arXiv subjects

André H. Hoang

Publications and source records attributed to André H. Hoang.

At least 19 recordsLinked to original sources

arXiv2025

Nonperturbative Corrections to Soft Drop Jet Mass

We provide a quantum field theory based description of the nonperturbative effects from hadronization for soft drop groomed jet mass distributions using the soft-collinear effective theory and the coherent branching formalism. There are two distinct regions of jet mass $m_J$ where grooming modifies hadronization effects. In a region with intermediate $m_J$ an operator expansion can be used, and the leading power corrections are given by three universal nonperturbative parameters that are independent of all kinematic variables and grooming parameters, and only depend on whether the parton initiating the jet is a quark or gluon. The leading power corrections in this region cannot be described by a standard normalized shape function. These power corrections depend on the kinematics of the subjet that stops soft drop through short distance coefficients, which encode a perturbatively calculable dependence on the jet transverse momentum, jet rapidity, and on the soft drop grooming parameters $z_{\rm cut}$ and $β$. Determining this dependence requires a resummation of large logarithms, which we carry out at LL order. For smaller $m_J$ there is a nonperturbative region described by a one-dimensional shape function that is unusual because it is not normalized to unity, and has a non-trivial dependence on $β$.

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arXiv2025

Matching Hadronization and Perturbative Evolution: The Cluster Model in Light of Infrared Shower Cutoff Dependence

In the context of Monte Carlo (MC) generators with parton showers that have next-to-leading-logarithmic (NLL) precision, the cutoff $Q_0$ terminating the shower evolution should be viewed as an infrared factorization scale so that parameters or non-perturbative effects of the MC generator may have a field theoretic interpretation with a controllable scheme dependence. This implies that the generator's parton level should be carefully defined within QCD perturbation theory with subleading order precision. Furthermore, it entails that the shower cut $Q_0$ is not treated as one of the generator's tuning parameters, but that the tuning can be carried out reliably for a range of $Q_0$ values and that the hadron level description is $Q_0$-invariant. This in turn imposes non-trival constraints on the behavior of the generator's hadronization model, so that its parameters can adapt accordingly when the $Q_0$ value is changed. We investigate these features using the angular ordered parton shower and the cluster hadronization model implemented in the Herwig~7.2 MC generator focusing in particular on the $e^+e^-$ 2-jettiness distribution, where the shower is known to be NLL precise and where QCD factorization imposes stringent constraints on the hadronization corrections. We show that the Herwig default cluster hadronization model does not exhibit these features or consistency with QCD factorization with a satisfying precision. We design a modification of the cluster hadronization model, where some dynamical parton shower aspects are added that are missing in the default model. For this novel dynamical cluster hadronization model these features and consistency with QCD factorization are realized much more accurately.

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arXiv2024

Three-Loop OPE Wilson Coefficients of Dimension-Four Operators for (Axial-)Vector and (Pseudo-)Scalar Current Correlators

We calculate the three-loop Wilson coefficients of all physically relevant dimension-four operators, i.e. $G_{μν}^a G^{a,μν}$, $m_i\bar q_j q_j$ and $m_i m_j m_k^2$, in the short-distance expansion of the time-ordered product of a pair of gauge-singlet vector, axial-vector, scalar and pseudo-scalar currents. The results are given for a general non-Abelian gauge theory with arbitrary (compact semi-simple) gauge group and $n_f$ light fermion flavors (quarks) in a common arbitrary representation of the gauge group, which includes QCD as a special case. In particular, we allow for arbitrary flavor contents of each of the currents. For the axial-vector current the included contributions from so-called singlet diagrams are consistent with the one-loop axial anomaly.

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arXiv2024

Determining $α_s(m_Z)$ from Thrust with Power Corrections

We update and extend a previous N$^3$LL$^\prime$+${\cal O}(α_s^3)$ strong coupling determination from thrust data. In particular, we carry out a fit with data fully restricted to the dijet region seeking to minimize the potential impact of power corrections that go beyond dijet configurations. In addition, we parametrize deviations from the dijet power correction in order to add an additional source of uncertainty in the result for $α_s(m_Z)$. We also show that the inclusion of resummation is important to achieve stability with respect to varying the fit region.

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arXiv2024

Beyond the Narrow-Width Limit for Off-Shell and Boosted Differential Top Quark Decays

The standard approaches for describing top quark production and its decay dynamics are currently mostly either based on the narrow-width (NW) limit or on off-shell fixed-order calculations. In this article we present a factorised approach for boosted top quarks that combines the properties of the NW limit and off-shell computations accounting for the dominant off-shell effects in an expansion in $m_t/Q$ with the hard scattering scale $Q$. We discuss the key ideas of our approach and show some preliminary results at tree-level.

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arXiv2023

Top Quark Mass Calibration for Monte Carlo Event Generators -- An Update

We generalize and update our former top quark mass calibration framework for Monte Carlo (MC) event generators based on the $e^+e^-$ hadron-level 2-jettiness $τ_2$ distribution in the resonance region for boosted $t\bar t$ production, that was used to relate the PYTHIA 8.205 top mass parameter $m_t^{\rm MC}$ to the MSR mass $m_t^{\rm MSR}(R)$ and the pole mass $m_t^{\rm pole}$. The current most precise direct top mass measurements specifically determine $m_t^{\rm MC}$. The updated framework includes the addition of the shape variables sum of jet masses $τ_s$ and modified jet mass $τ_m$, and the treatment of two more gap subtraction schemes to remove the ${\cal O}(Λ_{\rm QCD})$ renormalon related to large-angle soft radiation. These generalizations entail implementing a more versatile shape-function fit procedure and accounting for a certain type of $(m_t/Q)^2$ power corrections to achieve gap-scheme and observable independent results. The theoretical description employs boosted heavy-quark effective theory (bHQET) at next-to-next-to-logarithmic order (N$^2$LL), matched to soft-collinear effective theory (SCET) at N$^2$LL and full QCD at next-to-leading order (NLO), and includes the dominant top width effects. Furthermore, the software framework has been modernized to use standard file and event record formats. We update the top mass calibration results by applying the new framework to PYTHIA 8.205, HERWIG 7.2 and SHERPA 2.2.11. Even though the hadron-level resonance positions produced by the three generators differ significantly for the same top mass parameter $m_t^{\rm MC}$ value, the calibration shows that these differences arise from the hadronization modeling. Indeed, we find that $m_t^{\rm MC}$ agrees with $m_t^{\rm MSR}(1\,\mbox{GeV})$ within $200$ MeV for the three generators and differs from the pole mass by $350$ to $600$ MeV.

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arXiv2023

Mathematical Aspects of the Asymptotic Expansion in Contour Improved Perturbation Theory for Hadronic Tau Decays

Recently, it was demonstrated that the discrepancy between the fixed-order (FOPT) and contour-improved (CIPT) perturbative expansions for $τ$-lepton decay hadronic spectral function moments, which had been affecting the precision of $α_s$ determinations for many years, is related to the CIPT expansion being inconsistent with the standard formulation of the operator product expansion (OPE). Even though the problem can be alleviated phenomenologically for the most part by employing a renormalon-free scheme for the gluon-condensate matrix element, the principal inconsistency of CIPT remains. The CIPT expansion is special because it is not a power expansion, but represents an asymptotic expansion in a sequence of functions of the strong coupling. In this article we provide a closer look at the mathematical aspects of the asymptotic sequence of the functions the CIPT method is based on, and we expose the origin of the CIPT inconsistency as well as the reasons for its apparent good convergence at low orders. Our results are of general interest, and may in particular provide a useful tool to check for the consistency of expansion methods that are similar to CIPT.

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arXiv2023

Two-Loop Massive Quark Jet Functions in SCET

We calculate the $\mathcal O(α_s^2)$ corrections to the primary massive quark jet functions in Soft-Collinear Effective Theory (SCET). They are an important ingredient in factorized predictions for inclusive jet mass cross sections initiated by massive quarks emerging from a hard interaction with smooth quark mass dependence. Due to the effects coming from the secondary production of massive quark-antiquark pairs there are two options to define the SCET jet function, which we call universal and mass mode jet functions. They are related to whether or not a soft mass mode (zero) bin subtraction is applied for the secondary massive quark contributions and differ in particular concerning the infrared behavior for vanishing quark mass. We advocate that a useful alternative to the common zero-bin subtraction concept is to define the SCET jet functions through subtractions related to collinear-soft matrix elements. This avoids the need to impose additional power counting arguments as required for zero-bin subtractions. We demonstrate how the two SCET jet function definitions may be used in the context of two recently developed factorization approaches to treat secondary massive quark effects. We clarify the relation between these approaches and in which way they are equivalent. Our two-loop calculation involves interesting technical subtleties related to spurious rapidity divergences and infrared regularization in the presence of massive quarks.

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arXiv2022

Reconciling the Contour-Improved and Fixed-Order Approaches for $τ$ Hadronic Spectral Moments II: Renormalon Norm and Application in $α_s$ Determinations

In a previous article, we have shown that the discrepancy between the fixed-order (FOPT) and contour-improved (CIPT) perturbative expansions for $τ$ hadronic spectral function moments, which had affected the precision of $α_s$ determinations for many years, may be reconciled by employing a renormalon-free (RF) scheme for the gluon condensate (GC) matrix element. In addition, the perturbative convergence of spectral function moments with a sizeable GC correction can be improved. The RF GC scheme depends on an IR factorization scale $R$ and the normalization $N_g$ of the GC renormalon. In the present work, we use three different methods to determine $N_g$, yielding a result with an uncertainty of $40\%$. Following two recent state-of-the-art strong coupling determination analyses at ${\cal O}(α_s^5)$, we show that using the renormalon-free GC scheme successfully reconciles the results for $α_s({m_τ^2})$ based on CIPT and FOPT. The uncertainties due to variations of $R$ and the uncertainty of $N_g$ only lead to a small or moderate increase of the final uncertainty of $α_s(m_τ^2)$, and affect mainly the CIPT expansion method. The FOPT and CIPT results obtained in the RF GC scheme may be consistently averaged. The RF GC scheme thus constitutes a powerful new ingredient for future analyses of $τ$ hadronic spectral function moments.

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arXiv2022

Inclusive $τ$ Hadronic Decay Rate in a Renormalon-Free Gluon Condensate Scheme

In a recent work by some of us it was shown that the long-standing discrepancy between the QCD perturbation series for the inclusive hadronic tau decay rate computed in the CIPT and FOPT expansion approaches can be understood from the fact that CIPT has an infrared (IR) sensitivity that it not compatible with the standard form of the operator production expansion (OPE). For concrete IR renormalon models for the QCD Adler function the resulting CIPT-FOPT discrepancy, the asymptotic separation, can be calculated analytically from the Borel representation of the CIPT series expansion. If the known perturbative corrections for the QCD Adler function at the 5-loop level already have a sizeable contribution from the asymptotic behavior related to the gluon condensate (GC) renormalon, the asymptotic separation is dominated by that renormalon. This implies that the CIPT expansion can be reconciled with FOPT, when a renormalon-free scheme for the GC is adopted. In this talk we discuss such a renormalon-free scheme for the GC, which involves perturbative subtractions in analogy to using short-distance quark mass schemes instead of the pole mass. Using a concrete realistic high-order Borel model for the Adler function consistent with the known corrections up to 5 loops and containing a sizeable GC renormalon contribution, we show that the CIPT-FOPT discrepancy can be avoided when switching to the renormalon-free GC scheme. At the same time, the perturbative convergence of $τ$ hadronic spectral funtion moments strongly sensitive to the GC OPE corrections is considerably improved. We show that these improvements may lead to higher precision for strong coupling determinations.

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arXiv2022

Borel Representation of $τ$ Hadronic Spectral Function Moments in Contour-Improved Perturbation Theory

We show that the Borel representations of tau hadronic spectral function moments based on contour-improved perturbation theory (CIPT) in general differ from those obtained within fixed-order perturbation theory (FOPT) in the presence of IR renormalons in the underlying Adler function. The Borel sums obtained from both types of Borel representations in general differ as well, and the apparently conflicting behavior of the FOPT and CIPT spectral function moment series at intermediate orders, which has been subject to many studies in the past literature, can be understood quantitatively using concrete Borel function models. The difference between the CIPT and FOPT Borel sums, which we call the "asymptotic separation", can be computed analytically for any Borel function model and is proportional to inverse exponential terms in the strong coupling. Even though moments can be designed where the asymptotic separation is strongly suppressed, it is as a matter of principle unavoidable. If the Borel function of the Euclidean Adler function has a sizeable gluon condensate renormalon cut, the asymptotic separation can explain the observed disparity of the CIPT and FOPT spectral function moments at the 5-loop level. The existence of the asymptotic separation implies that the power corrections in the operator product expansion for the spectral function moments in the CIPT expansion approach do not have the commonly assumed analytic standard form.

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arXiv2021

On the Difference between FOPT and CIPT for Hadronic Tau Decays

In this article we review the results of our recent work on the difference between the Borel representations of tau hadronic spectral function moments obtained with the CIPT and FOPT methods. For the presentation of the theoretical results we focus on the large-$β_0$ approximation, where all expressions can be written down in closed form, and we comment on the generalization to full QCD. The results may explain the discrepancy in the behavior of the FOPT and CIPT series that has been the topic of intense discussions in previous literature and which represents a major part of the theoretical uncertainties in current strong coupling determinations from hadronic tau decays. The findings also imply that the OPE corrections for FOPT and CIPT differ and that the OPE corrections for CIPT do not have standard form.

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arXiv2021

Boosted Top Quarks in the Peak Region with N$^3$LL Resummation

We present results for the 2-jettiness differential distribution for boosted top quark pairs produced in $e^+e^-$ collisions in the peak region accounting for QCD large-logarithm resummation at next-to-next-to-next-to-leading logarithmic (N$^3$LL) order and fixed-order corrections to matrix elements at next-to-next-to-leading order (NNLO) calculated in the framework of soft-collinear effective theory and boosted heavy quark effective theory. Electroweak and finite-width effects are included at leading order. We study the perturbative convergence of the cross section in the pole and MSR mass schemes, with and without soft gap subtractions. We find that there is a partial cancellation between the pole mass and soft function renormalons. When renormalon subtractions concerning the top mass and the soft function are implemented, the perturbative uncertainties are, however, systematically smaller and an improvement in the stability of the peak position is observed. We find that the top MSR mass may be determined with perturbative uncertainties well below $100$\,MeV from the peak position of the 2-jettiness distribution. This result has important applications for Monte Carlo top quark mass calibrations.

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arXiv2020

What is the Top Quark Mass?

In this review I give an overview on the conceptual issues involved in the question how to interpret so-called `direct top quark mass measurements', which are based on the kinematic reconstruction of top quark decay products at the Large Hadron Collider (LHC). These measurements quote the top mass parameter $m_t^{\rm MC}$ of Monte-Carlo event generators with current uncertainties of around $0.5$ GeV. At present time the problem of finding a rigorous relation between $m_t^{\rm MC}$ and top mass renormalization schemes defined in field theory is unresolved and touches perturbative as well as nonperturbative aspects and the limitations of state-of-the-art Monte-Carlo event generators. I review the status of LHC top mass measurements, illustrate how conceptual limitations enter and explain a controversy that has permeated the community in the context of the interpretation problem. Recent advances in acquiring first principle insights are summarized, and it is outlined what else has to be understood to fully resolve the issue. For the time being, I give a recommendation how to deal with the interpretation problem when making top mass dependent theoretical predictions.

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arXiv2018

On the Cutoff Dependence of the Quark Mass Parameter in Angular Ordered Parton Showers

We show that the presence of an infrared cutoff $Q_0$ in the parton shower (PS) evolution for massive quarks implies that the generator quark mass corresponds to a $Q_0$-dependent short-distance mass scheme and is therefore not the pole mass. Our analysis considers an angular ordered parton shower based on the coherent branching formalism for quasi-collinear stable heavy quarks and splitting functions at next-to-leading logarithmic (NLL) order, and it is based on the analysis of the peak of hemisphere jet mass distributions. We show that NLL shower evolution is sufficient to describe the peak jet mass at full next-to-leading order (NLO). We determine the relation of this short-distance mass to the pole mass at NLO. We also show that the shower cut $Q_0$ affects soft radiation in a universal way for massless and quasi-collinear massive quark production. The basis of our analysis is (i) an analytic solution of the PS evolution based on the coherent branching formalism, (ii) an implementation of the infrared cut $Q_0$ of the angular ordered shower into factorized analytic calculations in the framework of Soft-Collinear-Effective-Theory (SCET) and (iii) the dependence of the peak of the jet mass distribution on the shower cut. Numerical comparisons to simulations with the HERWIG 7 event generator confirm our findings. Our analysis provides an important step towards a full understanding concerning the interpretation of top quark mass measurements based on direct reconstruction.

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arXiv2018

On the Light Massive Flavor Dependence of the Top Quark Mass

We provide a systematic renormalization group formalism to study the mass effects in the relation of the pole mass and short-distance masses such as the $\overline{\mathrm{MS}}$ mass of a heavy quark $Q$, coming from virtual loop insertions of massive quarks lighter than $Q$ with the main focus on the top quark. The formalism reflects the constraints from heavy quark symmetry and entails a combined matching and evolution procedure that allows to disentangle and successively integrate out the corrections coming from the lighter massive quarks and the momentum regions between them and also to precisely control the large order asymptotic behavior. The formalism is used to study the asymptotic behavior of light massive flavor contributions and is applied to predict the ${\cal O}(α_s^4)$ virtual quark mass corrections, calculate the pole mass differences for massive quark flavors with a precision of around 20 MeV, and determine the pole mass ambiguity which amounts to 250 MeV in the physical case of three massless quark flavors.

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arXiv2018

Monte Carlo Top Quark Mass Calibration

The most precise top quark mass measurements use kinematic reconstruction methods, determining the top mass parameter of a Monte Carlo event generator, $m_t^{\rm MC}$. Due to the complicated interplay of hadronization and parton shower dynamics in Monte Carlo event generators relevant for kinematic reconstruction, relating $m_t^{\rm MC}$ to field theory masses is a non-trivial task. In this talk we report on a calibration procedure to determine this relation using hadron level QCD predictions for 2-Jettiness in $e^+e^-$ annihilation, an observable which has kinematic top mass sensitivity and a close relation to the invariant mass of the particles coming from the top decay. The theoretical ingredients of the QCD prediction are reviewed. Fitting $e^+e^-$ 2-Jettiness calculations at NLL/NNLL order to PYTHIA 8.205, we find that $m_t^{\rm MC}$ agrees with the MSR mass $m_{t,1\,{\rm GeV}}^{\rm MSR}$ within uncertainties. At NNLL we find $m_t^{\rm MC} = m_{t,1\,{\rm GeV}}^{\rm MSR} + (0.18 \pm 0.22)\,{\rm GeV}$. $m_t^{\rm MC}$ can differ from the pole mass $m_t^{\rm pole}$ by up to $600\,{\rm MeV}$, and using the pole mass generally leads to larger uncertainties. At NNLL we find $m_t^{\rm MC} = m_t^{\rm pole} + (0.57 \pm 0.28)\,{\rm GeV}$ as the fit result. In contrast, converting $m_{t,1\,{\rm GeV}}^{\rm MSR}$ obtained at NNLL to the pole mass gives a result for $m_t^{\rm pole}$ that is substantially larger and incompatible with the fit result. We also explain some theoretical aspects relevant for employing the C-parameter as an alternative calibration observable.

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arXiv2015

A Precise Determination of $α_s$ from the C-parameter Distribution

We present a global fit for $α_s(m_Z)$, analyzing the available C-parameter data measured at center-of-mass energies between $Q=35$ and $207$ GeV. The experimental data is compared to a N$^3$LL$^\prime$ + $\mathcal{O}(α_s^3)$ + $Ω_1$ theoretical prediction (up to the missing 4-loop cusp anomalous dimension), which includes power corrections coming from a field theoretical nonperturbative soft function. The dominant hadronic parameter is its first moment $Ω_1$, which is defined in a scheme which eliminates the $\mathcal{O}(Λ_{\rm QCD})$ renormalon ambiguity. The resummation region plays a dominant role in the C-parameter spectrum, and in this region a fit for $α_s(m_Z)$ and $Ω_1$ is sufficient. We find $α_s(m_Z)=0.1123\pm 0.0015$ and $Ω_1=0.421\pm 0.063\,{\rm GeV}$ with $χ^2/\rm{dof}=0.988$ for $404$ bins of data. These results agree with the prediction of universality for $Ω_1$ between thrust and C-parameter within 1-$σ$.

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