Understanding single charged pion production via neutrino-nucleus charged current interaction in the neutrino energy region of a few GeV is essential for future neutrino oscillation experiments since this process is a dominant background for {nu}{sub {mu}} {yields} {nu}{sub x} oscillation measurements. There are two contributions to this process: single pion production via baryonic resonance ({nu}{sub {mu}}N {yields} {mu}{sup -} N{pi}{sup +}) and coherent pion production interacting with the entire nucleus ({nu}{sub {mu}}A {yields} {mu}{sup -} A{pi}{sup +}), where N is nucleon in the nucleus and A is the nucleus. The purpose of the study presented in this thesis is a precise measurement of charged current single charged pion productions, resonant and coherent pion productions, with a good final state separation in the neutrino energy region of a few GeV. In this thesis, we focus on the study of charged current coherent pion production from muon neutrinos scattering on carbon, {nu}{sub {mu}} {sup 12}C {yields} {mu}{sup -12}C{pi}{sup +}, in the SciBooNE experiment. This is motivated by the fact that without measuring this component first, the precise determination of resonant pion production cross section can not be achieved since the contribution of coherent pion production in the region of small muon scattering …

We present a search for standard model Higgs boson production in association with a W boson in proton-antiproton collisions (p{bar p} {yields} W{sup {+-}}H {yields} {ell}{nu}b{bar b}) at a center of mass energy of 1.96 TeV. WH candidate events have a signature of a single lepton (E{sup {+-}}/{mu}{sup {+-}}), missing transverse energy, and two jets. The search looks for candidate events in approximately 2.7 fb{sup -1} of data recorded with the CDF II detector. The high-p{sub T} lepton (e,{mu}) in the events provides a distinct signature for triggering and most of the events in the dataset come from high-p{sub t} lepton triggers. Our analysis improves on prior searches by including events recorded on the E{sub T} + 2 Jets trigger with a lepton reconstructed as an isolated high-p{sub T} charged particle. We increase the sample purity by identifying ('tagging') long-lived b-hadrons in jets. A neural network combines distinguishing kinematic information into a function optimized for WH sensitivity. The neural network output distributions are consistent with the standard model background expectations and we set limits upper limits on the rate of Higgs production. We set 95% confidence level upper limits on the WH production cross section times branching ratio for Higgs …

Arsenic in drinking water is a major public health problem threatening the lives of over 140 million people worldwide. In Bangladesh alone, up to 57 million people drink arsenic-laden water from shallow wells. ElectroChemical Arsenic Remediation(ECAR) overcomes many of the obstacles that plague current technologies and can be used affordably and on a small-scale, allowing for rapid dissemination into Bangladesh to address this arsenic crisis. In this work, ECAR was shown to effectively reduce 550 - 580 mu g=L arsenic (including both As[III]and As[V]in a 1:1 ratio) to below the WHO recommended maximum limit of 10 mu g=L in synthetic Bangladesh groundwater containing relevant concentrations of competitive ions such as phosphate, silicate, and bicarbonate. Arsenic removal capacity was found to be approximately constant within certain ranges of current density, but was found to change substantially between ranges. In order of decreasing arsenic removal capacity, the pattern was: 0.02 mA=cm2> 0.07 mA=cm2> 0.30 - 1.1 mA=cm2> 5.0 - 100 mA=cm2. Current processing time was found to effect arsenic removal capacity independent of either charge density or current density. Electrode polarization studies showed no passivation of the electrode in the tested range (up to current density 10 mA=cm2) and ruled out oxygen …

A method is presented to simultaneously separate the contributions to a sample of B{sub (s)}{sup 0} {yields} h{sup +}h{sup {prime}-} decays, where h = {pi} or K, and measure the B meson lifetimes in the sample while correcting for the bias in the lifetime distributions due to the hadronic trigger at the CDF experiment. Using 1 fb{sup -1} of data collected at CDF the B{sup 0} lifetime is measured as {tau}{sub B{sup 0}} = 1.558{sub -0.047}{sup +0.050}{sub stat} {+-} 0.028{sub syst} ps, in agreement with the world average measurement. The B{sub s}{sup 0} lifetime in the B{sub s}{sup 0} {yields} K{sup +}K{sup -} decay is measured as {tau}{sub B{sub s}{sup 0} {yields} K{sup +}K{sup -}} = 1.51{sub -0.11}{sup +0.13}{sub stat} {+-} 0.04{sub syst} ps. No difference is observed between the lifetime and other measurements of the average B{sub s}{sup 0} lifetime or the lifetime of the light B{sub s}{sup 0} mass eigenstate determined from B{sub s}{sup 0} {yields} J/{psi}{phi} decays. With the assumptions that B{sub s}{sup 0} {yields} K{sup +}K{sup -} is 100% CP-even and that {tau}{sub B{sub s}{sup 0}} = {tau}{sub B{sup 0}} the width difference in the B{sub s}{sup 0} system is determined as {Delta}{Lambda}{sup CP}/{Lambda} = 0.03{sub …

The author presents measurements of radiative B meson decays to the final states K{sub s}{sup 0}{pi}{sup 0}{gamma} and K{phi}{gamma} based on data collected at the {Upsilon}(4S) resonance with the BABAR detector at the PEP-II e{sup +}e{sup -} collider at SLAC. In a data sample of 467 million B{bar B} pairs, the time-dependent CP asymmetry in B{sup 0} {yields} K{sub s}{sup 0}{pi}{sup 0}{gamma} decays is measured in two regions of K{sub s}{sup 0}-{pi}{sup 0} invariant mass. In the K* region, 0.8 < m(K{sub s}{sup 0}{pi}{sup 0}) < 1.0 GeV/c{sup 2}, we find S{sub K*{gamma}} = -0.03 {+-} 0.29 {+-} 0.03 and C{sub K*{gamma}} = -0.14 {+-} 0.16 {+-} 0.03; in the range 1.1 < m(K{sub s}{sup 0}{pi}{sup 0}) < 1.8 GeV/c{sup 2}, they find S{sub K{sub s}{sup 0}{pi}{sup 0}{gamma}} = -0.78 {+-} 0.59 {+-} 0.09 and C{sub K{sub s}{sup 0}{pi}{sup 0}{gamma}} = -0.36 {+-} 0.33 {+-} 0.04. With a sample of 228 million B{bar B} pairs they measure the branching fraction {Beta}(B{sup +} {yields} K{sup +}{phi}{gamma}) = (3.5 {+-} 0.6 {+-} 0.4) x 10{sup -6} and set the limit {Beta}(B{sup 0} {yields} K{sup 0}{phi}{gamma}) < 2.7 x 10{sup -6} at 90% confidence level. The direct CP asymmetry in B{sup +} {yields} …

Researchers at the Lawrence Berkeley National Laboratory have invented ARUBA (Arsenic Removal Using Bottom Ash) a material that effectively and affordably removes high concentrations of arsenic from contaminated groundwater. The technology is cost-effective because the substrate?bottom ash from coal fired power plants?is a waste material readily available in South Asia. During fieldwork in four sub-districts ofBangladesh, ARUBA reduced groundwater arsenic concentrations as high as 680 ppb to below the Bangladesh standard of 50 ppb. Key results from three trips in Bangladesh and one trip to Cambodia include (1) ARUBA removes more than half of the arsenic from contaminated water within the first five minutes of contact, andcontinues removing arsenic for 2-3 days; (2) ARUBA?s arsenic removal efficiency can be improved through fractionated dosing (adding a given amount of ARUBA in fractions versus all at once); (3) allowing water to first stand for two to three days followed by treatment with ARUBA produced final arsenic concentrations ten times lower than treating water directly out of the well; and (4) the amount of arsenic removed per gram of ARUBA is linearly related to the initial arsenic concentrationof the water. Through analysis of existing studies, observations, and informal interviews in Bangladesh, eight design …

This dissertation presents the measurement of the Cp-odd fraction and time-dependent CP violation parameters for the B{sup 0} {yields} D*{sup +} D*{sup -} decay. These results are based on the full BABAR dataset of (467 {+-} 5) x 10{sup 6} B{bar B} pairs collected at the PEP-II B Factory at the Stanford Linear Accelerator Center. An angular analysis finds that the CP-odd fraction of the B{sup 0} {yields} D*{sup +} D*{sup -} decay is R{sub {perpendicular}} = 0.158 {+-} 0.028 {+-} 0.006, where the first uncertainty is statistical, and the second is systematic. A fit to the flavor-tagged, time-dependent, angular decay rate yields C{sub +} = 0.02 {+-} 0.12 {+-} 0.02; C{sub {perpendicular}} = 0.41 {+-} 0.50 {+-} 0.08; S{sub +} = -0.76 {+-} 0.16 {+-} 0.04; S{sub {perpendicular}} = -1.81 {+-} 0.71 {+-} 0.16, for the CP-odd ({perpendicular}) and CP-even (+) contributions. Constraining these two contributions to be the same results in C = 0.047 {+-} 0.091 {+-} 0.019; S = -0.71 {+-} 0.16 {+-} 0.03. These measurements are consistent with the Standard Model and with measurements of sin2{beta} from B{sup 0} {yields} (c{bar c})K{sup 0} decays.

In this thesis work we have measured the following upper limits at 90% of confidence level, for B meson decays (in units of 10{sup -6}), using a statistics of 465.0 x 10{sup 6} B{bar B} pairs: {Beta}(B{sup 0} {yields} {eta}K{sup 0}) < 1.6 {Beta}(B{sup 0} {yields} {eta}{eta}) < 1.4 {Beta}(B{sup 0} {yields} {eta}{prime}{eta}{prime}) < 2.1 {Beta}(B{sup 0} {yields} {eta}{phi}) < 0.52 {Beta}(B{sup 0} {yields} {eta}{omega}) < 1.6 {Beta}(B{sup 0} {yields} {eta}{prime}{phi}) < 1.2 {Beta}(B{sup 0} {yields} {eta}{prime}{omega}) < 1.7 We have no observation of any decay mode, statistical significance for our measurements is in the range 1.3-3.5 standard deviation. We have a 3.5{sigma} evidence for B {yields} {eta}{omega} and a 3.1 {sigma} evidence for B {yields} {eta}{prime}{omega}. The absence of observation of the B{sup 0} {yields} {eta}K{sup 0} open an issue related to the large difference compared to the charged mode B{sup +} {yields} {eta}K{sup +} branching fraction, which is measured to be 3.7 {+-} 0.4 {+-} 0.1 [118]. Our results represent substantial improvements of the previous ones [109, 110, 111] and are consistent with theoretical predictions. All these results were presented at Flavor Physics and CP Violation (FPCP) 2008 Conference, that took place in Taipei, Taiwan. They will be …

Summary and Conclusions - It was shown that segmentation and pulse-shape discrimination can improve the discovery sensitivity of a next-gen 0vBB-decay experiment by 90%. - However, when practical aspects are considered (such as instrumenting each segment with front-end electronics), the discovery sensitivity is decreased by 19%. - This has extremely important consequences to proposed next-gen experiments since the two active collaborations have strongly advocated the use of segmented detectors for all or part of the experiment. - New germanium detector technology, currently under development, has demonstrated excellent multi-site background rejection capabilities without the complexity of segmentation or complicated PSD algorithms. - The physically-segmented p-type germanium detector technology has proven to be a useful and practical tool in modern nuclear physics. The PSEG technology deserves further development as it has the potential for use in a variety of applications.

Various methods exist for fabrication of micron and submicron sized waveguide structures. However, most of them include expensive and time consuming semiconductor fabrication techniques. An economical method for fabricating waveguide structures is introduced and demonstrated in this thesis. This method is established based on previously well-developed photonic crystal fabrication method called two-polymer microtransfer molding. The waveguide in this work functions by a coupler structure that diffracts the incident light into submicron polymer rods. The light is then guided through the rods. Characterization is done by collecting the light that has been guided through the waveguide and exits the end of these submicron polymer bars. The coupling and waveguiding capabilities are demonstrated using two light sources, a laser and white light.

This thesis presents a measurement of the top quark mass obtained from p{bar p} collisions at {radical}s = 1.96 TeV at the Fermilab Tevatron using the CDF II detector. The measurement uses a matrix element integration method to calculate a t{bar t} likelihood, employing a Quasi-Monte Carlo integration, which enables us to take into account effects due to finite detector angular resolution and quark mass effects. We calculate a t{bar t} likelihood as a 2-D function of the top pole mass m{sub t} and {Delta}{sub JES}, where {Delta}{sub JES} parameterizes the uncertainty in our knowledge of the jet energy scale; it is a shift applied to all jet energies in units of the jet-dependent systematic error. By introducing {Delta}{sub JES} into the likelihood, we can use the information contained in W boson decays to constrain {Delta}{sub JES} and reduce error due to this uncertainty. We use a neural network discriminant to identify events likely to be background, and apply a cut on the peak value of individual event likelihoods to reduce the effect of badly reconstructed events. This measurement uses a total of 4.3 fb{sup -1} of integrated luminosity, requiring events with a lepton, large E{sub T}, and exactly four …

MINOS is a long-baseline two-detector neutrino oscillation experiment that uses a high intensity muon neutrino beam to investigate the phenomena of neutrino oscillations. By measuring the neutrino interactions in a detector near the neutrino source and again 735 km away from the production site, it is possible to probe the parameters governing neutrino oscillation. The majority of the {nu}{sub {mu}} oscillate to {nu}{sub {tau}} but a small fraction may oscillate instead to {nu}{sub e}. This thesis presents a measurement of the {nu}{sub e} appearance rate in the MINOS far detector using the first two years of exposure. Methods for constraining the far detector backgrounds using the near detector measurements is discussed and a technique for estimating the uncertainty on the background and signal selection are developed. A 1.6{sigma} excess over the expected background rate is found providing a hint of {nu}{sub e} appearance.

The standard model of elementary particle physics (SM) predicts, besides the top-quark pair production via the strong interaction, also the electroweak production of single top-quarks [19]. Up to now, the Fermilab Tevatron proton-antiproton-collider is the only place to produce and study top quarks emerging from hadron-hadron-collisions. Top quarks were directly observed in 1995 during the Tevatron Run I at a center-of-mass energy of {radical}s = 1.8 TeV simultaneously by the CDF and D0 Collaborations via the strong production of top-quark pairs. Run II of the Tevatron data taking period started 2001 at {radical}s = 1.96 TeV after a five year upgrade of the Tevatron accelerator complex and of both experiments. One main component of its physics program is the determination of the properties of the top quark including its electroweak production. Even though Run II is still ongoing, the study of the top quark is already a successful endeavor, confirmed by dozens of publications from both Tevatron experiments. A comprehensive review of top-quark physics can be found in reference. The reasons for searching for single top-quark production are compelling. As the electroweak top-quark production proceeds via a Wtb vertex, it provides the unique opportunity of the direct measurement of the …

Photonic crystals and metamaterials, both composed of artificial structures, are two interesting areas in electromagnetism and optics. New phenomena in photonic crystals and metamaterials are being discovered, including some not found in natural materials. This thesis presents my research work in the two areas. Photonic crystals are periodically arranged artificial structures, mostly made from dielectric materials, with period on the same order of the wavelength of the working electromagnetic wave. The wave propagation in photonic crystals is determined by the Bragg scattering of the periodic structure. Photonic band-gaps can be present for a properly designed photonic crystal. Electromagnetic waves with frequency within the range of the band-gap are suppressed from propagating in the photonic crystal. With surface defects, a photonic crystal could support surface modes that are localized on the surface of the crystal, with mode frequencies within the band-gap. With line defects, a photonic crystal could allow the propagation of electromagnetic waves along the channels. The study of surface modes and waveguiding properties of a 2D photonic crystal will be presented in Chapter 1. Metamaterials are generally composed of artificial structures with sizes one order smaller than the wavelength and can be approximated as effective media. Effective macroscopic parameters …

The top quark is generally produced in quark and anti-quark pairs. However, the Standard Model also predicts the production of only one top quark which is mediated by the electroweak interaction, known as 'Single Top'. Single Top quark production is important because it provides a unique and direct way to measure the CKM matrix element V{sub tb}, and can be used to explore physics possibilities beyond the Standard Model predictions. This dissertation presents the results of the observation of Single Top using 2.3 fb{sup -1} of Data collected with the D0 detector at the Fermilab Tevatron collider. The analysis includes the Single Top muon+jets and electron+jets final states and employs Boosted Decision Tress as a method to separate the signal from the background. The resulting Single Top cross section measurement is: (1) {sigma}(p{bar p} {yields} tb + X, tqb + X) = 3.74{sub -0.74}{sup +0.95} pb, where the errors include both statistical and systematic uncertainties. The probability to measure a cross section at this value or higher in the absence of signal is p = 1.9 x 10{sup -6}. This corresponds to a standard deviation Gaussian equivalence of 4.6. When combining this result with two other analysis methods, the resulting …

The Main Injector Neutrino Oscillation Search (MINOS) is a long-baseline accelerator neutrino experiment designed to measure properties of neutrino oscillation. Using a high intensity muon neutrino beam, produced by the Neutrinos at Main Injector (NuMI) complex at Fermilab, MINOS makes two measurements of neutrino interactions. The first measurement is made using the Near Detector situated at Fermilab and the second is made using the Far Detector located in the Soudan Underground laboratory in northern Minnesota. The primary goal of MINOS is to verify, and measure the properties of, neutrino oscillation between the two detectors using the {nu}{sub {mu}} {yields} V{sub {tau}} transition. A complementary measurement can be made to search for the existence of sterile neutrinos; an oft theorized, but experimentally unvalidated particle. The following thesis will show the results of a sterile neutrino search using MINOS RunI and RunII data totaling {approx}2.5 x 10{sup 20} protons on target. Due to the theoretical nature of sterile neutrinos, complete formalism that covers transition probabilities for the three known active states with the addition of a sterile state is also presented.

Homeland security relies heavily on analytical chemistry to identify suspicious materials and persons. Traditionally this role has focused on attribution, determining the type and origin of an explosive, for example. But as technology advances, analytical chemistry can and will play an important role in the prevention and preemption of terrorist attacks. More sensitive and selective detection techniques can allow suspicious materials and persons to be identified even before a final destructive product is made. The work presented herein focuses on the use of commercial and novel detection techniques for application to the prevention of terrorist activities. Although drugs are not commonly thought of when discussing terrorism, narcoterrorism has become a significant threat in the 21st century. The role of the drug trade in the funding of terrorist groups is prevalent; thus, reducing the trafficking of illegal drugs can play a role in the prevention of terrorism by cutting off much needed funding. To do so, sensitive, specific, and robust analytical equipment is needed to quickly identify a suspected drug sample no matter what matrix it is in. Single Particle Aerosol Mass Spectrometry (SPAMS) is a novel technique that has previously been applied to biological and chemical detection. The current work …

We present the search for the lepton flavour violating decay {tau} {yields} lK{sup 0}{sub s} with the BaBar experiment data. This process and many other lepton flavour violating {tau} decays, like {tau} {yields} {mu}{gamma} and {tau} {yields} lll, are one of the most promising channel to search for evidence of new physics. According to the Standard Model and the neutrino mixing parameters, branching fractions are estimated well below 10{sup -14}, but many models of new physics allow for branching fractions values close to the present experimental sensitivity. This analysis is based on a data sample of 469fb{sup -1} collected by BABAR detector at the PEP-II storage ring from 1999 to 2007, equivalent to 431 millions of {tau} pairs. the BABAR experiment, initially designed for studying CP violation in B mesons, has demonstrated to be one of the most suitable environments for studying {tau} decays. The tracking system, the calorimeter and the particle identification of BABAR, together with the knowledge of the {tau} initial energy, allow an extremely powerful rejection of background events that, for this analysis, is better than 10{sup -9}. Being {tau} {yields} lK{sup 0}{sub s} a decay mode without neutrinos, the signal {tau} decay can be fully reconstructed. …

Electricity and magnetism were unified into a common subject by James Clerk Maxwell in the nineteenth century yielding the electromagnetic theory. Four equations govern the dynamics of electric charges and magnetic fields, commonly known as Maxwell's equations. Maxwell's equations demonstrate that an accelerated charged particle can produce magnetic fields and a time varying magnetic field can induce a voltage - thereby linking the two phenomena. However, in solids, electric and magnetic ordering are most often considered separately and usually with good reason: the electric charges of electrons and ions are responsible for the charge effects, whereas the electron spin governs magnetic properties.

The lifetime of the B{sup {+-}} meson is measured using the decay channel B{sup +} {yields} {bar D}{sup 0}{pi}{sup +}. The measurement is made using approximately 1.0 fb{sup -1} of Tevatron proton-anti-proton collision data at {radical}s = 1.96 TeV collected by the CDF detector. The data were collected using impact parameter based triggers that were designed to select events with a secondary vertex. The trigger selection criteria result in data rich in a variety of B hadron decays, but intrinsically bias the lifetime distribution of the collected signal events. The traditional way to compensate for the bias is to use information from simulation. Presented here is a new method for correction of the lifetime bias using an analytical technique that uses information from the data only. This eliminates measurement uncertainty due to data and simulation agreement, ultimately resulting in a smaller systematic measurement uncertainty. The B{sup {+-}} lifetime measurement is the first measurement using this new technique and demonstrates its potential for use in future measurements. The B{sup {+-}} lifetime is measured to be {tau}(B{sup {+-}}) = 1.662 {+-} 0.023(stat) {+-} 0.015(syst)ps.

With data from the SELEX experiment we study charm hadro-production. We report the differential production cross sections as function of the longitudinal and transverse momentum, as well as for two different target materials, of 14 charmed hadron and/or their decay modes. This is the most extensive study to date. SELEX is a fixed target experiment at Fermilab with high forward acceptance; it took data during 1996-1997 with 600 GeV/c {Sigma}{sup -} and {pi}{sup -}, and 540 GeV/c proton and {pi}{sup +} beams. It used 5 target foils (two copper and three diamond). We use the results to determine {alpha}, used in parametrizing the production cross section as {infinity} A{sup {alpha}}, where A is the mass number of the target nuclei. We found within our statistics that {alpha} is independent of the longitudinal momentum fraction x{sub F} in the interval 0.1 < x{sub F} < 1.0, with {alpha} = 0.778 {+-} 0.014. The average value of {alpha} for charm production by pion beams is {alpha}{sub meson} = 0.850 {+-} 0.028. This is somewhat larger than the corresponding average {alpha}{sub baryon} = 0.755 {+-} 0.016 for charm production by baryon beams ({Sigma}{sup -} and protons).

The D0 detector underwent an upgrade to its silicon vertex detector and triggering systems during the transition from Run IIa to Run IIb to maximize its ability to fully exploit Run II at the Fermilab Tevatron. This thesis describes improvements made to the tracking and vertexing algorithms used by the high level trigger in both Run IIa and Run IIb, as well as a search for resonant di-J/{psi} states using both Run IIa and Run IIb data. Improvements made to the tracking and vertexing algorithms during Run IIa included the optimization of the existing tracking software to reduce overall processing time and the certification and testing of a new software release. Upgrades made to the high level trigger for Run IIb included the development of a new tracking algorithm and the inclusion of the new Layer 0 silicon detector into the existing software. The integration of Layer 0 into the high level trigger has led to an improvement in the overall impact parameter resolution for tracks of {approx}50%. The development of a new parameterization method for finding the error associated to the impact parameter of tracks returned by the high level tracking algorithm, in association with the inclusion of Layer …

In the past decades, there has been increasing interest in pulsed high power RF sources for building high-gradient high-energy particle accelerators. Passive RF pulse compression systems have been used in many applications to match the available RF sources to the loads requiring higher RF power but a shorter pulse. Theoretically, an active RF pulse compression system has the advantage of higher efficiency and compactness over the passive system. However, the key component for such a system an element capable of switching hundreds of megawatts of RF power in a short time compared to the compressed pulse width is still an open problem. In this dissertation, we present a switch module composed of an active window based on the bulk effects in semiconductor, a circular waveguide three-port network and a movable short plane, with the capability to adjust the S-parameters before and after switching. The RF properties of the switch module were analyzed. We give the scaling laws of the multiple-element switch systems, which allow the expansion of the system to a higher power level. We present a novel overmoded design for the circular waveguide three-port network and the associated circular-to-rectangular mode-converter. We also detail the design and synthesis process of …

We perform a search for {nu}{sub {mu}} {yields} {nu}{sub e} oscillations, a process which would manifest a nonzero value of the {theta}{sub 13} mixing angle, in the MINOS long-baseline neutrino oscillation experiment. The analysis consists of searching for an excess of {nu}{sub e} charged-current candidate events over the predicted backgrounds, made mostly of neutral-current events with high electromagnetic content. A novel technique to select electron neutrino events is developed, which achieves an improved separation between the signal and the backgrounds, and which consequently yields a better reach in {theta}{sub 13}. The backgrounds are predicted in the Far Detector from Near Detector measurements. An excess is observed in the Far Detector data over the predicted backgrounds, which is consistent with the background-only hypothesis at 1.2 standard deviations.