We compute the resummed hadronic transverse energy (E_T) distribution due to initial-state QCD radiation in vector boson and Higgs boson production at hadron colliders. The resummed exponent, parton distributions and coefficient functions are treated consistently to next-to-leading order. The results are matched to fixed-order calculations at large E_T and compared with parton-shower Monte Carlo predictions at Tevatron and LHC energies.
This writeup gives an introduction to the theoretical understanding that lies behind automated resummation. It then discusses its applications to hadron-collider event shapes.
We point out that a study of event shapes at hadron colliders allows to explore novel aspects of QCD. These studies are today made easier by the development of a program which automates the resummation.
A complete description of W and Z boson production at high-energy hadron colliders requires the resummation of large Sudakov double logarithms which dominate the transverse momentum (q_T) distribution at small q_T. We compare different prescriptions for performing this resummation, in particular implicit impact parameter space resummation versus explicit transverse momentum space resummation. We argue that the latter method can be formulated so as to retain the advantages of the former, while at the same time allowing a smooth transition to finite order dominance at high q_T.
The distribution of W and Z bosons produced with small transverse momentum (pt) at hadron colliders receives important contributions from large logarithms arising from soft gluon emission. Although conventionally the all-orders resummation of these `Sudakov' logarithms is performed in impact parameter (Fourier transform) space, pt-space resummation is also possible, and offers certain advantages.We present a detailed phenomenological analysis of W and Z production at small pt at the Tevatron $p \bar p$ collider, using pt-space resummation. A good description of the CDF and D0 data can be obtai…
We derive all order soft gluon resummation in dijet azimuthal angular correlation in hadronic collisions at the next-to-leading logarithmic level. The relevant coefficients for the Sudakov resummation factor, the soft and hard factors, are calculated. The theory predictions agree well with the experimental data from D0 Collaboration at the Tevatron. This provides a benchmark calculation for the transverse momentum dependent QCD resummation for jet productions in hadron collisions and can be readily applied at the CERN LHC.
We present a QCD calculation of the transverse momentum distribution of photon pairs produced at hadron colliders, including all-orders soft-gluon resummation valid at next-to-next-to-leading logarithmic accuracy. We specify the region of phase space in which the calculation is most reliable, compare our results with data from the Fermilab Tevatron, and make predictions for the Large Hadron Collider. The uncertainty of predictions for production of diphotons from fragmentation of final-state quarks is examined.
Resummation techniques are essential for high-precision phenomenology at current and future high-energy collider experiments. Perturbative computations of cross sections often suffer from large logarithmic corrections, which must be resummed to all orders to restore the reliability of predictions from first principles. The precise understanding of the all-order structure of field theories allows for fundamental tests of the Standard Model and new physics searches. In this white paper, we review recent progress in modern resummation techniques and outline future directions. In particular, we fo…
We consider the transverse-momentum distribution of colourless high-mass systems (lepton pairs, vector bosons, Higgs particles...) produced in hadronic collisions. We briefly review a formalism for the all-order resummation of the logarithmically-enhanced contributions at small transverse momenta, and we present an illustrative selection of numerical results obtained by using our method.
We compute the threshold-resummed cross section for pseudo-scalar MSSM Higgs boson production by gluon fusion at hadron colliders. The calculation is performed at next-to-next-to leading logarithmic accuracy. We present results for both the LHC and Tevatron Run II. We analyze the factorization and renormalization scale dependence of the results, finding that after performing the resummation the corresponding cross section can be computed with an accuracy better than 10%.
We present precision calculations of the transverse-momentum spectrum and the invariant-mass distribution for slepton pair production at hadron colliders. We implement the transverse-momentum, threshold and joint resummation formalisms at the next-to-leading logarithmic accuracy and consistently match the obtained result with the pure perturbative result at the first order in the strong coupling constant, i.e. at order alpha_s. We give numerical predictions for selectron and stau pair production, and compare the various resummed cross sections with the perturbative result.
A complete description of W and Z boson production at high-energy colliders requires the resummation of large Sudakov logarithms which dominate the production at small transverse momentum. Currently there are two techniques for performing this resummation: impact parameter space and transverse momentum space. We argue that the latter can be formulated in a way which retains the advantages of the former, while at the same time allowing a smooth transition to finite order dominance at high transverse momentum.
We present an implementation of the Yennie--\-Frautschi--\-Suura (YFS) scheme for the all-orders resummation of logarithms from the emission of soft real and virtual photons in processes that are critical for future lepton colliders. They include, in particular, $e^-e^+\to f\bar{f}$ and $e^-e^+\to W^-W^+$, where we validate the results of our implementation, improved with fixed-order corrections, with those obtained from the most precise calculations. We also show, for the first time, results for the Higgs-Strahlungs process, $e^-e^+\to ZH$, in YFS resummation including fixed-order improvement…
We investigate the resummation of large logarithmic perturbative corrections to hadron production in electron-positron annihilation and semi-inclusive deep-inelastic scattering. We find modest, but significant, enhancements of hadron multiplicities in the kinematic regimes accessible in present high-precision experiments. Our results are therefore relevant for the determination of hadron fragmentation functions from data for these processes.
We investigate the QCD effects in the production of neutral Higgs bosons via bottom quark fusion in both the standard model and the minimal supersymmetric standard model at the CERN Large Hadron Collider. We include the next-to-leading order (NLO) QCD corrections (including supersymmetric QCD) and the threshold resummation effects. We use the soft-collinear effective theory to resum the large logarithms near threshold from soft gluon emission. Our results show that the resummation effects can enhance the total cross sections by about 5% compared with the NLO results.
We study the nonperturbative functions in the Collins--Soper--Sterman resummation formalism by examing Drell--Yan data in both fixed target and collider experiments and then predict the transverse momentum distributions of the $W^\pm$ and $Z^0$ bosons at the Tevatron. Our results differ from that in the literature and agree better with published CDF data. Using statistical arguments, we find a $1\,$fb${}^{-1}$ luminosity at the Fermilab Tevatron should be able to provide useful constraints on the nonperturbative functions.
We use a recent approach to soft-gluon resummation based on effective field theory to implement soft-gluon resummation at NNNLL order for slepton-pair production in SUSY extensions of the Standard Model. This approach resums large logarithmic corrections arising from the dynamical enhancement of the partonic threshold region caused by steeply falling parton luminosities. We evaluate the resummed invariant-mass distribution and total cross section for slepton-pair production at the Tevatron and LHC, matching our results onto NLO fixed-order calculations. As a byproduct, we also study virtual SU…
We develop a framework for a systematic resummation of the transverse momentum distribution of top-quark pairs produced at hadron colliders based on effective field theory. Compared to Drell-Yan and Higgs production, a novel soft function matrix is required to account for the soft gluon emissions from the final states. We calculate this soft function at the next-to-leading order, and perform the resummation at the next-to-next-to-leading logarithmic accuracy. We compare our results with parton shower programs and with the experimental data at the Tevatron and the LHC. We also discuss the impli…
We examine the soft-gluon resummation effects, including the exact spin correlations among the final state particles, in the search of the Standard Model Higgs boson, via the process $gg\to H\to WW/ZZ \to 4 leptons, at the Tevatron and the LHC. A comparison between the resummation and the Next-to-Leading order (NLO) calculation is performed after imposing various kinematics cuts suggested in the literature for the Higgs boson search. For the $H\to ZZ$ mode, the resummation effects increase the acceptance of the signal events by about 25%, as compared to the NLO prediction, and dramatically alt…
We study the impact of initial-state multiple parton radiation on transverse momentum $(q_T)$ distribution of Higgs boson produced via bottom quark fusion at hadron colliders. The shape of the resulting $q_T$ distribution is affected by the bottom-quark mass corrections and by the strong kinematical behavior of the bottom-quark parton density. We account for both features in the full range of $q_T$. To do this, we formulate the resummation calculation in a general-mass factorization (S-ACOT) scheme and introduce a correction in the resummed-term to account for the effect from large-$q_T$ kinem…
We compute the resummed hadronic transverse-energy ($E_T$) distribution due to initial-state QCD radiation in the production of a Standard Model Higgs boson of mass 126 GeV by gluon fusion at the Large Hadron Collider, with matching to next-to-leading order calculations at large $E_T$. Effects of hadronization, underlying event and limited detector acceptance are estimated using aMC@NLO with the Herwig++ and Pythia 8 event generators.
We study the transverse-momentum (q_T) and rapidity (y) distributions of the Higgs boson in perturbative QCD, including the most advanced theoretical information presently available: fixed-order perturbation theory at Next-to-Leading Order (NLO) in the large-q_T region (q_T ~ M_H, being M_H the Higgs mass), and soft-gluon resummation at the Next-to-Next-to-Leading Logarithmic accuracy (NNLL) in the small-q_T region (q_T << M_H). We present numerical results for the doubly-differential (q_T and y) cross section for the production of a Standard Model Higgs boson at the Large Hadron Collider (LHC…
We present a first and extensive study of threshold resummation effects for supersymmetric (SUSY) particle production at hadron colliders, focusing on Drell-Yan like slepton-pair and slepton-sneutrino associated production. After confirming the known next-to-leading order (NLO) QCD corrections and generalizing the NLO SUSY-QCD corrections to the case of mixing squarks in the virtual loop contributions, we employ the usual Mellin N-space resummation formalism with the minimal prescription for the inverse Mellin-transform and improve it by resumming 1/N-suppressed and a class of N-independent un…
We present HEJ 2, a new implementation of the High Energy Jets formalism for high-energy resummation in hadron-collider processes as a flexible Monte Carlo event generator. In combination with a conventional fixed-order event generator, HEJ 2 can be used to obtain greatly improved predictions for a number of phenomenologically important processes by adding all-order logarithmic corrections in $\hat{s}/p_\perp^2$. A prime example for such a process is the gluon-fusion production of a Higgs boson in association with widely separated jets, which constitutes the dominant background to Higgs boson …
We study the resummation of large logarithmic perturbative corrections to the partonic cross sections relevant for di-hadron production in hadronic collisions, H1 H2 -> h1 h2 X, at high invariant mass of the produced hadron pair. These corrections arise near the threshold for the partonic reaction and are associated with soft-gluon emission. We perform the resummation to next-to-leading logarithmic accuracy, and show how to incorporate consistently cuts in rapidity and transverse momentum of the observed particles. We present numerical results for fixed-target and ISR regimes and find enhancem…
Direct photon production is an important process at hadron colliders, being relevant both for precision measurement of the gluon density, and as background to Higgs and other new physics searches. Here we explore the implications of recently derived results for high energy resummation of direct photon production for the interpretation of measurements at the Tevatron and the LHC. The effects of resummation are compared to various sources of theoretical uncertainties like PDFs and scale variations. We show how the high--energy resummation procedure stabilizes the logarithmic enhancement of the c…
We consider the associated production of a vector or Higgs boson with a jet in hadronic collisions. When the transverse momentum $q_T$ of the boson-jet system is much smaller than its invariant mass $Q$, the QCD perturbative expansion is affected by large logarithmic terms that must be resummed to all orders. We discuss the all-order resummation structure of the logarithmically enhanced contributions up to next-to-leading logarithmic accuracy. Resummation is performed at the differential level with respect to the kinematical variables of the boson-jet system. Soft-parton radiation produces azi…
We investigate the QCD effects in the associated production of the chargino and the neutralino, $\tildeχ^\pm_{1}$ and $\tildeχ^0_{2}$, in the Minimal Supersymmetric Standard Model (MSSM) at both the Fermilab Tevatron and the CERN Large Hadron Collider (LHC). We include the next-to-leading order (NLO) QCD corrections (including supersymmetric QCD) and the threshold resummation effects. Our results show that, compared to the NLO predictions, the threshold resummation effects can increase the total cross sections by 3.6% and 3.9% for the associated production of $\tildeχ^+_{1}\tildeχ^0_{2}$ and $…
We consider QCD corrections to Higgs boson production through gluon--gluon fusion in hadron collisions. We compute the cross section, performing the all-order resummation of multiple soft-gluon emission at next-to-next-to-leading logarithmic level. Known fixed-order results (up to next-to-next-to-leading order) are consistently included in our calculation. We give phenomenological predictions for Higgs boson production at the Tevatron and at the LHC. We estimate the residual theoretical uncertainty from perturbative QCD contributions. We also quantify the differences obtained by using the pres…
In R-parity conserving supersymmetric (SUSY) models, sleptons are produced in pairs at hadron colliders through neutral and charged electroweak currents. We demonstrate that the polarization of the initial hadron beams allows for a direct extraction of the slepton mixing angle and thus for a determination of the underlying SUSY-breaking mechanism. We also perform a first precision calculation of the transverse-momentum (q_T) spectrum of the slepton pairs by resumming soft multiple-gluon emission at next-to-leading logarithmic order. The results show a relevant contribution of resummation both …
A method is developed for calculating the jet mass distribution at hadron colliders using an expansion about the kinematic threshold. In particular, we consider the mass distribution of jets of size R produced in association with a hard photon at the Large Hadron Collider. Expanding around the kinematic threshold, where all the energy goes into the jet and the photon, provides a clean factorization formula and allows for the resummation of logarithms associated with soft and collinear divergences. All of the large logarithms of jet mass are resummed at next-to-leading logarithmic level (NLL), …
We compute the effects of soft gluon resummation for the production of high mass systems in hadronic collisions. We carefully analyse the growth of the perturbative expansion coefficients of the resummation formula. We propose an expression consistent with the known leading and next-to-leading resummation results, in which the coefficients grow much less than factorially. We apply our formula to Drell--Yan pair production, heavy flavour production, and the production of high invariant mass jet pairs in hadronic collisions. We find that, with our formula, resummation effects become important on…
We uncover a contribution to the NLO/NLL threshold resummed total cross section for top quark pair production at hadron colliders, which has not been taken into account in earlier literature. We derive this contribution - the difference between the singlet and octet hard (matching) coefficients - in exact analytic form. The numerical impact of our findings on the Sudakov resummed cross section turns out to be large, and comparable in size to the current estimates for the theoretical uncertainty of the total cross section. A rough estimate points toward a few percent decrease of the latter at t…
Incorporating all recent theoretical advances, we resum soft-gluon corrections to the total $t\bar t$ cross-section at hadron colliders at the next-to-next-to-leading logarithmic (NNLL) order. We perform the resummation in the well established framework of Mellin $N$-space resummation. We exhaustively study the sources of systematic uncertainty like renormalization and factorization scale variation, power suppressed effects and missing two- and higher-loop corrections. The inclusion of soft-gluon resummation at NNLL brings only a minor decrease in the perturbative uncertainty with respect to t…
We study the resummation of large logarithmic perturbative corrections to the partonic cross sections relevant for the process pp->h X at high transverse momentum of the hadron h. These corrections arise near the threshold for the partonic reaction and are associated with soft-gluon emission. We perform the resummation to next-to-leading logarithmic accuracy. We present numerical results for the fixed-target regime and find enhancements over the next-to-leading order cross section, which significantly improve the agreement between theoretical predictions and data. We also apply the resummation…
The perturbation series for electroweak vector boson production at small transverse momentum is dominated by large double logarithms at each order in perturbation theory. An accurate theoretical prediction therefore requires a resummation of these logarithms. This can be performed either directly in transverse momentum space or in impact parameter (Fourier transform) space. While both approaches resum the same leading double logarithms, the subleading logarithms are, in general, treated differently. We comment on two recent approaches to this problem, emphasising the particular subleading loga…
We evaluate the impact of heavy-quark masses on transverse momentum distributions of W, Z, and supersymmetric neutral Higgs bosons at the Tevatron and LHC. The masses of charm and bottom quarks act as non-negligible momentum scales at small transverse momentum, and affect resummation of soft and collinear radiation. We point out inconsistencies in the treatment of heavy-flavor channels at small transverse momentum in massless factorization schemes, and formulate small transverse momentum resummation in a general-mass variable flavor number factorization scheme. The improved treatment of the qu…
I discuss the motivation for resummation of the effects of initial-state soft gluon radiation, to all orders in the strong coupling strength, for processes in which the near-threshold region in the partonic subenergy is important. I summarize the method of "perturbative resummation" and its application to the calculation of the total cross section for top quark production at hadron colliders. Comments are included on the differences between the treatment of subleading logarithmic terms in this method and in other approaches.
We investigate the resummation of large logarithmic perturbative corrections to the partonic cross sections for single-inclusive high-p_T hadron production in collisions of transversely polarized hadrons. We perform the resummation to next-to-leading logarithmic accuracy. Phenomenological results are given for pbar-p collisions at center-of-mass energy of 14.5 GeV and for p-p collisions at 62.4 GeV and at 10 GeV, which are relevant for possible experiments at the GSI-FAIR, RHIC and J-PARC facilities, respectively. We find significant enhancements of the spin-dependent and spin-averaged cross s…
We study the transverse momentum resummation for dijet correlation in hadron collisions based on the Collins-Soper-Sterman formalism. The complete one-loop calculations are carried out in the collinear factorization framework for the differential cross sections at low imbalance transverse momentum between the two jets. Important cross checks are performed to demonstrate that the soft divergences cancelled out between different diagrams, and in particular, those associated with final state jets. The leading and sub-leading logarithms are identified. All order resummation is derived following th…
We study the application of the joint resummation to electroweak boson production at hadron colliders. The joint resummation formalism resums both threshold and transverse momentum corrections to the transverse momentum distribution at next-to-leading logarithmic accuracy. We obtain a good description of the transverse momentum distribution of Z bosons produced at the Tevatron collider.
We present results relevant for the extension of threshold resummation beyond the next-to-leading logarithmic (NLL) order for QCD hard-scattering processes. As an example, we consider di-hadron production $H_1 H_2\to h_1 h_2 X$, where the produced pair has a large invariant mass. Taking into account the non-trivial color structure of the partonic hard-scattering process, we determine the hard and soft matrices in color space. In our numerical studies we find a significant improvement compared to previous results at NLL accuracy. In particular, the scale dependence of the resummed cross section…
We investigate QCD threshold resummation effects beyond the next-to-leading logarithmic (NLL) order for the process H1 H2->h1 h2 X at high invariant mass of the produced hadron pair. We take into account the color structure of the underlying partonic hard-scattering cross sections and determine the relevant hard and soft matrices in color space that contribute to the resummed cross section at next-to-next-to-leading logarithmic (NNLL) accuracy. We present numerical results for fixed-target and collider regimes. We find a significant improvement compared to previous results at NLL accuracy. In …
We derive a factorization formula for the production of pairs of heavy coloured particles in hadronic collisions near the production threshold that establishes factorization of soft and Coulomb effects. This forms the basis for a combined resummation of Coulomb and soft corrections, including the non-trivial interference of the two effects. We develop a resummation formalism valid at NNLL accuracy using the momentum-space approach to soft gluon resummation. We present numerical results for the NLL resummed squark-antisquark production cross section at the LHC and Tevatron, including also the c…
We present a formalism that improves the applicability of perturbative QCD in the current region of semi-inclusive deep inelastic scattering. The formalism is based on all-order resummation of large logarithms arising in the perturbative treatment of hadron multiplicities and energy flows in this region. It is shown that the current region of semi-inclusive DIS is similar to the region of small transverse momenta in vector boson production at hadron colliders. We use this resummation formalism to describe transverse energy flows and charged particle multiplicity measured at the electron-proton…
We consider the resummation of soft-gluon emission in the transverse-momentum distribution of vector mesons in hadronic collisions. We find that the resummed expression in the impact-parameter formulation has an expansion in $\as$ with factorially growing terms with oscillating signs. These diverging terms arise from the small impact-parameter region of integration, and are of a subleading nature. We also obtain a closed expression for the next-to-leading logarithm resummation in $\qt$-space, and we study its analytic structure. We find in this case that, although no factorially growing terms …
We perform the transverse-momentum resummation for $W^{+}W^{-}$, $ZZ$, and $W^{\pm}Z$ pair productions at the next-to-next-to-leading logarithmic accuracy using soft-collinear effective theory for $\sqrt{S}=8 \text{TeV}$ and $\sqrt{S}=14 \text{TeV}$ at the LHC, respectively. Especially, this is the first calculation of $W^{\pm}Z$ transverse-momentum resummation. We also include the non-perturbative effects and discussions on the PDF uncertainties. Comparing with the next-to-leading logarithmic results, the next-to-next-to-leading logarithmic resummation can reduce the dependence of the transve…
We investigate the effect of QCD resummation to kinematical correlations in the Higgs boson plus high transverse momentum (Pt) jet events produced at hadron colliders. We show that at the complete one-loop order, the Collins-Soper-Sterman resummation formalism can be applied to derive the Sudakov form factor, which is found to be independent of jet-finding algorithm. We compare the singular behavior of resummation calculation to fixed order prediction in the case that Higgs boson and high Pt jet are produced nearly back-to-back in their transverse momenta, and find a perfect agreement. The phe…
We report on the study of soft gluon effects in the production of squarks and gluinos at hadron colliders. Close to production threshold, the emission of soft gluon results in the appearence of large logarithmic corrections in the theoretical expressions. In order to resum these corrections at next-to-leading-logarithmic accuracy appropriate one-loop anomalous dimensions have to be calculated. We present the calculation of the anomalous dimensions for all production channels of squarks and gluinos and provide numerical predictions for the Tevatron and the LHC.
We review the basic concepts of all-order calculations in Quantum Chromodynamics (QCD) and their application to collider phenomenology. We start by discussing the factorization properties of QCD amplitudes and cross-sections in the soft and collinear limits and their resulting all-order exponentiation. We then discuss several applications of this formalism to observables which are of great interest at particle colliders. In this context, we describe the all-order resummation of event-shape distributions, as well as observables that probe the internal structure of hadronic jets.
We present calculations of next-to-leading order and resummed QCD corrections for semi-inclusive deep-inelastic scattering and single-inclusive e+e- annihilation. The resummation is performed to next-to-leading logarithmic accuracy. Knowing these QCD corrections is important in order to extract parton distribution functions and fragmentation functions from present and future data for these reactions. We present comparisons of our results to recent data by the COMPASS, HERMES, Belle, and BaBar experiments.
We study the cross section for the photoproduction process $γN\rightarrow h X$ where the incident photon and nucleon are longitudinally polarized and a hadron $h$ is observed at high transverse momentum. Specifically, we address the "direct" part of the cross section, for which the photon interacts in a pointlike way. For this contribution we perform an all-order resummation of logarithmic threshold corrections generated by soft or collinear gluon emission to next-to-leading logarithmic accuracy. We present phenomenological results relevant for the COMPASS experiment and compare to recent COMP…
We parameterize the enhancement of threshold effects away from hadronic endpoint that arise due to the steeply falling nature of parton distribution functions, within the context of soft-collinear effective theory. This is accomplished in a process-independent way by directly linking the charac- teristic scale of soft and collinear radiation, λ, to the shape of the pdfs. This allows us quantify the power corrections to partonic threshold resummation as a function of the invariant mass and rapidity of the final state. In the context of SCET, being able to compute λin a process-independent manne…
We thoroughly investigate both transverse momentum and threshold resummation effects on scalar-pseudoscalar pair production via quark-antiquark annihilation at the $13~ \text{TeV}$ Large Hadron Collider at QCD NLO+NLL accuracy. A factorization method is introduced to properly supplement the soft-gluon (threshold) resummation contribution from parton distribution functions to the resummed results obtained by the Collins-Soper-Sterman resummation approach. We find that the impact of the threshold-resummation improved PDFs is comparable to the resummation effect of the partonic matrix element and…
We discuss a model for soft gluon re-summation based on a statistical description of independent emissions during inelastic collisions. The model is applied to estimate Survival Probabilities at the LHC. A comparison with other models and experimental data is presented.
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.
We study QCD effects in single graviton production at the CERN Large Hadron Collider (LHC) in the Randall-Sundrum (RS) Model. We present in detail the complete next-to-leading order (NLO) QCD corrections to the inclusive total cross sections. The NLO QCD corrections enhance significantly the total cross sections and decrease efficiently the dependence of the total cross sections on the factorization and renormalization scales. We also examine the uncertainty of the total cross sections due to the parton distribution function (PDF) uncertainties. For the differential cross sections on the trans…
We investigate QCD effects in the production of a single slepton at hadron colliders in the Minimal Supersymmetric Standard Model without R-parity. We calculate the total cross sections and the transverse momentum distributions at next-to-leading order in QCD. The NLO corrections enhance the total cross sections and decrease the dependence of the total cross sections on the factorization and renormalization scales. For the differential cross sections, we resum all order soft gluon effects to give reliable predictions for the transverse momentum distributions. We also compare two approaches to …
