Higher-order Perturbative Corrections Research Articles

Heavy quarks in polarised deep-inelastic scattering at the electron-ion collider

We extend the FONLL general-mass variable-flavour-number scheme to the case of longitudinally polarised DIS structure functions, accounting for perturbative corrections up to Oαs2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}\\left( \\alpha _s^2\\right) $$\\end{document}. We quantify the impact of charm quark mass and higher-order perturbative corrections on projected measurements of inclusive and charm-tagged longitudinal asymmetries at the Electron-Ion Collider (EIC) and at the Electron-ion collider in China (EicC). We demonstrate how the inclusion of these corrections is essential to compute predictions with an accuracy that matches the projected precision of the measurements. The computation is made publicly available through the open-source EKO and YADISM programs.

Quantum control of tunable-coupling transmons using dynamical invariants of motion

We analyze the implementation of a fast nonadiabatic CZ gate between two transmon qubits with tunable coupling. The gate control method is based on a theory of dynamical invariants which leads to reduced leakage and robustness against decoherence. The gate is based on a description of the resonance between the and using an effective Hamiltonian with the six lowest energy states. A modification of the protocol allows us to take into account the higher-order perturbative corrections of this effective model. This enables a gate fidelity several orders of magnitude higher than other quasiadiabatic protocols, with gate times that approach the theoretical limit.

Unpolarized transverse momentum distributions from a global fit of Drell-Yan and semi-inclusive deep-inelastic scattering data

We present an extraction of unpolarized transverse-momentum-dependent parton distribution and fragmentation functions based on more than two thousand data points from several experiments for two different processes: semi-inclusive deep-inelastic scattering and Drell-Yan production. The baseline analysis is performed using the Monte Carlo replica method and resumming large logarithms at N3LL accuracy. The resulting description of the data is very good (χ2/Ndat = 1.06). For semi-inclusive deep-inelastic scattering, predictions for multiplicities are normalized by factors that cure the discrepancy with data introduced by higher-order perturbative corrections.

Mass-derivative relations and unitarity constraints for CP asymmetries at finite temperature

Within the seesaw type-I leptogenesis, we formulate CPT and unitarity constraints for the equilibrium reaction rate CP asymmetries and consider thermal mass and quantum statistics. We demonstrate that including higher-order perturbative corrections in the classical Boltzmann equation remarkably induces quantum effects into the kinetic theory.

Logarithmic corrections for jet production at the LHC

Several important processes and analyses at the LHC are sensitive to higher-order perturbative corrections beyond what can currently be calculated at fixed order. One important class of logarithmic corrections are those which appear when the centre-of-mass energy of a QCD collision is much larger than the transverse momenta of the observed jets. We describe the High Energy Jets (HEJ) framework, which includes the dominant high-energy logarithms to provide all-order predictions for several LHC processes including Higgs, W, or Z boson production in association with jets. We will summarise some recent developments, in particular the first matching of HEJ to a NLO calculation.

Measurement of the production cross section of pairs of isolated photons in pp collisions at 13 TeV with the ATLAS detector

A measurement of prompt photon-pair production in proton-proton collisions at sqrt{s} = 13 TeV is presented. The data were recorded by the ATLAS detector at the LHC with an integrated luminosity of 139 fb−1. Events with two photons in the well-instrumented region of the detector are selected. The photons are required to be isolated and have a transverse momentum of {p}_{mathrm{T}{,}_{gamma 1(2)}} > 40 (30) GeV for the leading (sub-leading) photon. The differential cross sections as functions of several observables for the diphoton system are measured and compared with theoretical predictions from state-of-the-art Monte Carlo and fixed-order calculations. The QCD predictions from next-to-next-to-leading-order calculations and multi-leg merged calculations are able to describe the measured integrated and differential cross sections within uncertainties, whereas lower-order calculations show significant deviations, demonstrating that higher-order perturbative QCD corrections are crucial for this process. The resummed predictions with parton showers additionally provide an excellent description of the low transverse-momentum regime of the diphoton system.

Determination of alpha _{S} beyond NNLO using event shape averages

We consider a method for determining the QCD strong coupling constant using fits of perturbative predictions for event shape averages to data collected at the LEP, PETRA, PEP and TRISTAN colliders. To obtain highest accuracy predictions we use a combination of perturbative {{{mathcal {O}}}}(alpha _{S}^{3}) calculations and estimations of the {{{mathcal {O}}}}(alpha _{S}^{4}) perturbative coefficients from data. We account for non-perturbative effects using modern Monte Carlo event generators and analytic hadronization models. The obtained results show that the total precision of the alpha _{S} determination cannot be improved significantly with the higher-order perturbative QCD corrections alone, but primarily requires a deeper understanding of the non-perturbative effects.

Simultaneous extraction of fragmentation functions of light charged hadrons with mass corrections

Achieving the highest possible precision for theoretical predictions at the present and future high-energy lepton and hadron colliders requires a precise determination of fragmentation functions (FFs) of light and heavy charged hadrons from a global QCD analysis with great accuracy. We describe a simultaneous determination of unpolarized FFs of charged pions, charged kaons and protons/antiprotons from single-inclusive hadron production in electron-positron annihilation (SIA) data at next-to-leading order and next-to-next-to-leading order accuracy in perturbative QCD. A new set of FFs, called SGKS20, is presented. We include data for identified light charged hadrons (${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$, ${K}^{\ifmmode\pm\else\textpm\fi{}}$ and $p/\overline{p}$) as well as for unidentified light charged hadrons, ${h}^{\ifmmode\pm\else\textpm\fi{}}$ and show that these data have a significant impact on both size and uncertainties of the fragmentation functions. We examine the inclusion of higher-order perturbative QCD corrections and finite-mass effects. We compare the new SGKS20 FFs with other recent FFs available in the literature and find in general reasonable agreement, but also important differences for some parton species. We show that theoretical predictions obtained from our new FFs are in very good agreement with the analyzed SIA data, especially at small values of $z$. The SGKS20 FF sets presented in this work are available via the LHAPDF interface.

Accurate single- and double-differential resummation of colour-singlet processes with MATRIX+RADISH: W+W\u2212 production at the LHC

We present the combination of fully differential cross sections for colour-singlet production processes at next-to-next-to-leading order (NNLO) QCD obtained with Matrix and all-order resummation through RadISH. This interface allows us to achieve unprecedented accuracy for various transverse observables in 2 → 2 production processes. As an important application we consider W+W− production at the LHC, more precisely the full leptonic process pp → {mathrm{ell}}^{+}mathrm{ell}{prime}^{-}{nu}_{mathrm{ell}}{overline{nu}}_{mathrm{ell}prime } + X with ℓ′ ≠ ℓ, and we present resummed predictions for differential distributions in presence of fiducial selection cuts. In particular, we resum the transverse-momentum spectrum of the W+W− pair at next-to-next-to-next-to-leading logarithmic (N3LL) accuracy and match it to the integrated NNLO cross section. The transverse-momentum spectrum of the leading jet in W+W− production is calculated at NNLO+NNLL accuracy. Finally, the joint resummation for the transverse-momentum spectrum of the W+W− pair in the presence of a jet veto is performed at NNLO+NNLL. Our phenomenological study highlights the importance of higher-order perturbative and logarithmic corrections for precision phenomenology at the LHC.

A note on higher-order perturbative corrections to squirming speed in weakly viscoelastic fluids

Many microorganisms swim in fluids with complex rheological properties. Although much is now understood about motion of these swimmers in Newtonian fluids, the understanding is still developing in non-Newtonian fluids—this understanding is crucial for various biomimetic and biomedical applications. Here we study a common model for microswimmers, the squirmer model, in two common viscoelastic fluid models, the Giesekus fluid model and fluids of differential type (grade three), at zero Reynolds number. Through this article we address a recent commentary that discussed suitable values of parameters in these models and pointed at higher-order viscoelastic effects on squirming motion.

Monte Carlo explicitly correlated many-body Green's function theory.

A highly scalable stochastic algorithm is proposed and implemented for computing the basis-set-incompleteness correction to the diagonal, frequency-independent self-energy of the second-order many-body Green's function (GF2) theory within the explicitly correlated (F12) formalism. The 6-, 9-, 12-, and 15-dimensional integrals comprising the F12 correction are directly evaluated by the Monte Carlo method using appropriate weight functions for importance sampling. The method is naturally and easily parallelized, involves minimal memory space and no disk I/O, and can use virtually any mathematical form of a correlation factor. Its computational cost to correct all ionization energies (IEs) is observed to increase as the fourth power of system size, as opposed to the fifth power in the case of the deterministic counterparts. The GF2 calculations and their F12 corrections for the first IEs of C60 and C70 were executed on 128 graphical processing units (GF2) and 896 central processing units (F12), respectively, to reach the results with statistical errors of 0.04 eV or less. They showed that the basis-set-incompleteness (from aug-cc-pVDZ) accounts for only 50%-60% of the deviations from experiments, suggesting the significance of higher-order perturbation corrections.

Analytical Method for Next-to-Leading-Order QCD Corrections to Double-Higgs Production.

We propose a new method to calculate analytically higher-order perturbative corrections and we apply it to the calculation of the two-loop virtual corrections to Higgs pair production through gluon fusion. The method is based on the expansion of the amplitudes in terms of a small Higgs transverse momentum. This approach gives a very good approximation (better than per mille) of the partonic cross section in the center-of-mass energy region sqrt[s[over ^]]≲750 GeV, where ∼95% of the total hadronic cross section is concentrated. The presented method is general and can be applied in a straightforward way to the computation of virtual higher-order corrections to other 2→2 processes, representing an improvement with respect to calculations based on heavy mass expansions.

Higgs-boson plus dijets: higher-order matching for high-energy predictions

Several important processes and analyses at the LHC are sensitive to higher-order perturbative corrections beyond what can currently be calculated at fixed order. The formalism of High Energy Jets (HEJ) calculates the corrections systematically enhanced for a large ratio of the centre-of-mass energy to the transverse momentum of the observed jets. These effects are relevant in the analysis of e.g. Higgs-boson production in association with dijets within the cuts devised to enhance the contribution from Vector Boson Fusion (VBF).HEJ obtains an all-order approximation, based on logarithmic corrections which are matched to fixed-order results in the cases where these can be readily evaluated. In this paper we present an improved framework for the matching utilised in HEJ, which for merging of tree-level results is mathematically equivalent to the one used so far. However, by starting from events generated at fixed order and supplementing these with the all-order summation, it is computationally simpler to obtain matching to calculations of high multiplicity.We demonstrate that the impact of the higher-multiplicity matching on predictions is small for the gluon-fusion (GF) contribution of Higgs-boson production in association with dijets in the VBF-region, so perturbative stability against high-multiplicity matching has been achieved within HEJ. We match the improved HEJ prediction to the inclusive next-to-leading order (NLO) cross section and compare to pure NLO in the h → γγ channel with standard VBF cuts.

XYZ-SU3 breakings from Laplace sum rules at higher orders

We present new compact integrated expressions of SU3 breaking corrections to QCD spectral functions of heavy–light molecules and four-quark [Formula: see text]-like states at lowest order (LO) of perturbative (PT) QCD and up to [Formula: see text] condensates of the Operator Product Expansion (OPE). Including next-to-next-to-leading order (N2LO) PT corrections in the chiral limit and next-to-leading order (NLO) SU3 PT corrections, which we have estimated by assuming the factorization of the four-quark spectral functions, we improve previous LO results for the [Formula: see text]-like masses and decay constants from QCD spectral sum rules (QSSR). Systematic errors are estimated from a geometric growth of the higher order PT corrections and from some partially known [Formula: see text] nonperturbative contributions. Our optimal results, based on stability criteria, are summarized in Tables 18–21 while the [Formula: see text] and [Formula: see text] channels are compared with some existing LO results in Table 22. One can note that, in most channels, the SU3 corrections on the meson masses are tiny: [Formula: see text] (respectively [Formula: see text]) for the [Formula: see text] (respectively [Formula: see text])-quark channel but can be large for the couplings ([Formula: see text]). Within the lowest dimension currents, most of the [Formula: see text] and [Formula: see text] states are below the physical thresholds while our predictions cannot discriminate a molecule from a four-quark state. A comparison with the masses of some experimental candidates indicates that the [Formula: see text] [Formula: see text] might have a large [Formula: see text] molecule component while an interpretation of the [Formula: see text] candidates as four-quark ground states is not supported by our findings. The [Formula: see text] [Formula: see text] and [Formula: see text] are compatible with the [Formula: see text], [Formula: see text] molecules and/or with the axial-vector [Formula: see text] four-quark ground state. Our results for the [Formula: see text], [Formula: see text] and for different beauty states can be tested in the future data. Finally, we revisit our previous estimates1 for the [Formula: see text] and [Formula: see text] and present new results for the [Formula: see text].

On the relation between pole and running heavy quark masses beyond the four-loop approximation

The effective charges motivated method is applied to the relation between pole and M̅S̅-scheme heavy quark masses to study high order perturbative QCD corrections in the observable quantities proportional to the running quark masses. The non-calculated five- and six-loop perturbative QCD coefficients are estimated. This approach predicts for these terms the sign-alternating expansion in powers of number of lighter flavors nl, while the analyzed recently infrared renormalon asymptotic expressions do not reproduce the same behavior. We emphasize that coefficients of the quark mass relation contain proportional to π2 effects, which result from analytical continuation from the Euclidean region, where the scales of the running masses and QCD coupling constant are initially fixed, to the Minkowskian region, where the pole masses and the running QCD parameters are determined. For the t-quark the asymptotic nature of the non-resummed PT mass relation does not manifest itself at six-loops, while for the b-quark the minimal PT term appears at the probed by direct calculations four-loop level. The recent infrared renormalon based studies support these conclusions.

Four-dimensional unsubtraction from the loop-tree duality

We present a new algorithm to construct a purely four dimensional representation of higher-order perturbative corrections to physical cross-sections at next-to-leading order (NLO). The algorithm is based on the loop-tree duality (LTD), and it is implemented by introducing a suitable mapping between the external and loop momenta of the virtual scattering amplitudes, and the external momenta of the real emission corrections. In this way, the sum over degenerate infrared states is performed at integrand level and the cancellation of infrared divergences occurs locally without introducing subtraction counter-terms to deal with soft and final-state collinear singularities. The dual representation of ultraviolet counter-terms is also discussed in detail, in particular for self-energy contributions. The method is first illustrated with the scalar three-point function, before proceeding with the calculation of the physical cross-section for $\gamma^* \to q \bar{q}(g)$, and its generalisation to multi-leg processes. The extension to next-to-next-to-leading order (NNLO) is briefly commented.

On the cusp anomalous dimension in the ladder limit of N = 4 $$ \mathcal{N}=4 $$ SYM

We analyze the cusp anomalous dimension in the (leading) ladder limit of $\mathcal N=4$ SYM and present new results for its higher-order perturbative expansion. We study two different limits with respect to the cusp angle $\phi$. The first is the light-like regime where $x = e^{i\,\phi}\to 0$. This limit is characterised by a non-trivial expansion of the cusp anomaly as a sum of powers of $\log x$, where the maximum exponent increases with the loop order. The coefficients of this expansion have remarkable transcendentality features and can be expressed by products of single zeta values. We show that the whole logarithmic expansion is fully captured by a solvable Woods-Saxon like one-dimensional potential. From the exact solution, we extract generating functions for the cusp anomaly as well as for the various specific transcendental structures appearing therein. The second limit that we discuss is the regime of small cusp angle. In this somewhat simpler case, we show how to organise the quantum mechanical perturbation theory in a novel efficient way by means of a suitable all-order Ansatz for the ground state of the associated Schr\"odinger problem. Our perturbative setup allows to systematically derive higher-order perturbative corrections in powers of the cusp angle as explicit non-perturbative functions of the effective coupling. This series approximation is compared with the numerical solution of the Schr\"odinger equation to show that we can achieve very good accuracy over the whole range of coupling and cusp angle. Our results have been obtained by relatively simple techniques. Nevertheless, they provide several non-trivial tests useful to check the application of Quantum Spectral Curve methods to the ladder approximation at non zero $\phi$, in the two limits we studied.

Optics in a nonlinear gravitational plane wave

Gravitational waves can act like gravitational lenses, affecting the observed positions, brightnesses, and redshifts of distant objects. Exact expressions for such effects are derived here in general relativity, allowing for arbitrarily-moving sources and observers in the presence of plane-symmetric gravitational waves. At least for freely falling sources and observers, it is shown that the commonly-used predictions of linear perturbation theory can be generically overshadowed by nonlinear effects; even for very weak gravitational waves, higher-order perturbative corrections involve secularly-growing terms which cannot necessarily be neglected when considering observations of sufficiently distant sources. Even on more moderate scales where linear effects remain at least marginally dominant, nonlinear corrections are qualitatively different from their linear counterparts. There is a sense in which they can, for example, mimic the existence of a third type of gravitational wave polarization.

Resumming double logarithms in the QCD evolution of color dipoles

The higher-order perturbative corrections, beyond leading logarithmic accuracy, to the BFKL evolution in QCD at high energy are well known to suffer from a severe lack-of-convergence problem, due to radiative corrections enhanced by double collinear logarithms. Via an explicit calculation of Feynman graphs in light cone (time-ordered) perturbation theory, we show that the corrections enhanced by double logarithms (either energy-collinear, or double collinear) are associated with soft gluon emissions which are strictly ordered in lifetime. These corrections can be resummed to all orders by solving an evolution equation which is non-local in rapidity. This equation can be equivalently rewritten in local form, but with modified kernel and initial conditions, which resum double collinear logs to all orders. We extend this resummation to the next-to-leading order BFKL and BK equations. The first numerical studies of the collinearly-improved BK equation demonstrate the essential role of the resummation in both stabilizing and slowing down the evolution.

Higgs-boson production through gluon fusion at NNLO QCD with parton showers

We discuss how the ${\mathrm{UN}}^{2}\mathrm{LOPS}$ scheme for matching next-to-next-to-leading order (NNLO) calculations to parton showers can be applied to processes with large higher-order perturbative QCD corrections. We focus on Higgs-boson production through gluon fusion as an example. We also present an NNLO fixed-order event generator for this reaction.