Transverse Momentum Dependent Parton Densities Research Articles

Measurements of jet multiplicity and jet transverse momentum in multijet events in proton–proton collisions at {sqrt{s}=13, text {TeV}}

Multijet events at large transverse momentum (p_{textrm{T}}) are measured at sqrt{s}=13,text {TeV} using data recorded with the CMS detector at the LHC, corresponding to an integrated luminosity of 36.3{,text {fb}^{-1}} . The multiplicity of jets with p_{textrm{T}} >50,text {GeV} that are produced in association with a high-p_{textrm{T}} dijet system is measured in various ranges of the p_{textrm{T}} of the jet with the highest transverse momentum and as a function of the azimuthal angle difference varDelta phi _{1,2} between the two highest p_{textrm{T}} jets in the dijet system. The differential production cross sections are measured as a function of the transverse momenta of the four highest p_{textrm{T}} jets. The measurements are compared with leading and next-to-leading order matrix element calculations supplemented with simulations of parton shower, hadronization, and multiparton interactions. In addition, the measurements are compared with next-to-leading order matrix element calculations combined with transverse-momentum dependent parton densities and transverse-momentum dependent parton shower.

Transverse momentum dependent parton densities in processes with heavy quark generations

To study the heavy quark production processes, we use the transverse momentum dependent (TMD, or unintegrated) gluon distribution function in a proton obtained recently using the Kimber-Martin-Ryskin prescription from the Bessel-inspired behavior of parton densities at small Bjorken $x$ values. We obtained a good agreement of our results with the latest HERA experimental data for reduced cross sections $\sigma^{c\overline{c}}_{\rm red}(x,Q^2)$ and $\sigma^{b\overline{b}}_{\rm red}(x,Q^2)$, and also for deep inelastic structure functions $F_2^c(x,Q^2)$ and $F_2^b(x,Q^2)$ in a wide range of $x$ and $Q^2$ values. Comparisons with the predictions based on the Ciafaloni-Catani-Fiorani-Marchesini evolution equation and with the results of conventional pQCD calculations performed at first three orders of perturbative expansion are presented.

Factorization of e+e\u2212 \u2192 H X cross section, differential in zh, PT and thrust, in the 2-jet limit

Factorizing the cross section for single hadron production in e+e− annihilations is a highly non trivial task when the transverse momentum of the outgoing hadron with respect to the thrust axis is taken into account. We work in a scheme that allows to factorize the e+e−→ H X cross section as a convolution of a calculable hard coefficient and a Transverse Momentum Dependent (TMD) fragmentation function. The result, differential in zh, PT and thrust, will be given to all orders in perturbation theory and explicitly computed to Next to Leading Order (NLO) and Next to Leading Log (NLL) accuracy. The predictions obtained from our computation, applying the simplest and most natural ansatz to model the non-perturbative part of the TMD, are in exceptional agreement with the experimental measurements of the BELLE Collaboration. The factorization scheme we propose relates the TMD parton densities defined in 1-hadron and 2-hadron processes, restoring the possi- bility to perform global phenomenological studies of TMD physics including experimental data from semi-inclusive deep inelastic scattering, Drell-Yan processes, e+e−→ H1H2X and e+e−→ H X annihilations.

Universality-breaking effects in e^+e^- hadronic production processes

Recent BELLE measurements provide the cross section for single hadron production in e^+e^- annihilations, differential in thrust and in the hadron transverse momentum with respect to the thrust axis. Universality breaking effects due to process-dependent soft factors make it very difficult to relate this cross sections to those corresponding to hadron-pair production in e^+e^- annihilations, where transverse momentum dependent (TMD) factorization can be applied. The correspondence between these two cross sections is examined in the framework of the Collins-Soper-Sterman factorization, in the collinear as well as in the TMD approach. We propose a scheme that allows to relate the TMD parton densities defined in 1-hadron and in 2-hadron processes, neatly separating, within the soft and collinear parts, the non-perturbative terms from the contributions that can be calculated perturbatively. The regularization of rapidity divergences introduces cut-offs, the arbitrariness of which will be properly reabsorbed by means of a mechanism closely reminiscent of a gauge transformation. In this way, we restore the possibility to perform global phenomenological studies of TMD physics, simultaneously analyzing data belonging to different hadron classes.

Transverse moments of TMD parton densities and ultraviolet divergences

I review some open questions relating to the large transverse momentum divergences in transverse moments of transverse momentum dependent (TMD) parton correlation functions. I also explain, in an abbreviated and summarized form, recent work that shows that the resulting violations of a commonly used integral relation are not perturbatively suppressed. I argue that this implies a need for more precise definitions for the correlation functions used to describe transverse moments.

Transverse momentum dependent parton densities in a proton from the generalized DAS approach

We use the Bessel-inspired behavior of parton densities at small Bjorken x values, obtained in the case of the flat initial conditions for DGLAP evolution equations in the double scaling QCD approximation (DAS), to evaluate the transverse momentum dependent (TMD, or unintegrated) quark and gluon distribution functions in a proton. The calculations are performed analytically using the Kimber-Martin-Ryskin (KMR) prescription with different implementation of kinematical constraint, reflecting the angular and strong ordering conditions. The relations between the differential and integral formulation of the KMR approach is discussed. Several phenomenological applications of the proposed TMD parton densities to the LHC processes are given.

Collinear and TMD parton densities from fits to precision DIS measurements in the parton branching method

Collinear and transverse momentum dependent (TMD) parton densities are obtained from fits to precision measurements of deep inelastic scattering (DIS) cross sections at HERA. The parton densities are evolved by DGLAP evolution with next-to-leading-order (NLO) splitting functions using the parton branching method, allowing one to determine simultaneously collinear and TMD densities for all flavors over a wide range in $x$, $\mu^2$ and $k_t$, relevant for predictions at the LHC. The DIS cross section is computed from the parton densities using perturbative NLO coefficient functions. Parton densities satisfying angular ordering conditions are presented. Two sets of parton densities are obtained, differing in the renormalization scale choice for the argument in the strong coupling alpha_s. This is taken to be either the evolution scale $\mu$ or the transverse momentum $q_t$. While both choices yield similarly good $\chi^2$ values for the fit to DIS measurements, especially the gluon density turns out to differ between the two sets. The TMD densities are used to predict the transverse momentum spectrum of Z-bosons at the LHC.

Testing the parton evolution with the use of two-body final states

We consider the production of b{bar{b}} quarks and Drell–Yan lepton pairs under LHC conditions focusing attention on the total transverse momentum of the produced pair and on the azimuthal angle between the momenta of the outgoing particles. Plotting the corresponding distributions in bins of the final-state invariant mass, one can reconstruct the full map of the transverse momentum dependent parton densities in a proton. We give examples of how these distributions can look like at the LHC energies.

Significance of gluon density at soft and hard processes at LHC

We study the role of the non-perturbative input to the transverse momentum dependent (TMD) gluon density in hard processes at the LHC. We derive the TMD gluon distribution from the fit of the inclusive hadron spectra measured at low transverse momenta in [Formula: see text] collisions at the LHC and demonstrate that the best description of these spectra for larger hadron transverse momenta can be achieved by matching the derived TMD gluon distribution with the exact solution of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation obtained at small transverse momenta outside the saturation region. A special attention is put to the phenomenological applications of presented TMD parton densities to some LHC processes, which are sensitive to the quark and gluon content of a proton.

Transverse momentum dependent parton densities in associated real and virtual photon and jet production at the LHC

We study the associated production of real (isolated) or virtual photons (with their subsequent leptonic decay) and hadronic jets in proton-proton collisions at the LHC using the ${k}_{T}$-factorization approach of QCD. The consideration is based on the off-shell quark-gluon QCD Compton scattering subprocesses. In the case of virtual photon production, the contributions from $Z$ boson exchange as well as ${\ensuremath{\gamma}}^{*}\ensuremath{-}Z$ interference with the full spin correlations are included. The transversemomentum-dependent (TMD) quark and gluon densities in a proton are determined from the Kimber-Martin-Ryskin prescription or Catani-Ciafoloni-Fiorani-Marchesini (CCFM) equation. In the latter, we restrict to the case where the gluon-to-quark splitting occurs at the last evolution step and calculate the sea quark density as a convolution of the CCFM-evolved gluon distribution and the TMD gluon-to-quark splitting function. Our numerical predictions are compared with the recent experimental data taken by the ATLAS Collaboration. We discuss the theoretical uncertainties of our calculations and argue that further studies are capable of constraining the TMD parton densities in the proton.

TRANSVERSE-MOMENTUM-DEPENDENT PARTON DISTRIBUTIONS AT THE EDGE OF THE LIGHTCONE

We present a completely gauge-invariant operator definition of transverse-momentum-dependent parton densities (TMD), supplied with longitudinal lightlike gauge links as well as transverse gauge links at lightcone infinity. Within this framework, we consider the consistent treatment of specific divergences, emerging in the "unsubtracted" TMD beyond the tree approximation, and construct the soft factors to cancel unphysical singularities. We confront this approach with factorization schemes, which make use of covariant gauges with off-the-lightcone gauge links, and discuss their mutual connection.

Importance of Lorentz structure in the parton model: Target mass corrections, transverse momentum dependence, positivity bounds

We show that respecting the underlying Lorentz structure in the parton model has very strong consequences. Failure to insist on the correct Lorentz covariance is responsible for the existence of contradictory results in the literature for the polarized structure function ${g}_{2}(x)$, whereas with the correct imposition we are able to derive the Wandzura-Wilczek relation for ${g}_{2}(x)$ and the target-mass corrections for polarized deep inelastic scattering without recourse to the operator product expansion. We comment briefly on the problem of threshold behavior in the presence of target-mass corrections. Careful attention to the Lorentz structure has also profound implications for the structure of the transverse momentum dependent parton densities often used in parton model treatments of hadron production, allowing the ${\mathbit{k}}_{T}$ dependence to be derived explicitly. It also leads to stronger positivity and Soffer-type bounds than usually utilized for the collinear densities.

Transverse momentum in semi-inclusive deep inelastic scattering

Within the framework of perturbative quantum chromodynamics we derive the evolution equations for transverse momentum dependent distributions and apply them to the case of semi-inclusive deep inelastic scattering. The evolution equations encode the perturbative component of transverse momentum generated by collinear parton branchings. The current fragmentation is described via transverse momentum dependent parton densities and fragmentation functions. Target fragmentation instead is described via fracture functions. We present, to leading logarithmic accuracy, the corresponding semi-inclusive deep inelastic scattering cross-section, which applies to the entire phase space of the detected hadron. Some phenomenological implications and further developments are briefly outlined.