Resummation Of Logarithms Research Articles

Fiducial Higgs and Drell-Yan distributions at N3LL\u2032+NNLO with RadISH

We present state-of-the-art predictions for transverse observables relevant to colour-singlet production at the LHC, in particular the transverse momentum of the colour singlet in gluon-fusion Higgs production and in neutral Drell-Yan lepton-pair production, as well as the {phi}_{eta}^{ast } observable in Drell Yan. We perform a next-to-next-to-next-to-leading logarithmic (N3LL) resummation of such observables in momentum space according to the RadISH formalism, consistently including in our prediction all constant terms of relative order {alpha}_s^3 with respect to the Born, thereby achieving N3LL′ accuracy. The calculation is fully exclusive with respect to the Born kinematics, which allows the application of arbitrary fiducial selection cuts on the decay products of the colour singlet. We supplement our results with a transverse-recoil prescription, accounting for dominant classes of subleading-power corrections in a fiducial setup. The resummed predictions are matched with fixed-order differential spectra at next-to-next-to-leading order (NNLO) accuracy. A phenomenological comparison is carried out with 13 TeV LHC data relevant to the Higgs to di-photon channel, as well as to neutral Drell-Yan lepton-pair production. Overall, the inclusion of mathcal{O} ( {alpha}_s^3 ) constant terms, and to a lesser extent of transverse-recoil effects, proves beneficial for the comparison of theoretical predictions to data, leaving a residual theoretical uncertainty in the resummation region at the 2–5% level for Drell-Yan observables, and 5–7% in Higgs production.

Precision Global Determination of the B→X_{s}γ Decay Rate.

We perform the first global fit to inclusive B→X_{s}γ measurements using a model-independent treatment of the nonperturbative b-quark distribution function, with next-to-next-to-leading logarithmic resummation and O(α_{s}^{2}) fixed-order contributions. The normalization of the B→X_{s}γ decay rate, given by |C_{7}^{incl}V_{tb}V_{ts}^{*}|^{2}, is sensitive to physics beyond the standard model (SM). We determine |C_{7}^{incl}V_{tb}V_{ts}^{*}|=(14.77±0.51_{fit}±0.59_{theory}±0.08_{param})×10^{-3}, in good agreement with the SM prediction, and the b-quark mass m_{b}^{1S}=(4.750±0.027_{fit}±0.033_{theory}±0.003_{param}) GeV. Our results suggest that the uncertainties in the extracted B→X_{s}γ rate have been underestimated by up to a factor of 2, leaving more room for beyond-SM contributions.

Hunting BFKL in semi-hard reactions at the LHC

The agreement between calculations inspired by the resummation of energy logarithms, known as BFKL approach, and experimental data in the semi-hard sector of QCD has become manifest after a wealthy series of phenomenological analyses. However, the contingency that the same data could be concurrently portrayed at the hand of fixed-order, DGLAP-based calculations, has been pointed out recently, but not yet punctually addressed. Taking advantage of the richness of configurations gained by combining the acceptances of CMS and CASTOR detectors, we give results in the full next-to-leading logarithmic approximation of cross sections, azimuthal correlations and azimuthal distributions for three distinct semi-hard processes, each of them featuring a peculiar final-state exclusiveness. Then, making use of disjoint intervals for the transverse momenta of the emitted objects, i.e. kappa -windows, we clearly highlight how high-energy resummed and fixed-order driven predictions for semi-hard sensitive observables can be decisively discriminated in the kinematic ranges typical of current and forthcoming analyses at the LHC. The scale-optimization issue is also introduced and explored, while the uncertainty coming from the use of different PDF and FF set is deservedly handled. Finally, a brief overview of JETHAD, a numerical tool recently developed, suited for the computation of inclusive semi-hard reactions is provided.

Factorization at subleading power, Sudakov resummation, and endpoint divergences in soft-collinear effective theory

Starting from the first renormalized factorization theorem for a process described at subleading power in soft-collinear effective theory, we discuss the resummation of Sudakov logarithms for such processes in renormalization-group improved perturbation theory. Endpoint divergences in convolution integrals, which arise generically beyond leading power, are regularized and removed by systematically rearranging the factorization formula. We study in detail the example of the $b$-quark induced $h\to\gamma\gamma$ decay of the Higgs boson, for which we resum large logarithms of the ratio $M_h/m_b$ at next-to-leading logarithmic order. We also briefly discuss the related $gg\to h$ amplitude.

Small-pT and large-x regions for Higgs transverse momentum distributions

It was shown recently that standard resummation of logarithms of Q/pT can be supplemented with the resummation of logarithmic contributions at large x = Q2/s in the case of a colourless final state such as Higgs produced via gluon fusion or the production of a lepton pair via Drell–Yan mechanism. Such an improved transverse momentum resummation takes into account soft emissions that are emitted at very small angles. We report on recent phenomenological studies of a combined threshold-improved pT and threshold resummation formalism to the Higgs boson produced at the LHC where small-pT and threshold logarithms are resummed up to NNLL and NNLL* respectively. We show that the effect of the modified pT resummation yields a faster perturbative convergence in the small-pT region while the effect of the threshold one improves the agreement with fixed-order calculations in the medium and large-pT regions.

Jet angularities in Z+jet production at the LHC

We present a phenomenological study of angularities measured on the highest transverse-momentum jet in LHC events that feature the associate production of a Z boson and one or more jets. In particular, we study angularity distributions that are measured on jets with and without the SoftDrop grooming procedure. We begin our analysis exploiting state-of-the-art Monte Carlo parton shower simulations and we quantitatively assess the impact of next-to-leading order (NLO) matching and merging procedures. We then move to analytic resummation and arrive at an all-order expression that features the resummation of large logarithms at next-to-leading logarithmic accuracy (NLL) and is matched to the exact NLO result. Our predictions include the effect of soft emissions at large angles, treated as a power expansion in the jet radius, and non-global logarithms. Furthermore, matching to fixed-order is performed in such a way to ensure what is usually referred to as NLL′ accuracy. Our results account for realistic experimental cuts and can be easily compared to upcoming measurements of jet angularities from the LHC collaborations.

Origin and resummation of threshold logarithms in the lattice QCD calculations of PDFs

Many present lattice QCD approaches to calculate the parton distribution functions (PDFs) rely on a factorization formula or effective theory expansion of certain Euclidean matrix elements in boosted hadron states. In the quasi- and pseudo-PDF methods, the matching coefficient in the factorization or expansion formula includes large logarithms near the threshold, which arise from the subtle interplay of collinear and soft divergences of an underlying 3D momentum distribution. We use the standard prescription to resum such logarithms in the Mellin-moment space at next-to-leading logarithmic accuracy, which also accounts for the DGLAP evolution, and we show that it can suppress the PDF at large $x$. Unlike the deep inelastic scattering and Drell-Yan cross sections, the resummation formula is away from the Landau pole. We then apply our formulation to reanalyze the recent lattice results for the pion valence PDF, and find that within the current data sensitivity, the effect of threshold resummation is marginal for the accessible moments and the PDF at large $x$.

Three-loop soft function for energetic electroweak boson production at hadron colliders

We calculate the three-loop soft function for the production of an electroweak boson (Higgs, γ, W±, Z) with large transverse momentum at a hadron collider. It is the first time a soft function for a three-parton process is computed at next-to-next-to-next-to-leading order (N3LO). As a technical novelty, we perform the calculation in terms of forward-scattering-type loop diagrams rather than evaluating phase space integrals. Our three-loop result contains color-tripole contributions and explicitly confirms predictions on the universal infrared structure of QCD scattering amplitudes with three massless parton legs. The soft function is a central ingredient in the factorized cross section for electroweak boson production near the kinematic endpoint (threshold), where the invariant mass of the recoiling hadronic radiation is small compared to its transverse momentum. Our result is required for predictions of the near-threshold cross sections at N3LO and for the resummation of threshold logarithms at primed next-to-next-to-next-to-leading logarithmic (N3LL′) accuracy.

Diffractive production of Λ hyperons in the high-energy limit of strong interactions

We propose the study of the inclusive production of two $\Lambda$ hyperons or a single $\Lambda$-particle in association with a jet, featuring high transverse momenta and large separation in rapidity, as a probe channel of the resummation of energy logarithms in the QCD perturbative series. We give predictions, shaped on kinematic ranges typical of CMS and of the backward CASTOR detector, for cross section and azimuthal-correlation moments between the two emitted objects, showing how considering the tag of $\Lambda$ baryons eases the comparison between theoretical results and experimental data in the phenomenological context of semi-hard reactions.

Higgsino and gaugino pair production at the LHC with aNNLO+NNLL precision

We present a calculation of higgsino and gaugino pair production at the LHC at next-to-next-to-leading logarithmic (NNLL) accuracy, matched to approximate next-to-next-to-leading order (aNNLO) QCD corrections. We briefly review the formalism for the resummation of large threshold logarithms and highlight the analytical results required at aNNLO+NNLO accuracy. Our numerical results are found to depend on the mass and nature of the produced charginos and neutralinos. The differential and total cross sections for light higgsinos, which like sleptons are produced mostly at small x and in the s-channel, are found to be again moderately increased with respect to our previous results. The differential and total cross sections for gauginos are, however, not increased any more due to the fact that gauginos, like squarks, are now constrained by ATLAS and CMS to be heavier than about 1 TeV, so that also t- and u-channels play an important role. The valence quarks probed at large x then also induce substantially different cross sections for positively and negatively charged gauginos. The higgsino and gaugino cross sections are both further stabilized at aNNLO+NNLL with respect to the variation of renormalization and factorization scales. We also now take mixing in the squark sector into account and study the dependence of the total cross sections on the squark and gluino masses as well as the trilinear coupling controlling the mixing in particular in the sbottom sector.

Jet energy drop

We study the jet energy drop, which is the relative difference between the groomed and ungroomed jet energy or transverse momentum. It is one of the fundamental quantities that characterizes the impact of grooming on jets produced in high energy collisions. We consider three different grooming algorithms i) soft drop, ii) iterated soft drop, and iii) trimming. We carry out the resummation of large logarithms of the jet energy drop, the jet radius as well as relevant grooming parameters at next-to-leading logarithmic (NLL′) accuracy. In addition, we account for non-global and clustering logarithms, and determine the next-to-leading order corrections. For soft drop we perform a joint resummation of the jet energy drop and the groomed jet radius, which is necessary to achieve the correct all-order structure of the cross section, in particular for the Sudakov-safe case of soft drop with β = 0. We present numerical results for LHC energies and compare to Pythia simulations as well as CMS data. Our factorization framework predicts the onset of nonperturbative effects in the jet energy distribution, in line with what we find in Pythia. The jet energy drop observables stand out because they only probe soft radiation, making them ideal candidates for the tuning of parton shower Monte Carlo event generators and for probing medium effects in heavy-ion collisions.

One-loop jet functions by geometric subtraction

In factorization formulae for cross sections of scattering processes, final-state jets are described by jet functions, which are a crucial ingredient in the resummation of large logarithms. We present an approach to calculate generic one-loop jet functions, by using the geometric subtraction scheme. This method leads to local counterterms generated from a slicing procedure; and whose analytic integration is particularly simple. The poles are obtained analytically, up to an integration over the azimuthal angle for the observable- dependent soft counterterm. The poles depend only on the soft limit of the observable, characterized by a power law, and the finite term is written as a numerical integral. We illustrate our method by reproducing the known expressions for the jet function for angularities, the jet shape, and jets defined through a cone or kT algorithm. As a new result, we obtain the one-loop jet function for an angularity measurement in e+e− collisions, that accounts for the formally power-suppressed but potentially large effect of recoil. An implementation of our approach is made available as the GOJet Mathematica package accompanying this paper.

Large-x resummation of off-diagonal deep-inelastic parton scattering from d-dimensional refactorization

The off-diagonal parton-scattering channels g + γ* and q + ϕ* in deep-inelastic scattering are power-suppressed near threshold x → 1. We address the next-to-leading power (NLP) resummation of large double logarithms of 1 − x to all orders in the strong coupling, which are present even in the off-diagonal DGLAP splitting kernels. The appearance of divergent convolutions prevents the application of factorization methods known from leading power resummation. Employing d-dimensional consistency relations from requiring 1/ϵ pole cancellations in dimensional regularization between momentum regions, we show that the resummation of the off-diagonal parton-scattering channels at the leading logarithmic order can be bootstrapped from the recently conjectured exponentiation of NLP soft-quark Sudakov logarithms. In particular, we derive a result for the DGLAP kernel in terms of the series of Bernoulli numbers found previously by Vogt directly from algebraic all-order expressions. We identify the off-diagonal DGLAP splitting functions and soft-quark Sudakov logarithms as inherent two-scale quantities in the large-x limit. We use a refactorization of these scales and renormalization group methods inspired by soft-collinear effective theory to derive the conjectured soft-quark Sudakov exponentiation formula.

Factorization Theorem Connecting the Light-Cone Distribution Amplitudes of Heavy-Flavor Mesons in QCD and Heavy-Quark Effective Theory.

The light-cone distribution amplitude (LCDA) of a heavy-light meson defined in heavy quark effective theory (HQET) is a fundamental nonperturbative input to account for innumerable B meson exclusive decay and production processes. On the other hand, the conventional heavy-flavored meson LCDA defined in QCD also ubiquitously enters the factorization formula for hard exclusive B production processes. Inspired by the observation that these two LCDAs exhibit the identical infrared behaviors, yet differ in the ultraviolet scale of order m_{b} or greater, we propose a novel factorization theorem for the heavy-light mesons, that the LCDA defined in QCD can be further expressed as a convolution between the LCDA in HQET and a perturbatively calculable coefficient function thanks to asymptotic freedom. This refactorization program can be invoked to fully disentangle the effects from three disparate scales Q, m_{b}, and Λ_{QCD} for a hard exclusive B production process, particularly to facilitate the resummation of logarithms of type lnQ/m_{b} and lnm_{b}/Λ_{QCD} in a systematic fashion.

Heavy-flavor PDF evolution and variable-flavor-number scheme uncertainties in deep-inelastic scattering

We consider a detailed account on the construction of the heavy-quark parton distribution functions for charm and bottom, starting from $n_f=3$ light flavors in the fixed-flavor number (FFN) scheme and by using the standard decoupling relations for heavy quarks in QCD. We also account for two-mass effects. Furthermore, different implementations of the variable-flavor-number (VFN) scheme in deep-inelastic scattering (DIS) are studied, with the particular focus on the resummation of large logarithms in $Q^2/m_h^2$, the ratio the virtuality of the exchanged gauge-boson $Q^2$ to the heavy-quark mass squared $m_h^2$. A little impact of resummation effects if found in the kinematic range of the existing data on the DIS charm-quark production so that they can be described very well within the FFN scheme. Finally, we study the theoretical uncertainties associated to the VFN scheme, which manifest predominantly at small $Q^2$.

Resummation of non-global logarithms in cross sections with massive particles

A factorization formalism for jet processes involving massive colored particles such as the top quark is developed, extending earlier results for the massless case. The factorization of soft emissions from the underlying hard process is implemented in an effective field theory framework, which forms the basis for the resummation of large logarithms. The renormalization group evolution giving rise to non-global logarithms is implemented into a parton shower code in the large-Nc limit. After a comparison of the massive and massless radiation patterns, the cross section for toverline{t} production with a veto on additional central jet activity is computed, taking into account radiation both from the production and the decay of the top quarks. The resummation of the leading logarithms leads to an improved description of ATLAS measurements at sqrt{s} = 7 TeV.

Determination of \u03b1(Mz) from an hyperasymptotic approximation to the energy of a static quark-antiquark pair

We give the hyperasymptotic expansion of the energy of a static quark-antiquark pair with a precision that includes the effects of the subleading renormalon. The terminants associated to the first and second renormalon are incorporated in the analysis when necessary. In particular, we determine the normalization of the leading renormalon of the force and, consequently, of the subleading renormalon of the static potential. We obtain {Z}_3^F (nf = 3) = 2{Z}_3^V (nf = 3) = 0.37(17). The precision we reach in strict perturbation theory is next-to-next-to-next-to-leading logarithmic resummed order both for the static potential and for the force. We find that the resummation of large logarithms and the inclusion of the leading terminants associated to the renormalons are compulsory to get accurate determinations of {Lambda}_{overline{mathrm{MS}}} when fitting to short-distance lattice data of the static energy. We obtain {Lambda}_{overline{mathrm{MS}}}^{left({n}_f=3right)} = 338(12) MeV and α(Mz) = 0.1181(9). We have also MS found strong consistency checks that the ultrasoft correction to the static energy can be computed at weak coupling in the energy range we have studied.

The Zγ transverse-momentum spectrum at NNLO+N3LL

We consider the transverse-momentum (pT) distribution of Zγ pairs produced in hadronic collisions. Logarithmically enhanced contributions at small pT are resummed to all orders in QCD perturbation theory and combined with the fixed-order prediction. We achieve the most advanced prediction for the ZγpT spectrum by matching next-to-next-to-next-to-leading logarithmic (N3LL) resummation to the integrated cross section at next-to-next-to-leading order (NNLO). By considering ℓ+ℓ−γ production at the fully differential level, including spin correlations, interferences and off-shell effects, arbitrary cuts can be applied to the leptons and the photon. We present results at the LHC in presence of fiducial cuts and find agreement with the 13TeV ATLAS data at the few-percent level.

J/ψ meson production in association with an open charm hadron at the LHC: A reappraisal

We critically (re)examine the associated production process of a $J/\psi$ meson plus an open charm hadron at the LHC in the proton-proton ($pp$) and proton-lead ($p{\rm Pb}$) collisions. Such a process is very intriguing in the sense of tailoring to explore the double parton structure of nucleons and to determine the geometry of partons in nuclei. In order to interpret the existing $pp$ data with the LHCb detector at the center-of-mass energy $\sqrt{s}=7$ TeV, we introduce two overlooked mechanisms for the double parton scattering (DPS) and single parton scattering (SPS) processes. Besides the conventional DPS mode, where the two mesons are produced almost independently in the two separate scattering subprocesses, we propose a novel DPS mechanism that the two constituent (heavy) quarks stemming from two hard scatterings can form into a composite particle, like the $J/\psi$ meson, during the hadronization phase. However, it turns out the corresponding contribution is small in $J/\psi+c\bar{c}$ hadroproduction. On the contrary, we point out that the resummation of the initial state logarithms due to gluon splitting into a charm quark pair is crucial to understand the LHCb measurement, which was overlooked in the literature. We perform a proper matching between the perturbative calculations in different initial-quark flavor number schemes, generically referring to the variable flavor number scheme. The new variable flavor number scheme calculation for the process strongly enhance the SPS cross sections, almost closing the discrepancies between theory and experiment. Finally, we present our predictions for the forthcoming LHCb measurement in $p{\rm Pb}$ collisions at $\sqrt{s_{NN}}=8.16$ TeV. Some interesting observables are exploited to set up the control regions of the DPS signal and to probe the impact-parameter dependent parton densities in lead.

Groomed jet mass at high precision

We present predictions of the distribution of groomed heavy jet mass in electron-positron collisions at the next-to-next-to-leading order accuracy matched with the resummation of large logarithms to next-to-next-to-next-to-leading logarithmic accuracy. Resummation at this accuracy is possible through extraction of necessary two-loop constants and three-loop anomalous dimensions from fixed-order codes.