Resummation Formula Research Articles

Renormalon-based resummation of Bjorken polarised sum rule in holomorphic QCD

Approximate knowledge of the renormalon structure of the Bjorken polarised sum rule (BSR) Γ‾1p−n(Q2) leads to the corresponding BSR characteristic function that allows us to evaluate the leading-twist part of BSR. In our previous work [1], this evaluation (resummation) was performed using perturbative QCD (pQCD) coupling a(Q2)≡αs(Q2)/π in specific renormalisation schemes. In the present paper, we continue this work, by using instead holomorphic couplings [a(Q2)↦A(Q2)] that have no Landau singularities and thus require, in contrast to the pQCD case, no regularisation of the resummation formula. The D=2 and D=4 terms are included in the Operator Product Expansion (OPE) of inelastic BSR, and fits are performed to the available experimental data in a specific interval (Qmin2,Qmax2) where Qmax2=4.74GeV2. We needed relatively high Qmin2≈1.7GeV2 in the pQCD case since the pQCD coupling a(Q2) has Landau singularities at Q2≲1GeV2. Now, when holomorphic (AQCD) couplings A(Q2) are used, no such problems occur: for the 3δAQCD and 2δAQCD variants the preferred values are Qmin2≈0.6GeV2. The preferred values of αs in general cannot be unambiguously extracted, due to large uncertainties of the experimental BSR data. At a fixed value of αsMS‾(MZ2), the values of the D=2 and D=4 residue parameters are determined in all cases, with the corresponding uncertainties.

Jettiness formulation of the MiNNLOPS method

We present a new formulation of the MiNNLOPS method to match NNLO QCD calculations with parton showers by using jettiness as a resummation variable. The full derivation for colour-singlet processes is presented using 0-jettiness starting from the NNLL′ resummation formula. We show phenomenological results for Drell-Yan and Higgs-boson production at the LHC and compare our predictions to ATLAS and CMS data. Differences to the original MiNNLOPS formulation using the transverse momentum of the colour singlet as resummation variable are discussed. We further present a comparison of MiNNLOPS predictions with Geneva. Finally, we extend the formulation of the MiNNLOPS method to 1-jettiness which is applicable to processes with a colour singlet plus one jet in the final state.

N3LL resummation of one-jettiness for Z -boson plus jet production at hadron colliders

We present the resummation of one-jettiness for the color-singlet plus jet production process pp→(γ*/Z→ℓ+ℓ−)+jet at hadron colliders up to the fourth logarithmic order (N3LL). This is the first resummation at this order for processes involving three colored partons at the Born level. We match our resummation formula to the corresponding fixed-order predictions, extending the validity of our results to regions of the phase space where further hard emissions are present. This result paves the way for the construction of next-to-next-to-leading order simulations for color-singlet plus jet production matched to parton showers in the framework. Published by the American Physical Society 2024

Soft-parton contributions to heavy-quark production at low transverse momentum

We consider QCD radiative corrections to the production of a heavy-quark pair in hadronic collisions. We present the computation of the soft-parton contributions at low transverse momentum of the heavy-quark pair up to second order in the QCD coupling αS. These results complete the evaluation at the next-to-next-to-leading order (NNLO) of the transverse-momentum resummation formula for this process. Moreover, they give all the ingredients that are needed for the NNLO implementation of the qT subtraction formalism for heavy-quark production. We discuss the details of the computation and we provide a code that can be used to obtain the relevant results in numerical form.

Collinear functions for QCD resummations

The singular behaviour of QCD squared amplitudes in the collinear limit is factorized and controlled by splitting kernels with a process-independent structure. We use these kernels to define collinear functions that can be used in QCD resummation formulae of hard-scattering observables. Different collinear functions are obtained by integrating the splitting kernels over different phase-space regions that depend on the hard-scattering observables of interest. The collinear functions depend on an auxiliary vector nμ that can be either light-like (n2 = 0) or time-like (n2> 0). In the case of transverse-momentum dependent (TMD) collinear functions, we show that the use of a time-like auxiliary vector avoids the rapidity divergences, which are instead present if n2 = 0. The perturbative computation of the collinear functions lead to infrared (IR) divergences that can be properly factorized with respect to IR finite functions that embody the logarithmically-enhanced collinear contributions to hard-scattering cross sections. We evaluate various collinear functions and their nμ dependence at mathcal{O} (αS). We compute the azimuthal-correlation component of the TMD collinear functions at mathcal{O}left({alpha}_{textrm{S}}^2right) , and we present the results of the mathcal{O}left({alpha}_{textrm{S}}^2right) contribution of linearly-polarized gluons to transverse-momentum resummation formulae. Beyond mathcal{O}left({alpha}_{textrm{S}}^2right) the collinear functions of initial-state colliding partons are process dependent, as a consequence of the violation of strict collinear factorization of QCD squared amplitudes.

Azimuthal asymmetries of muon pair production in ultraperipheral heavy ion collisions

In this paper we study azimuthal asymmetries of the muon pair production in ultraperipheral heavy ion collisions within the joint impact parameter and transverse momentum dependent framework. The final state QED radiation effects are resummed to all orders in perturbation theory, where the complete muon mass corrections are also taken into account. We further make numerical estimations for azimuthal asymmetries in the different kinematic regions accessible at RHIC and LHC with the derived resummation formula. We find that the lepton mass effects can give sizable corrections to the asymmetries at relatively large pair transverse momentum at RHIC energy.

Resummation of threshold logarithms in deeply-virtual Compton scattering

I derive an all-order resummation formula for the logarithmically enhanced contributions proportional to frac{alpha_s^n}{xpm xi } log {left(frac{xi pm x}{2xi}right)}^k in the quark coefficient function of deeply-virtual-Compton scattering and the pion-photon transition form factor in momentum space. The resummation is performed at the next-to-next-to-leading logarithmic accuracy. The key observation is that the quark coefficient function itself factorizes in the x → ±ξ limit, which allows for a resummation using renormalization group equations. A preliminary numerical analysis suggests that the corrections due to resummation for the quark contribution might be small.

Zero-jettiness resummation for top-quark pair production at the LHC

We study the resummation of the 0-jettiness resolution variable mathcal{T} 0 for the top-quark pair production process in hadronic collisions. Starting from an effective theory framework we derive a factorisation formula for this observable which allows its resummation at any logarithmic order in the mathcal{T} 0 → 0 limit. We then calculate the mathcal{O} (αs) corrections to the soft function matrices and, by employing renormalisation group equation methods, we obtain the ingredients for the resummation formula up to next-to-next-to-leading logarithmic (NNLL) accuracy. We study the impact of these corrections to the 0-jettiness distribution by comparing predictions at different accuracy orders: NLL, NLL′, NNLL and approximate NNLL′ ( {mathrm{NNLL}}_{mathrm{a}}^{prime } ). We match these results to the corresponding fixed order calculations both at leading order and next-to-leading order for the t overline{t} +jet production process, obtaining the most accurate prediction of the 0-jettiness distribution for the top-quark pair production process at {mathrm{NNLL}}_{mathrm{a}}^{prime } +NLO accuracy.

{t {{bar{t}}}H} production at NNLO: the flavour off-diagonal channels

We consider QCD radiative corrections to the associated production of a heavy-quark pair (Q{{bar{Q}}}) with a generic colourless system F at hadron colliders. We discuss the resummation formalism for the production of the Q{{bar{Q}}}F system at small values of its total transverse momentum q_T. We present the results of the corresponding resummation coefficients at next-to-leading and, partly, next-to-next-to-leading order. The perturbative expansion of the resummation formula leads to the explicit ingredients that can be used to apply the q_T subtraction formalism to fixed-order calculations for this class of processes. We use the q_T subtraction formalism to perform a fully differential perturbative computation for the production of a top-antitop quark pair and a Higgs boson. At next-to-leading order we compare our results with those obtained with established subtraction methods and we find complete agreement. We present, for the first time, the results for the flavour off-diagonal partonic channels at the next-to-next-to-leading order.

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 $x$.

QCD resummation on single hadron transverse momentum distribution with the thrust axis

We derive the transverse momentum dependent (TMD) factorization and resummation formula of the unpolarized transverse momentum distribution (jT) for the single hadron production with the thrust axis in an electron-positron collision. Two different kinematic regions are considered, including small transverse momentum limit jT « Q, and joint transverse momentum and threshold limit jT « Q(1 − zh) « Q, where Q and zh are the hard scattering energy and the observed hadron momentum fraction. Using effective theory methods, we resum logarithms ln(Q/jT) and ln(1 − zh) to all orders. In the end, we present the differential cross sections and Gaussian widths calculated for the inclusive charged pion production and find that our results are consistent with the measurements reported by the Belle collaboration.

Top quark pair production near threshold: single/double distributions and mass determination

We investigate top quark pair production near the threshold where the pair invariant mass {M}_{toverline{t}} approaches 2mt, which provides sensitive observables to extract the top quark mass mt. Using the effective field theory methods, we derive a factorization and resummation formula for kinematic distributions in the threshold limit up to the next-to- leading power, which resums higher order Coulomb corrections to all orders in the strong coupling constant. Our formula is similar to those in the literature but differs in several important aspects. We apply our formula to the {M}_{toverline{t}} distribution, as well as to the double differential cross section with respect to {M}_{toverline{t}} and the rapidity of the toverline{t} pair. We find that the resummation effects significantly increase the cross sections near the threshold, and lead to predictions better compatible with experimental data than the fixed-order ones. We demonstrate that incorporating resummation effects in the top quark mass determination can shift the extracted value of mt by as large as 1.4 GeV. The shift is much larger than the estimated uncertainties in previous experimental studies, and leads to a value of the top quark pole mass more consistent with the current world average.

QCD resummation in hard diffractive dijet production at the electron-ion collider

Diffractive dijet production at the electron-ion collider (EIC) has been proposed to study the gluon Wigner distribution at small-x. We investigate the soft gluon radiation associated with the final state jets and an all order resummation formula is derived. We show that the soft gluon resummation plays an important role to describe E791 data on π-induced diffractive dijet production at Fermilab. Predictions for the EIC are presented, and we emphasize that the soft gluon resummation is an important aspect to explore the nucleon/nucleus tomography through these processes.

Infrared resummation for derivative interactions in de Sitter space

In de Sitter space, scale invariant fluctuations give rise to infrared logarithmic corrections to physical quantities, which eventually spoil perturbation theories. For models without derivative interactions, it has been known that the field equation reduces to a Langevin equation with white noise in the leading logarithm approximation. The stochastic equation allows us to evaluate the infrared effects nonperturbatively. We extend the resummation formula so that it is applicable to models with derivative interactions. We first consider the nonlinear sigma model and next consider a more general model which consists of a noncanonical kinetic term and a potential term. The stochastic equations derived from the infrared resummation in these models can be understood as generalizations of the standard one to curved target spaces.

Configurational entropy of the energy-energy correlation in e+e− annihilation processes

In this paper the configurational entropy of the energy-energy correlation function is scrutinized, in e+e− collisions to hadrons in the back-to-back region, within the QCD perturbative theory. The critical points of the configurational entropy concept, in the hot nuclear system, is shown to correspond to the critical angle between the two scattered hadrons, corroborating this with phenomenological data with great accuracy. The main tools employ the main coefficients of the soft-gluon resummation formula, taking into account logarithmically enhanced contributions up to next-to-next-to-leading logarithmic accuracy.

Momentum-space resummation for transverse observables and the Higgs p\u22a5 at N3LL+NNLO

We present an approach to the momentum-space resummation of global, recursively infrared and collinear safe observables that can vanish away from the Sudakov region. We focus on the hadro-production of a generic colour singlet, and we consider the class of observables that depend only upon the total transverse momentum of the radiation, prime examples being the transverse momentum of the singlet, and ϕ∗ in Drell-Yan pair production. We derive a resummation formula valid up to next-to-next-to-next-to-leading-logarithmic accuracy for the considered class of observables. We use this result to compute state-of-the-art predictions for the Higgs-boson transverse-momentum spectrum at the LHC at next-to-next-to-next-to-leading-logarithmic accuracy matched to fixed next-to-next-to-leading order. Our resummation formula reduces exactly to the customary resummation performed in impact-parameter space in the known cases, and it also predicts the correct power-behaved scaling of the cross section in the limit of small value of the observable. We show how this formalism is efficiently implemented by means of Monte Carlo techniques in a fully exclusive generator that allows one to apply arbitrary cuts on the Born variables for any colour singlet, as well as to automatically match the resummed results to fixed-order calculations.

Associated production of a top pair and a Z boson at the LHC to NNLL accuracy

We study the resummation of soft gluon emission corrections to the production of a top-antitop pair in association with a Z boson at the Large Hadron Collider to next-to-next-to-leading logarithmic accuracy. By means of an in-house parton level Monte Carlo code we evaluate the resummation formula for the total cross section and several differential distributions at a center-of-mass energy of 13 TeV, and we match these calculations to next-to-leading order results.

NNLL resummation for the associated production of a top pair and a Higgs boson at the LHC

We study the resummation of soft gluon emission corrections to the production of a top-antitop pair in association with a Higgs boson at the Large Hadron Collider. Starting from a soft-gluon resummation formula derived in previous work, we develop a bespoke parton-level Monte Carlo program which can be used to calculate the total cross section along with differential distributions. We use this tool to study the phenomenological impact of the resummation to next-to-next-to-leading logarithmic (NNLL) accuracy, finding that these corrections increase the total cross section and the differential distributions with respect to NLO calculations of the same observables.

Associated production of a top pair and a W boson at next-to-next-to-leading logarithmic accuracy

We consider soft gluon emission corrections to the production of a top-antitop pair in association with a W boson at the Large Hadron Collider. We obtain a soft-gluon resummation formula for this production process which is valid up to next-to-next-to-leading logarithmic accuracy. We evaluate the soft gluon resummation formula in Mellin space by means of an in-house parton level Monte Carlo code which allows us to obtain predictions for the total cross section as well as for several differential distributions. We study the impact of the soft-gluon resummation corrections in comparison to fixed order calculations.

Resummed Differential Cross Sections for Top-Quark Pairs at the LHC.

We present state of the art resummation predictions for differential cross sections in top-quark pair production at the LHC. They are derived from a formalism which allows the simultaneous resummation of both soft and small-mass logarithms, which endanger the convergence of fixed-order perturbative series in the boosted regime, where the partonic center-of-mass energy is much larger than the mass to the top quark. We combine such a double resummation at next-to-next-to-leading logarithmic^{'} (NNLL^{'}) accuracy with standard soft-gluon resummation at next-to-next-to-leading logarithmic accuracy and with next-to-leading-order calculations, so that our results are applicable throughout the whole phase space. We find that the resummation effects on the differential distributions are significant, bringing theoretical predictions into better agreement with experimental data compared to fixed-order calculations. Moreover, such effects are not well described by the next-to-next-to-leading-order approximation of the resummation formula, especially in the high-energy tails of the distributions, highlighting the importance of all-orders resummation in dedicated studies of boosted top production.