Uncertainties In Theoretical Predictions Research Articles

Neutrino Flavor Model Building and the Origins of Flavor and CP Violation

The neutrino sector offers one of the most sensitive probes of new physics beyond the Standard Model of Particle Physics (SM). The mechanism of neutrino mass generation is still unknown. The observed suppression of neutrino masses hints at a large scale, conceivably of the order of the scale of a rand unified theory (GUT), which is a unique feature of neutrinos that is not shared by the charged fermions. The origin of neutrino masses and mixing is part of the outstanding puzzle of fermion masses and mixings, which is not explained ab initio in the SM. Flavor model building for both quark and lepton sectors is important in order to gain a better understanding of the origin of the structure of mass hierarchy and flavor mixing, which constitute the dominant fraction of the SM parameters. Recent activities in neutrino flavor model building based on non-Abelian discrete flavor symmetries and modular flavor symmetries have been shown to be a promising direction to explore. The emerging models provide a framework that has a significantly reduced number of undetermined parameters in the flavor sector. In addition, such a framework affords a novel origin of CP violation from group theory due to the intimate connection between physical CP transformation and group theoretical properties of non-Abelian discrete groups. Model building based on non-Abelian discrete flavor symmetries and their modular variants enables the particle physics community to interpret the current and anticipated upcoming data from neutrino experiments. Non-Abelian discrete flavor symmetries and their modular variants can result from compactification of a higher-dimensional theory. Pursuit of flavor model building based on such frameworks thus also provides the connection to possible UV completions: in particular, to string theory. We emphasize the importance of constructing models in which the uncertainties of theoretical predictions are smaller than, or at most compatible with, the error bars of measurements in neutrino experiments. While there exist proof-of-principle versions of bottom-up models in which the theoretical uncertainties are under control, it is remarkable that the key ingredients of such constructions were discovered first in top-down model building. We outline how a successful unification of bottom-up and top-down ideas and techniques may guide us towards a new era of precision flavor model building in which future experimental results can give us crucial insights into the UV completion of the SM.

Isospin-breaking corrections to light-meson leptonic decays from lattice simulations at physical quark masses

The decreasing uncertainties in theoretical predictions and experimental measurements of several hadronic observables related to weak processes, which in many cases are now smaller than O(1%), require theoretical calculations to include subleading corrections that were neglected so far. Precise determinations of leptonic and semi-leptonic decay rates, including QED and strong isospin-breaking effects, can play a central role in solving the current tensions in the first-row unitarity of the CKM matrix. In this work we present the first RBC/UKQCD lattice calculation of the isospin-breaking corrections to the ratio of leptonic decay rates of kaons and pions into muons and neutrinos. The calculation is performed at fixed lattice spacing (a−1 ≃ 1.730 GeV) on a 483× 96 volume with Nf = 2 + 1 dynamical quarks close to the physical point and domain wall fermions in the Möbius formulation are employed. Long-distance QED interactions are included according to the QEDL prescription and the crucial role of finite-volume electromagnetic corrections in the determination of leptonic decay rates, which produce a large systematic uncertainty, is extensively discussed. Finally, we study the different sources of uncertainty on |Vus|/|Vud| and observe that, if finite-volume systematics can be reduced, the error from isospin-breaking corrections is potentially sub-dominant in the final precision of the ratio of the CKM matrix elements.

Uncertainties in theoretical predictions for γd → π 0d observables near threshold due to the use of different elementary amplitudes

We discuss possible uncertainties in theoretical predictions for γd → π 0 d observables near threshold due to the use of different elementary γN → πN amplitudes using an approach which is based on time-ordered perturbation theory. Results are presented for unpolarized cross sections and all possible spin asymmetries of differential and total cross sections. Our results indicate that the estimations of the uncertainty on the γd → π 0 d observables show important sensitivity to the modeling of the elementary γN → πN operator. A comparison to presently available experimental data is given. The results presented here are of particular interest for the evaluation of the systematic uncertainties caused by the use of different elementary operators in the analyses of γd → π 0 d measurements to extract information on the free neutron amplitude from deuteron data.

NLO QCD corrections to pseudoscalar quarkonium production with two heavy flavors in photon-photon collision

We calculate the next-to-leading order (NLO) QCD corrections to $\ensuremath{\gamma}+\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\eta}}_{c}+c+\overline{c}$, $\ensuremath{\gamma}+\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\eta}}_{b}+b+\overline{b,}$ and $\ensuremath{\gamma}+\ensuremath{\gamma}\ensuremath{\rightarrow}{B}_{c}+b+\overline{c}$ processes in the framework of nonrelativistic QCD factorization formalism. The cross sections at the SuperKEKB electron-positron collider, as well as the future collider like the Circular Electron Positron Collider, are evaluated. Numerical results indicate that the NLO corrections are significant, and the uncertainties in theoretical predictions with NLO corrections are reduced as expected. Due to the high luminosity of the SuperKEKB collider, the ${\ensuremath{\eta}}_{c}+c+\overline{c}$ production is hopefully observable in the near future.

Correlation of theoretical uncertainties in PDF fits and theoretical uncertainties in predictions

We show how to account for correlations between theoretical uncertainties incorporated in parton distribution function (PDF) fits, and the theoretical uncertainties in the predictions made using these PDFs. We demonstrate by explicit calculations, both analytical and numerical, that these correlations can lead to corrections to the central values of the predictions, and reductions in both the PDF uncertainties and the theoretical uncertainties in the prediction. We illustrate our results with predictions for top production rapidity distributions and the Higgs total cross-section at the LHC, using the NLO NNPDF3.1 PDF set which incorporates missing higher order uncertainties. We conclude that the inclusion of correlations can increase both the accuracy and precision of predictions involving PDFs, particularly for processes with data already included in the PDF fit.

The electron-capture origin of supernova 2018zd

In the transitional mass range (~8–10 solar masses) between white dwarf formation and iron core-collapse supernovae, stars are expected to produce an electron-capture supernova. Theoretically, these progenitors are thought to be super-asymptotic giant branch stars with a degenerate O + Ne + Mg core, and electron capture onto Ne and Mg nuclei should initiate core collapse1,2,3,4. However, no supernovae have unequivocally been identified from an electron-capture origin, partly because of uncertainty in theoretical predictions. Here we present six indicators of electron-capture supernovae and show that supernova 2018zd is the only known supernova with strong evidence for or consistent with all six: progenitor identification, circumstellar material, chemical composition5,6,7, explosion energy, light curve and nucleosynthesis8,9,10,11,12. For supernova 2018zd, we infer a super-asymptotic giant branch progenitor based on the faint candidate in the pre-explosion images and the chemically enriched circumstellar material revealed by the early ultraviolet colours and flash spectroscopy. The light-curve morphology and nebular emission lines can be explained by the low explosion energy and neutron-rich nucleosynthesis produced in an electron-capture supernova. This identification provides insights into the complex stellar evolution, supernova physics, cosmic nucleosynthesis and remnant populations in the transitional mass range.

Exploring the uncertainties in theoretical predictions of nuclear β-decay half-lives * *Partly supported by the National Natural Science Foundation of China under (11805004, 11875070), the Key Research Foundation of Education Ministry of Anhui Province (KJ2020A0485), and the Open fund for Discipline Construction, Institute of Physical Science and Information Technology, Anhui University

Nuclear -decay half-lives are predicted based on an empirical formula and the mass predictions from various nuclear models. It is found that the empirical formula can reproduce the nuclear -decay half-lives well, especially for short-lived nuclei with s. The theoretical half-life uncertainties from -decay energies and the parameters of the empirical formula are further investigated. It is found that the uncertainties of the half-lives are relatively large for heavy nuclei and nuclei near the neutron-drip line. For nuclei on the r-process path, the uncertainties for those with are about one order of magnitude, which are much larger than the uncertainties for those with and . However, theoretical uncertainties from the parameters of the empirical formula are relatively small for the nuclei on the r-process path, which indicates that the empirical formula is very suitable for predicting the -decay half-lives in r-process simulations.

NLO QCD corrections to inclusive charmonium and Bc meson production in W+ decays

We calculate the next-to-leading order (NLO) quantum chromodynamics (QCD) corrections to inclusive processes $W^+\to J/\psi(\eta_c)+c+\bar{s}+X$ and $W^+\to B_c(B_c^{*})+b+\bar{s}+X$ in the framework of nonrelativistic QCD (NRQCD) factorization formalism. Result indicates that the NLO corrections are significant, and the uncertainties in theoretical predictions with NLO corrections are greatly reduced. The charmonium and $B_c$ meson yielding rates at the Large Hadron Collider (LHC) are given.

Bayesian Analysis of Theoretical Rotational Constants from Low-Cost Electronic Structure Methods.

With an ever-increasing usage of electronic structure programs by the microwave spectroscopy community, there is a growing need to assess the performance of commonly used, low-cost quantum chemical methods, particularly with respect to rotational constants because these quantities are central in guiding experiments. Here, we systematically benchmark the predictive power afforded by several low-level ab initio and density functionals combined with a variety of basis sets that are commonly employed in the rotational spectroscopy literature. The data set in our analysis consists of 6916 optimized geometries of 76 representative species where high-resolution experimental gas-phase rotational constants are available. We adopted a Bayesian approach for analyzing the performance of each method and basis set combination, employing Hamiltonian Monte Carlo sampling to determine the uncertainty in theoretical predictions of rotational constants and dipole moments. Our analysis establishes a hierarchy of accuracy and uncertainty, with commonly used methods in the rotational spectroscopy literature such as B3LYP and MP2 yielding lower accuracy and higher uncertainty than newer-generation functionals such as those from the Minnesota family, and ωB97X-D, which, when paired with a modestly sized 6-31+G(d) basis, provides optimal performance with respect to computational cost. Additionally, we provide statistical scaling factors that can be used to empirically correct for vibration-rotation effects, as a means to further improve the accuracy of rotational constants predicted from these relatively low-cost theoretical methods. As part of this, we demonstrate that the uncertainties can be used in simulations of rotational spectra to cross-correlate with broadband spectra, a methodology that could be used to quickly and efficiently survey experimental spectra for new molecules.

NLO QCD corrections to exclusive electroproduction of quarkonium

The process of exclusive electroproduction of vector quarkonium (EEQ), ep→epV, is per se an interesting topic in studies of quarkonium production mechanism, QCD description of diffractive interaction and nucleon structure. We investigate this process in the framework of nonrelativistic QCD and QCD collinear factorization at the next-to-leading order QCD accuracy. The perturbative convergence behavior is discussed in a large range of photon virtuality Q2. The J/ψ large-Q2 electroproduction data at HERA can be well explained, and the ϒ differential production rate is predicted. The uncertainties in theoretical predictions with radiative corrections are greatly reduced. Notice the EEQ process is extremely sensitive to the gluon distribution in nucleon, the generalized parton distribution, our results will constraint the gluon density with high precision while confronting to the future experimental data. For the sake of comparing convenience, the analytic expressions are provided.

Directed searches for gravitational waves from ultralight bosons

Gravitational-wave detectors can search for yet-undiscovered ultralight bosons, including those conjectured to solve problems in particle physics, high-energy theory and cosmology. Ground-based instruments could probe boson masses between $10^{-15}$ eV to $10^{-11}$ eV, which are largely inaccessible to other experiments. In this paper, we explore the prospect of searching for the continuous gravitational waves generated by boson clouds around known black holes. We carefully study the predicted waveforms and use the latest-available numerical results to model signals for different black-hole and boson parameters. We then demonstrate the suitability of a specific method (hidden Markov model tracking) to efficiently search for such signals, even when the source parameters are not perfectly known and allowing for some uncertainty in theoretical predictions. We empirically study this method's sensitivity and computational cost in the context of boson signals, finding that it will be possible to target remnants from compact-binary mergers localized with at least three instruments. For signals from scalar clouds, we also compute detection horizons for future detectors (Advanced LIGO, LIGO Voyager, Cosmic Explorer and the Einstein Telescope). Among other results, we find that, after one year of observation, an Advanced LIGO detector at design sensitivity could detect these sources up to over 100 Mpc, while Cosmic Explorer could reach over $10^4$ Mpc. These projections offer a more complete picture than previous estimates based on analytic approximations to the signal power or idealized search strategies. Finally, we discuss specific implications for the followup of compact-binary coalescences and black holes in x-ray binaries. Along the way, we review the basic physics of bosons around black holes, in the hope of providing a bridge between the theory and data-analysis literatures.

Generic assembly patterns in complex ecological communities

The study of ecological communities often involves detailed simulations of complex networks. However, our empirical knowledge of these networks is typically incomplete and the space of simulation models and parameters is vast, leaving room for uncertainty in theoretical predictions. Here we show that a large fraction of this space of possibilities exhibits generic behaviors that are robust to modeling choices. We consider a wide array of model features, including interaction types and community structures, known to generate different dynamics for a few species. We combine these features in large simulated communities, and show that equilibrium diversity, functioning, and stability can be predicted analytically using a random model parameterized by a few statistical properties of the community. We give an ecological interpretation of this "disordered" limit where structure fails to emerge from complexity. We also demonstrate that some well-studied interaction patterns remain relevant in large ecosystems, but their impact can be encapsulated in a minimal number of additional parameters. Our approach provides a powerful framework for predicting the outcomes of ecosystem assembly and quantifying the added value of more detailed models and measurements.

The impact of the photon PDF and electroweak corrections on [Formula: see text] distributions.

We discuss the impact of EW corrections on differential distributions in top-quark pair production at the LHC and future hadron colliders, focussing on the effects of initial-state photons. Performing a calculation at Next-to-Leading Order QCD+EW accuracy, we investigate in detail the impact of photon-initiated channels on central values as well as PDF and scale uncertainties, both at order alpha _salpha and alpha _s^2alpha . We present predictions at 13 and 100 TeV, and provide results for the 8 TeV differential measurements performed by ATLAS and CMS. A thorough comparison of results obtained with the NNPDF2.3QED and CT14QED PDF sets is performed. While contributions due to the photon PDF are negligible with CT14QED, this is not the case for NNPDF2.3QED, where such contributions are sizeable and show large PDF uncertainties. On the one hand, we show that differential observables in top-pair production, in particular top-quark and tbar{t} rapidities, can be used to improve the determination of the photon PDF within the NNPDF approach. On the other hand, with current PDF sets, we demonstrate the necessity of including EW corrections and photon-induced contributions for a correct determination of both the central value and the uncertainties of theoretical predictions.

Global uncertainty analysis for RRKM/master equation based kinetic predictions: A case study of ethanol decomposition

A precise understanding of the accuracy of reaction rate constants, whether determined experimentally or theoretically, is of considerable importance to kinetic modelers. While the uncertainties of experimentally measured rate constants are commonly provided, the “error bars” of computed (temperature- and pressure-dependent) rate constants are rarely evaluated rigorously. In this work, global uncertainty and sensitivity analysis is applied to the propagation of the uncertainties in the input parameters (e.g. barrier heights, frequencies and collisional energy transfer parameters et al.) to those in the rate constants computed by the RRKM/master equation method for the decomposition of ethanol. This case study provides a systematic exploration of the effect of temperature and pressure on the parametric uncertainties in RRKM/master equation calculations for a prototypical single-well multiple-channel dissociation. In the high pressure limit, the uncertainties in the theoretical predictions are controlled by the uncertainties in the input parameters involved in the transition state theory calculations, with the most important ones being those describing the energetics of the decomposition. At lower pressures, where fall-off is important, the uncertainties in the collisional energy transfer parameters play a significant role, particularly for the higher energy of the two channels. Remarkably, the competition between dissociation and collisional excitation leads to uncertainties of more than a factor of 100 in the predictions for the higher energy channel. These large uncertainties are related to the need for large-scale single-collision-induced transitions in energy in order to produce the higher energy products in the low pressure limit. The present study illustrates the value of detailed qualitative and quantitative studies of the uncertainties in theoretical kinetics predictions.

Top quark forward-backward asymmetry in e+ e- annihilation at next-to-next-to-leading order in QCD.

We report on a complete calculation of electroweak production of top-quark pairs in e+ e- annihilation at next-to-next-to-leading order in quantum chromodynamics. Our setup is fully differential in phase space and can be used to calculate any infrared-safe observable. Especially we calculated the next-to-next-to-leading-order corrections to the top-quark forward-backward asymmetry and found sizable effects. Our results show a large reduction of the theoretical uncertainties in predictions of the forward-backward asymmetry, and allow for a precision determination of the top-quark electroweak couplings at future e+ e- colliders.

Higher order corrections and unification in the minimal supersymmetric standard model: SOFTSUSY3.5

We explore the effects of three-loop minimal supersymmetric standard model renormalisation group equation terms and some leading two-loop threshold corrections on gauge and Yukawa unification: each being one loop higher order than current public spectrum calculators. We also explore the effect of the higher order terms (often 2–3 GeV) on the lightest CP even Higgs mass prediction. We illustrate our results in the constrained minimal supersymmetric standard model. Neglecting threshold corrections at the grand unified scale, the discrepancy between the unification scale αs and the other two unified gauge couplings changes by 0.1% due to the higher order corrections and the difference between unification scale bottom-tau Yukawa couplings neglecting unification scale threshold corrections changes by up to 1%. The difference between unification scale bottom and top Yukawa couplings changes by a few percent. Differences due to the higher order corrections also give an estimate of the size of theoretical uncertainties in the minimal supersymmetric standard model spectrum. We use these to provide estimates of theoretical uncertainties in predictions of the dark matter relic density (which can be of order one due to its strong dependence on sparticle masses) and the LHC sparticle production cross-section (often around 30%). The additional higher order corrections have been incorporated into SOFTSUSY, and we provide details on how to compile and use the program. We also provide a summary of the approximations used in the higher order corrections. Program SummaryNature of problem: Calculating supersymmetric particle spectrum and mixing parameters in the minimal supersymmetric standard model. The solution to the renormalisation group equations must be consistent with boundary conditions on supersymmetry breaking parameters, as well as the weak-scale boundary condition on gauge couplings, Yukawa couplings and the Higgs potential parameters.Program title:SOFTSUSYCatalogue identifier: ADPM_v5_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADPM_v5_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 240528No. of bytes in distributed program, including test data, etc.: 2597933Distribution format: tar.gzProgramming language: C++, Fortran.Computer: Personal computer.Operating system: Tested on Linux 3.4.6.Word size: 64 bits.Classification: 11.1, 11.6.External routines: At least GiNaC1.3.5 [1] and CLN1.3.1 (both freely obtainable from http://www.ginac.de).Does the new version supersede the previous version?: YesCatalogue identifier of previous version: ADPM_v4_0Journal reference of previous version: Comput. Phys. Comm. 185 (2014) 2322Solution method: Nested iterative algorithm.Reasons for new version: Extension to include additional two and three-loop terms.Summary of revisions: All quantities in the minimal supersymmetric standard model are extended to have three-loop renormalisation group equations (including 3-family mixing) in the limit of real parameters and some leading two-loop threshold corrections are incorporated to the third family Yukawa couplings and the strong gauge coupling.Restrictions:SOFTSUSY will provide a solution only in the perturbative regime and it assumes that all couplings of the model are real (i.e. CP-conserving). If the parameter point under investigation is non-physical for some reason (for example because the electroweak potential does not have an acceptable minimum), SOFTSUSY returns an error message. The higher order corrections included are for the real R-parity conserving minimal supersymmetric standard model (MSSM) only.Running time: A minute per parameter point. The tests provided with the package only take a few seconds to run.

A meta-analysis of parton distribution functions

A "meta-analysis" is a method for comparison and combination of nonperturbative parton distribution functions (PDFs) in a nucleon obtained with heterogeneous procedures and assumptions. Each input parton distribution set is converted into a "meta-parametrization" based on a common functional form. By analyzing parameters of the meta-parametrizations from all input PDF ensembles, a combined PDF ensemble can be produced that has a smaller total number of PDF member sets than the original ensembles. The meta-parametrizations simplify the computation of the PDF uncertainty in theoretical predictions and provide an alternative to the 2010 PDF4LHC convention for combination of PDF uncertainties. As a practical example, we construct a META ensemble for computation of QCD observables at the Large Hadron Collider using the next-to-next-to-leading order PDF sets from CTEQ, MSTW, and NNPDF groups as the input. The META ensemble includes a central set that reproduces the average of LHC predictions based on the three input PDF ensembles and Hessian eigenvector sets for computing the combined PDF+$\alpha_s$ uncertainty at a common QCD coupling strength of 0.118.

Outer core compositional layering and constraints on core liquid transport properties

A variety of studies of the Earth's outer core report wave speeds near the top of the core slightly lower than reference models for core properties. One interpretation of the slower wavespeed profile is that it could represent a change in the core's light element concentration with depth in the core. I explore the consequences of this idea by interpreting the velocity profile as arising from diffusion gradients imposed in the outer core by various mechanisms. In order to estimate relative diffusion rates for light elements in liquid iron I also examine theories for transport properties of high pressure metallic liquids that are based on hard-sphere models. From the seismic wavespeed profile, an effective diffusivity may be obtained, which ranges from 0.1 to 10×10−7 m2s−1 depending on the particular boundary condition or initial condition chosen. The upper bound of the range is higher than expected from high pressure experiments and models of diffusivity in liquid metals for all elements except H. The lower bound is within the uncertainty of theoretical predictions and experimental determinations given the range of expected outer core temperatures if diffusion involves low Z elements. Plausible agreement arises from a class of models that represent diffusion out of a compositionally different layer existing from the time of the formation of the Earth. If the wavespeed profile in the core is diffusive in nature, the data suggest that it is an original feature of the core.

Theoretical uncertainties in inflationary predictions

With present and future observations becoming of higher and higher quality, it is timelyand necessary to investigate the most significant theoretical uncertainties in the predictionsof inflation. We show that our ignorance of the entire history of the universe, including thephysics of reheating after inflation, translates to considerable errors in observationally relevantparameters. Using the inflationary flow formalism, we estimate that for a spectral indexn and tensor/scalarratio r in the region favoured by current observational constraints, the theoretical errors are of orderΔn/|n−1| ∼ 0.1–1 and Δr/r ∼ 0.1–1. These errors represent the dominant theoretical uncertainties in the predictions ofinflation, and are generically of the order of or larger than the projected uncertainties infuture precision measurements of the cosmic microwave background. We also show that thelowest order classification of models into small field, large field and hybrid breaks downwhen higher order corrections to the dynamics are included. Models can flow from oneregion to another.

Short-range three-nucleon forces and low-energy constants

The $3N$ forces due to $\ensuremath{\pi}\text{\ensuremath{-}}\ensuremath{\rho},\ensuremath{\pi}\text{\ensuremath{-}}\ensuremath{\sigma}$, and $\ensuremath{\pi}\text{\ensuremath{-}}\ensuremath{\omega}$ exchanges following from the nucleon Born diagrams and diagrams with an intermediate ${N}^{*}(1440)$ are reanalyzed. The cancellation between $\ensuremath{\pi}\text{\ensuremath{-}}\ensuremath{\sigma}$ and $\ensuremath{\pi}\text{\ensuremath{-}}\ensuremath{\omega}$ forces is rather sensitive to the values of the coupling constants and to the form of the $\ensuremath{\pi}NN$ vertex. Experimental uncertainties in the parameters of the Tucson-Melbourne $\ensuremath{\pi}\text{\ensuremath{-}}\ensuremath{\pi}$ potential are assessed. They lead to uncertainties in theoretical predictions of the triton binding energy of about $\ifmmode\pm\else\textpm\fi{}0.4\phantom{\rule{0.3em}{0ex}}\text{MeV}$. The low-energy limit of $\ensuremath{\pi}\text{\ensuremath{-}}\ensuremath{\sigma}$ and $\ensuremath{\pi}\text{\ensuremath{-}}\ensuremath{\omega}$ potentials is performed. It defines the coupling constants of effective contact $\ensuremath{\pi}NNNN$ vertices, which are compared with the corresponding contact vertices of chiral perturbation theory.