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DOE OSTI2018

Probing gravity with a joint analysis of galaxy and CMB lensing and SDSS spectroscopy

We present measurements of EG, a probe of gravity from large-scale structure, using BOSS LOWZ and CMASS spectroscopic samples, with lensing measurements from SDSS (galaxy lensing) and Planck (CMB lensing). Using SDSS lensing and the BOSS LOWZ sample, we measure ⟨ E G ⟩ = 0.40 − 0.04 + 0.05 (stat), ±0.026 (systematic), consistent with the predicted value from the Planck ΛCDM model, EG=0.46. Using CMB lensing, we measure ⟨ E G ⟩ = 0.46 − 0.09 + 0.08 (stat) for LOWZ (statistically consistent with galaxy lensing and Planck predictions) and ⟨ E G ⟩ = 0.39 − 0.05 + 0.05 (stat) for the CMASS sample, consistent with the Planck prediction of E G =0.40 given the higher redshift of the sample. We also study the redshift evolution of E G by splitting the LOWZ sample into two samples based on redshift, with results being consistent with model predictions. We estimate systematic uncertainties on the above $\langle$E G $\rangle$ numbers to be ~6% (when using galaxy-galaxy lensing) or ~3% (when using CMB lensing), subdominant to the quoted statistical errors. These systematic error budgets are dominated by observational systematics in galaxy-galaxy lensing and by theoretical modeling uncertainties, respectively. We do not estimate observational systematics in galaxy-CMB lensing cros-correlations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2019

Dark Energy Survey Year 1 results: weak lensing mass calibration of redMaPPer galaxy clusters

We constrain the mass-richness scaling relation of redMaPPer galaxy clusters identified in the Dark Energy Survey Year 1 data using weak gravitational lensing. We split clusters into 4 x 3 bins of richness lambda and redshift z for lambda >= 20 and 0.2 <= z <= 0.65 and measure the mean masses of these bins using their stacked weak lensing signal. By modelling the scaling relation as M-200m|lambda, M-0(lambda/40)(F)((1 + /1.35)(G), we constrain the normalization of the scaling relation at the 5.0 per cent level, finding M-0 = [3.081 +/- 0.075(stat) +/- 0.133(sys)] center dot 10(14) M-aS (TM) at lambda = 40 and = 0.35. The recovered richness scaling index is F = 1.356 +/- 0.051 (stat) +/- 0.008 (sys) and the redshift scaling index G = -0.30 +/- 0.30 (stat) +/- 0.06 (sys). These are the tightest measurements of the normalization and richness scaling index made to date from a weak lensing experiment. We use a semi-analytic covariance matrix to characterize the statistical errors in the recovered weak lensing profiles. Our analysis accounts for the following sources of systematic error: shear and photometric redshift errors, cluster miscentring, cluster member dilution of the source sample, systematic uncertainties in the modelling of the halo-mass correlation function, halo triaxiality, and projection effects. We discuss prospects for reducing our systematic error budget, which dominates the uncertainty on M-0. Our result is in excellent agreement with, but has significantly smaller uncertainties than, previous measurements in the literature, and augurs well for the power of the DES cluster survey as a tool for precision cosmology and upcoming galaxy surveys such as LSST, Euclid, and WFIRST

clusters↗

DOE OSTI2018

Photometric classification and redshift estimation of LSST Supernovae

Supernova (SN) classification and redshift estimation using photometric data only have become very important for the Large Synoptic Survey Telescope (LSST), given the large number of SNe that LSST will observe and the impossibility of spectroscopically following up all the SNe. We investigate the performance of an SN classifier that uses SN colours to classify LSST SNe with the Random Forest classification algorithm. Our classifier results in an area-under-the-curve of 0.98 which represents excellent classification. We are able to obtain a photometric SN sample containing 99 percent SNe Ia by choosing a probability threshold. We estimate the photometric redshifts (photo-z) of SNe in our sample by fitting the SN light curves using the SALT2 model with nested sampling. We obtain a mean bias ($\langle$z phot - z spec $\rangle$) of 0.012 with σ($\frac{zphot-zspec}{1+zspec}$)=0.0294 σ(zphot-zspec1+zspec)=0.0294 without using a host-galaxy photo-z prior, and a mean bias ($\langle$z phot - z spec $\rangle$) of 0.0017 with σ($\frac{zphot-zspec}{1+zspec}$)=0.0116 using a host-galaxy photo-z prior. Assuming a flat ΛCDM model with Ω m = 0.3, we obtain Ω m of 0.305 ± 0.008 (statistical errors only), using the simulated LSST sample of photometric SNe Ia (with intrinsic scatter σ int = 0.11) derived using our methodology without using host-galaxy photo-z prior. Our method will help boost the power of SNe from the LSST as cosmological probes.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2019

Estimating redshift distributions using hierarchical logistic Gaussian processes

ABSTRACT This work uses hierarchical logistic Gaussian processes to infer true redshift distributions of samples of galaxies, through their cross-correlations with spatially overlapping spectroscopic samples. We demonstrate that this method can accurately estimate these redshift distributions in a fully Bayesian manner jointly with galaxy-dark matter bias models. We forecast how systematic biases in the redshift-dependent galaxy-dark matter bias model affect redshift inference. Using published galaxy-dark matter bias measurements from the Illustris simulation, we compare these systematic biases with the statistical error budget from a forecasted weak gravitational lensing measurement. If the redshift-dependent galaxy-dark matter bias model is mis-specified, redshift inference can be biased. This can propagate into relative biases in the weak lensing convergence power spectrum on the 10–30 per cent level. We, therefore, showcase a methodology to detect these sources of error using Bayesian model selection techniques. Furthermore, we discuss the improvements that can be gained from incorporating prior information from Bayesian template fitting into the model, both in redshift prediction accuracy and in the detection of systematic modelling biases.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

First Limits on Light Dark Matter Interactions in a Low Threshold Two-Channel Athermal Phonon Detector from the TESSERACT Collaboration

We present results of a search for spin-independent dark matter-nucleus interactions in a 1 cm 2 by 1 mm thick (0.233 g) high-resolution silicon athermal phonon detector operated above ground. For interactions in the substrate, this detector achieves an rms baseline energy resolution of 361.5⁢(4) m⁢ eV (statistical error), the best for any athermal phonon detector to date. With an exposure of 0.233 g ×12 hours, we place the most stringent constraints on dark matter masses between 44 and 87 M⁢ eV/c 2 , with the lowest unexplored cross section of 4⁢ × 10 −32 c⁢m 2 at 87 M⁢ eV/c 2 . We employ a conservative salting technique to reach the lowest dark matter mass ever probed via direct detection experiment. This constraint is enabled by two-channel rejection of low energy backgrounds that are coupled to individual sensors.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Cohesion and excitations of diamond-structure silicon by quantum Monte Carlo: Benchmarks and control of systematic biases

We have carried out quantum Monte Carlo (QMC) calculations of silicon crystal focusing on the accuracy and systematic biases that affect the electronic structure characteristics. The results show that 64 and 216 atom supercells provide an excellent consistency for extrapolated energies per atom in the thermodynamic limit for ground, excited, and ionized states. We have calculated the ground state cohesion energy with both systematic and statistical errors below ≈ 0.05 eV. The ground state exhibits a fixed-node error of only 1.3(2)% of the correlation energy, suggesting an unusually high accuracy of the corresponding single-reference trial wave function. We obtain a very good agreement between optical and quasiparticle gaps that affirms the marginal impact of excitonic effects. Our most accurate results for band gaps differ from the experiments by about 0.2 eV. This difference is assigned to a combination of residual finite-size and fixed-node errors. In conclusion, we have estimated the crystal Fermi level referenced to vacuum that enabled us to calculate the edges of valence and conduction bands in agreement with experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Equation of state of boron nitride combining computation, modeling, and experiment

The equation of state (EOS) of materials at warm dense conditions poses significant challenges to both theory and experiment. We report a combined computational, modeling, and experimental investigation leveraging new theoretical and experimental capabilities to investigate warm-dense boron nitride (BN). The simulation methodologies include path integral Monte Carlo (PIMC), several density functional theory (DFT) molecular dynamics methods [plane-wave pseudopotential, Fermi operator expansion (FOE), and spectral quadrature (SQ)], activity expansion (actex), and all-electron Green's function Korringa-Kohn-Rostoker (mecca), and compute the pressure and internal energy of BN over a broad range of densities and temperatures. Our experiments were conducted at the Omega laser facility and the Hugoniot response of BN to unprecedented pressures (1200–2650 GPa). The EOSs computed using different methods cross validate one another in the warm-dense matter regime, and the experimental Hugoniot data are in good agreement with our theoretical predictions. By comparing the EOS results from different methods, we assess that the largest discrepancies between theoretical predictions are ≲ 4% in pressure and ≲ 3% in energy and occur at 10 6 K, slightly below the peak compression that corresponds to the K -shell ionization regime. At these conditions, we find remarkable consistency between the EOS from DFT calculations performed on different platforms and using different exchange-correlation functionals and those from PIMC using free-particle nodes. This provides strong evidence for the accuracy of both PIMC and DFT in the high-pressure, high-temperature regime. Moreover, the recently developed SQ and FOE methods produce EOS data that have significantly smaller statistical error bars than PIMC, and so represent significant advances for efficient computation at high temperatures. The shock Hugoniot predicted by PIMC, actex, and mecca shows a maximum compression ratio of 4.55 ± 0.05 for an initial density of 2.26 g/cm 3 , higher than the Thomas-Fermi predictions by about 5%. In addition, we construct tabular EOS models that are consistent with the first-principles simulations and the experimental data. Our findings clarify the ionic and electronic structure of BN over a broad range of temperatures and densities and quantify their roles in the EOS and properties of this material. The tabular models may be utilized for future simulations of laser-driven experiments that include BN as a candidate ablator material.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Test of nuclear decay rate variation due to an antineutrino flux

Unexplained variations of the decay rate parameter for weak interaction decays such as β ± decay, electron capture, as well as strong interaction α decay have been reported. Because these variations have been presented by a number of groups, at various locations, using various types of detectors, different isotopes, and over extended periods of time, some researchers have interpreted the source of these variations as not from ambient environmental factors such as temperature, pressure, and humidity but via an unexplained fundamental interaction. The state of decay rate parameter variations experiments is reviewed, and the reported results are placed into a common comparable context by defining a phenomenological cross section. After that we make decay parameter measurements as a function of time at the level of 10 -5 in the presences of an antineutrino flux with an on-off cycle time of ≈ 30 days. This level of precision requires a detailed understanding of both systematic and statistical errors; otherwise, systematic errors in the measurement may mimic the decay events of fundamental interactions. The experiment searched for variation of the $^{54}_{25}$Mn, e - capture decay rate parameter and $^{137}_{55}$Cs, β - decay rate parameter both to a level of precision of 1 part in ≈10 5 by comparing the difference between the decay rate in the presence of an antineutrino flux ≈ 3 x 10 12 $\bar{ν}$ cm -2 s -1 and no flux measurements. The experiment was located 6.53 m from the reactor core of the High Flux Isotope Reactor at the Oak Ridge National Laboratory. Two weak interaction decays, one via electron capture and the other via β - decay, were selected because the final state and the time reverse state each contain a neutrino and antineutrino, covering arguments that the antineutrino flux may interact differently or not at all in one of the cases. The $\gamma$ spectra from both decays were collected and analyzed independently. The measured variation in the decay rate parameters are found to be δλ/λ =(0.034 ± 1.38) x10 -5 for $^{54}_{25}$Mn and δλ/λ =(0.67±1.56) x10 -5 for $^{137}_{55}$Cs. These results are consistent with no measurable decay rate parameter variation due to an antineutrino flux, yielding a 68% confidence level upper limit sensitivity for $^{54}_{25}$Mn δλ/λ ≤ 1.31 x 10 -5 or σ ≤ 1.29 x10 -25 cm 2 in cross section and for $^{137}_{55}$Cs δλ/λ ≤ 2.23 x 10 -5 or σ ≤ 5.69 x10 -27 cm 2 . The cross-section upper limit obtained in these null or no observable effect measurements are ≈ 10 4 times more sensitive than past experiments reporting positive results in 54 Mn and 137 Cs. . .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Uncertainty quantification of transition operators in the empirical shell model

While empirical shell model calculations have successfully described low-lying nuclear data for decades, only recently has significant effort been made to quantify the uncertainty in such calculations. Here, in this study, we quantify the statistical error in effective parameters for transition operators in empirical calculations in the sd (1s 1/2 -0d 3/2 -0d 5/2 ) valence space, specifically the quenching of Gamow-Teller transitions, effective charges for electric quadrupole (E2) transitions, and the effective orbital and spin couplings for magnetic dipole (M1) transitions and moments. We find the quenching factor for Gamow-Teller transitions relative to free-space values is tightly constrained. For effective M1 couplings, we found isoscalar components more constrained than isovector. This detailed quantification of uncertainties, while highly empirical, nonetheless is an important step towards interpretation of experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2016

Measurement of elliptic flow of light nuclei at s N N = 200 , 62.4, 39, 27, 19.6, 11.5, and 7.7 GeV at the BNL Relativistic Heavy Ion Collider

Here we present measurements of second-order azimuthal anisotropy ( v 2 ) at midrapidity ( |y| < 1.0 ) for light nuclei d , t , 3 He (for $\sqrt{s}$$_{NN}$ = 200 , 62.4, 39, 27, 19.6, 11.5, and 7.7 GeV) and antinuclei$\bar{d}$ ( $\sqrt{s}$$_{NN}$ = 200 , 62.4, 39, 27, and 19.6 GeV) and 3 ¯¯¯¯¯ He ( $\sqrt{s}$$_{NN}$ = 200 GeV) in the STAR (Solenoidal Tracker at RHIC) experiment. The v 2 for these light nuclei produced in heavy-ion collisions is compared with those for p and $\bar{p}$. We observe mass ordering in nuclei v 2 ( p T ) at low transverse momenta ( p T < 2.0 GeV/c). We also find a centrality dependence of v 2 for d and $\bar{d}$ . The magnitude of v 2 for t and 3 He agree within statistical errors. Light-nuclei v 2 are compared with predictions from a blast-wave model. Atomic mass number ( A ) scaling of light-nuclei v 2 (p T ) seems to hold for p T / A < 1.5 GeV/c . Results on light-nuclei v 2 from a transport-plus-coalescence model are consistent with the experimental measurements.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2017

Quantified Gamow shell model interaction for p s d -shell nuclei

Background: The structure of weakly bound and unbound nuclei close to particle drip lines is one of the major science drivers of nuclear physics. A comprehensive understanding of these systems goes beyond the traditional configuration interaction approach formulated in the Hilbert space of localized states (nuclear shell model) and requires an open quantum system description. The complex-energy Gamow shell model (GSM) provides such a framework as it is capable of describing resonant and nonresonant many-body states on equal footing. Purpose: To make reliable predictions, quality input is needed that allows for the full uncertainty quantification of theoretical results. In this study, we carry out the optimization of an effective GSM (one-body and two-body) interaction in the psdf-shell-model space. The resulting interaction is expected to describe nuclei with 5 ≤ A ≲ 12 at the p-sd-shell interface. Method: The one-body potential of the 4 He core is modeled by a Woods-Saxon + spin-orbit + Coulomb potential, and the finite-range nucleon-nucleon interaction between the valence nucleons consists of central, spin-orbit, tensor, and Coulomb terms. The GSM is used to compute key fit observables. The χ 2 optimization is performed using the Gauss-Newton algorithm augmented by the singular value decomposition technique. The resulting covariance matrix enables quantification of statistical errors within the linear regression approach. Results: The optimized one-body potential reproduces nucleon- 4 He scattering phase shifts up to an excitation energy of 20 MeV. The two-body interaction built on top of the optimized one-body field is adjusted to the bound and unbound ground-state binding energies and selected excited states of the helium, lithium, and beryllium isotopes up to A = 9 . A very good agreement with experimental results was obtained for binding energies. First applications of the optimized interaction include predictions for two-nucleon correlation densities and excitation spectra of light nuclei with quantified uncertainties. In conclusion: The new interaction will enable comprehensive and fully quantified studies of structure and reactions aspects of nuclei from the psd region of the nuclear chart.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Perturbation theory models for LSST-era galaxy clustering: Tests with subpercent mock catalog measurements in Fourier and configuration space

Here, we analyze the clustering of galaxies using the z = 1.006 snapshot of the CosmoDC2 simulation, a high-fidelity synthetic galaxy catalog designed to validate analysis methods for the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST). We present sub-percent measurements of the galaxy auto-correlation and galaxy-dark matter cross correlations in Fourier space and configuration space for a magnitude-limited galaxy sample. At these levels of precision, the statistical errors of the measurement are comparable to the systematic effects present in the simulation and measurement procedure; nevertheless, using a hybrid-PT model, we are able to model non-linear galaxy bias with 0.5% precision up to scales of k max = 0.5 h/Mpc and r min = 4 Mpc/h. While the linear bias parameter is measured with 0.01% precision, other bias parameters are determined with considerably weaker constraints and sometimes bimodal posterior distributions. We compare our fiducial model with lower dimensional models where the higher-order bias parameters are fixed at their co-evolution values and find that leaving these parameters free provides significant improvements in our ability to model small scale information. We also compare bias parameters for galaxy samples defined using different magnitude bands and find agreement between samples containing equal numbers of galaxies. Finally, we compare bias parameters between Fourier space and configuration space and find moderate to significant tension between the two approaches. Although our model is often unable to fit the CosmoDC2 galaxy samples within the 0.1% precision of our measurements, our results suggest that the hybrid-PT model used in this analysis is capable of modeling non-linear galaxy bias within the percent level precision needed for upcoming galaxy surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Lattice QCD estimates of thermal photon production from the QGP

Thermal photons produced in heavy-ion collision experiments are an important observable for understanding quark-gluon plasma (QGP). The thermal photon rate from the QGP at a given temperature can be calculated from the spectral function of the vector current correlator. Extraction of the spectral function from the lattice correlator is known to be an ill-conditioned problem, as there is no unique solution for a spectral function for a given lattice correlator with statistical errors. The vector current correlator, on the other hand, receives a large ultraviolet contribution from the vacuum, which makes the extraction of the thermal photon rate difficult from this channel. We therefore consider the difference between the transverse and longitudinal part of the spectral function, only capturing the thermal contribution to the current correlator, simplifying the reconstruction significantly. The lattice correlator is calculated for light quarks in quenched QCD at T = 470 MeV ( ∼ 1.5 T c ), as well as in 2 + 1 flavor QCD at T = 220 MeV ( ∼ 1.2 T p c ) with m π = 320 MeV . In order to quantify the nonperturbative effects, the lattice correlator is compared with the corresponding NLO + LPM LO estimate of correlator. The reconstruction of the spectral function is performed in several different frameworks, ranging from physics-informed models of the spectral function to more general models in the Backus-Gilbert method and Gaussian process regression. We find that the resulting photon rates agree within errors. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

DOE OSTI2015

Isovector and isoscalar tensor charges of the nucleon from lattice QCD

We present results for the iso-vector and flavor diagonal tensor charges $g$$^{u−d}_{T}$, $g$$^{u}_{T}$, $g$$^{d}_{T}$, and $g$$^{s}_{T}$ needed to probe novel tensor interactions at the TeV scale in neutron and nuclear β-decays and the contribution of the quark electric dipole moment (EDM) to the neutron EDM. The lattice QCD calculations were done using nine ensembles of gauge configurations generated by the MILC collaboration using the HISQ action with 2+1+1 dynamical flavors. These ensembles span three lattice spacings a ≈ 0.06, 0.09 and 0.12 fm and three quark masses corresponding to the pion masses M π ≈ 130, 220 and 310 MeV. Using estimates from these ensembles, we quantify all systematic uncertainties and perform a simultaneous extrapolation in the lattice spacing, volume and light quark masses for the connected contributions. The final estimates of the connected nucleon (proton) tensor charge for the iso-vector combination is $g$$^{u−d}_{T}$ = 1.020(76) in the MS scheme at 2 GeV. The additional disconnected quark loop contributions needed for the flavor-diagonal matrix elements are calculated using a stochastic estimator employing the truncated solver method with the all-mode-averaging technique. We find that the size of the disconnected contribution is smaller than the statistical error in the connected contribution. This allows us to bound the disconnected contribution and include it as an additional uncertainty in the flavor-diagonal charges. After a continuum extrapolation, we find $g$$^{u}_{T}$ = 0.774(66), $g$$^{d}_{T}$ = −0.233(28) and $g$$^{u+d}_{T}$ = 0.541(67). The strangeness tensor charge, that can make a significant contribution to the neutron EDM due to the large ratio ms/mu,d, is $g$$^{s}_{T}$ = 0.008(9) in the continuum limit.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

Lattice calculation of hadronic light-by-light contribution to the muon anomalous magnetic moment

The quark-connected part of the hadronic light-by-light scattering contribution to the muon’s anomalous magnetic moment is computed using lattice QCD with chiral fermions. Here we report several significant algorithmic improvements and demonstrate their effectiveness through specific calculations which show a reduction in statistical errors by more than an order of magnitude. The most realistic of these calculations is performed with a near-physical 171 MeV pion mass on a (4.6 fm) 3 spatial volume using the 32 3 ×64 Iwasaki+DSDR gauge ensemble of the RBC/UKQCD Collaboration.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

Neutron and proton electric dipole moments from N f =2+1 domain-wall fermion lattice QCD

We present a lattice calculation of the neutron and proton electric dipole moments (EDM’s) with N f = 2 + 1 flavors of domain-wall fermions. The neutron and proton EDM form factors are extracted from three-point functions at the next-to-leading order in the θ vacuum of QCD. In this computation, we use pion masses 330 and 420 MeV and 2.7 fm 3 lattices with Iwasaki gauge action and a 170 MeV pion and 4.6 fm 3 lattice with I-DSDR gauge action, all generated by the RBC and UKQCD collaborations. The all-mode-averaging technique enables an efficient, high statistics calculation; however the statistical errors on our results are still relatively large, so we investigate a new direction to reduce them, reweighting with the local topological charge density which appears promising. Furthermore, we discuss the chiral behavior and finite size effects of the EDM’s in the context of baryon chiral perturbation theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2017

Probing the top-quark width using the charge identification of b jets

We propose a new method for measuring the top-quark width based on the on-/off-shell ratio of b -charge asymmetry in pp → Wbj production at the LHC. The charge asymmetry removes virtually all backgrounds and related uncertainties, while remaining systematic and theoretical uncertainties can be taken under control by the ratio of cross sections. Limited only by statistical error, in an optimistic scenario, we find that our approach leads to good precision at high integrated luminosity, at a few hundred MeV assuming 300 – 3000 fb -1 at the LHC. The approach directly probes the total width, in such a way that model-dependence can be minimized. It is complementary to existing cross section measurements which always leave a degeneracy between the total rate and the branching ratio, and provides valuable information about the properties of the top quark. Here, the proposal opens up new opportunities for precision top measurements using a b-charge identification algorithm.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

Effects of nonequilibrated topological charge distributions on pseudoscalar meson masses and decay constants

We study the effects of failure to equilibrate the squared topological charge Q 2 on lattice calculations of pseudoscalar masses and decay constants. The analysis is based on chiral perturbation theory calculations of the dependence of these quantities on the QCD vacuum angle θ. For the light-light partially quenched case, we rederive the known chiral perturbation theory results of Aoki and Fukaya, but using the nonperturbatively valid chiral theory worked out by Golterman, Sharpe and Singleton, and by Sharpe and Shoresh. We then extend these calculations to heavy-light mesons. Results when staggered taste violations are important are also presented. The derived Q 2 dependence is compared to that of simulations using the MILC Collaboration’s ensembles of lattices with four flavors of dynamical highly improved staggered quarks. We find agreement, albeit with large statistical errors. These results can be used to correct for the leading effects of unequilibrated Q 2 , or to make estimates of the systematic error coming from the failure to equilibrate Q 2 . In an appendix, we show that the partially quenched chiral theory may be extended beyond a lower bound on valence masses discovered by Sharpe and Shoresh. Subtleties occurring when a sea-quark mass vanishes are discussed in another appendix.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗