An Erratum to this paper has been published: https://doi.org/10.1007/JHEP01(2018)044

Germany

Maarten Buffing

Markus Diehl

Netherlands

Tomas Kasemets

Erratum to: Transverse momentum in double parton scattering: factorisation, evolution and matching

The future runs of LHC offer a unique opportunity to measure correlations between two partons inside the proton, which have never been experimentally detected. The process of interest is the production of two positively charged W-bosons decaying in the muon channel. We present a detailed analysis of proton-proton collisions at   <math> <msqrt> <mi>s</mi> </msqrt> </math>  $$ \sqrt{s} $$  = 13 TeV, where we combine Monte Carlo event generators with our calculations of parton correlations. We carefully compare double parton scattering to relevant background processes and trace a path towards a clean signal sample. Several observables are constructed to demonstrate the effect of parton correlations with respect to clear benchmark values for uncorrelated scatterings. We find that especially spin correlations can be responsible for large effects in the variables we study, because of their direct relation with the parton angular momentum and, therefore, the directions of the muon momenta. We estimate the significance of the measurements as a function of the integrated luminosity and conclude that the LHC has the potential to detect, or put strong limits on, parton correlations in the near future.

France

Sabrina Cotogno

Czechia

Miroslav Myska

Confronting same-sign W-boson production with parton correlations

We demonstrate that the LHC will be sensitive to quantum correlations between two quarks inside the proton. Same-sign <math><mi>W</mi></math>-boson pair production is the most promising channel for clear measurements of double parton scattering. The left-handed nature of the coupling between quarks and <math><mi>W</mi></math> bosons makes it a prime probe to measure parton spin correlations. We perform a detailed analysis of double parton scattering, including relevant backgrounds. The analysis reveals that measurements comparing the rate at which two muons from <math><mi>W</mi></math> boson decays are produced in the same, compared to opposite, hemispheres are especially sensitive to spin correlations between two quarks inside the proton. We provide estimates of the significance of the measurements as a function of the integrated luminosity.

Spin on same-sign <math><mi>W</mi></math>-boson pair production

In this review, we describe the status of transverse momentum dependence (TMD) in double parton scattering (DPS). The different regions of TMD DPS are discussed, and expressions are given for the DPS cross section contributions that make use of as much perturbative information as possible. The regions are then combined with each other as well as single parton scattering to obtain a complete expression for the cross section. Particular emphasis is put on the differences and similarities to transverse momentum dependence in single parton scattering. We further discuss the status of the factorisation proof for double colour singlet production in DPS, which is now on a similar footing to the proofs for TMD factorisation in single Drell-Yan, discuss parton correlations, and give an outlook on possible research on DPS in the near future.

CERN

Jonathan R. Gaunt

Transverse Momentum Dependence in Double Parton Scattering

We propose a new fast method to match factorization theorems applicable in different kinematical regions, such as the transverse-momentum-dependent and the collinear factorization theorems in Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate the unknown complete matched cross section from an inverse-error-weighted average. The method is simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated with the uncertainties from the power corrections to the factorization theorems (additional uncertainties, such as the nonperturbative ones, should be added for a proper comparison with experimental data). Its usage is illustrated with several basic examples, such as Z boson, W boson, <math><msup><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msup></math> boson and Drell–Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins–Soper–Sterman subtraction scheme. It is also not limited to the transverse-momentum spectrum, and can straightforwardly be extended to match any (un)polarized cross section differential in other variables, including multi-differential measurements.

Italy

Miguel G. Echevarria

Jean-Philippe Lansberg

Cristian Pisano

United States

Andrea Signori

Matching factorization theorems with an inverse-error weighting

We give a description of double parton scattering with measured transverse momenta in the final state, extending the formalism for factorisation and resummation developed by Collins, Soper and Sterman for the production of colourless particles. After a detailed analysis of their colour structure, we derive and solve evolution equations in rapidity and renormalisation scale for the relevant soft factors and double parton distributions. We show how in the perturbative regime, transverse momentum dependent double parton distributions can be expressed in terms of simpler nonperturbative quantities and compute several of the corresponding perturbative kernels at one-loop accuracy. We then show how the coherent sum of single and double parton scattering can be simplified for perturbatively large transverse momenta, and we discuss to which order resummation can be performed with presently available results. As an auxiliary result, we derive a simple form for the square root factor in the Collins construction of transverse momentum dependent parton distributions.

Transverse momentum in double parton scattering: factorisation, evolution and matching

Miguel Echevarria

Piet Mulders

Belgium

Erratum to: QCD evolution of (un)polarized gluon TMDPDFs and the Higgs q T -distribution

We present an efficient way to calculate the effect of soft QCD radiation at one loop, which is needed for predictions at next-to-next-to-leading logarithmic accuracy. We use rapidity coordinates and isolate the divergences in the integrand. By performing manipulations with cumulative variables, we avoid complications from plus distributions. We address rapidity divergences, divergences with an azimuthal dependence, complicated jet boundaries and multi-differential measurements. The process and measurements can be easily adjusted, as we demonstrate by reproducing many existing soft functions. The results for a general LHC process with multiple Wilson lines are obtained by treating Wilson lines that are not back-to-back using a boost. We also obtain, for the first time, the N -jettiness soft function for generic jet angularities, and the collinear-soft function for the measurement of two angularities.

Wouter Waalewijn

Lisa Zeune

Calculating soft radiation at one loop

We provide the proper definition of all the leading-twist (un)polarized gluon transverse momentum dependent parton distribution functions (TMDPDFs), by considering the Higgs boson transverse momentum distribution in hadron-hadron collisions and deriving the factorization theorem in terms of them. We show that the evolution of all the (un)polarized gluon TMDPDFs is driven by a universal evolution kernel, which can be resummed up to next-to-next-to-leading-logarithmic accuracy. Considering the proper definition of gluon TMDPDFs, we perform an explicit next-to-leading-order calculation of the unpolarized ( f 1 g ), linearly polarized ( h 1 ⊥  g ) and helicity ( g 1 L g ) gluon TMDPDFs, and show that, as expected, they are free from rapidity divergences. As a byproduct, we obtain the Wilson coefficients of the refactorization of these TMDPDFs at large transverse momentum. In particular, the coefficient of g 1 L g , which has never been calculated before, constitutes a new and necessary ingredient for a reliable phenomenological extraction of this quantity, for instance at RHIC or the future AFTER@LHC or Electron-Ion Collider. The coefficients of f 1 g and h 1 ⊥  g have never been calculated in the present formalism, although they could be obtained by carefully collecting and recasting previous results in the new TMD formalism. We apply these results to analyze the contribution of linearly polarized gluons at different scales, relevant, for instance, for the inclusive production of the Higgs boson and the C -even pseudoscalar bottomonium state η b . Applying our resummation scheme we finally provide predictions for the Higgs boson q T -distribution at the LHC.

QCD evolution of (un)polarized gluon TMDPDFs and the Higgs q T -distribution

Double open-charm production is one of the most promising channels to disentangle single from double parton scattering (DPS) and study different properties of DPS. Several studies of the DPS contributions have been made. A missing ingredient so far has been the study of polarization effects, arising from spin correlations between the two partons inside an unpolarized proton. We investigate the impact polarization has on the double open-charm cross section. We show that the longitudinally polarized gluons can give significant contributions to the cross section, but for most of the considered kinematic region only have a moderate effect on the shape. We compare our findings to the LHCb data in the D 0 D 0 final state, identify observables where polarization does have an impact on the distribution of the final state particles, and suggest measurements which could lead to first experimental indications of, or limits on, polarization in DPS.