I present the latest results on the theoretical cross section for top-antitop pair production as well as for single top production at the Tevatron and the LHC. The calculations include higher-order soft-gluon corrections which are dominant near threshold. The top quark transverse momentum distribution is also presented.
The charge asymmetry in hadronic top-antitop-quark production is a powerful test observable of perturbative quantum chromodynamics. Since its origin in terms of Feynman diagrams is distinct from charge-symmetric top-antitop production, probing the charge asymmetry provides complementary information to cross section measurements. Furthermore, asymmetric observables offer new ways to distinguish new physics beyond the standard model. This article summarizes prospects to investigate the top-quark charge asymmetry at the LHC in and beyond the standard model. Particular attention is given to observ…
The associated production of a Higgs boson with a top-antitop quark pair is a crucial process at the LHC since it allows for a direct measurement of the top-quark Yukawa coupling. We present the computation of the radiative corrections to this process at the next-to-next-to-leading order (NNLO) in QCD perturbation theory. This is the very first computation for a $2 \to 3$ process with massive coloured particles at this perturbative order. We develop a soft Higgs boson approximation for loop amplitudes, which enables us to reliably quantify the impact of the yet unknown two-loop contribution. A…
Several models predict the existence of heavy colored resonances decaying to top quarks in the TeV energy range that might be discovered at the LHC. In some of those models, moreover, a sizable charge asymmetry of top versus antitop quarks might be generated. The detection of these exotic resonances, however, requires selecting data samples where the top and the antitop quarks are highly boosted, which is experimentally very challenging. We asses that the measurement of the top quark charge asymmetry at the LHC is very sensitive to the existence of excited states of the gluon with axial-vector…
Recent measurements of the top quark charge asymmetry at Tevatron disfavor the existence of flavor universal axigluons and colorons at 2 sigmas. In this letter we explore the possibility to reconcile the data with these models and use the charge asymmetry and the invariant mass distribution of top-antitop quark pair events to constrain the mass and couplings of massive color-octet gauge bosons decaying to top quarks.
We perform a general parton level analysis for the search of heavy resonant states in the production of top-antitop pairs at the LHC with an integrated luminosity of 30 fb^-1. We assume the existence of resonances that only couple to quarks and propose kinematic cuts in order to increase the amount of events produced through quark-annihilation. We study the interplay between different variables and their impact on the purity of the selected sample. We make focus on the longitudinal ($β$) and transverse ($p_T$) momentum of the top-antitop pair, and the scattering angle ($θ$) in the center of ma…
We study the kinematic distributions of top--antitop quark pairs produced at the Tevatron, including the effects of initial state and final state multiple soft gluon emission, using the Collins--Soper--Sterman resummation formalism. The resummed results are compared with those predicted by the showering event generator PYTHIA for various distributions involving the top--antitop quark pair and the individual top quark or antiquark. The comparison between the experimental and predicted distributions will be a strong test of our understanding and application of perturbative QCD. Our results indic…
We propose selection cuts on the LHC top-antitop production sample which should enhance the sensitivity to New Physics signals in the study of the top-antitop invariant mass distribution. We show that selecting events in which the top-antitop object has little transverse and large longitudinal momentum enlarges the quark-fusion fraction of the sample and therefore increases its sensitivity to New Physics which couples to quarks and not to gluons. We find that systematic error bars play a fundamental role and assume a simple model for them. We check how a non-visible new particle would become v…
We present a determination of the strong coupling constant $α_s(m_Z)$ using inclusive top-quark pair production cross section measurements performed at the LHC and at the Tevatron. Following a procedure first applied by the CMS collaboration, we extract individual values of $α_s(m_Z)$ from measurements by different experiments at several centre-of-mass energies, using QCD predictions complete in NNLO perturbation theory, supplemented with NNLL approximations to all orders, and suitable sets of parton distribution functions. The determinations are then combined using a likelihood-based approach…
The dependence of the top-quark mass measurement in top-quark production on the parton distribution functions is explored through the differential distribution of the invariant mass of the top-antitop system in top-quark pair production at hadron colliders. Several different proton-proton collider options are considered: 8 TeV, 13 TeV, 13.6 TeV, 14 TeV, and 100 TeV. The top-quark mass is obtained from a chi-squared fit to the invariant mass of the top-antitop-quark pair. The parton distribution function uncertainties are used in the chi-square evaluation. The uncertainties are reduced through …
We present a calculation of the cross section for the process p pbar -> Zt' -> t tbar, the production of a Topcolor Z' with subsequent decay to top quark pairs in proton anti-proton collisions at 1.8 TeV. Variations of the cross section with varying assumptions about the model, the resonance width, the parton distributions and the renormalization scale are presented.
The searches for extra-dimensions, top resonances, 4th generation quarks and leptoquark signatures are presented. The results are based on proton-proton collision data for a center-of mass energy of7 or 8 TeV, corresponding to various integrated luminosities. No signal of physics beyond the Standard Model has been observed so far.
Selected topics of the top-quark mass measurements in well-defined schemes are presented. The measurements have been performed using data recorded with the ATLAS and CMS detectors at the LHC at proton-proton centre-of-mass energies of 7 and 8 TeV. Precision theoretical QCD calculations for both inclusive top-antitop quark pair production and top-antitop quark pair production with an additional jet to extract the top quark mass in the pole-mass scheme have been used.
We study the effects of the complete supersymmetric QCD and electroweak one-loop corrections to the ttbar forward-backward asymmetry at the Fermilab Tevatron collider. We work in the complex Minimal Supersymmetric Standard Model (MSSM), only restricted by the condition of minimal flavor violation (MFV). We perform a comprehensive scan over the relevant parameter space of the complex MFV-MSSM and determine the maximal possible contributions of these MSSM loop corrections to the forward-backward asymmetry in the ttbar center-of-mass frame.
We discuss the top-antitop production cross section near threshold at a future linear collider accounting for the NNLL QCD corrections to the anomalous dimension of the leading S-wave production current computed recently within renormalization-group-improved NRQCD perturbation theory. We argue that the still unknown soft NNLL mixing corrections are negligible so that the NNLL QCD corrections to the total cross section can be considered complete for practical purposes. Based on combined variations of the renormalization and matching scales and the overall size of the perturbative corrections we…
The PowHel framework allows to make predictions of total and differential cross-sections of multiparticle hadroproduction processes at both NLO QCD accuracy and NLO QCD matched to Parton Shower, on the basis of the interface between the POWHEG-BOX and HELAC-NLO codes. It has already been applied to study several processes involving a top-antitop pair in association with a third particle or hadronic jet. Our most recent predictions concern top-antitop-V hadroproduction (with V = W or Z), at both parton and hadron level, by considering different decay channels (hadronic and leptonic) of the heav…
The production of top-antitop pairs at the Fermilab Tevatron shows a forward-backward asymmetry in which the top quark tends to follow the proton direction, while the antitop tends to follow the antiproton direction. The effect grows with increasing effective mass $m_{t \bar t}$ of the top-antitop pair, and with increasing rapidity difference between the top and antitop. The observed effect is about three times as large as predicted by next-to-leading-order QCD, but with the same sign. An estimate of non-factorizable effects based on a QCD string picture finds they are negligible, but that sma…
The production of top-quark pairs that subsequently decay hadronically and leptonically (lepton+jets channel) is one of the key processes for the study of top-quark properties at the LHC. In this article, NLO QCD corrections of order $\mathcal{O}{\left(α_{\rm s}^3α^{4}\right)}$ to the hadronic process ${\rm p}{\rm p}\to μ^-\barν_μ{\rm b}\bar{\rm b} {\rm j} {\rm j}$ are presented. The computation includes off-shell as well as non-resonant contributions, and experimental event selections are used in order to provide realistic predictions. The results are provided in the form of cross sections an…
I present high-order calculations, including soft-gluon corrections, for single-top and top-antitop production cross sections and differential distributions. For single-top production, results are presented for the three different channels in the Standard Model, for associated production with a charged Higgs, and for processes involving anomalous couplings. For top-antitop pair production, total cross sections and top-quark transverse-momentum and rapidity distributions are presented for various LHC energies.
We propose a charged, electrically neutral, and flavour changing Z' model to conciliate the apparent disagreement between the important excess found in the top-antitop Tevatron forward-backward asymmetry and the null -compatible with negative- results found in the LHC charge asymmetry. We show that this model contributes positively to the forward-backward asymmetry, whereas naturally a new cancellation is turned on at the LHC, yielding a null, or even negative, charge asymmetry. We found the region in parameter space that is simultaneously allowed by the stringent Tevatron and LHC observables.…
We present the NNLO corrections to top pair production in the quark-antiquark channel proportional to the number of light quark flavors $N_l$. While the double real corrections were derived previously, here we compute the real-virtual and virtual-virtual contributions in this partonic channel. Using the antenna subtraction formalism, we show that the subtraction terms correctly approximate the real-virtual contributions in all their infrared limits. Combined with the integrated forms of the double real and real-virtual subtraction terms, we show analytically that the explicit infrared poles ca…
We study $bt\bar t$ production via subprocesses initiated by $b$-quarks at the Large Hadron Collider. Both QCD and electroweak interactions are included in the elementary scattering amplitudes for $bg\to b t\bar t$. Since the additional jet in the final state (arising from the bottom quark) is in most cases at very low transverse momentum and very high pseudorapidity, it tends to escape detection. Therefore, such a process can act as a background to double-top as well as to single-top channels exploited in top quark phenomenology at present and future hadron colliders. Furthermore, if the addi…
In the Randall-Sundrum model, we study top-antitop pair production and top spin correlations at the Large Hadron Collider. In addition to the Standard Model processes, there is a new contribution to the top-antitop pair production process mediated by graviton Kaluza-Klein modes in the s-channel. We calculate the density matrix for the top-antitop pair production including the new contribution. With a reasonable parameter choice in the Randall-Sundrum model, we find a sizable deviation of the top-antitop pair production cross section and the top spin correlations from those in the Standard Mode…
We perform a model-independent study for top-antitop and top-top resonances in the dilepton channel at the Large Hadtron Collider. In this channel, we can solve the kinematic system to obtain the momenta of all particles including the two neutrinos, and hence the resonance mass and spin. For discovering top-antitop resonances, the dilepton channel is competitive to the semileptonic channel because of the good resolution of lepton momentum measurement and small standard model backgrounds. Moreover, the charges of the two leptons can be identified, which makes the dilepton channel advantageous f…
We study top-antitop pair production and top spin correlations in a model with an electrically neutral massive gauge boson, Z', at the Large Hadron Collider. In addition to the Standard Model processes, the Z' contributes to the top-antitop pair production process in the s-channel. Choosing a kinematical region of top invariant mass around the Z' resonance pole, we find sizable deviations of the top-antitop pair production cross section and the top spin correlations from those of the Standard Model.
With the next start of LHC, a huge production of top quarks is expected. There are several models that predict the existence of heavy colored resonances decaying to top quarks in the TeV energy range. A peak in the differential cross section could reveal the existence of such a resonance, but this is experimentally challenging, because it requires selecting data samples where top and antitop quarks are highly boosted. Nonetheless, the production of such resonances might generate a sizable charge asymmetry of top versus antitop quarks. We consider a toy model with general flavour independent co…
We present results from the analytic calculation of top+antitop+Higgs hadronic production at Next-to-Leading Order in QCD interfaced with parton-shower Monte Carlo event generators in the POWHEG BOX framework. We consider kinematic distributions of the top quark and Higgs boson at the 8 TeV Large Hadron Collider and study the theoretical uncertainties due to specific choices of renormalization/factorization scales and parton-showering algorithms, namely PYTHIA and HERWIG. The importance of spin-correlations in the production and decay stages of a top/antitop quark is discussed on the example o…
We present an update to the NNLL RG-improved QCD prediction of top-antitop production in electron-positron annihilation at threshold. It includes for the first time a complete NNLL resummation of ultrasoft logarithms, which are dominant at this order and give a sizable correction. The renormalization scale dependence of the total resonance cross section decreases substantially compared to earlier predictions, where the ultrasoft logarithms were included only partially.
We study the top quark pair production process p+p(anti-p)-->top+antitop in various kinds of technicolor (TC) models at the Fermilab Tevatron Run II and the CERN LHC. The s-channel neutral pseudo-Goldstone bosons (PGB's) contribute dominately to the production amplitudes from its coupling to the gluons through the triangle loops of techniquarks and the top quark. Cross sections in different TC models with s-channel PGB contributions are calculated. It is shown that the PGB effects can be experimentally tested and different TC models under consideration can be distinguished at the LHC. Therefor…
We report on a calculation of the effects of supersymmetry on the cross-section for top-antitop production at LHC. A numerical study is carried out for the ten benchmarks of the Snowmass accord. It is found that the higher order effects involving supersymmetric particles in internal loops can be as high as 6%, both for the cross-section and the (parity even) helicity asymmetry, for one particular benchmark. For other benchmarks smaller but nonetheless observable corrections are found.
The LHC is the perfect environment for the study of new physics in the top quark sector. We study the possibility of detecting signals of heavy color-octet vector resonances, through the charge asymmetry, in top-antitop+jet events. Besides contributions with the top-antitop pair in a color-singlet state, the asymmetry gets also contributions which are proportional to the color factor f_{abc}^2. This process is particularly interesting for extra-dimensional models, where the inclusive charge asymmetry generated by Kaluza-Klein excitations of the gluon vanishes at the tree level. We find that th…
The associated production of top-antitop-bottom-antibottom quarks is a relevant irreducible background for Higgs boson analyses in the top-antitop-Higgs production channel, with Higgs decaying into a bottom-antibottom quark pair. We implement this process in the PowHel event generator, considering the bottom quarks as massive in all steps of the computation which involves hard-scattering matrix-elements in the 4-flavour number scheme combined with 4-flavour Parton Distribution Functions. Predictions with NLO QCD + Parton Shower accuracy, as obtained by PowHel + PYTHIA, are compared to those wh…
The status of the theoretical predictions for the top-anti top production in hadronic collisions is shortly reviewed, paying a articular attention to the analytic calculation of the two-loop QCD corrections to the parton-level matrix elements.
The recent developments on the computation of non-resonant corrections to the e+ e- -> W+ W- b bbar cross section in the top-antitop resonance region are reviewed in this talk. Non-resonant production of the final state W+ W- b bbar starts to contribute at NLO in the nonrelativistic power-counting v ~ alpha_s ~ sqrt(alpha_EW). The corrections induced by non-resonant effects reduce the cross section in the top-antitop resonance peak region at a level which is comparable to the expected experimental precision at the future linear collider, and are thus relevant for a high-precision top mass and …
We describe the off-diagonal spin basis for observing angular correlations in top quark pair production events at the Fermilab Tevatron. For events initiated by quark-antiquark annihilation, the top and antitop quark spins are 100% correlated in this basis: a spin-up top quark is always accompanied by a spin-down antitop quark and vice versa. Inclusion of the gluon-gluon initial state lowers the fraction of unlike spin events to 92%. Nevertheless, the angular correlations between the top and antitop quark decay products are twice as large in the off-diagonal basis as those in the more traditio…
We emphasize the role that the associated production of a Higgs boson with a pair of top-antitop quarks can play at present and future hadron colliders. Results of recent calculations of the NLO total cross section for the associated production of a Standard Model like Higgs boson with a pair of top-antitop quarks at the Tevatron (sqrt(s)=2 TeV) are presented.
I present a calculation of next-to-next-to-next-to-leading-order (NNNLO) soft-gluon corrections for top-antitop pair production in hadronic collisions. Approximate NNNLO (aNNNLO) results are obtained by adding the NNNLO soft-gluon corrections to the complete next-to-next-to-leading-order (NNLO) cross section. Theoretical predictions are shown for the total aNNNLO $t{\bar t}$ cross section at LHC and Tevatron energies. The aNNNLO cross sections are larger but have smaller theoretical uncertainties than at NNLO.
We compute the hadronic production of top-antitop pairs in association with a Higgs boson at next-to-leading-order QCD, including the decay of the top and antitop quark into bottom quarks and leptons. Our computation is based on full leading and next-to-leading-order matrix elements for $e^+ ν_e μ^-\barν_μb \bar{b} H(j)$ and includes all non-resonant contributions, off-shell effects and interferences. Numerical results for the integrated cross section and several differential distributions are given for the LHC operating at 13 TeV using a fixed and a dynamical factorization and renormalization…
The effects of the finite top quark width in the top pair production cross section close to the threshold are discussed in this talk. We introduce a $t\bar{t}$ cross section with a cut on the invariant masses of the top and antitop that can be calculated theoretically with effective field theory (EFT) methods. The matching procedure to implement the physical phase-space boundaries in the NRQCD framework (``phase-space matching'') is briefly outlined.
We present details of a calculation of the cross section for hadronic top-antitop production in next-to-leading order (NLO) QCD, including the decays of the top and antitop into bottom quarks and leptons. This calculation is based on matrix elements for νe e+ μ- \barν_μb\bar{b} production and includes all non-resonant diagrams, interferences, and off-shell effects of the top quarks. Such contributions are formally suppressed by the top-quark width and turn out to be small in the inclusive cross section. However, they can be strongly enhanced in exclusive observables that play an important role…
We present the results of the computation of the next-to-leading order QCD corrections to the production cross section of a Higgs boson in association with a top-antitop pair at the LHC, including the three relevant dimension-six operators ($O_{t φ}, O_{φG}, O_{tG}$) of the standard model effective field theory. These operators also contribute to the production of Higgs bosons in loop-induced processes at the LHC, such as inclusive Higgs, $Hj$ and $HH$ production, and modify the Higgs decay branching ratios for which we also provide predictions. We perform a detailed study of the cross section…
We consider two polarization asymmetries in the process of top-antitop production at LHC. We show that the theoretical predictions for these two quantities, at the strong and electroweak partonic one-loop level, are free of QCD and QED effects. At this perturbative level we derive two sum rules, that relate measurable quantities of top-antitop production to genuinely weak inputs. This would allow to perform two independent tests of the candidate theoretical model, with a precision that will be fixed by the future experimental accuracies of the different polarization measurements. A tentative q…
We present NLO electroweak corrections to Higgs production in association with off-shell top-antitop quark pairs. The full process $\text{p}\text{p}\to\text{e}^+ν_{\text{e}} μ^-\barν_μ\text{b}\bar{\text{b}} \text{H}$ is considered, and hence all interference, off-shell, and non-resonant contributions are taken into account. The electroweak corrections turn out to be below one per cent for the integrated cross section but can exceed $10\%$ in certain phase-space regions. In addition to its phenomenological relevance, the computation constitutes a major technical achievement as the full NLO virt…
Muon colliders are expected to naturally have a small spread in beam energy making them an ideal place to study the excitation curve. We present the parameter determinations that are possible from measuring the total cross section near threshold at a $μ^+μ^-$ collider.
We study the sensitivity of top-antitop samples produced at all energy stages of the Large Hadron Collider (LHC) to the nature of an underlying Z' boson, in presence of full tree level standard model (SM) background effects and relative interferences. We concentrate on differential mass spectra as well as both spatial and spin asymmetries thereby demonstrating that exploiting combinations of these observables will enable one to distinguish between sequential Z's and those pertaining to Left-Right symmetric models as well as E6 inspired ones, assuming realistic final state reconstruction effici…
Top-antitop pairs produced in the decay of a new heavy resonance will exhibit spin correlations that contain valuable coupling information. When the tops decay, these correlations imprint themselves on the angular patterns of the final quarks and leptons. While many approaches to the measurement of top spin correlations are known, the most common ones require detailed kinematic reconstructions and are insensitive to some important spin interference effects. In particular, spin-1 resonances with mostly-vector or mostly-axial couplings to top cannot be easily discriminated from one another witho…
At the LHC, top quark pairs are dominantly produced from gluons, making it difficult to measure the top quark forward-backward asymmetry. To improve the asymmetry measurement, we study variables that can distinguish between top quarks produced from quarks and those from gluons: the invariant mass of the top pair, the rapidity of the top-antitop system in the lab frame, the rapidity of the top quark in the top-antitop rest frame, the top quark polarization and the top-antitop spin correlation. We combine all the variables in a likelihood discriminant method to separate quark-initiated events fr…
We present numerical calculations of the production cross section of a heavy Z' resonance in hadron-hadron collisions with subsequent decay into top-antitop pairs. In particular, we consider the leptophobic topcolor Z' discussed under Model IV of hep-ph/9911288 which has predicted cross sections large enough to be experimentally accessible at the Fermilab Tevatron and the Large Hadron Collider at CERN. This article presents an updated calculation valid for the Tevatron and all proposed LHC collision energies. Cross sections are presented for various Z' widths, in p-pbar collisions at \sqrt{s}=…
In this talk electroweak corrections related to the finite top quark lifetime to the total top pair threshold e+e- cross section at NNLL order are discussed. We include the absorptive parts in electroweak matching conditions of the NRQCD operators related to the top decay and use the optical theorem. Gauge invariance is maintained. The corrections lead to ultraviolet phase space divergences and NLL mixing effects. The corrections can amount to several percent and are phenomenologically relevant.
Quantum field theory near thresholds of ultra-heavy particles is considered. We focus especially on the top-antitop and the stop-antistop systems. The question of the possible large corrections due to a running width of the top quark could be solved in this work. It was shown that a previously not considered contribution gives rise to large cancellations and leads especially to a gauge independent result. With the help of a new zero order equation and a Ward identity it was further possible to derive a general therorem for bound state corrections to the width. Furthermore a systematic derivati…
We compute the dominant term in the expansion in rho=1-M_W/m_t of the unknown next-to-next-to-leading order (NNLO) nonresonant contributions to the e+ e- -> W+ W- b bbar total cross section at energies close to the top-antitop threshold. Our analytic result disagrees with a previous calculation by other authors [1]. We show that our determination has the correct infrared structure needed to cancel the divergences proportional to the top width arising in the resonant production of the same final state, and we point out to a missing contribution in the computation of [1] to explain the discrepan…
We study the sensitivity of top pair production at the Large Hadron Collider (LHC) to the nature of an underlying Z' boson, including full tree level standard model background effects and interferences while assuming realistic final state reconstruction efficiencies. We demonstrate that exploiting asymmetry observables represents a promising way to distinguish between a selection of benchmark Z' models due to their unique dependences on the chiral couplings of the new gauge boson
Entanglement is a central subject in quantum mechanics. Due to its genuine relativistic behavior and fundamental nature, high-energy colliders are attractive systems for the experimental study of fundamental aspects of quantum mechanics. We propose the detection of entanglement between the spins of top-antitop-quark pairs at the LHC, representing the first proposal of entanglement detection in a pair of quarks, and also the entanglement observation at the highest energy scale so far. We show that entanglement can be observed by direct measurement of the angular separation between the leptons a…
We explore the sensitivity of the LHC at 14 TeV centre-of-mass energy (LHC14) to the single production and decay of top-antitop resonances in the four-top final state. We focus on the same-sign dilepton channel, and work within a simplified model with a vector boson coupling to the Standard Model only via its interactions with right-handed top quarks. We find it is possible to discover (exclude) such a vector boson with 300 fb$^{-1}$ of integrated luminosity up to a mass of 1.2 (1.6) TeV for a modest coupling to tops of $g_ρ$=2. We present our results as an exclusion limit on the cross-section…
We present the calculation of scalar and pseudoscalar Higgs production in association with a top-antitop pair to the next-to-leading order (NLO) accuracy in QCD, interfaced with parton showers according to the MC@NLO formalism. We apply our results to the cases of light and very light Higgs boson production at the LHC, giving results for total rates as well as for sample differential distributions, relevant to the Higgs, to the top quarks, and to their decay products. This work constitutes the first phenomenological application of aMC@NLO, a fully automated approach to complete event generatio…
We present the computation of the double real and real-virtual contributions to top-antitop pair production in the quark-antiquark channel at leading colour. The $q \bar q \to t \bar{t} g$ amplitudes contributing to the real-virtual part are computed with OpenLoops, and their numerical stability in the soft and collinear regions is found to be sufficiently high to perform a realistic NNLO calculation in double precision. The subtraction terms required at real-real and real-virtual levels are constructed within the antenna subtraction formalism extended to deal with the presence of coloured mas…
The process e+e- -> Htt can be exploited at future Linear Colliders to measure the Higgs-top Yukawa coupling. In this note, we estimate the size of the irreducible backgrounds in the channel Htt -> bbbb WW -> bbbb ln qq, for the case of a Standard Model Higgs boson with mass between 100 and 140 GeV.
We consider the top-antitop invariant mass distributions for production of unpolarized and polarized top quark pairs at LHC, in the theoretical framework of the MSSM. Assuming a "moderately" light SUSY scenario, we derive the leading logarithmic electroweak contributions at one loop in a region of large invariant mass, $M_{t\bar t}\simeq1$ TeV, for the unpolarized differential cross section $dσ/dM_{t\bar t}$ and for the differential longitudinal top polarization asymmetry $A_t(M_{t\bar t})$. We perform a realistic evaluation of the expected uncertainties of the two quantities, both from a theo…