Carlo is used. Based on our knowledge of Chandra and the reported detection of the line by other instruments, an instrumental origin for the line remains unlikely. We cannot, however, rule out a statistical fluctuation, and in that case our results provide a 3σ upper limit at 1.85 × 10−6 ph cm−2 s−1. We discuss the interpretation of this observed line in terms of the iron line background, S xvi charge exchange, as well as potentially being from sterile neutrino decay. We note that our detection is consistent with previous measurements of this line toward the Galactic center and can be modeled as the result of sterile neutrino decay from the Milky Way for the dark matter distribution modeled as a Navarro–Frenk–White profile. For this case, we estimate a mass m ν ∼ 7.01 keV and a mixing angle sin2(2θ) = (0.83–2.75) × 10−10. These derived values are in agreement with independent estimates from galaxy clusters, the Galactic center, and M31.

Learning from Higgs physics at future Higgs factories

Future Higgs factories can reach impressive precision on Higgs property measurements. In this paper, instead of conventional focus of Higgs precision in certain interaction bases, we explore its sensitivity to new physics models at the electron-positron colliders. In particular, we study two categories of new physics models, Standard Model (SM) with a real scalar singlet extension, and Two Higgs Double Model (2HDM) as examples of weakly-interacting models, Minimal Composite Higgs Model (MCHM) and three typical patterns of the more general operator counting for strong interacting models as examples of strong dynamics. We perform a global fit to various Higgs search channels to obtain the 95% C.L. constraints on the model parameter space. In the SM with a singlet extension, we obtain the limits on the singlet-doublet mixing angle sin θ, as well as the more general Wilson coefficients of the induced higher dimensional operators. In the 2HDM, we analyze tree level effects in tan β vs. cos(β − α) plane, as well as the one-loop contributions from the heavy Higgs bosons in the alignment limit to obtain the constraints on heavy Higgs masses for different types of 2HDM. In strong dynamics models, we obtain lower limits on the strong dynamics scale. In addition, once deviations of Higgs couplings are observed, they can be used to distinguish different models. We also compare the sensitivity of various future Higgs factories, namely Circular Electron Positron Collider (CEPC), Future Circular Collider (FCC)-ee and International Linear Collider (ILC).

Measurement of polarization angular coefficients in Z boson leptonic decays with ATLAS at the LHC

This paper presents the complete set of polarization angular coefficients A 0−7 describing lepton angular distributions in Z boson decay, which were measured at the ATLAS experiment in proton–proton collisions with the energy √s = 8 TeV. Theoretical values for the difference A 0 − A 2 calculated in the fixed-order QCD perturbation theory O(α 2 ), demonstrate significant deviation from the measured data, which indicates the necessity of taking into account higher order corrections. The evidence of nonzero coefficients A 5,6,7 was obtained for the first time, in accordance with theoretical calculations in O(α 2 ) approximation. Measurement of the polarization angular coefficients A i is important for subsequent precision measurement of parameters of the electroweak model at the LHC, such as the sine of Weinberg electroweak mixing angle sin2 θ W and the W boson mass.

Stellar cooling bounds on new light particles: plasma mixing effects

Strong constraints on the coupling of new light particles to the Standard Model (SM) arise from their production in the hot cores of stars, and the effects of this on stellar cooling. For new light particles which have an effective in-medium mixing with the photon, plasma effects can result in parametrically different production rates to those obtained from a naive calculation. Taking these previously-neglected contributions into account, we make updated estimates for the stellar cooling bounds on light scalars and vectors with a variety of SM couplings. In particular, we improve the bounds on light (m ≲ keV) scalars coupling to electrons or nucleons by up to 3 orders of magnitude in the coupling squared, significantly revise the supernova cooling bounds on dark photon couplings, and qualitatively change the mass dependence of stellar bounds on new vectors. Scalars with mass ≲ 2 keV that couple through the Higgs portal are constrained to mixing angle sin θ ≲ 3 × 10−10, which gives the dominant bound for scalar masses above ∼ 0.2eV.

Global analysis of the source and detector nonstandard interactions using the short baselineν−eandν¯−escattering data

We present a global analysis of the semileptonic and purely Leptonic nonuniversal and flavor-changing nonstandard neutrino interactions in all the known short-baseline neutrino- and antineutrino-electron scattering experiments. The nonstandard effects at the source and at the detector can be more transparent in these experiments because of the negligibly small ratio between the baselines and the neutrino energies, which is not enough for the neutrinos to oscillate, and thus can be sensitive to the new physics at the both ends. We use data from two electron-neutrino electron scattering experiments and six electron-antineutrino electron scattering experiments and combine them to find the best fits on the nonstandard parameters using the source-only, detector-only analyses, and then find the interplay between the two cases. The bounds obtained in some cases are stronger and new, in some cases comparable to the current ones, and in the other cases weaker. For instance, the bound obtained from the interplay between the source and detector nonstandard physics on the nonstandard parameter {\epsilon}_{ee}^{udL} at the source is much stronger and is comparable with the indirect bound, but the bounds on the parameters {\epsilon}_{{\mu}e}^{udL} and {\epsilon}_{{\tau}e}^{udL} are weaker in this study in comparison with the indirect bounds. We also find a global fit on the standard weak mixing angle sin{\theta}_{W}=0.249+-0.020 with 2% improvement in its precision in comparison with the previous studies.

Subdominant Dark Matter sterile neutrino resonant production in the light of PLANCK

Few independent detections of a weak X-ray line at an energy of ∼ 3.5 keV seen toward a number of astrophysical sites have been reported. If this signal will be confirmed to be the signature of decaying DM sterile neutrino with a mass of ∼ 7.1 keV, then the cosmological observables should be consistent with its properties.In this paper we make a coupled treatment of the weak decoupling, primordial nucleosynthesis and photon decoupling epochs in the sterile neutrino resonant production scenario, including the extra radiation energy density via Neff. We compute the radiation and matter perturbations including the full resonance sweep solution for να/ν̄α → νs flavor conversion in the expanding Universe.We show that the cosmological measurements are in agreement with subdominant Dark Matter sterile neutrino resonant production with following parameters (errors at 95% CL): mass mνs=6.08 ± 3.22 keV, mixing angle sin2 2θ < 5.61 × 10−10, lepton number per flavor L4 = 1.23 ± 0.04 (L4 ≡ 104 Lνa) and sterile neutrino mass fraction fνs< 0.078.Our results are in good agreement with the sterile neutrino resonant production parameters inferred in ref. [1] from the linear large scale structure constraints to produce full Dark Matter density.

Muon neutrino disappearance at T2K

The T2K experiment has observed the disappearance of muon neutrinos from the J-PARC muon-neutrino beam. Using data corresponding to 3.01 × 1020 protons on target, 58 muon neutrino event candidates were observed; 205 ± 17 (syst.) events are expected under the no-oscillation hypothesis. A fit to the observed rate and energy spectrum in a neutrino oscillation framework with three active neutrino flavours in constant density matter, assuming the normal mass hierarchy, yields a best fit mixing angle sin2 θ23 = 0.514 ± 0.082 and best fit mass squared splitting |Δm232| = 2.44+0.17−0.15 × 10-3 eV2/c4, which corresponds to the maximal disappearance probability.

DETECTION OF AN UNIDENTIFIED EMISSION LINE IN THE STACKED X-RAY SPECTRUM OF GALAXY CLUSTERS

We detect a weak unidentified emission line at E=(3.55-3.57)+/-0.03 keV in a stacked XMM spectrum of 73 galaxy clusters spanning a redshift range 0.01-0.35. MOS and PN observations independently show the presence of the line at consistent energies. When the full sample is divided into three subsamples (Perseus, Centaurus+Ophiuchus+Coma, and all others), the line is significantly detected in all three independent MOS spectra and the PN "all others" spectrum. It is also detected in the Chandra spectra of Perseus with the flux consistent with XMM (though it is not seen in Virgo). However, it is very weak and located within 50-110eV of several known faint lines, and so is subject to significant modeling uncertainties. On the origin of this line, we argue that there should be no atomic transitions in thermal plasma at this energy. An intriguing possibility is the decay of sterile neutrino, a long-sought dark matter particle candidate. Assuming that all dark matter is in sterile neutrinos with m_s=2E=7.1 keV, our detection in the full sample corresponds to a neutrino decay mixing angle sin^2(2theta)=7e-11, below the previous upper limits. However, based on the cluster masses and distances, the line in Perseus is much brighter than expected in this model. This appears to be because of an anomalously bright line at E=3.62 keV in Perseus, possibly an Ar XVII dielectronic recombination line, although its flux would be 30 times the expected value and physically difficult to understand. In principle, such an anomaly might explain our line detection in other subsamples as well, though it would stretch the line energy uncertainties. Another alternative is the above anomaly in the Ar line combined with the nearby 3.51 keV K line also exceeding expectation by factor 10-20. Confirmation with Chandra and Suzaku, and eventually Astro-H, are required to determine the nature of this new line.(ABRIDGED)

ICARUS-NESSiE: a sensitive search for sterile neutrinos at CERN SPS

A new experimental search for sterile neutrinos beyond the Standard Model at a new CERN-SPS neutrino beam aiming at measuring the electron and muon neutrino events with a Near and Far detectors (1600 and 330 m from the proton target) is presented. The project will exploit the ICARUS T600 LAr-TPC moved from LNGS to the CERN Far position and a new additional LAr-TPC detector, 1/4 of the T600, located in the Near position. Two magnetic spectrometers will be placed downstream of the two LAr-TPC detectors to greatly complement the physics capabilities. Comparing the two detectors, in absence of oscillations, all cross sections and experimental biases cancel out. Any difference of the event distributions at the two locations should be attributed to the possible existence of oscillations, presumably due to additional neutrinos with a mixing angle sin2(2θnew) and a mass squared difference Δm2new larger than the measured for the standard neutrinos. The superior quality of the LAr imaging TPC, in particular its unique electron-π0 discrimination allows for full rejection of backgrounds and offers a lossless νe detection capability. The determination of the muon charge with the spectrometers allows for the full separation of νμ from ν̄μ and therefore controlling systematics from muon mis-identification mainly at high momenta.

ICARUS+NESSiE: A proposal for short baseline neutrino anomalies with innovative LAr imaging detectors coupled with large muon spectrometers

The proposal for an experimental search for sterile neutrinos beyond the Standard Model with a new CERN-SPS neutrino beam is presented. The experiment is based on two identical LAr-TPCʼs followed by magnetized spectrometers, observing the electron and muon neutrino events at 1600 and 300 m from the proton target. This project will exploit the ICARUS T600, moved from LNGS to the CERN “Far” position. An additional 1/4 of the T600 detector will be constructed and located in the “Near” position. Two spectrometers will be placed downstream of the two LAr-TPC detectors to greatly complement the physics capabilities. Comparing the two detectors, in absence of oscillations, all cross sections and experimental biases cancel out. Any difference of the event distributions at the locations of the two detectors might be attributed to the possible existence of ν-oscillations, presumably due to additional neutrinos with a mixing angle sin2(2θnew) and a larger mass difference Δmnew2. The superior quality of the LAr imaging TPC, in particular its unique electron-π0 discrimination allows full rejection of backgrounds and offers a lossless νe detection capability. The determination of the muon charge with the spectrometers allows the full separation of νμ from anti-νμ and therefore controlling systematics from muon mis-identification largely at high momenta.

Effects of the nuclear medium and non-isoscalarity in extractingsin2θWusing the Paschos-Wolfenstein relation

We study the nuclear medium effects and nonisoscalarity correction in the extraction of weak mixing angle sin$^2\theta_W$ using Paschos-Wolfenstein (PW) relation. The calculations are performed for the iron nucleus. The results are discussed along with the experimental result inferred by NuTeV collaboration. The nuclear medium effects like Fermi motion, binding, shadowing and antishadowing corrections and pion and rho meson cloud contributions have been taken into account. Calculations have been performed in the local density approximation using a relativistic nuclear spectral function which includes nucleon correlations. These studies may be useful for the ongoing MINER$\nu$A experiment as well as for the proposed NuSOnG experiment.

Measurement of the Z/γ* forward-backward asymmetry in muon pairs with the ATLAS experiment at the LHC

A study on muon pairs produced through an intermediate Z/γ*, in pp collisions at the LHC, at a center-of-mass energy of 7 TeV, is presented. After a selection aimed at enhancing the contribution from Z boson decay, the topology of the events is analyzed, and the forward-backward asymmetry is measured. The result is then used to test a method to measure the effective weak mixing angle sin2 θeffw. This note summarizes the results obtained with 2011 data collected by the ATLAS experiment at the LHC, corresponding to an integrated luminosity of 4.8 fb−1.

Searches for Physics beyond the Standard Model

The Thomas Jefferson National Accelerator Laboratory has the demonstrated ability to test the fundamental symmetries of nature to very great precision and thereby probe for new physics beyond the Standard Model (SM). In the following objectives and descriptions will be given of three Jefferson Laboratory (JLab) experiments: Qweak, MOLLER, and PVDIS. The Qweak experiment is to measure the weak charge of the proton (via the vector coupling of the Z0 boson to the proton). The MOLLER experiment is to measure the weak charge of the electron. The PV-DIS experiment will measure combinations of vector couplings and axial-vector couplings to the quarks of the nucleons. These three experiments follow from the advances made in precision parity-violating electron scattering measurements at the CEBAF of JLab. The Standard Model makes accurate predictions of the 'running' of the electroweak mixing angle or sin2(θw) from the Z0 pole down to low energies and therefore of the weak charges of the proton and electron. The Qweak experiment will make the first precision determination of the weak charge of the proton, Qpw = 1 – 4 sin2 (θw), from a measurement of the parity-violating asymmetry in the elastic scattering of longitudinally polarized electrons from the protons in a liquid hydrogen target at very low momentum transfer. The projected result will determine the proton's weak charge with a 4.1% total error and consequently sin2 (θw) with a 0.3% error. The Qweak experiment is at present three months into its commissioning run. The MOLLER experiment is to measure the parity-violating asymmetry in the scattering of 11 GeV longitudinally polarized electrons from the atomic electrons in a liquid hydrogen target. The longitudinal analyzing power Az is predicted to be 35.6 ppb at the kinematics of the experiment and is to be determined with a precision of 0.73 ppb, which would make the MOLLER experiment the most precise parity-violation experiment ever undertaken. The result would yield a measurement of the weak charge of the electron to 2.3% at an average Q2 value of 0.0056 (GeV/c)2 and in turn a determination of the electroweak mixing angle sin2(θw) with an uncertainty of ±0.00026 (stat) ±0.00013 (syst), comparable to the accuracy of the two best determinations at the Z0 pole. The PVDIS experiment is to measure the parity-violating asymmetry in deep inelastic scattering of longitudinally polarized electrons from an unpolarized deuterium target. The longitudinal analyzing power can be expressed in terms of the quark distribution functions of the deuterium target and the couplings C1q (axial electron x vector quark) and C2q (vector electron x axial quark), which in the Standard Model can be expressed in terms of sin2(θw).

Design of the local trigger board for the Daya Bay reactor neutrino experiment

We have designed a local trigger board for the Daya Bay reactor neutrino experiment, which is aimed to measure the neutrino mixing angle sin 2 2 θ 13 with a precision down to 1% level. The local trigger board processes both the total number of coincident photomultiplier tube (PMT) hits and the PMT energy sum to make trigger decisions. With this design, a high trigger probability is achieved to meet the system requirement. The design of the local trigger board is presented.

AN UPDATED NUMERICAL ANALYSIS OF eV SEESAW WITH FOUR GENERATIONS

We consider the so-called "eV seesaw" scenario, with right-handed Majorana mass MR at eV order, extended to four lepton generations. The fourth generation gives a heavy pseudo-Dirac neutral lepton, which largely decouples from other generations and is relatively stable. The framework naturally gives three active and three sterile neutrinos. We update a previous numerical analysis of a 3+3 study of the LSND anomaly, taking into account the more recent results from the MiniBooNE experiment. In particular, we study the implications for the third mixing angle sin 2 θ13, as well as CP violation. We find that current data do not seriously constrain more than one sterile neutrinos.