Theoretical Uncertainties Research Articles

Statistical patterns of theory uncertainties

A comprehensive uncertainty estimation is vital for the precision program of the LHC. While experimental uncertainties are often described by stochastic processes and well-defined nuisance parameters, theoretical uncertainties lack such a description. We study uncertainty estimates for cross-section predictions based on scale variations across a large set of processes. We find patterns similar to a stochastic origin, with accurate uncertainties for processes mediated by the strong force, but a systematic underestimate for electroweak processes. We propose an improved scheme, based on the scale variation of reference processes, which reduces outliers in the mapping from leading order to next-to-leading-order in perturbation theory.

Probing the delay time of supermassive black hole binary mergers with gravitational waves

ABSTRACT Merging supermassive black hole binaries are expected as a consequence of galaxy mergers, yet the detailed evolution path and underlying merging mechanisms of these binaries are still subject to large theoretical uncertainties. In this work, we propose to combine the (future) gravitational wave measurements of supermassive black hole binary merger events with the galaxy merger rate distributions from galaxy surveys/cosmological simulations, to infer the delay time of binary mergers, as a function of binary mass. The delay time encodes key information about binary evolution, which can be used to test the predictions of various evolution models. With a Mock data set of supermassive black hole binary merger events, we discuss how to infer the distribution of delay time with hierarchical Bayesian inference and test evolution models with the Bayesian model selection method. The astrophysical model uncertainties are also considered in the hierarchical Bayesian inference and Bayesian model selection.

Muon capture on the deuteron in chiral effective field theory

We consider the capture of a muon on a deuteron. An uncertainty analysis of the dominant channels is important for a careful analysis of forthcoming experimental data. We quantify the theoretical uncertainties of chiral effective-field-theory predictions of the muon-deuteron capture rate from the relevant neutron-neutron partial wave channels in the final state. We study the dependence on the cutoff used to regularize the interactions, low-energy constants calibrated using different fitting data and strategies, and truncation of the effective-field-theory expansion of the currents. Combining these approaches gives as an estimate of ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\mu}d}^{1/2}=399.1\ifmmode\pm\else\textpm\fi{}7.6\ifmmode\pm\else\textpm\fi{}4.4\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ for capture from the atomic doublet state, and ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\mu}d}^{3/2}=12.31\ifmmode\pm\else\textpm\fi{}0.47\ifmmode\pm\else\textpm\fi{}0.04\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ for capture from the quartet state and the first and second uncertainties given here are due to the effective field theory truncation error and the uncertainty in the axial radius, respectively.

Minihalos as probes of the inflationary spectrum:accurate boost factor calculation and new CMB constraints

Although the spectrum of primordial fluctuations has been accurately measured on scales above ∼ 0.1 Mpc, only upper limits exist on smaller scales. In this study, we investigate generic monochromatic enhancements to the ΛCDM spectrum that trigger the collapse of ultracompact minihalos (UCMHs) well before standard structure formation. We refine previous treatments by considering a mixed population of halos with different density profiles, that should realistically arise as a consequence of late-time accretion and mergers. Assuming that dark matter (DM) can self-annihilate, we find, as expected, that UCMHs can greatly enhance the annihilation rate around recombination, significantly imprinting the cosmic microwave background (CMB) anisotropies. However, we provide additional insight on the theoretical uncertainties that currently impact that boost and which may affect late-time probes such as the 21 cm line or γ-ray signals. We derive constraints on the primordial power spectrum on small scales using the ExoCLASS/HYREC codes and the Planck legacy data. We account for the velocity dependence of the DM annihilation cross-section (s- or p-wave), annihilation channel, the DM particle mass and the inclusion of late-time halo mergers. Our s-wave constraints are competitive with previous literature, excluding primordial amplitudes \U0001d49c*≳ 10-6.5 at wavenumbers k ∼ 104 - 107 Mpc-1. For the first time, we highlight that even p-wave processes have constraining power on the primordial spectrum for cross-sections still allowed by currently the strongest astrophysical constraints. Finally, we provide an up-to-date compilation of the most stringent limits on the primordial power spectrum across a wide range of scales.

Theoretical uncertainties of (d,$$^{3}$$He) and ($$^{3}$$He,d) reactions owing to the uncertainties of optical model potentials

Theoretical uncertainties of (d,$$^{3}$$He) and ($$^{3}$$He,d) reactions owing to the uncertainties of optical model potentials

Constraining the gravitational-wave spectrum from cosmological first-order phase transitions using data from LIGO-Virgo first three observing runs

We search for a first-order phase transition (PT) gravitational wave (GW) signal from Advanced LIGO and Advanced Virgo's first three observing runs. Due to the large theoretical uncertainties, four shapes of GW energy spectral from bubble and sound wave collisions widely adopted in literature are investigated, separately. Our results indicate that there is no evidence for the existence of such GW signals, and therefore we give the upper limits on the amplitude of GW energy spectrum Ωpt(f *) in the peak frequency range of f * ∈ [5,500] Hz for these four theoretical models, separately. We find that Ωpt(f * ≃ 40 Hz) < 1.3 × 10-8 at 95% credible level, and roughly H */β ≲ 0.1 and α ≲ 1 at 68% credible level in the peak frequency range of 20 ≲ f * ≲ 100 Hz corresponding to the mostsensitive frequency band of Advanced LIGO and Advanced Virgo's first three observing runs, where H * is the Hubble parameter when PT happens, β is the bubble nucleation rate and α is the normalized latent heat.

Observational constraint from the heaviest pulsar PSR J0952-0607 on the equation of state of dense matter in relativistic mean field model

In the present work, we constrain the equation of state of dense matter in the context of heaviest observed neutron-star mass ${M}_{\mathrm{max}}=(2.35\ifmmode\pm\else\textpm\fi{}0.17){M}_{\ensuremath{\bigodot}}$ for the black widow pulsar PSR J0952-0607. We propose three interactions HPU1, HPU2 and HPU3 (named after Himachal Pradesh University) for the relativistic mean-field model, which include different combinations of nonlinear, self-couplings, and cross couplings among isoscalar-scalar $\ensuremath{\sigma}$, and isoscalar-vector $\ensuremath{\omega}$ and isovector-vector $\ensuremath{\rho}$ meson fields up to the quartic order. These interactions are in harmony with the finite nuclei and bulk nuclear matter properties. The equations of state computed by using newly generated interactions for the $\ensuremath{\beta}$-equilibrated nucleonic matter satisfy the heaviest observed neutron-star mass ${M}_{\mathrm{max}}=(2.35\ifmmode\pm\else\textpm\fi{}0.17){M}_{\ensuremath{\bigodot}}$ for the black widow pulsar PSR J0952-0607. The results for the radius ${R}_{1.4}$ and dimensionless tidal deformability ${\mathrm{\ensuremath{\Lambda}}}_{1.4}$ corresponding to the canonical mass are also presented and agree well with the GW170817 event and astrophysical observations. The radius of $2.08{M}_{\ensuremath{\bigodot}}$ neutron-star mass is predicted to be in the range ${R}_{2.08}=12.98$--13.09 km which also satisfy the NICER observations by Miller et al. [Astrophys. J. Lett. 918, L28 (2021)] and Riley et al. [Astrophys. J. Lett. 918, L27 (2021)]. A covariance analysis is also performed to assess the theoretical uncertainties of model parameters and to determine their correlations with nuclear matter observables.

Study of exclusive two-body W decays with fully reconstructible kinematics

In the framework of electroweak theory and perturbative quantum chromodynamics, we examine various exclusive decay channels of [Formula: see text] bosons that can be fully or partially reconstructed. Our findings provide predictions for the partial widths and address some gaps in previous literature. We also place a strong emphasis on understanding and estimating the associated theoretical uncertainties.

Branching fraction of the decay B+ → π+τ+τ− and lepton flavor universality test via the ratio Rπ(τ/μ)

Among (semi)leptonic rare B-decays induced by the b→d flavor changing neutral current, the decay B+→π+μ+μ− is the only one observed so far experimentally. Related decays involving the e+e− and τ+τ− pairs are the targets for the ongoing experiments at the LHC, in particular LHCb, and Belle II. The muonic and electronic semileptonic decays have almost identical branching fractions in the Standard Model (SM). However, the tauonic decay B+→π+τ+τ− differs from the other two due to the higher reaction threshold which lies slightly below the ψ(2S)-resonance. We present calculations of the ditauon (τ+τ−) invariant-mass distribution and the branching fraction Br(B+→π+τ+τ−) in the SM based on the Effective Electroweak Hamiltonian approach, taking into account also the so-called long-distance contributions. The largest theoretical uncertainty in the short-distance part of the decay rates is due to the B→π form factors, which we quantify using three popular parametrizations. The long-distance contribution can be minimized by a cut on the ditauon mass mτ+τ−>Mψ(2S). Once available, the branching fractions in the tauonic and muonic (and electronic) modes provide stringent test of the lepton flavor universality in the b→d transitions. We illustrate this by calculating the ratio Rπ(τ/μ)≡Br(B+→π+τ+τ−)/Br(B+→π+μ+μ−) in the SM for the total and binned ratios of the branching fractions.

Computational budget optimization for Bayesian parameter estimation in heavy-ion collisions

Bayesian parameter estimation provides a systematic approach to compare heavy-ion collision models with measurements, leading to constraints on the properties of nuclear matter with proper accounting of experimental and theoretical uncertainties. Aside from statistical and systematic model uncertainties, interpolation uncertainties can also play a role in Bayesian inference, if the model’s predictions can only be calculated at a limited set of model parameters. This uncertainty originates from using an emulator to interpolate the model’s prediction across a continuous space of parameters. In this work, we study the trade-offs between the emulator (interpolation) and statistical uncertainties. We perform the analysis using spatial eccentricities from the TRENTo model of initial conditions for nuclear collisions. Given a fixed computational budget, we study the optimal compromise between the number of parameter samples and the number of collisions simulated per parameter sample. For the observables and parameters used in the present study, we find that the best constraints are achieved when the number of parameter samples is slightly smaller than the number of collisions simulated per parameter sample.

Warm giant exoplanet characterisation: current state, challenges and outlook

The characterisation of giant exoplanets is crucial to constrain giant planet formation and evolution theory and for putting the solar-system’s giant planets in perspective. Typically, mass-radius (M-R) measurements of moderately irradiated warm Jupiters are used to estimate the planetary bulk composition, which is an essential quantity for constraining giant planet formation, evolution and structure models. The successful launch of the James Webb Space Telescope (JWST) and the upcoming ARIEL mission open a new era in giant exoplanet characterisation as atmospheric measurements provide key information on the composition and internal structure of giant exoplanets. In this review, we discuss how giant planet evolution models are used to infer the planetary bulk composition, and the connection between the compositions of the interior and atmosphere. We identify the important theoretical uncertainties in evolution models including the equations of state, atmospheric models, chemical composition, interior structure and main energy transport processes. Nevertheless, we show that atmospheric measurements by JWST and ARIEL and the accurate determination of stellar ages by PLATO can significantly reduce the degeneracy in the inferred bulk composition. Furthermore, we discuss the importance of evolution models for the characterisation of direct-imaged planets. We conclude that giant planet theory has a critical role in the interpretation of observation and emphasise the importance of advancing giant planet theory.

CREX- and PREX-II-motivated relativistic interactions and their implications for the bulk properties of nuclear matter and neutron stars

We investigate the implications of parity-violating electron scattering experiment on neutron skin thickness of $^{48}\mathrm{Ca}$ [calcium radius experiment (CREX)] and $^{208}\mathrm{Pb}$ [lead radius experiment (PREX-II)] data on the bulk properties of finite nuclei, nuclear matter, and neutron stars. The neutron skin thickness from the CREX and PREX-II data is employed to constrain the parameters of relativistic mean-field models which includes different nonlinear, self- and cross-couplings among isoscalar-scalar $\ensuremath{\sigma}$, isoscalar-vector $\ensuremath{\omega}$, isovector-scalar $\ensuremath{\delta}$, and isovector-vector $\ensuremath{\rho}$ meson fields up to the quartic order. Three parametrizations of RMF model are proposed by fitting CREX, PREX-II, and both CREX as well as PREX-II data to assess their implications. A covariance analysis is performed to assess the theoretical uncertainties of model parameters and nuclear matter observables along with correlations among them. The RMF model parametrization obtained with the CREX data acquires much smaller value of symmetry energy ($J=28.97\ifmmode\pm\else\textpm\fi{}0.99$ MeV) and its slope parameter ($L=30.61\ifmmode\pm\else\textpm\fi{}6.74$ MeV) in comparison to those obtained with PREX-II data. The neutron star properties are studied by employing the equations of state composed of nucleons and leptons in $\ensuremath{\beta}$ equilibrium.

The nucleon-induced deuteron breakup process as a laboratory for chiral dynamics

The nucleon-induced deuteron breakup reaction is studied within the Faddeev approach at incoming nucleon laboratory energies of 135 and 200 MeV. The chiral semilocal momentum-space (SMS) potential developed up to N4LO+, supplemented by the N2LO three-nucleon interaction, is used. Our investigation is focused on the determination of theoretical uncertainties in a predicted cross section related to its dependence on the value of the cutoff parameter of the regulator. We also compare predictions based on the complete N2LO potential with those based on the two-nucleon force upgraded to the N4LO+ order and augmented with the N2LO three-nucleon force. In addition, we study the three-nucleon force effects predicted by this model of interaction. Our systematic study covers the entire kinematically allowed phase space; however, our main results are obtained when additional restrictions on energies and cross section values are imposed. In such a case, we observe that the dependence of the differential cross sections on the regulator cutoff is moderate at 135 MeV and much stronger at 200 MeV. For the latter energy, it can amount to up to 45% in specific kinematic configurations. Taking into account terms beyond, N2LO in a two-body interaction changes the cross section up to 20% (27%) at E = 135(200) MeV. The inclusion of the three-nucleon force leads to effects of approximately 27% at both energies. We illustrate these dependencies with a few examples of the exclusive cross section as a function of the arc length of the S-curve.

Optical potentials for the rare-isotope beam era

We review recent progress and motivate the need for further developments in nuclear optical potentials that are widely used in the theoretical analysis of nucleon elastic scattering and reaction cross sections. In regions of the nuclear chart away from stability, which represent a frontier in nuclear science over the coming decade and which will be probed at new rare-isotope beam facilities worldwide, there is a targeted need to quantify and reduce theoretical reaction model uncertainties, especially with respect to nuclear optical potentials. We first describe the primary physics motivations for an improved description of nuclear reactions involving short-lived isotopes, focusing on its benefits for fundamental science discoveries and applications to medicine, energy, and security. We then outline the various methods in use today to build optical potentials starting from phenomenological, microscopic, and ab initio methods, highlighting in particular, the strengths and weaknesses of each approach. We then discuss publicly-available tools and resources facilitating the propagation of recent progresses in the field to practitioners. Finally, we provide a set of open challenges and recommendations for the field to advance the fundamental science goals of nuclear reaction studies in the rare-isotope beam era. This paper is the outcome of the Facility for Rare Isotope Beams Theory Alliance (FRIB-TA) topical program ‘Optical Potentials in Nuclear Physics’ held in March 2022 at FRIB. Its content is non-exhaustive, was chosen by the participants and reflects their efforts related to optical potentials.

NNLO QCD predictions for Z-boson production in association with a charm jet within the LHCb fiducial region

We compute next-to-next-to-leading order (NNLO) QCD corrections to neutral vector boson production in association with a charm jet at the LHC. This process is studied in the forward kinematics at sqrt{s}=13 TeV, which may provide valuable constraints on the intrinsic charm component of the proton. A comparison is performed between fixed order and NLO predictions matched to a parton shower showing mutual compatibility within the respective uncertainties. NNLO corrections typically lead to a reduction of theoretical uncertainties by a factor of two and the perturbative convergence is further improved through the introduction of a theory-inspired constraint on the transverse momentum of the vector boson plus jet system. A comparison between these predictions with data will require an alignment of a flavour-tagging procedure in theory and experiment that is infrared and collinear safe.

Cross Sections for Coherent Elastic and Inelastic Neutrino-Nucleus Scattering

The prospects of extracting new physics signals in coherent elastic neutrino–nucleus scattering (CEνNS) processes are limited by the precision with which the underlying nuclear structure physics, embedded in the weak nuclear form factor, is known. We present calculations of charge and weak nuclear form factors and CEνNS cross sections on 12C, 16O, 40Ar, 56Fe and 208Pb nuclei. We obtain the proton and neutron densities, and charge and weak form factors by solving Hartree–Fock (HF) equations with a Skyrme (SkE2) nuclear potential. We validate our approach by comparing 208Pb and 40Ar charge form factor predictions with available elastic electron scattering data. Since CEνNS experiments at stopped-pion sources are also well suited to measure inelastic charged–current and neutral–current neutrino–nucleus cross sections, we also present calculations for these processes, incorporating a continuum Random Phase Approximation (CRPA) description on top of the HF–SkE2 picture of the nucleus. Providing both coherent as well as inelastic cross sections in a consistent framework, we aim at obtaining a reliable and detailed comparison of the strength of these processes in the energy region below 100 MeV. Furthermore, we attempt to gauge the level of theoretical uncertainty pertaining to the description of the 40Ar form factor and CEνNS cross sections by comparing relative differences between recent microscopic nuclear theory and widely-used phenomenological form factor predictions. Future precision measurements of CEνNS will potentially help in constraining these nuclear structure details that will in turn improve prospects of extracting new physics.

Lund multiplicity in QCD jets

We compute the average Lund multiplicity of high-energy QCD jets. This extends an earlier calculation, done for event-wide multiplicity in e+e− collisions [1], to the large energy range available at the LHC. Our calculation achieves next-to-next-to-double logarithmic (NNDL) accuracy. Our results are split into a universal collinear piece, common to the e+e− calculation, and a non-universal large-angle contribution. The latter amounts to 10–15% of the total multiplicity. We provide accurate LHC predictions by matching our resummed calculation to fixed-order NLO results and by incorporating non-perturbative corrections via Monte Carlo simulations. Including NNDL terms leads to a 50% reduction of the theoretical uncertainty, with non-perturbative corrections remaining below 5% down to transverse momentum scales of a few GeV. This proves the suitability of Lund multiplicities for robust theory-to-data comparisons at the LHC.

Jet-veto resummation at N3LLp + NNLO in boson production processes

Vetoing energetic jet activity is a crucial tool for suppressing backgrounds and enabling new physics searches at the LHC, but the introduction of a veto scale can introduce large logarithms that may need to be resummed. We present an implementation of jet-veto resummation for color-singlet processes at the level of N3LLp matched to fixed-order NNLO predictions. Our public code MCFM allows for predictions of a single boson, such as Z/γ*, W± or H, or with a pair of vector bosons, such as W+W−, W±Z or ZZ. The implementation relies on recent calculations of the soft and beam functions in the presence of a jet veto over all rapidities, with jets defined using a sequential recombination algorithm with jet radius R. However one of the ingredients that is required to reach full N3LL accuracy is only known approximately, hence N3LLp. We describe in detail our formalism and compare with previous public codes that operate at the level of NNLL. Our higher-order predictions improve significantly upon NNLL calculations by reducing theoretical uncertainties. We demonstrate this by comparing our predictions with ATLAS and CMS results.

Determination of the top-quark mass from top-quark pair events with the matrix element method at next-to-leading order: Potential and prospects

In 2004 the matrix element method was used in a pioneering work by the Tevatron experiment D0 to determine the top-quark mass from a handful of events. Since then the method has been matured into a powerful analysis tool. While the first applications were restricted to leading-order accuracy, in the meantime also the extension to next-to-leading order (NLO) accuracy has been studied. In this article we explore the potential of the matrix element method at NLO to determine the top-quark mass using events with pair-produced top quarks. We simulate a toy experiment by generating unweighted events with a fixed input mass and apply the matrix element method to construct an estimator for the top-quark mass. Two different setups are investigated: unweighted events obtained from the fixed-order cross section at NLO accuracy as well as events obtained using POWHEG matched to a parton shower. The latter lead to a more realistic simulation and allow to study the impact of higher-order corrections as well as the robustness of the approach. We find that the matrix element method in NLO accuracy leads to a significant reduction of the theoretical uncertainties compared to leading order. In view of the high luminosity phase of the LHC, this observation is especially relevant in analyses which are no longer dominated by statistical uncertainties.

Assessing theoretical uncertainties for cosmological constraints from weak lensing surveys

ABSTRACT Weak gravitational lensing is a powerful probe, which is used to constrain the standard cosmological model and its extensions. With the enhanced statistical precision of current and upcoming surveys, high-accuracy predictions for weak lensing statistics are needed to limit the impact of theoretical uncertainties on cosmological parameter constraints. For this purpose, we present a comparison of the theoretical predictions for the non-linear matter and weak lensing power spectra, based on the widely used fitting functions ($\texttt {mead}$ and $\texttt {rev-halofit}$ ), emulators ($\texttt {EuclidEmulator}$ , $\texttt {EuclidEmulator2}$ , $\texttt {BaccoEmulator}$ , and $\texttt {CosmicEmulator}$ ), and N-body simulations (pkdgrav3). We consider the forecasted constraints on the $\Lambda \texttt {CDM}$ and $\texttt {wCDM}$ models from weak lensing for stage III and stage IV surveys. We study the relative bias on the constraints and their dependence on the assumed prescriptions. Assuming a $\Lambda \texttt {CDM}$ cosmology, we find that the relative agreement on the S8 parameter is between 0.2 and 0.3σ for a stage III-like survey between the above predictors. For a stage IV-like survey the agreement becomes 1.4–3.0σ. In the $\texttt {wCDM}$ scenario, we find broader S8 constraints, and agreements of 0.18–0.26σ and 0.7–1.7σ for stage III and stage IV surveys, respectively. The accuracies of the above predictors therefore appear adequate for stage III surveys, whereas the fitting functions would need improvements for future stage IV surveys. Furthermore, we find that, of the fitting functions, $\texttt {mead}$ provides the best agreement with the emulators. We discuss the implication of these findings for the preparation of future weak lensing surveys, and the relative impact of theoretical uncertainties to other systematics.