Theoretical Uncertainties Research Articles

Differential toverline{t} cross-section measurements using boosted top quarks in the all-hadronic final state with 139 fb−1 of ATLAS data

Measurements of single-, double-, and triple-differential cross-sections are presented for boosted top-quark pair-production in 13 TeV proton–proton collisions recorded by the ATLAS detector at the LHC. The top quarks are observed through their hadronic decay and reconstructed as large-radius jets with the leading jet having transverse momentum (pT) greater than 500 GeV. The observed data are unfolded to remove detector effects. The particle-level cross-section, multiplied by the toverline{t}to WWboverline{b} branching fraction and measured in a fiducial phase space defined by requiring the leading and second-leading jets to have pT> 500 GeV and pT> 350 GeV, respectively, is 331 ± 3(stat.) ± 39(syst.) fb. This is approximately 20% lower than the prediction of {398}_{-49}^{+48} fb by Powheg+Pythia 8 with next-to-leading-order (NLO) accuracy but consistent within the theoretical uncertainties. Results are also presented at the parton level, where the effects of top-quark decay, parton showering, and hadronization are removed such that they can be compared with fixed-order next-to-next-to-leading-order (NNLO) calculations. The parton-level cross-section, measured in a fiducial phase space similar to that at particle level, is 1.94 ± 0.02(stat.) ± 0.25(syst.) pb. This agrees with the NNLO prediction of {1.96}_{-0.17}^{+0.02} pb. Reasonable agreement with the differential cross-sections is found for most NLO models, while the NNLO calculations are generally in better agreement with the data. The differential cross-sections are interpreted using a Standard Model effective field-theory formalism and limits are set on Wilson coefficients of several four-fermion operators.

Z′-boson dilepton searches and the high-x quark density

We study the influence of theoretical systematic uncertainties due to the quark density on LHC experimental searches for Z′-bosons. Using an approach originally proposed in the context of the ABMP16 PDF set for the high-x behaviour of the quark density, we present results on observables commonly used to study Z′ signals in dilepton channels.

Prospects for strong coupling measurement at hadron colliders using soft-drop jet mass

We compute the soft-drop jet-mass distribution from pp collisions to NNLL accuracy while including nonperturbative corrections through a field-theory based formalism. Using these calculations, we assess the theoretical uncertainties on an αs precision measurement due to higher order perturbative effects, nonperturbative corrections, and PDF uncertainty. We identify which soft-drop parameters are well-suited for measuring αs, and find that higher-logarithmic resummation has a qualitatively important effect on the shape of the jet-mass distribution. We find that quark jets and gluon jets have similar sensitivity to αs, and emphasize that experimentally distinguishing quark and gluon jets is not required for an αs measurement. We conclude that measuring αs to the 10% level is feasible now, and with improvements in theory a 5% level measurement is possible. Getting down to the 1% level to be competitive with other state-of-the-art measurements will be challenging.

Elimination of QCD Renormalization Scale and Scheme Ambiguities

The setting of the renormalization scale (μr) in the perturbative QCD (pQCD) is one of the crucial problems for achieving precise fixed-order pQCD predictions. The conventional prescription is to take its value as the typical momentum transfer Q in a given process, and theoretical uncertainties are then evaluated by varying it over an arbitrary range. The conventional scale-setting procedure introduces arbitrary scheme-and-scale ambiguities in fixed-order pQCD predictions. The principle of maximum conformality (PMC) provides a systematic way to eliminate the renormalization scheme-and-scale ambiguities. The PMC method has rigorous theoretical foundations; it satisfies the renormalization group invariance (RGI) and all of the self-consistency conditions derived from the renormalization group. The PMC has now been successfully applied to many physical processes. In this paper, we summarize recent PMC applications, including event shape observables and heavy quark pair production near the threshold region in e+e− annihilation and top-quark decay at hadronic colliders. In addition, estimating the contributions related to the uncalculated higher-order terms is also summarized. These results show that the major theoretical uncertainties caused by different choices of μr are eliminated, and the improved pQCD predictions are thus obtained, demonstrating the generality and applicability of the PMC.

Quark-hadron duality at work: lifetimes of bottom baryons

In the 1990s, very low experimental values for the lifetime ratio τ(Λb)/τ(Bd) triggered a considerable amount of doubt in the applicability of the heavy quark expansion (HQE), which is based on the assumption of quark-hadron duality (QHD) for inclusive total decay rates. However, these low values turned out to be the result of purely experimental problems, and the current HFLAV average reads τ(Λb)/τ(Bd) = 0.969(6). In this work, we present the Standard Model predictions for the b-baryon lifetimes within the framework of the HQE. In particular, we include for the first time the contribution of the Darwin term and we update the estimates for the matrix elements of the dimension-six four-quark operators. Within experimental and theoretical uncertainties, we find excellent agreement between the data and the HQE predictions, and thus no indication for any visible violation of QHD. Our numerical results can be summarised by the ratios τ(Λb)/τ(Bd) = 0.955(14), tau left({varOmega}_b^{-}right) /τ(Bd) = 1.081(42), and tau left({Xi}_b^0right)/tau left({Xi}_b^{-}right) = 0.929(28).

Neutrinoless ββ -decay nuclear matrix elements from two-neutrino ββ -decay data

We study two-neutrino ($2\nu\beta\beta$) and neutrinoless double-$\beta$ ($0\nu\beta\beta$) decays in the nuclear shell model and proton-neutron quasiparticle random-phase approximation (pnQRPA) frameworks. Calculating the decay half-life of several dozens of nuclei ranging from calcium to xenon with the shell model, and of $\beta\beta$ emitters with a wide range of proton-neutron pairing strengths in the pnQRPA, we observe good linear correlations between $2\nu\beta\beta$- and $0\nu\beta\beta$-decay nuclear matrix elements for both methods. We then combine the correlations with measured $2\nu\beta\beta$-decay half-lives to predict $0\nu\beta\beta$-decay matrix elements with theoretical uncertainties based on our systematic calculations. Our results include two-body currents and the short-range $0\nu\beta\beta$-decay operator.

Correlations between nuclear Schiff moment and electromagnetic measurements

We study the nuclear Schiff moments of 129Xe and 199Hg induced by the nucleon electric dipole moment using large-scale shell model calculations. For 129Xe, we find a linear relation between the leading-order contribution and magnetic moment, which would be useful in reducing the theoretical uncertainty. The conventional model space does not contain the 0g9/2 and 0h9/2 orbitals, which are connected to the spin-orbit partners by large matrix elements. Thus, to evaluate the influence of the relevant single-particle orbitals outside the conventional model space, we apply the quasiparticle vacua shell model method. Moreover, the next-to-leading-order contribution arises from parity and time-reversal violation in the nucleus. We demonstrate that these secondary effects do not induce any significant disturbance to the correlation. Additionally, we report the shell model results for the nuclear Schiff moment coefficients of 199Hg. Compared to previous studies, the results obtained in this study are rather large, indicating a higher sensitivity to the neutron electric dipole moment.

Non-local contribution from small scales in galaxy–galaxy lensing: comparison of mitigation schemes

ABSTRACT Recent cosmological analyses with large-scale structure and weak lensing measurements, usually referred to as 3 × 2pt, had to discard a lot of signal to noise from small scales due to our inability to accurately model non-linearities and baryonic effects. Galaxy–galaxy lensing, or the position–shear correlation between lens and source galaxies, is one of the three two-point correlation functions that are included in such analyses, usually estimated with the mean tangential shear. However, tangential shear measurements at a given angular scale θ or physical scale R carry information from all scales below that, forcing the scale cuts applied in real data to be significantly larger than the scale at which theoretical uncertainties become problematic. Recently, there have been a few independent efforts that aim to mitigate the non-locality of the galaxy–galaxy lensing signal. Here, we perform a comparison of the different methods, including the Y-transformation, the point-mass marginalization methodology, and the annular differential surface density statistic. We do the comparison at the cosmological constraints level in a combined galaxy clustering and galaxy–galaxy lensing analysis. We find that all the estimators yield equivalent cosmological results assuming a simulated Rubin Observatory Legacy Survey of Space and Time (LSST) Year 1 like set-up and also when applied to DES Y3 data. With the LSST Y1 set-up, we find that the mitigation schemes yield ∼1.3 times more constraining S8 results than applying larger scale cuts without using any mitigation scheme.

Theoretical Study of the d(d, p)^{3}H and d(d, n)^{3}He Processes at Low Energies.

We present a theoretical study of the processes d(d,p)^{3}H and d(d,n)^{3}He at energies of interest for energy production and for big-bang nucleosynthesis. We accurately solve the four body scattering problem using the abinitio hyperspherical harmonics method, starting from nuclear Hamiltonians which include modern two- and three-nucleon interactions, derived in chiral effective field theory. We report results for the astrophysical S factor, the quintet suppression factor, and various single and double polarized observables. A first estimate of the theoretical uncertainty for all these quantities is provided by varying the cutoff parameter used to regularize the chiral interactions at high momentum.

Impact of fluctuating initial conditions on bottomonium suppression in 5.02 TeV heavy-ion collisions

We compute bottomonium suppression and elliptic flow within the pNRQCD effective field theory using an open quantum systems approach. For the hydrodynamical background, we use 2+1D MUSIC second-order viscous hydrodynamics with IP-Glasma initial conditions and evolve bottom/antibottom quantum wave packets in real time in these backgrounds. We find that the impact of fluctuating initial conditions is small when compared to results obtained using smooth initial conditions. Including the effect of fluctuating initial conditions, we find that the Upsilon(1S) integrated elliptic flow is v_2[1S] = 0.005 +/- 0.002 +/- 0.001, with the first and second variations corresponding to statistical and systematic theoretical uncertainties, respectively.

Refined theoretical values of field and mass isotope shifts in thallium to extract charge radii of Tl isotopes.

Electronic factors for the field and mass isotope shifts in the 6p 2P3/2 → 7s 2S1/2 (535nm), 6p 2P1/2 → 6d 2D3/2 (277nm), and 6p 2P1/2 → 7s 2S1/2 (378nm) transitions in neutral thallium were calculated within the high-order relativistic coupled cluster approach. These factors were used to reinterpret previous experimental isotope shift measurements in terms of charge radii of a wide range of Tl isotopes. Good agreement between theoretical and experimental King-plot parameters was found for the 6p 2P3/2 → 7s 2S1/2 and 6p 2P1/2 → 6d 2D3/2 transitions. It was shown that the value of the specific mass shift factor for the 6p 2P3/2 → 7s 2S1/2 transition is not negligible compared with the value of normal mass shift in contrast to what had been suggested previously. Theoretical uncertainties in the mean square charge radii were estimated. They were substantially reduced compared with the previously ascribed ones and amounted to less than 2.6%. The achieved accuracy paves the way for a more reliable comparison of the charge radii trends in the lead region.

Approximate N^{3}LO parton distribution functions with theoretical uncertainties: MSHT20aN^3LO PDFs

We present the first global analysis of parton distribution functions (PDFs) at approximate N^{3}LO in the strong coupling constant alpha _{s}, extending beyond the current highest NNLO achieved in PDF fits. To achieve this, we present a general formalism for the inclusion of theoretical uncertainties associated with the perturbative expansion in the strong coupling. We demonstrate how using the currently available knowledge surrounding the next highest order (N^{3}LO) in alpha _{s} can provide consistent, justifiable and explainable approximate N^{3}LO (aN^{3}LO) PDFs. This includes estimates for uncertainties due the currently unknown N^{3}LO ingredients, but also implicitly some missing higher order uncertainties (MHOUs) beyond these. Specifically, we approximate the splitting functions, transition matrix elements, coefficient functions and K-factors for multiple processes to N^{3}LO. Crucially, these are constrained to be consistent with the wide range of already available information about N^{3}LO to match the complete result at this order as accurately as possible. Using this approach we perform a fully consistent approximate N^{3}LO global fit within the MSHT framework. This relies on an expansion of the Hessian procedure used in previous MSHT fits to allow for sources of theoretical uncertainties. These are included as nuisance parameters in a global fit, controlled by knowledge and intuition based prior distributions. We analyse the differences between our aN^{3}LO PDFs and the standard NNLO PDF set, and study the impact of using aN^{3}LO PDFs on the LHC production of a Higgs boson at this order. Finally, we provide guidelines on how these PDFs should be used in phenomenological investigations.

The Ages of Galactic Bulge Stars with Realistic Uncertainties

Using modern isochrones with customized physics and carefully considered statistical techniques, we recompute the age distribution for a sample of 91 microlensed dwarfs in the Galactic bulge presented by Bensby et al. and do not produce an age distribution consistent with their results. In particular, our analysis finds that only 15 of 91 stars have ages younger than 7 Gyr, compared to their finding of 42 young stars in the same sample. While we do not find a constituency of very young stars, our results do suggest the presence of an ∼8 Gyr population at the highest metallicities, thus contributing to the long-standing debate about the age–metallicity distribution of the Galactic bulge. We supplement this with attempts at independent age determinations from two sources of photometry, BDBS and Gaia, but find that the imprecision of photometric measurements prevents reliable age and age uncertainty determinations. Lastly, we present age uncertainties derived using a first-order consideration of global modeling uncertainties in addition to standard observational uncertainties. The theoretical uncertainties are based on the known variance of free parameters in the 1D stellar evolution models used to generate isochrones, and when included, result in age uncertainties of 2–5 Gyr for this spectroscopically well-constrained sample. These error bars, which are roughly twice as large as typical literature values, constitute realistic lower limits on the true age uncertainties.

Theoretical uncertainties count: parity violating asymmetry and dipole polarizability in 208Pb

In this contribution, we overview a recent theoretical work [1] where a sound statistical and systematic analysis based on nuclear Energy Density Functionals of the parity violating asymmetry and dipole polarizability in 208Pb has been presented. Based on our results, we predict a neutron skin thickness in 208Pb which barely overlaps the lower-edge of the estimation presented in [2] and is consistent with much of the previous work.

Toward the ultimate reach of current imaging atmospheric Cherenkov telescopes and their sensitivity to TeV dark matter

Indirect detection opens a unique window for probing thermal dark matter (DM): the same annihilation process that determined the relic abundance in the early Universe drives the present day astrophysical signal. While TeV-scale particles weakly coupled to the Standard Model face undoubted challenges from decades of null searches, the scenario remains compelling, and simple realizations such as Higgsino DM remain largely unexplored. The fate of such scenarios could be determined by gamma-ray observations of the centre of the Milky Way with Imaging Atmospheric Cherenkov Telescopes (IACTs). We consider the ultimate sensitivity of current IACTs to a broad range of TeV-scale DM candidates - including specific ones such as the Wino, Higgsino, and Quintuplet. To do so, we use realistic mock H.E.S.S.-like observations of the inner Milky Way halo, and provide a careful assessment of the impact of recent Milky Way mass modeling, instrumental and astrophysical background uncertainties in the Galactic Center region, and the theoretical uncertainty on the predicted signal. We find that the dominant systematic for IACT searches in the inner Galaxy is the unknown distribution of DM in that region, however, beyond this the searches are currently statistically dominated indicating a continued benefit from more observations. For two-body final states at $1~{\rm TeV}$, we find a H.E.S.S.-like observatory is sensitive to $\langle \sigma v \rangle \sim 3 \times 10^{-26}-4 \times 10^{-25}~{\rm cm}^3{\rm s}^{-1}$, except for neutrino final states, although we find results competitive with ANTARES. In addition, the thermal masses for the Wino and Quintuplet can be probed; the Higgsino continues to be out of reach by at least a factor of a few. Our conclusions are also directly relevant to the next generation Cherenkov Telescope Array, which remains well positioned to be the discovery instrument for thermal DM.

Introducing a novel event generator for electron-nucleus and neutrino-nucleus scattering

We present a novel lepton-nucleus event generator: ACHILLES, A CHIcagoLand Lepton Event Simulator. The generator factorizes the primary interaction from the propagation of hadrons in the nucleus, which allows for a great deal of modularity, facilitating further improvements and interfaces with existing codes. We validate our generator against high quality electron-carbon scattering data in the quasielastic regime, including the recent CLAS/e4v reanalysis of existing data. We find good agreement in both inclusive and exclusive distributions. By varying the assumptions on the propagation of knocked out nucleons throughout the nucleus, we estimate a component of theoretical uncertainties. We also propose novel observables that will allow for further testing of lepton-nucleus scattering models. ACHILLES is readily extendable to generate neutrino-nucleus scattering events.

What is ab initio in nuclear theory?

Ab initio has been used as a label in nuclear theory for over two decades. Its meaning has evolved and broadened over the years. We present our interpretation, briefly review its historical use, and discuss its present-day relation to theoretical uncertainty quantification.

Nuclear Equation of State for Arbitrary Proton Fraction and Temperature Based on Chiral Effective Field Theory and a Gaussian Process Emulator.

We calculate the equation of state of asymmetric nuclear matter at finite temperature based on chiral effective field theory interactions to next-to-next-to-next-to-leading order. Our results assess the theoretical uncertainties from the many-body calculation and the chiral expansion. Using a Gaussian process emulator for the free energy, we derive the thermodynamic properties of matter through consistent derivatives and use the Gaussian process to access arbitrary proton fraction and temperature. This enables a first nonparametric calculation of the equation of state in beta equilibrium, and of the speed of sound and the symmetry energy at finite temperature. Moreover, our results show that the thermal part of the pressure decreases with increasing densities.

Production of tensor glueball in ultraperipheral pp, AuAu and PbPb collisions

In this work, we discuss the production of a tensor glueball in the proton–proton and nuclei–nuclei ultraperipheral collisions (UPCs). The cross section is calculated in the equivalent photon approximation (EPA). The total UPCs cross section is related to the matrix elements of gamma gamma rightarrow pi ^0 G_2 process, which can be described in terms of the neutral pion and tensor glueball G_2’s distribution amplitudes. The predictions for the rapidity distributions of UPCs cross sections and total cross sections are presented. The theoretical uncertainty of the whole calculation is considered. We consider the decay modes of the final-state tensor glueball and estimate the corresponding number of events. We estimate that there are about 10 tensor glueball G_2rightarrow phi phi signal events in PbPb collisions at the LHC. We also argue that the lead–lead UPC experiments at future HE-LHC and FCC experiments will provide larger opportunities to measure tensor glueballs.

Low-energy positronium scattering from O2

The total cross section of positronium (Ps) scattering from molecular oxygen has been measured in the velocity range 0.27--1.50 a.u. (energy range 2--61 eV) and has been found to be close to the corresponding equivelocity electron cross section above 0.87 a.u. $(20\phantom{\rule{0.16em}{0ex}}\mathrm{eV})$, as previously found by Brawley et al., [Science 330, 789 (2010)]. However, below this value the cross section for positronium is observed to exceed that for electrons by up to a factor of 4 at the lowest energy. Measurements are compared to the predictions of low-energy resonant peaks in the elastic-scattering cross section calculated within a free-electron-gas model refined by applying corrections to the correlation energy for the interaction between Ps and the electron gas. Additionally, cross sections for ${\mathrm{O}}_{2}^{\ensuremath{-}}$ formation and positronium breakup have been calculated using a classical-trajectory Monte Carlo approach. Comparisons are made with earlier calculations and discussed in terms of both experimental and theoretical uncertainties.