Tomas Kasemets

Transverse momentum dependent (TMD) parton distribution functions: Status and prospects*

We review transverse momentum dependent (TMD) parton distribution functions, their application to topical issues in high-energy physics phenomenology, and their theoretical connections with QCD resummation, evolution and factorization theorems. We illustrate the use of TMDs via examples of multi-scale problems in hadronic collisions. These include transverse momentum q(T) spectra of Higgs and vector bosons for low q(T), and azimuthal correlations in the production of multiple jets associated with heavy bosons at large jet masses. We discuss computational tools for TMDs, and present the application of a new tool, TMDLIB, to parton density fits and parameterizations.

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

A bstractWe 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 (f1g), linearly polarized (h1⊥ g) and helicity (g1Lg) 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 g1Lg, 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 f1g and h1⊥ 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 ηb. Applying our resummation scheme we finally provide predictions for the Higgs boson qT -distribution at the LHC.

Correlations in double parton distributions: effects of evolution

A bstractWe numerically investigate the impact of scale evolution on double parton distributions, which are needed to compute multiple hard scattering processes. Assuming correlations between longitudinal and transverse variables or between the parton spins to be present at a low scale, we study how they are affected by evolution to higher scales, i.e. by repeated parton emission. We find that generically evolution tends to wash out correlations, but with a speed that may be slow or fast depending on kinematics and on the type of correlation. Nontrivial parton correlations may hence persist in double parton distributions at the high scales relevant for hard scattering processes.

Angular correlations in the double Drell-Yan process

A bstractWe study the impact of parton correlations on the double Drell-Yan process, i.e. on the production of two electroweak gauge bosons by double parton scattering in a single proton-proton collision. Spin correlations between two partons in a proton are shown to change the overall rate of the process and to induce characteristic angular correlations between the decay leptons of the two gauge bosons.

Positivity bounds on double parton distributions

A bstractDouble hard scattering in proton-proton collisions is described in terms of double parton distributions. We derive bounds on these distributions that follow from their interpretation as probability densities, taking into account all possible spin correlations between two partons in an unpolarized proton. These bounds constrain the size of the polarized distributions and can for instance be used to set upper limits on the effects of spin correlations in double hard scattering. We investigate the stability of the bounds under leading-order DGLAP evolution to higher scales.

Constraining double-parton correlations and interferences

Double-parton scattering (DPS) has become very relevant as a background to interesting analyses performed by the experiments at the LHC. It encodes knowledge of correlations between the proton constituents not accessible in single-parton scattering. Within perturbative QCD DPS is described in terms of partonic subprocesses and double-parton distributions (DPDs). There exists a large number of different DPDs describing the different possible states of two partons inside a proton. They include correlations between the two partons and interferences between the two hard subprocesses. Taking the probability interpretation of the DPDs as a starting point, we derive limits on the interference DPDs and thereby constrain the size of correlations between two partons inside an unpolarized proton.

Polarization effects in double open-charm production at LHCb

A bstractDouble 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 D0D0 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.

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

A bstractWe 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.

Calculating Soft Radiation at One Loop

A bstractWe 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.

Quark-gluon double parton distributions in the light-front dressed quark model

We study parton distributions for two partons, a quark and a gluon, in the light-front dressed quark model, with a focus on the correlations between the two partons. The model calculation leads to sizable spin-spin and spin-kinematic correlations of interest for studies of double parton scattering in high-energy collisions. In particular, we find that the transverse dependence of the double parton distributions (DPDs) does not factorize within the model. The results give insight into the strengths of the correlations in different kinematical regions, which can help in constructing input DPDs in cross-section calculations.