The new precision era of jet quenching observables at both RHIC and the LHC calls for an improved and more precise description of in-medium gluon emissions. The development of new theoretical tools and analytical calculations to tackle this challenge has been hampered by the inability to include the effects of multiple scatterings with the medium using a realistic model for the parton-medium interactions. In this paper, we show how the analytical expressions for the full in-medium spectrum, including the resummation of all multiple scatterings, can be written in a form where the numerical evaluation can be easily performed without the need of the usually employed harmonic or single hard approximations. We present the transverse momentum and energy-dependent medium-induced gluon emission distributions for known realistic interaction models to illustrate how our framework can be applied beyond the limited kinematic regions of previous calculations.
We present a systematic study of differences between NLL resummation and parton showers. We first construct a Markovian Monte-Carlo algorithm for resummation of additive observables in electron-positron annihilation. Approximations intrinsic to the pure NLL result are then removed, in order to obtain a traditional, momentum and probability conserving parton shower based on the coherent branching formalism. The impact of each approximation is studied, and an overall comparison is made between the parton shower and pure NLL resummation. Differences compared to modern parton-shower algorithms for…
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 discuss perturbative solutions of renormalization group equations, and propose the use of resummation scale techniques in assessing theoretical uncertainties on the extraction of parton distribution functions from data.
I report on precision comparisons of theoretical predictions for Drell-Yan (DY) transverse momentum spectra from two approaches: the analytical resummation approach based on Collins-Soper-Sterman (CSS) formalism and the parton branching (PB) approach to the evolution of transverse momentum dependent (TMD) parton distributions.
We demonstrate that theoretical predictions using current resummation techniques for the lepton pair production (LPP) rapidity and $x_F$ distributions can be inconsistent with data in high rapidity and $x_F$ kinematic regions by observing their effect in global fits of parton distribution functions (PDFs). We present an enhanced resummation technique for the LPP rapidity and $x_F$ distributions that agrees with LPP data. The enhanced resummation method is used in conjunction with threshold resummation in deep inelastic scattering (DIS) to perform two global fits of PDFs using the minimal and B…
The precise knowledge of parton distribution functions (PDFs) is indispensable to the accurate calculation of hadron-initiated QCD hard scattering observables. Much of our information on PDFs is extracted by comparing deep inelastic scattering (DIS) and lepton pair production (LPP) data to convolutions of the PDFs with the partonic cross sections of these processes. It is known that partonic cross sections receive large corrections in regions of phase space near partonic thresholds that can be resummed using threshold resummation techniques. The effect of threshold resummation on DIS and LPP d…
Threshold resummation for gluon fusion $ZH$ production at the LHC
RWTH Aachen University（亚琛工业大学）；Indian Institute of Technology Kanpur（坎普尔印度理工学院）；Physical Research Laboratory（物理研究实验室）；Indian Institute of Technology Guwahati（古瓦哈提印度理工学院）；Durham University（杜伦大学）
Infrared divergences of QCD scattering amplitudes can be derived from an anomalous dimension matrix, which is also an essential ingredient for the resummation of large logarithms due to soft gluon emissions. We report a recent analytical calculation of the anomalous dimension matrix with both massless and massive partons at two-loop level, which describes the two-loop infrared singularities of any scattering amplitudes with an arbitrary number of massless and massive partons, and also enables soft gluon resummation at next-to-next-to-leading-logarithmic order. As an application, we calculate t…
We present a determination of the parton distribution functions of the proton in which NLO and NNLO fixed-order calculations are supplemented by NLLx small-x resummation. Deep inelastic structure functions are computed consistently at NLO+NLLx or NNLO+NLLx, while for hadronic processes small-x resummation is included only in the PDF evolution, with kinematic cuts introduced to ensure the fitted data lie in a region where the fixed-order calculation of the hard cross-sections is reliable. In all other respects, the fits use the same methodology and are based on the same global dataset as the re…
We describe a new framework for soft gluon resummation, based on path integral methods. The approach recovers previous results obtained in the eikonal approximation, in which all emitted gluons become soft. Furthermore, a clear physical interpretation allows straightforward extension of the framework to beyond the eikonal approximation, and we use this to classify the structure of next-to-eikonal corrections to matrix elements.
We discuss the resummation of the large logarithmic terms appearing in the heavy quark effects on parton distribution functions inside the virtual photon. We incorporate heavy quark mass effects by changing the initial condition of the leading-order DGLAP evolution equation. In a certain kinematical limit, we recover the logarithmic terms of the next-to-leading order heavy quark effects obtained in the previous work. This method enables us to resum the large logarithmic terms due to heavy quark mass effects on the parton distributions in the virtual photon. We numerically calculate parton dist…
LHC measurements involve cuts on several observables, but resummed calculations are mostly restricted to single variables. We show how the resummation of a class of double-differential measurements can be achieved through an extension of Soft-Collinear Effective Theory (SCET). A prototypical application is $pp \to Z + 0$ jets, where the jet veto is imposed through the beam thrust event shape ${\mathcal T}$, and the transverse momentum $p_T$ of the $Z$ boson is measured. A standard SCET analysis suffices for $p_T \sim m_Z^{1/2} {\mathcal T}^{1/2}$ and $p_T \sim {\mathcal T}$, but additional col…
I discuss the effectiveness of soft-gluon resummations in describing higher-order corrections. I present a comparison of recent resummation approaches and their relative successes in approximating complete NNLO corrections. I also discuss fixed-order expansions through NNNLO and present some recent applications to QCD hard-scattering processes, including top-antitop pair production, single-top production, and W production at large transverse momentum.
We determine the valence parton distribution function of the pion by performing a new analysis of data for the Drell-Yan process $π^- N\to μ^+μ^-X$. Compared to previous analyses, we include next-to-leading-logarithmic threshold resummation effects in the calculation of the Drell-Yan cross section. As a result of these, we find a considerably softer valence distribution at high momentum fractions $x$ than obtained in previous next-to-leading order analyses, in line with expectations based on perturbative-QCD counting rules or Dyson-Schwinger equations.
We analyze soft and collinear gluon resummation effects at the N$^3$LL level for Standard Model Higgs boson production via gluon fusion $gg\to H$ and the neutral scalar and pseudoscalar Higgs bosons of the minimal supersymmetric extension at the N$^3$LL and NNLL level, respectively. We introduce refinements in the treatment of quark mass effects and subleading collinear gluon effects within the resummation. Soft and collinear gluon resummation effects amount to up to about 5% beyond the fixed-order results for scalar and pseudoscalar Higgs boson production.
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 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 perform the first global QCD analysis of pion valence, sea quark, and gluon distributions within a Bayesian Monte Carlo framework with threshold resummation on Drell-Yan cross sections at next-to-leading log accuracy. Exploring various treatments of resummation, we find that the large-$x$ asymptotics of the valence quark distribution $\sim (1-x)^{β_v}$ can differ significantly, with $β_v$ ranging from $\approx 1$ to $> 2.5$ at the input scale. Regardless of the specific implementation, however, the resummation induced redistribution of the momentum between valence quarks and gluons boosts t…
We discuss the GENEVA Monte Carlo framework, which combines higher-order resummation (NNLL) of large Sudakov logarithms with multiple next-to-leading-order (NLO) matrix-element corrections and parton showering (using PYTHIA8) to give a complete description at the next higher perturbative accuracy in alpha_s at both small and large jet resolution scales. Results for e+e- -> jets compared to LEP data and for Drell-Yan production are presented.
A strategy for calculating the color structure needed for soft gluon resummation for processes with any number of colored partons is introduced using a N_c --> infinity inspired basis. In this basis a general formalism can be found at the same time as the calculations are simplified. The advantages are illustrated by recalculating the soft anomalous dimension matrix for the processes gg --> gg, q\qbar --> q \qbar g and q\qbar --> ggg.
We perform resummation of soft gluon corrections to the total cross section for the process $pp \to t\bar{t}H$. The resummation is carried out at next-to-leading-logarithmic (NLL) accuracy using the Mellin space technique, extending its application to the class of $2 \to 3$ processes. We present an analytical result for the soft anomalous dimension for a hadronic production of two coloured massive particles in association with a colour singlet. We discuss the impact of resummation on the numerical prediction for the associated Higgs boson production with top quarks at the LHC.
We present our results on soft gluon resummation in the invariant mass threshold applied to the associated production of a top quark pair with a W boson at the LHC in the Mellin space formalism.
Inclusion of down to zero-momentum gluons and their k_t resummation is shown to quench the too fast rise of the mini jet cross section and thereby obtain realistic total cross-sections.
In the following we present our recent results on the resummation of soft gluon corrections to the $pp\rightarrow t\bar{t}H$ cross section at the LHC. The resummation was carried out at next-to-next-to-leading-logarithmic (NNLL) accuracy using the Mellin space technique. Obtained results were matched to the NLO cross section. We show that the resummation leads to reduction of scale-variation uncertainty of the total $pp\rightarrow t\bar{t}H$ cross section.
We study the effect of soft gluon resummation on the gaps-between-jets cross-section at the LHC. We review the theoretical framework that enables one to sum logarithms of the hard scale over the veto scale to all orders in perturbation theory. We then present a study of the phenomenological impact of Coulomb gluon contributions and super-leading logarithms on the gaps between jets cross-section at the LHC.
The off-diagonal parton-scattering channels $g+γ^*$ and $q+ϕ^*$ in deep-inelastic scattering are power-suppressed near threshold $x\to 1$. 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 …
Novel PDFs taking into account resummation-improved matrix elements, albeit only in the fit of a reduced data set, allow for consistent NLO+NLL calculations of slepton pair production at the LHC. We apply a factorisation method to this process that minimises the effect of the data set reduction, avoids the problem of outlier replicas in the NNPDF method for PDF uncertainties and preserves the reduction of the scale uncertainty. For Run II of the LHC, left-handed selectron/smuon, right-handed and maximally mixed stau production, we confirm that the consistent use of threshold-improved PDFs part…
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.
We study the effect of soft gluon emission on the total cross section predictions for the $gg\to HZ$ associated Higgs production process at the LHC. To this end, we perform resummation of threshold corrections at the NLL accuracy in the absolute threshold production limit and in the threshold limit for production of a $ZH$ system with a given invariant mass. Analytical results and numerical predictions for various possible LHC collision energies are presented. The perturbative stability of the results is verified by including universal NNLL effects. We find that resummation significantly reduc…
