N-jettiness in electroweak high-energy processes

We study N-jettiness in electroweak processes at extreme high energies, in which the mass of the weak gauge bosons can be regarded as small. The description of the scattering process such as e−e+ → μ−μ+ + X is similar to QCD. The incoming leptons emit initial-state radiation and the resultant particles, highly off-shell, participate in the hard scattering, which are expressed by the beam functions. After the hard scattering, the final- state leptons or leptonic jets are observed, described by the fragmenting jet functions or the jet functions respectively. At present, electroweak processes are prevailed by the processes induced by the strong interaction, but they will be relevant at future e−e+ colliders at high energy. The main difference between QCD and electroweak processes is that the initial- and final-state particles should appear in the form of hadrons, that is, color singlets in QCD, while there can be weak nonsinglets as well in electroweak interactions. We analyze the factorization theorems for the N-jettiness in e−e+ → μ−μ+ + X, and compute the factorized parts to next-to-leading logarithmic accuracy. To simplify the comparison with QCD, we only consider the SU(2)W gauge interaction, and the extension to the Standard Model is straightforward. Put it in a different way, it corresponds to an imaginary world in which colored particles can be observed in QCD, and the richer structure of effective theories is probed. Various nonzero nonsinglet matrix elements are interwoven to produce the factorized results, in contrast to QCD in which there are only contributions from the singlets. Another distinct feature is that the rapidity divergence is prevalent in the contributions from weak nonsinglets due to the different group theory factors between the real and virtual corrections. We verify that the rapidity divergence cancels in all the contributions with a different number of nonsinglet channels. We also consider the renormalization group evolution of each factorized part to resum large logarithms, which are distinct from QCD.

Advancing MıNNLOPS to diboson processes: Zγ production at NNLO+PS

We consider Zγ production in hadronic collisions and present the first computation of next-to-next-to-leading order accurate predictions consistently matched to parton showers (NNLO+PS). Spin correlations, interferences and off-shell effects are included by calculating the full process pp → ℓ+ℓ−γ. We extend the recently developed MiNNLOPS method to genuine 2 → 2 hard scattering processes at the LHC, which paves the way for NNLO+PS simulations of all diboson processes. This is the first 2 → 2 NNLO+PS calculation that does not require an a-posteriori multi-differential reweighting. We find that both NNLO corrections and matching to parton showers are crucial for an accurate simulation of the Zγ process. Our predictions are in very good agreement with recent ATLAS data.

Mixed EW-QCD two-loop amplitudes for $$ q\overline{q}\to {\mathrm{\ell}}^{+}{\mathrm{\ell}}^{-} $$ and γ5 scheme independence of multi-loop corrections

We perform a dedicated study of the $$ q\overline{q} $$ q q ¯ -initiated two-loop electroweak-QCD Drell-Yan scattering amplitude in dimensional regularization schemes for vanishing light quark and lepton masses. For the relative order α and αs one-loop Standard Model corrections, details of our comparison to the original literature are given. The infrared pole terms of the mixed two-loop amplitude are governed by a known generalization of the dipole formula and we show explicitly that exactly the same two-loop polarized hard scattering functions are obtained in both the standard ’t Hooft-Veltman-Breitenlohner-Maison γ5 scheme and Kreimer’s anticommuting γ5 scheme.

Energetic boundary element method for accurate solution of damped waves hard scattering problems

The paper deals with the numerical solution of 2D wave propagation exterior problems including viscous and material damping coefficients and equipped by Neumann boundary condition, hence modeling the hard scattering of damped waves. The differential problem, which includes, besides diffusion, advection and reaction terms, is written as a space–time boundary integral equation (BIE) whose kernel is given by the hypersingular fundamental solution of the 2D damped waves operator. The resulting BIE is solved by a modified Energetic Boundary Element Method, where a suitable kernel treatment is introduced for the evaluation of the discretization linear system matrix entries represented by space–time quadruple integrals with hypersingular kernel in space variables. A wide variety of numerical results, obtained varying both damping coefficients and discretization parameters, is presented and shows accuracy and stability of the proposed technique, confirming what was theoretically proved for the simpler undamped case. Post-processing phase is also taken into account, giving the approximate solution of the exterior differential problem involving damped waves propagation around disconnected obstacles and bounded domains.

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.

Improved opacity expansion at NNLO for medium induced gluon radiation

When an energetic parton propagates in a hot and dense QCD medium it loses energy by elastic scatterings or by medium-induced gluon radiation. The gluon radiation spectrum is suppressed at high frequency due to the LPM effect and encompasses two regimes that are known analytically: at high frequencies $$ \omega >{\omega}_c=\hat{q}{L}^2 $$ ω > ω c = q ̂ L 2 , where $$ \hat{q} $$ q ̂ is the jet quenching transport coefficient and L the length of the medium, the spectrum is dominated by a single hard scattering, whereas the regime ω < ωc is dominated by multiple low momentum transfers. In this paper, we extend a recent approach (dubbed the Improved Opacity Expansion (IOE)), which allows an analytic (and systematic) treatment beyond the multiple soft scattering approximation, matching this result with the single hard emission spectrum. We calculate in particular the NNLO correction analytically and numerically and show that it is strongly suppressed compared to the NLO indicating a fast convergence of the IOE scheme and thus, we conclude that it is sufficient to truncate the series at NLO. We also propose a prescription to compare the GW and the HTL potentials and relate their parameters for future phenomenological works.

Soft Anomalous Dimensions and Resummation in QCD

I discuss and review soft anomalous dimensions in QCD that describe soft-gluon threshold resummation for a wide range of hard-scattering processes. The factorization properties of the cross section in moment space and renormalization-group evolution are implemented to derive a general form for differential resummed cross sections. Detailed expressions are given for the soft anomalous dimensions at one, two, and three loops, including some new results, for a large number of partonic processes involving top quarks, electroweak bosons, Higgs bosons, and other particles in the standard model and beyond.

General recipe to form input space for deep learning analysis of HEP scattering processes

Deep learning neural network (DNN) technique is one of the most efficient and general approach of multivariate data analysis of the collider experiments. The important step of the analysis is the optimization of the input space for multivariate technique. In the paper we propose the general recipe how to form the set of low-level observables sensitive to the differences in hard scattering processes at the colliders. It is shown in the paper that without any sophisticated analysis of the kinematic properties one can achieve close to optimal performance of DNN with the proposed general set of low-level observables.