Cristian Pisano

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.

Direct Probes of Linearly Polarized Gluons inside Unpolarized Hadrons

We show that linearly polarized gluons inside unpolarized hadrons can be directly probed in jet or heavy quark pair production in electron-hadron collisions. We discuss the simplest cos2ϕ asymmetries and estimate their maximal value, concluding that measurements of the unknown linearly polarized gluon distribution in the proton should be feasible in future Electron-Ion Collider or Large Hadron electron Collider experiments. Analogous asymmetries in hadron-hadron collisions suffer from factorization breaking contributions and would allow us to quantify the importance of initial- and final-state interactions.

Linearly Polarized Gluons and the Higgs Transverse Momentum Distribution

We study how gluons carrying linear polarization inside an unpolarized hadron contribute to the transverse momentum distribution of Higgs bosons produced in hadronic collisions. They modify the distribution produced by unpolarized gluons in a characteristic way that could be used to determine whether the Higgs boson is a scalar or a pseudoscalar particle.

Linear polarization of gluons and photons in unpolarized collider experiments

A bstractWe study azimuthal asymmetries in heavy quark pair production in unpolarized electron-proton and proton-proton collisions, where the asymmetries originate from the linear polarization of gluons inside unpolarized hadrons. We provide cross section expressions and study the maximal asymmetries allowed by positivity, for both charm and bottom quark pair production. The upper bounds on the asymmetries are shown to be very large depending on the transverse momentum of the heavy quarks, which is promising especially for their measurements at a possible future Electron-Ion Collider or a Large Hadron electron Collider. We also study the analogous processes and asymmetries in muon pair production as a means to probe linearly polarized photons inside unpolarized protons. For increasing invariant mass of the muon pair the asymmetries become very similar to the heavy quark pair ones. Finally, we discuss the process dependence of the results that arises due to differences in color flow and address the problem with factorization in case of proton-proton collisions.

Polarized gluon studies with charmonium and bottomonium at LHCb and AFTER

Recently it has been put forward that linearly polarized gluons inside unpolarized protons affect the transverse momentum distribution of final state particles in hadronic collisions. They lead to a characteristic modulation of the differential cross section in Higgs production and to azimuthal asymmetries in, for instance, heavy quark pair production. Here we study the effect on charmonium and bottomonium production in hadronic collisions, such as at LHCb and at the proposed fixed target experiment AFTER at LHC. We focus mainly on the scalar and pseudoscalar quarkonia, eta(c), chi(c0), eta(b), chi(b0), which allow for an angular independent investigation. Within the framework of transverse momentum dependent factorization in combination with the nonrelativistic QCD based color-singlet quarkonium model, we show for small transverse momentum (q(T)(2)

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.

Accessing the transverse dynamics and polarization of gluons inside the proton at the LHC

We argue that the study of heavy quarkonia, in particular that of Υ, produced back to back with an isolated photon in pp collisions at the LHC is the best - and currently unique - way to access the distribution of both the transverse momentum and the polarization of the gluon in an unpolarized proton. These encode fundamental information on the dynamics of QCD. We derive analytical expressions for various transverse-momentum distributions that can be measured at the LHC and which allow for a direct extraction of the aforementioned quantities. To assess the feasibility of such measurements, we evaluate the expected yields and the relevant transverse-momentum distributions for different models of the gluon dynamics inside a proton.

Extraction of partonic transverse momentum distributions from semi-inclusive deep-inelastic scattering, Drell-Yan and Z-boson production

A bstractWe present an extraction of unpolarized partonic transverse momentum distributions (TMDs) from a simultaneous fit of available data measured in semi-inclusive deep-inelastic scattering, Drell-Yan and Z boson production. To connect data at different scales, we use TMD evolution at next-to-leading logarithmic accuracy. The analysis is restricted to the low-transverse-momentum region, with no matching to fixed-order calculations at high transverse momentum. We introduce specific choices to deal with TMD evolution at low scales, of the order of 1 GeV2. This could be considered as a first attempt at a global fit of TMDs.

Determining the Higgs Spin and Parity in the Diphoton Decay Channel

We calculate the diphoton distribution in the decay of arbitrary spin-0 and spin-2 bosons produced from gluon fusion, taking into account the fact that gluons inside an unpolarized proton are generally linearly polarized. The gluon polarization brings about a difference in the transverse momentum distribution of positive and negative parity states. At the same time, it causes the azimuthal distribution of the photon pair to be nonisotropic for several spin-2 coupling hypotheses, allowing one to distinguish these from the isotropic scalar and pseudoscalar distributions.

Spin physics and TMD studies at A Fixed-Target ExpeRiment at the LHC (AFTER@LHC)

We report on the opportunities for spin physics and Transverse-Momentum Dependent distribution (TMD) studies at a future multi-purpose fixed-target experiment using the proton or lead ion LHC beams extracted by a bent crystal. The LHC multi-TeV beams allow for the most energetic fixed-target experiments ever performed, opening new domains of particle and nuclear physics and complementing that of collider physics, in particular that of RHIC and the EIC projects. The luminosity achievable with AFTER@LHC using typical targets would surpass that of RHIC by more that 3 orders of magnitude in a similar energy region. In unpolarised proton-proton collisions, AFTER@LHC allows for measurements of TMDs such as the Boer-Mulders quark distributions, the distribution of unpolarised and linearly polarised gluons in unpolarised protons. Using the polarisation of hydrogen and nuclear targets, one can measure transverse single-spin asymmetries of quark and gluon sensitive probes, such as, respectively, Drell-Yan pair and quarkonium production. The fixed-target mode has the advantage to allow for measurements in the target-rapidity region, namely at large x^uparrow in the polarised nucleon. Overall, this allows for an ambitious spin program which we outline here.