Particle Physics

This report describes the research conducted in the High Energy Physics Division of Argonne National Laboratory during the period of July 1 through December 31, 2003. Topics covered here include experimental and theoretical particle physics, advanced accelerator physics, detector development, and experimental facilities research. Lists of Division publications and colloquia are included. i Table of Contents I. EXPERIMENTAL RESEARCH PROGRAM.

We summarize what is known about the transverse spatial distribution of gluons in the nucleon and its x-dependence from exclusive J/ψ photo/electroproduction in ep fixed-target and collider experiments (HERA H1 and ZEUS). This information can be used to predict the impact parameter dependence of the cross section for certain hard QCD processes (dijet production) in pp and pp collisions at the Tevatron and LHC.

Efficient water resource management is a topic of major importance in the field of sustainable development. In arid and semi-arid regions characterized by limited and irregular water availability, the agricultural sector is under constant pressure to receive and ensure water for their crops. Finding an optimal way to share this limited resource requires numerous negotiations between water suppliers and farmers. A multi-agent system, as presented in this paper, is a computer simulation that models the interactions between different types of agents in order to gain insight into the group’s behavior as a whole. This paper claims that such a system can be used at the beginning of the agricultural season to predict potential outcomes of the interactions between water suppliers and farmers, which can inform management on how to optimally plan for the allocation of water. One objective was to take an interdisciplinary approach in order to simulate imagined consequences to complex decisions...

Efficient water resource management is a topic of major importance in the field of sustainable development. In arid and semi-arid regions characterized by limited and irregular water availability, the agricultural sector is under constant pressure to receive and ensure water for their crops. Finding an optimal way to share this limited resource requires numerous negotiations between water suppliers and farmers. A multi-agent system, as presented in this paper, is a computer simulation that models the interactions between different types of agents in order to gain insight into the group’s behavior as a whole. This paper claims that such a system can be used at the beginning of the agricultural season to predict potential outcomes of the interactions between water suppliers and farmers, which can inform management on how to optimally plan for the allocation of water. One objective was to take an interdisciplinary approach in order to simulate imagined consequences to complex decisions...

Efficient water resource management is a topic of major importance in the field of sustainable development. In arid and semi-arid regions characterized by limited and irregular water availability, the agricultural sector is under constant pressure to receive and ensure water for their crops. Finding an optimal way to share this limited resource requires numerous negotiations between water suppliers and farmers. A multi-agent system, as presented in this paper, is a computer simulation that models the interactions between different types of agents in order to gain insight into the group’s behavior as a whole. This paper claims that such a system can be used at the beginning of the agricultural season to predict potential outcomes of the interactions between water suppliers and farmers, which can inform management on how to optimally plan for the allocation of water. One objective was to take an interdisciplinary approach in order to simulate imagined consequences to complex decisions...

We determine the charm quark mass mc ( mc ) from QCD sum rules of moments of the vector current correlator calculated in perturbative QCD. Only experimental data for the charm resonances below the continuum threshold are needed in our approach, while the continuum contribution is determined by requiring self-consistency between various sum rules, including the one for the zeroth moment. Existing data from the continuum region can then be used to bound the theoretical error. Our result is mc ( mc ) = 1272 ± 8 MeV for αs (M Z ) = 0.1182. Special attention is given to the question how to quantify and justify the uncertainty.

Measurements of the W ± → ± ν and Z → + -production cross sections (where ± = e ± , µ ± ) in proton-proton collisions at √ s = 13 TeV are presented using data recorded by the ATLAS experiment at the Large Hadron Collider, corresponding to a total integrated luminosity of 81 pb -1 . The total inclusive W ± -boson production cross sections times the singlelepton-flavour branching ratios are σ tot W + = 11.83 ± 0.02 (stat) ± 0.32 (sys) ± 0.25 (lumi) nb and σ tot W -= 8.79 ± 0.02 (stat) ± 0.24 (sys) ± 0.18 (lumi) nb for W + and W -, respectively. The total inclusive Z-boson production cross section times leptonic branching ratio, within the invariant mass window 66 < m < 116 GeV, is σ tot Z = 1.981 ± 0.007 (stat) ± 0.038 (sys) ± 0.042 (lumi) nb. The W + , W -, and Z-boson production cross sections and cross-section ratios within a fiducial region defined by the detector acceptance are also measured. The crosssection ratios benefit from significant cancellation of experimental uncertainties, resulting in σ fid W + /σ fid W -= 1.295±0.003 (stat)±0.010 (sys) and σ fid W ± /σ fid Z = 10.31±0.04 (stat)±0.20 (sys). Theoretical predictions, based on calculations accurate to next-to-next-to-leading order for quantum chromodynamics and to next-to-leading order for electroweak processes and which employ different parton distribution function sets, are compared to these measurements.

With a data sample of 86 000 Z ---+ r+r -(y) events collected in 1990 through 1993 we have measured the polarization of rleptons as a function of the production polar angle using the following 1-prong r decay modes: r-~ e-~evT, r---+/.t-Vuv~, r----+ 7r-(K-)v~, r-~ p-v, and r----+ a~'v, We obtain for the ratio of vector to axial-vector weak neutral couplings for electrons gve/gA~ = 0.0791 -t-0.0099(Stat) + 0.0025(syst) and taus gvT/gA, = 0.0752 -t-0.0063(stat) + 0.0045(syst) consistent with the hypothesis of e -r universality. Assuming universality of the e -r neutral current we determine the effective electroweak mixing angle to be sin 2 0~ fr = 0.2309 + 0.0016.

We review the theoretical and experimental status of minimal grand unified theories (GUTS), contrasting the failure of minimal non-supersymmetric SU (5) with the success of the minimal supersymmetric SU (5) and minimal supersymmetric Flipped SU (5) × U (1) models. We show that a reasonable value for the universal soft supersymmetry-breaking gaugino mass, 45 GeV < m 1/2 < 1 TeV, and a 1 -σ range of the other inputs constrains the strong coupling, α 3 (m Z ) > .114. We define the supersymmetric standard model (SSM), the minimal supersymmetric extension of the standard model with gauge coupling unification and universal soft supersymmetry-breaking at the unification scale, as a baseline model for unified theories. We review the structure of the allowed parameter space of the SSM and suggest sparticle spectroscopy as the experimental means to determine the parameters of the SSM and search for departures from the baseline SSM.

We apply to nucleon decay the knowledge about the short-distance structure of baryon wave functions gleaned from QCD form factor calculations and the J/$ --) pp decay rate. We review the uncertainties arising when current algebra and PCAC are aused to relate N + z+ meson decay rates to (OlqqqjN) matrix elements. We show that the relevant matrix elements are not directly related to those of the leading twist operators "measured" in conventional high momentum transfer physics, but argue for -an indirect relation based on models that fit both form factor and J/q decay data. We use these inputs to calculate the p * e+s" decay rate in minimal SU(5) and other grand unified theories (GUTS) for a specified value of the heavy vector boson mass mx. Our results combined with the recent experimental lower limit on this mode indicate that rnx > 2 X 10 l5 GeV in the minimal SU(5) GUT, and we derive analogous bounds for super-symmetric GUTS. Our calculated lifetime for a given value of rnx is considerably shorter than previous estimates made using non-relativistic SU(6) or the bag model, a difference traceable to the different normalizations of 2 and 3 quark wave functions at short distances.

We discuss the pair production of massive photinos +or other neutral gauginos in e e annihilation. We present +-cross sections for e e +--+ yy and e e -t yyy including finite mass effects for both the selectron and the gaugino. * Work supported by the Department of Energy, contract DE-AC03-76SF00515. § On leave of absence from Theory Division,

We derive a one-loop expression, including all thresholds, for the mass of the proton decay mediating color triplets, M D c , in minimal supersymmetric SU(5). The result for M D c does not depend on other heavy thresholds or extra representations with SU(5) invariant masses which might be added to the minimal model. We numerically correct our result to two-loop accuracy. Choosing inputs to maximize M D c and τ P , within experimental limits on the inputs and a 1 T eV naturalness bound, we derive a strict bound α 3 > 0.117. We discuss how this bound will change as experimental limits improve. Measurements of α 3 from deep inelastic scattering and the charmonium spectrum are below the bound α 3 > 0.117 by more than 3σ. We briefly review several ideas of how to resolve the discrepancy between these low values of α 3 and the determinations of α 3 from LEP event shapes.

Work supported by the Department of Energy, contract DEAC03-76SF00515 aBSTR.ACT Weak interaction gauge symmetry breaking can be generated by radiative corrections in a spontaneously broken supergravity theory, provided the top quark is heavy enough. In one class of such theories the weak Higgs vacuum expectation values are determined by dimensional transmutation ;5 la Coleman-Weinberg, and may be considerably larger than the magnitudes of susy breaking mass parameters. In this scenario rnt 2 65 GeV, the supersymmetric partners of known particles may have masses << pnw, the mass of the lighter neutral scalar Higgs boson is determined by radiative corrections, and there is some variant of a light pseudoscalar axion. In contrast to conventional Coleman-Weinberg models, the weak phase transition is second order and there is no likelihood of excess entropy production. -

Many models of broken supersymmetry predict the existence of supersymmetric fermions x*7' with masses less than the W* and 2'. Often there are two light neutral fermions x0, even in models with large gaugino masses. The W* have large branching ratios for decays into X* +x0, with the X* subsequently decaying into x0 plus hadrons or leptons. We propose looking at the CERN pp collider for W* production and decay * This terminology is motivated by the zen koan: 'You can make the sound of two hands clapping. Now what is the sound of one hand?" See ref. [lq for important background information.

We use recent information on the b lifetime to improve bounds on shortdistance contributions arising from the t quark to various weak amplitudes. In particular, our previous lower bound on c'/t is substantially increased, while the upper bound on K + WVP is reduced.

We demonstrate that supergravity models containing the Standard Model, dilaton and modulus naturally lead to dynamical symmetry breaking with excellent phenomenology. We assume primordial supersymmetry breaking in the form of a constant contribution to the superpotential. String inspired relations link fundamental couplings to the dilaton vev. We specialize to a class of models inspired by the 4-D fermionic string. Non-renormalizable terms in the superpotential naturally produce the Higgs mixing parameter µ suitable for our mechanism. We discuss extensions and limitations of our approach.

We present the most general supersymmetric amplitude for [Formula: see text] and [Formula: see text] mixing resulting from gluino box diagrams. We use this amplitude to place general constraints on the magnitude of flavor-changing squark mass mixings, and compare these constraints with theoretical predictions both in and beyond the Minimal Supersymmetric Standard Model.

Work supported by the Department of Energy, contract DEAC03-76SF00515 aBSTR.ACT Weak interaction gauge symmetry breaking can be generated by radiative corrections in a spontaneously broken supergravity theory, provided the top quark is heavy enough. In one class of such theories the weak Higgs vacuum expectation values are determined by dimensional transmutation ;5 la Coleman-Weinberg, and may be considerably larger than the magnitudes of susy breaking mass parameters. In this scenario rnt 2 65 GeV, the supersymmetric partners of known particles may have masses << pnw, the mass of the lighter neutral scalar Higgs boson is determined by radiative corrections, and there is some variant of a light pseudoscalar axion. In contrast to conventional Coleman-Weinberg models, the weak phase transition is second order and there is no likelihood of excess entropy production. -

The Karlsruhe Tritium Neutrino (KATRIN) experiment is designed to measure a high-precision integral spectrum of the endpoint region of T2β decay, with the primary goal of probing the absolute mass scale of the neutrino. After a first tritium commissioning campaign in 2018, the experiment has been regularly running since 2019, and in its first two measurement campaigns has already achieved a sub-eV sensitivity. After 1000 days of data-taking, KATRIN’s design sensitivity is 0.2 eV at the 90% confidence level. In this white paper we describe the current status of KATRIN; explore prospects for measuring the neutrino mass and other physics observables, including sterile neutrinos and other beyond-Standard-Model hypotheses; and discuss research-and-development projects that may further improve the KATRIN sensitivity.

Field theories naturally give rise to multiple jets of hadrons in short-distance processes, such as e+e -annihilation. In particular, a low-energy jet of hadrons distributed in some cone of opening angle 6 would be naively expected to evolve at high energies into multiple jets within the angle 6. We explore to what extent this will happen in quantum chromodynamics. * Permanent address. ** Jet opening angles decrease very roughly as Nhadrons/Eje t. * To ensure that the quanta are made at short distances we think of Ej~ t -~ ~/~ (in e + e-) or Ejet = (PT)jet (in pp---~high-pT jets ). ** Extracted from the work of Polyakov [4]. (This proliferation can be nicely interpreted as a branching process [5] .) It is by now common wisdom that this conjectural picture should in some way apply to QCD. *** We will not discuss the case where one observes some' fixed number of jets at large fixed angles to one another. The probability of such a configuration vanishes roughly as a power of 1/In E. * We always measure p2 in units of A2~ (1 GeV)2. In this section we ignore the difference between q--* qG and G--* GG. The picture does not warrant any better. ** For reasons of symmetry we assume that each breakup is into two partons of essentially equal p2. * The azimuthal angle of the partons is entirely random. ** We choose a u-quark jet for all partons. This should be acceptable, as we are interested in calorimetric properties, not flavor. * Quantities such as (p~-Had), which are not linear as is (45), are probably more sensitive to perturbative broadening.

Hadron production and lepton-pair production in e + e -collisions are studied with data collected with the L3 detector at LEP at centre-of-mass energies √ s = 192-208 GeV. Using a total integrated luminosity of 453 pb -1 , 36 057 hadronic events and 12 863 lepton-pair events are selected. The cross sections for hadron production and lepton-pair production are measured for the full sample and for events where no high-energy initial-state-radiation photon is emitted prior to the collisions. Lepton-pair events are further investigated and forward-backward asymmetries are measured. Finally, the differential cross sections for electron-positron pair-production is determined as a function of the scattering angle. An overall good agreement is found with Standard Model predictions.

We show that the measured abundance of ultra-faint lensed galaxies at » z 6 in the Hubble Frontier Fields (HFF) provides stringent constraints on the parameter space of (i) dark matter models based onkeV sterile neutrinos; (ii) "fuzzy" wavelike dark matter models, based on Bose-Einstein condensates of ultra-light particles. For the case of sterile neutrinos, we consider two production mechanisms: resonant production through mixing with active neutrinos and the decay of scalar particles. For the former model, we derive constraints for the combination of sterile neutrino mass n m and mixing parameter q sin 2 2 ( ) which provide the tightest lower bounds on the mixing angle (and hence on the lepton asymmetry) derived so far by methods independent of baryonic physics. For the latter we compute the allowed combinations of the scalar mass, its coupling to the Higgs field, and the Yukawa coupling of scalar to sterile neutrinos. We compare our results to independent existing astrophysical bounds on sterile neutrinos in the same mass range. For the case of "fuzzy" dark matter, we show that the observed number density »1 Mpc 3 of high-redshift galaxies in the HFF sets a lower limit  y m 8 10 22 • eV (at the 3-σ confidence level) on the particle mass, a result that strongly disfavors wavelike bosonic dark matter as a viable model for structure formation. We discuss the impact on our results of uncertainties due to systematics in the selection of highly magnified, faint galaxies at high redshift.

Sterile neutrinos with mass in the range of one to a few keV are important as extensions of the Standard Model of particle physics and are serious dark matter (DM) candidates. This DM mass scale (warm DM) is in agreement with both cosmological and galactic observations. We study the role of a keV sterile neutrino through its mixing with a light active neutrino in Rhenium 187 and Tritium beta decays. We pinpoint the energy spectrum of the beta particle, 0 Te (Q β -ms), as the region where a sterile neutrino could be detected and where its mass ms could be measured. This energy region is at least 1 keV away from the region suitable to measure the mass of the light active neutrino, located near the endpoint Q β . The emission of a keV sterile neutrino in a beta decay could show up as a small kink in the spectrum of the emitted beta particle. With this in view, we perform a careful calculation of the Rhenium and Tritium beta spectra and estimate the size of this perturbation by means of the dimensionless ratio R of the sterile neutrino to the active neutrino contributions. We comment on the possibility of searching for sterile neutrino signatures in two experiments which are currently running at present, MARE and KATRIN, focused on the Rhenium 187 and Tritium beta decays respectively.

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We uncover the general mechanism and the nature of the today dark energy (DE). This is only based on well known quantum physics and cosmology. We show that the observed DE today originates from the cosmological quantum vacuum of light particles which provides a continuous energy distribution able to reproduce the data. Bosons give positive contributions to the DE while fermions yield negative contributions. As usual in field theory, ultraviolet divergences are subtracted from the physical quantities. The subtractions respect the symmetries of the theory and we normalize the physical quantities to be zero for the Minkowski vacuum. The resulting finite contributions to the energy density and the pressure from the quantum vacuum grow as log a(t) where a(t) is the scale factor, while the particle contributions dilute as 1/a 3 (t), as it must be for massive particles. We find the explicit today dark energy equation of state P = w(z) H: It turns to be slightly w(z) < -1 with w(z) asymptotically reaching the value -1 from below. A scalar particle can produce the observed dark energy through its quantum cosmological vacuum provided: (i) Its mass is of the order of 10 -3 eV = 1 meV, (ii) It is very weakly coupled, and (iii) it is stable on the time scale of the age of the universe. The axion vacuum thus appears as a natural candidate. The neutrino vacuum (especially the lightest mass eigenstate) can give negative contributions to the dark energy. We find that w(z = 0) is slightly below -1 by an amount ranging from (-1.5 × 10 -3 ) to (-8 × 10 -3 ) and we predict the axion mass be in the range between 4 and 5 meV . We find that the universe will expand in the future faster than the de Sitter universe, as an exponential in the square of the cosmic time. Dark energy today arises from the quantum vacuum of light particles in FRW cosmological space-time in an analogous way to the Casimir vacuum effect of quantum fields in Minkowski space-time with non-trivial boundary conditions. (+) passed away (a): Contents I. Introduction and Results 2 II. Scalar Fields in Cosmological Space-Times III. Fermion Fields in Cosmological Space-Times IV. The Cosmological Quantum Vacuum. V. Vacuum Energy Density and Pressure for Late Times VI. The Quantum Nature of the Cosmological Vacuum. VII. Dark Energy from the Cosmological Quantum Vacuum. VIII. Neutrino Mass Eigenstates IX. Light Particle Masses and the Dark Energy Density Today X. The Future Evolution of the Universe XI. Discussion XII. Conclusions A. Dimensional and Cutoff Regularization of the Vacuum Energy References I. INTRODUCTION AND RESULTS Since the discovery of the dark energy in the present universe [1], [2], an intense observational activity has improved our knowledge about it [3], [4], [5], and more activity is expected to provide new data and understanding eg. [6], [7]. Many different approachs and models have been proposed to explain the dark energy [8], [9], [10], [11], [12]. For reviews and approachs on the dark energy see for example Refs. [10], [8], [9], [11, 12].

Cumulative observational evidence confirms that the surface gravity of dark matter (DM) halos μ0 D = r0ρ0, where r0 and ρ0 are the halo core radius and central density, respectively, is nearly constant and independent of galaxy luminosity for a high number of galactic systems (spirals, dwarf irregular and spheroidals, elliptics) spanning over 14 magnitudes in luminosity and of different Hubble types. Remarkably, its numerical value, μ0D ≃140M⊙/ pc 2 = (18.6 MeV )3, is approximately the same (up to a factor of 2) in all these systems. First, we present the physical consequences of the independence of μ0D from r0: the energy scales as the volume [Formula: see text], while the mass and the entropy scale as the surface [Formula: see text] and the surface times log r0, respectively. Namely, the entropy scales similarly to the black hole entropy but with a much smaller coefficient. Second, we compute the surface gravity and the density profile for small scales from first principles and th...

The FOCUS photoproduction experiment took data in the ninenties and produced a wealth of results in charm physics. Some of the studies were seminal for contemporary experiments, and even paved the way for the technology of many charm and beauty analysis tools.

The result of a search at the LHC for heavy stable charged particles produced in pp collisions at √ s = 7 TeV is described. The data sample was collected with the CMS detector and corresponds to an integrated luminosity of 3.1 pb -1 . Momentum and ionization-energy-loss measurements in the inner tracker detector are used to identify tracks compatible with heavy slow-moving particles. Additionally, tracks passing muon identification requirements are also analyzed for the same signature. In each case, no candidate passes the selection, with an expected background of less than 0.1 events. A lower limit at the 95% confidence level on the mass of a stable gluino is set at 398 GeV/c 2 , using a conventional model of nuclear interactions that allows charged hadrons containing this particle to reach the muon detectors. A lower limit of 311 GeV/c 2 is also set for a stable gluino in a conservative scenario of complete charge suppression, where any hadron containing this particle becomes neutral before reaching the muon detectors.

We review genetic programming principles, their application to FOCUS data samples, and use the method to study the doubly Cabibbo suppressed decay D + → K + π + π -relative to its Cabibbo favored counterpart, D + → K -π + π + . We find that this technique is able to improve upon more traditional analysis methods. To our knowledge, this is the first application of the genetic programming technique to High Energy Physics data.

A measurement of the b-hadron production cross section in proton-proton collisions at √ s = 7 TeV is presented. The dataset, corresponding to 85 nb -1 , was recorded with the CMS experiment at the LHC using a low-threshold single-muon trigger. Events are selected by the presence of a muon with transverse momentum p µ T > 6 GeV with respect to the beam direction and pseudorapidity |η µ | < 2.1. The transverse momentum of the muon with respect to the closest jet discriminates events containing b hadrons from background. The inclusive b-hadron production cross section is presented as a function of muon transverse momentum and pseudorapidity. The measured total cross section in the kinematic acceptance is σ(pp → b + X → µ + X ) = 1.32 ± 0.01(stat) ± 0.30(syst) ± 0.15(lumi)µb.

A search for narrow resonances at high mass in the dimuon and dielectron channels has been performed by the CMS experiment at the CERN LHC, using pp collision data recorded at √ s = 7 TeV. The event samples correspond to integrated luminosities of 40 pb -1 in the dimuon channel and 35 pb -1 in the dielectron channel. Heavy dilepton resonances are predicted in theoretical models with extra gauge bosons (Z ′ ) or as Kaluza-Klein graviton excitations (G KK ) in the Randall-Sundrum model. Upper limits on the inclusive cross section of Z ′ (G KK ) → ℓ + ℓ -relative to Z → ℓ + ℓ -are presented. These limits exclude at 95% confidence level a Z ′ with standard-model-like couplings below 1140 GeV, the superstring-inspired Z ′ ψ below 887 GeV, and, for values of the coupling parameter k/M Pl of 0.05 (0.1), Kaluza-Klein gravitons below 855 (1079) GeV.

A search for the standard model Higgs boson decaying into two Z bosons with subsequent decay into a final state containing two quark jets and two leptons, H → ZZ(*) → q $ \overline {\text{q}} $ ℓ − ℓ + is presented. Results are based on data corresponding to an integrated luminosity of 4.6 fb−1 of proton-proton collisions at $ \sqrt {s} = 7 $ TeV, collected with the CMS detector at the LHC. In order to discriminate between signal and background events, kinematic and topological quantities, including the angular spin correlations of the decay products, are employed. Events are further classified according to the probability of the jets to originate from quarks of light or heavy flavor or from gluons. No evidence for the Higgs boson is found, and upper limits on its production cross section are determined for a Higgs boson of mass between 130 and 600 GeV.

Using a large sample of charm semileptonic decays collected by the FOCUS photoproduction experiment at Fermilab, we present evidence for a small, even spin K -π + amplitude that interferes with the dominant K * 0 component in the D + → K -π + µ + ν final state. Although this interference significantly distorts the D + → K -π + µ + ν decay angular distributions, the new amplitude creates only a very small distortion to the observed kaon pion mass distribution when integrated over the other kinematic variables describing the decay. Our data can be described by K * 0 interference with either a constant amplitude or broad spin zero resonance.

Using a high statistics sample of photoproduced charm particles from the FOCUS experiment at Fermilab, we compare the lifetimes of neutral D mesons decaying via D 0 → K -π + and K -K + to measure the lifetime differences between CP even and CP odd final states. These measurements bear on the phenomenology of D 0 -D0 mixing. If the D 0 → K -π + is an equal mixture of CP even and CP odd eigenstates, we measure y CP = (Γ(CP even) -Γ(CP odd))/(Γ(CP even) + Γ(CP odd)) = 0.0342 ± 0.0139 ± 0.0074.

A high statistics sample of photoproduced charm particles from the FOCUS (E831) experiment at Fermilab has been used to search for CP violation in the Cabibbo suppressed decay modes We have measured the following CP asymmetry parameters: A CP (K -K + π + ) = +0.006 ± 0.011 ± 0.005, A CP (K -K + ) = -0.001 ± 0.022 ± 0.015 and A CP (π -π + ) = +0.048 ± 0.039 ± 0.025 where the first error is statistical and the second error is systematic. These asymmetries are consistent with zero with smaller errors than previous measurements.