QCD Cross Sections Research Articles

Hadronic total cross sections, Wilson loop correlators and the QCD spectrum

We show how to obtain rising hadronic total cross sections in QCD, in the framework of the nonperturbative approach to soft high-energy scattering based on Wilson-loop correlators. Total cross sections turn out to be of “Froissart”-type, i.e., the leading energy dependence is of the form σtot∼Blog2⁡s, in agreement with experiments. The observed universality of the prefactor B is obtained rather naturally in this framework. In this case, B is entirely determined by the stable spectrum of QCD, and predicted to be Bth=0.22 mb, in fair agreement with experiments.

Fragmentation functions at next-to-next-to-leading order accuracy

We present a first analysis of parton-to-pion fragmentation functions at next-to-next-to-leading order accuracy in QCD based on single-inclusive pion production in electron-positron annihilation. Special emphasis is put on the technical details necessary to perform the QCD scale evolution and cross section calculation in Mellin moment space. We demonstrate how the description of the data and the theoretical uncertainties are improved when next-to-next-to-leading order QCD corrections are included.

QCD corrections to W + W − production through gluon fusion

We compute the next-to-leading order (NLO) QCD corrections to the $gg \to W^+ W^- \to l^+_1 \nu_1 l^-_2 \bar \nu_2$ process, mediated by a massless quark loop, at the LHC. This process first contributes to the hadroproduction of $W^+W^-$ at $\mathcal{O}(\alpha_s^2)$, but, nevertheless, has a sizable impact on the total production rate. We find that the NLO QCD corrections to the $gg \to W^+W^-$ process amount to ${\cal O}(50)$%, and increase the NNLO QCD cross sections of $pp \to W^+W^-$ by approximately two percent, at both the 8 TeV and 13 TeV LHC. We also compute the NLO corrections to gluonic $W^+W^-$ production within a fiducial volume used by the ATLAS collaboration in their 8 TeV measurement of the $W^+W^-$ production rate and find that the QCD corrections are significantly smaller than in the inclusive case. While the current experimental uncertainties are still too large to make these differences relevant, the observed strong dependence of perturbative corrections on kinematic cuts underscores that extrapolation from a fiducial measurement to the total cross section is an extremely delicate matter, and calls for the direct comparison of fiducial volume measurements with corresponding theoretical computations.

Introducing MCgrid 2.0: Projecting cross section calculations on grids

MCgrid is a software package that provides access to interpolation tools for Monte Carlo event generator codes, allowing for the fast and flexible variation of scales, coupling parameters and PDFs in cutting edge leading- and next-to-leading-order QCD calculations. We present the upgrade to version 2.0 which has a broader scope of interfaced interpolation tools, now providing access to fastNLO, and features an approximated treatment for the projection of MC@NLO-type calculations onto interpolation grids. MCgrid 2.0 also now supports the extended information provided through the HepMC event record used in the recent SHERPA version 2.2.0. The additional information provided therein allows for the support of multi-jet merged QCD calculations in a future update of MCgrid. New version program summaryProgram title: MCgridCatalogue identifier: AESS_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AESS_v2_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 512334No. of bytes in distributed program, including test data, etc.: 4263504Distribution format: tar.gzProgramming language: C++, shell, Python.Computer: PC running Linux, Mac.Operating system: Linux, Mac OS.RAM: VaryingCatalogue identifier of previous version: AESS_v1_0Journal reference of previous version: Comput. Phys. Comm. 185(2014)2115Classification: 11.2, 11.5, 11.9.External routines: HepMC [1], Rivet [2], APPLgrid [3] and fastNLO [4]. A SHERPA [5] installation is also required.Does the new version supersede the previous version?: YesNature of problem: Efficient filling of cross section grid files from fully exclusive parton level Monte Carlo events.Solution method: Analyse Monte Carlo events via the Rivet program, which projects events on discretized cross section tables from APPLgrid [3] or fastNLO [4].Reasons for new version:•Previous MCgrid releases, cf. [6], supported only a single interpolation tool: APPLgrid [3]. Interfacing to more than one is important for cross checks and allows the use of MCgrid in a wider range of existing workflows.•The recently released SHERPA 2.2.0 provides more information in the HepMC [1] event record, allowing for the filling of the exact next-to-leading-order expansion of an MC@NLO calculation, see e.g. [7] for details, into an interpolation grid. To process the additional information and adopt the new weight naming convention used in SHERPA 2.2.0, modifications on the MCgrid side have been necessary. The possibility of filling grids for MC@NLO-type calculations broadens the scope of MCgrid. It allows for the quantification of the residual dependencies on the parton showers that are beyond the fixed-order approximation. Understanding these dependencies and eventually taking them into account during the creation of interpolation grids in an automated way would help in the fitting of PDFs to data that are not appropriately described by fixed-order calculations.Summary of revisions:•As an additional interpolation tool fastNLO [4] is now supported. This is the first time the fastNLO package can be used in conjunction with a multi-purpose Monte Carlo event generator. The required version of the fastNLO toolkit [8] is 2.3.1pre-2125 or later. With APPLgrid and fastNLO, all currently available interpolation tools for fixed-order QCD cross sections can now be used in conjunction with MCgrid.•Modifications have been made in order to adopt the new naming conventions in the HepMC event record format introduced in SHERPA 2.2.0.•The filling of the exact next-to-leading-order expansion of MC@NLO calculations has been implemented. The required information must be provided with the HepMC event record, which is the case for SHERPA 2.2.0.•The MCgrid::BinnedGrid class has been added. It corresponds to the Rivet::BinnedHistogram class and allows for the direct creation of grids for every Rivet histogram combined therein.•MCGRID_OUTPUT_PATH has been introduced, an environmental variable for specifying the grid output directory.•An automatic counter suffix for grid file names has been added to prevent overwriting.•The API has been streamlined for easier enabling of Rivet analyses for MCgrid.•The provided examples have been updated for use with SHERPA 2.2.0 and Rivet 2.2.1.Running time: Approximately 6 min per 1 million Drell–Yan events from SHERPA. This includes both the event generation and the MCgrid computations. The times can vary quite dramatically. The process used in the test case (which is a relatively quick one) takes about 2 min 30 s for the initial (phase-space fill) run and about 3 min for the second and final run. This is for 1 million events on a 2.9GhZ Ivy Bridge i7 processor.

General formulation of the sector-improved residue subtraction

The main theoretical tool to provide precise predictions for scattering cross sections of strongly interacting particles is perturbative QCD. Starting at next-to-leading order (NLO) the calculation suffers from unphysical IR-divergences that cancel in the final result. At NLO there exist general subtraction algorithms to treat these divergences during a calculation. Since the LHC demands for more precise theoretical predictions, general subtraction methods at next- to-next-to-leading order (NNLO) are needed.These proceedings outline the four-dimensional formulation of the sector improved residue subtraction. The subtraction scheme STRIPPER and in particular its extension to arbitrary multiplicities is explained. Therefore, it furnishes a general framework for the calculation of NNLO cross sections in perturbative QCD.

Comments on high-energy total cross sections in QCD

We discuss how hadronic total cross sections at high energy depend on the details of QCD, namely on the number of colours Nc and the quark masses. We find that while a “Froissart”-type behaviour σtot∼Blog2⁡s is rather general, relying only on the presence of higher-spin stable particles in the spectrum, the value of B depends quite strongly on the quark masses. Moreover, we argue that B is of order O(Nc0) at large Nc, and we discuss a bound for B which does not become singular in the Nf=2 chiral limit, unlike the Froissart–Łukaszuk–Martin bound.

Jets production in peripheral interactions of high energy leptons, quarks, photons, and gluons with the proton

The paper presents short historical reviews of the processes of lepton pairs production in peripheral interaction of leptons and ions at high energies. The orders of magnitude of the QED and QCD cross sections with the production of two and three jets are given. The technique of the analysis is described in detail based on the parameterization of Sudakov 4-momentum tasks and writing the amplitude in an explicit gaugeinvariant form.

Toward multi-differential cross sections: measuring two angularities on a single jet

The analytic study of differential cross sections in QCD has typically focused on individual observables, such as mass or thrust, to great success. Here, we present a first study of double differential jet cross sections considering two recoil-free angularities measured on a single jet. By analyzing the phase space defined by the two angularities and using methods from soft-collinear effective theory, we prove that the double differential cross section factorizes at the boundaries of the phase space. We also show that the cross section in the bulk of the phase space cannot be factorized using only soft and collinear modes, excluding the possibility of a global factorization theorem in soft-collinear effective theory. Nevertheless, we are able to define a simple interpolation procedure that smoothly connects the factorization theorem at one boundary to the other. We present an explicit example of this at next-to-leading logarithmic accuracy and show that the interpolation is unique up to $\alpha_s^4$ order in the exponent of the cross section, under reasonable assumptions. This is evidence that the interpolation is sufficiently robust to account for all logarithms in the bulk of phase space to the accuracy of the boundary factorization theorem. We compare our analytic calculation of the double differential cross section to Monte Carlo simulation and find qualitative agreement. Because our arguments rely on general structures of the phase space, we expect that much of our analysis would be relevant for the study of phenomenologically well-motivated observables, such as $N$-subjettiness, energy correlation functions, and planar flow.

Measurement of inclusive W and Z boson production cross sections in pp collisions at sqrt[s] = 8 TeV.

A measurement of total and fiducial inclusive W and Z boson production cross sections in pp collisions at sqrt[s] = 8 TeV is presented. Electron and muon final states are analyzed in a data sample collected with the CMS detector corresponding to an integrated luminosity of 18.2 ± 0.5 pb(-1). The measured total inclusive cross sections times branching fractions are σ(pp → WX)×B(W → ℓν) = 12.21 ± 0.03(stat) ± 0.24(syst) ± 0.32(lum) nb and σ(pp → ZX) × B(Z → ℓ+ℓ-) = 1.15 ± 0.01(stat) ± 0.02(syst) ± 0.03(lum) nb for the dilepton mass in the range of 60-120 GeV. The measured values agree with next-to-next-to-leading-order QCD cross section calculations. Ratios of cross sections are reported with a precision of 2%. This is the first measurement of inclusive W and Z boson production in proton-proton collisions at sqrt[s] = 8 TeV.

Higgs production in gluon fusion beyond NNLO

We construct an approximate expression for the cross section for Higgs production in gluon fusion at next-to-next-to-next-to-leading order (N3LO) in αs with finite top mass. We argue that an accurate approximation can be constructed by exploiting the analyticity of the Mellin space cross section, and the information on its singularity structure coming from large N (soft gluon, Sudakov) and small N (high energy, BFKL) all order resummation. We support our argument with an explicit comparison of the approximate and the exact expressions up to the highest (NNLO) order at which the latter are available. We find that the approximate N3LO result amounts to a correction of 17% to the NNLO QCD cross section for production of a 125 GeV Higgs at the LHC (8 TeV), larger than previously estimated, and it significantly reduces the scale dependence of the NNLO result.

NLO EW and QCD proton–proton cross section calculations with mcsanc-v1.01

mcsanc is a Monte Carlo tool based on the SANC (Support for Analytic and Numeric Calculations for experiments at colliders) modules for higher order calculations in hadron collider physics. It allows to evaluate NLO QCD and EW cross sections for Drell–Yan processes (inclusive), associated Higgs and gauge boson production and single-top quark production in s- and t-channels. The paper contains theoretical description of the SANC approach, numerical validations and manual. Program summaryProgram title: mcsanc-v1.01Catalogue identifier: AEPO_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPO_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 144207No. of bytes in distributed program, including test data, etc.: 1115648Distribution format: tar.gzProgramming language: Fortran, C, C++.Computer: x86(-64) architecture.Operating system: Linux.RAM: 2 GBClassification: 11.1, 11.6.External routines: LHAPDF [1]. LoopTools [2], Cuba [3] (included in the distribution file).Nature of problem:Theoretical calculations at next-to-leading order in perturbation theory allow the computation of higher precision amplitudes for Standard Model processes and decays, provided proper treatments of UV divergences and IR singularities are performed.Solution method:Numerical integration of the precomputed differential expressions for partonic cross sections of certain processes implemented as SANC modules [4].Restrictions:The list of processes is limited to Drell–Yan, associated Higgs and gauge boson production and single-top production in s- and t-channels.Running time:From hours to days depending on the requested precision and kinematic conditions. The example provided takes approximately 10–15 min.

High-energy behavior of hadronic total cross sections from lattice QCD

By means of a nonperturbative approach to soft high-energy hadron-hadron scattering, based on the analytic continuation of Wilson-loop correlation functions from Euclidean to Minkowskian theory, we shall investigate the asymptotic energy dependence of hadron-hadron total cross sections in lattice QCD: we will show, using best fits of the lattice data with proper functional forms satisfying unitarity and other physical constraints, how indications emerge in favor of a universal asymptotic high-energy behavior of the kind Blog2s for hadronic total cross sections.

General mass scheme for jet production in DIS

We propose a method for calculating DIS jet production cross sections in QCD at NLO accuracy with consistent treatment of heavy quarks. The scheme relies on the dipole subtraction method for jets, which we extend to all possible initial state splittings with heavy partons, so that the Aivazis-Collins-Olness-Tung massive collinear factorization scheme can be applied. As a first check of the formalism we recover the Aivazis-Collins-Olness-Tung result for the heavy quark structure function using a dedicated Monte Carlo program.

Setting the renormalization scale in QCD: The principle of maximum conformality

A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale $\mu$ of the running coupling $\alpha_s(\mu^2).$ The purpose of the running coupling in any gauge theory is to sum all terms involving the $\beta$ function; in fact, when the renormalization scale is set properly, all non-conformal $\beta \ne 0$ terms in a perturbative expansion arising from renormalization are summed into the running coupling. The remaining terms in the perturbative series are then identical to that of a conformal theory; i.e., the corresponding theory with $\beta=0$. The resulting scale-fixed predictions using the "principle of maximum conformality" (PMC) are independent of the choice of renormalization scheme -- a key requirement of renormalization group invariance. The results avoid renormalon resummation and agree with QED scale-setting in the Abelian limit. The PMC is also the theoretical principle underlying the BLM procedure, commensurate scale relations between observables, and the scale-setting method used in lattice gauge theory. The number of active flavors $n_f$ in the QCD $\beta$ function is also correctly determined. We discuss several methods for determining the PMC scale for QCD processes. We show that a single global PMC scale, valid at leading order, can be derived from basic properties of the perturbative QCD cross section. The elimination of the renormalization scale ambiguity and the scheme dependence using the PMC will not only increase the precision of QCD tests, but it will also increase the sensitivity of collider experiments to new physics beyond the Standard Model.

Asymptotic energy dependence of hadronic total cross sections from lattice QCD

The nonperturbative approach to soft high-energy hadron-hadron scattering, based on the analytic continuation of Wilson-loop correlation functions from Euclidean to Minkowskian theory, allows to investigate the asymptotic energy dependence of hadron-hadron total cross sections in lattice QCD. In this paper we will show, using best fits of the lattice data with proper functional forms satisfying unitarity and other physical constraints, how indications emerge in favor of a universal asymptotic high-energy behavior of the kind B log^2 s for hadronic total cross sections.

Ultra-high energy probes of classicalization

Classicalizing theories are characterized by a rapid growth of the scattering cross section. This growth converts these sort of theories in interesting probes for ultra-high energy experiments even at relatively low luminosity, such as cosmic rays or Plasma Wakefield accelerators. The microscopic reason behind this growth is the production of N-particle states, classicalons, that represent self-sustained lumps of soft Bosons. For spin-2 theories this is the quantum portrait of what in the classical limit are known as black holes. We emphasize the importance of this quantum picture which liberates us from the artifacts of the classical geometric limit and allows to scan a much wider landscape of experimentally-interesting quantum theories. We identify a phenomenologically-viable class of spin-2 theories for which the growth of classicalon production cross section can be as efficient as to compete with QCD cross section already at 100TeV energy, signaling production of quantum black holes with graviton occupation number N ∼ 104.

Experiences on QCD Monte Carlo simulations: a user point of view on the inclusive jet cross-section simulations

In the last years, important progresses in the theoretical description of the QCD high pT processes have been carried out. In this proceeding, a review of the tools and techniques used to simulate QCD cross sections will be presented from a user point of view. The benchmark process selected for the discussion is the inclusive jet cross section. The proceeding will focus on the uncertainties of the Next to Leading Order (NLO) cross sections, on the strategies adopted to correct for the non-perturbative effects such as the hadronization and the underlying event, and the new techniques derived during the last years to incorporate in a coherent way the NLO matrix elements in the Monte Carlo generators.

Measurement of the inclusive W and Z production cross sections in pp collisions at $ \sqrt {s} = 7 $ TeV with the CMS experiment

A measurement of inclusive W and Z production cross sections in pp collisions at sqrt(s)=7 TeV is presented. The electron and muon decay channels are analyzed in a data sample collected with the CMS detector at the LHC and corresponding to an integrated luminosity of 36 inverse picobarns. The measured inclusive cross sections are sigma(pp-> WX) B(W-> l nu) = 10.30 +/- 0.02 (stat.) +/- 0.10 (syst.) +/- 0.10 (th.) +/- 0.41 (lumi.) nb and sigma(pp -> ZX) B(Z-> l^+l^-) = 0.974 +/- 0.007 (stat.) +/- 0.007 (syst.) +/- 0.018 (th.) +/- 0.039 (lumi.) nb, limited to the dilepton invariant mass range 60 to 120 GeV. The luminosity-independent cross section ratios are [sigma(pp->WX) B(W-> l nu)]/[sigma(pp-> ZX) B(Z->l^+l^-)] = 10.54 +/- 0.07 (stat.) +/- 0.08 (syst.) +/- 0.16 (th.) and [sigma(pp->W^+X) B(W^+ -> l^+nu)] / [sigma(pp->W^- X) B(W^- -> l^- nu)] = 1.421 +/- 0.006 (stat.) +/- 0.014 (syst.) +/- 0.029 (th.). The measured values agree with next-to-next-to-leading order QCD cross section calculations based on recent parton distribution functions.

Colourful FKS subtraction

I formulate in a colour-friendly way the FKS method for the computation of QCD cross sections at the next-to-leading order accuracy. This is achieved through the definition of subtraction terms for squared matrix elements, constructed with single colour-dressed or pairs of colour-ordered amplitudes. The latter approach relies on the use of colour flows, is exact to all orders in $N$, and is thus particularly suited to being organized as a systematic expansion in 1/N.

An off-shell IR regularization strategy in the analysis of collinear divergences

We present a method for the analysis of singularities of Feynman amplitudes based on the Speer sector decomposition of the Schwinger parametric integrals combined with the Mellin–Barnes transform. The sector decomposition method is described in some detail. We suggest the idea of applying the method to the analysis of collinear singularities in inclusive QCD cross sections in the mass-less limit regularizing the forward amplitudes by an off-shell choice of the initial particle momenta. It is shown how the suggested strategy works in the well-known case of the one loop corrections to deep inelastic scattering.