Transverse Parton Distribution Research Articles

Influence of the Nucleon Hard Partons Distribution on J/Ψ Suppression in a GMC Framework

In a Glauber Monte Carlo framework, taking into account the transverse spatial distribution of hard partons in the nucleon, we analyze the nuclear modification factor Rd Au for J/Ψ in d+Au collisions with EPS09 shadowing parametrization. After the influence of nucleon hard partons distribution is considered, a clearly upward correction is revealed for the dependence of Rd Au on Ncoll in peripheral d+Au collisions, however, an unconspicuous correction is shown for the results versus pT. The theoretical results are in good agreement with the experimental data from PHENIX.

Multiple hard partonic collisions with correlations in proton-proton scattering

We propose a simple method for incorporating correlations into the impact parameter space description of multiple (semi-)hard partonic collisions in high energy hadron-hadron scattering. The perturbative QCD input is the standard factorization theorem for inclusive dijet production with a lower cutoff on transverse momentum. The width of the transverse distribution of hard partons is fixed by parameterizations of the two-gluon form factor. We then reconstruct the hard contribution to the total inelastic profile function and obtain corrections due to correlations to the more commonly used eikonal description. Estimates of the size of double correlation corrections are based on the rate of double collisions measured at the Tevatron. We find that, if typical values for the lower transverse momentum cutoff are used in the calculation of the inclusive hard dijet cross section, then the correlation corrections are necessary for maintaining consistency with expectations for the total inelastic proton-proton cross section at LHC energies.

Parton promenade into the nucleon

Generalized parton distributions (GPDs) offer a comprehensive picture of the nucleon struture and dynamics and provide a link between microscopic and macroscopic properties of the nucleon. These quantities, which can be interpreted as the transverse distribution of partons carrying a certain longitudinal momentum fraction of the nucleon, can be accessed in deep exclusive processes. This lecture reviews the main features of the nucleon structure as obtained from elastic and inelastic lepton scatterings and unified in the context of the GPDs framework. Particular emphasis is put on the experimental methods to access these distributions and the today experimental status.

Jet evolution in Yang-Mills-Wong simulations

We present results for collisional energy loss and momentum broadening of high momentum partons in a hot and dense non-Abelian plasma obtained by solving the coupled system of Yang-Mills-Wong equations on a lattice in real time. Including hard elastic collisions among the particles we obtain cutoff independent results for the collisional energy loss d E / d x and the transport coefficient q ˆ . The latter is found to receive a sizable contribution from a power-law tail in the transverse momentum distribution of high-momentum partons. We further argue that the effect of instabilities on jet broadening should be accessible by experiment when employing jet cones with elliptical bases or studying correlations within the cone in full jet reconstruction methods.

Probing the Nucleon’s Transversity and the Photon’s Distribution Amplitude in Lepton Pair Photoproduction

We describe a new way to access the chiral-odd transversity parton distribution in the proton through the photoproduction of lepton pairs. The basic ingredient is the interference of the usual Bethe-Heitler or Drell-Yan amplitudes with the amplitude of a process, where the photon couples to quarks through its chiral-odd distribution amplitude, which is normalized to the magnetic susceptibility of the QCD vacuum. A promising phenomenology of single and double spin observables emerges from the unusual features of this amplitude.

Deeply inelastic pions in the exclusive reactionp(e,e′π+)nabove the resonance region

A model for the $p(e,{e}^{\ensuremath{'}}{\ensuremath{\pi}}^{+})n$ reaction which combines an improved treatment of gauge invariant meson-exchange currents and hard deep-inelastic scattering (DIS) of virtual photons off nucleons is proposed. It is shown that DIS dominates and explains the transverse response at moderate and high photon virtualities ${Q}^{2}$, whereas the longitudinal response is dominated by hadronic degrees of freedom and the pion electromagnetic form factor. This leads to a combined description of the longitudinal and transverse components of the cross section in a wide range of photon virtuality ${Q}^{2}$ and momentum transfer to the target $t$ and solves the longstanding problem of the observed large transverse cross sections. The latter are shown to be sensitive to the intrinsic transverse momentum distribution of partons.

Di-hadron correlations and parton intrinsic transverse momentum

The transverse momentum distribution of partons in the proton is studied with the help of di-hadron correlations. A simple randomization model is compared to the data.

Bound state effects in transverse momentum parton distributions

We derive a nonperturbative transverse momentum distribution for partons using a potential model to describe the quark-quark interaction inside the proton. We use this distribution in the calculation of the differential cross section of ${\ensuremath{\pi}}^{0}$ production for intermediate transverse momentum values in $p\ensuremath{-}p$ collisions at high energies. Assuming a variable string tension constant for the quark-quark potential we obtain a very good description of the experimental data at different energies. The corresponding values of the mean transverse momentum of the partons are essentially lower than those obtained using a Gaussian transverse momentum parton distribution. Using the same approach we can also describe the proton production data in the Chicago-Princeton experiment. Our analysis indicates that bound state effects may be important for the description of the experimental data in proton-proton collisions.

Azimuthal asymmetries in unpolarized Drell–Yan events on nuclear targets

We show that for Drell–Yan events by unpolarized hadronic projectiles and nuclear targets, azimuthal asymmetries can arise from the nuclear distortion of the hadronic projectile wavefunction, typically a spin–orbit effect occurring on the nuclear surface. The asymmetry depends on quantities that enter also the spin asymmetry in the corresponding Drell–Yan event on polarized free nucleonic targets. Hence, this study can be of help in exploring the spin structure of the nucleon, in particular the transverse spin distribution of partons inside the proton. All arguments can be extended also to antinucleon projectiles and, consequently, apply to possible future measurements involving nuclear targets at the foreseen HESR ring at GSI.

3D parton imaging of the nucleon in high-energypp andpA collisions

We discuss several examples of how the transverse spatial distribution of partons in the nucleon, as well as multiparton correlations, can be probed by observing hard processes (dijets) in high-energy pp (pbar p) and pA (dA) collisions. Such studies can complement the information gained from measurements of hard exclusive processes in ep scattering. The transverse spatial distribution of partons determines the distribution over pp impact parameters of events with hard dijet production. Correlations in the transverse positions of partons can be studied in multiple dijet production. We find that the correlation cross section measured by the CDF Collaboration, sigma_eff = 14.5 +/- 1.7^{+ 1.7}_{-2.3} mb, can be explained by "constituent quark" type quark-gluon correlations with r_q ~ r_N / 3, as suggested by the instanton liquid model of the QCD vacuum. Longitudinal and transverse multiparton correlations can be separated in a model-independent way by comparing multiple dijet production in pp and pA collisions. Finally, we estimate the cross section for exclusive diffractive Higgs production in pp collisions at LHC (rapidity gap survival probability), by combining the impact parameter distribution implied by the hard partonic process with information about soft interactions gained in pp elastic scattering.

3D parton imaging of the nucleon in high‐energy pp and pA collisions*

AbstractWe discuss several examples of how the transverse spatial distribution of partons in the nucleon, as well as multiparton correlations, can be probed by observing hard processes (dijets) in high‐energy and pA (dA collisions. Such studies can complement the information gained from measurements of hard exclusive processes in ep scattering. The transverse spatial distribution of partons determines the distribution over pp impact parameters of events with hard dijet production. Correlations in the transverse positions of partons can be studied in multiple dijet production. We find that the correlation cross section measured by the CDF Collaboration, σeff = 14.5±1.7+ 1.7‐2.3 mb, can be explained by “constituent quark” type quark–gluon correlations with rq ≊ rN / 3, as suggested by the instanton liquid model of the QCD vacuum. Longitudinal and transverse multiparton correlations can be separated in a model‐independent way by comparing multiple dijet production in pp and pA collisions. Finally, we estimate the cross section for exclusive diffractive Higgs production in pp collisions at LHC (rapidity gap survival probability), by combining the impact parameter distribution implied by the hard partonic process with information about soft interactions gained in pp elastic scattering.

Dijet production as a centrality trigger forppcollisions at CERN LHC

We demonstrate that a trigger on hard dijet production at small rapidities allows us to establish a quantitative distinction between central and peripheral collisions in $\overline{p}p$ and pp collisions at Tevatron and LHC energies. Such a trigger strongly reduces the effective impact parameters as compared to minimum bias events. This happens because the transverse spatial distribution of hard partons $(x\ensuremath{\gtrsim}{10}^{\ensuremath{-}2})$ in the proton is considerably narrower than that of soft partons, whose collisions dominate the total cross section. In the central collisions selected by the trigger, most of the partons with $x\ensuremath{\gtrsim}{10}^{\ensuremath{-}2}$ interact with a gluon field whose strength rapidly increases with energy. At LHC (and to some extent already at Tevatron) energies the strength of this interaction approaches the unitarity (``blackbody'') limit. This leads to specific modifications of the final state, such as a higher probability of multijet events at small rapidities, a strong increase of the transverse momenta and depletion of the longitudinal momenta at large rapidities, and the appearance of long-range correlations in rapidity between the forward or backward fragmentation regions. The same pattern is expected for events with production of new heavy particles (Higgs boson, SUSY). Studies of these phenomena would be feasible with the CMS-TOTEM detector setup, and would have considerable impact on the exploration of the physics of strong gluon fields in QCD, as well as the search for new particles at LHC.

Structure of the nucleon

Generalized parton distributions provide information on the longitudinal and transverse distribution of partons in the fast moving nucleon. Furthermore, they contain information on the spin structure of the nucleon. First results of a lattice study of generalized parton distributions are presented.

Next-to-leading order QCD corrections toATTfor prompt photon production

We present a next-to-leading order QCD calculation of the cross section for isolated large-p_T prompt photon production in collisions of transversely polarized protons. We devise a simple method of dealing with the phase space integrals in dimensional regularization in the presence of the cos(2 phi) azimuthal-angular dependence occurring for transverse polarization. Our results allow to calculate the double-spin asymmetry A_TT for this process at next-to-leading order accuracy, which may be used at BNL-RHIC to measure the transversity parton distributions of the proton.

High-pTpion and kaon production in relativistic nuclear collisions

High-p_T pion and kaon production is studied in relativistic proton-proton, proton-nucleus, and nucleus-nucleus collisions in a wide energy range. Cross sections are calculated based on perturbative QCD, augmented by a phenomenological transverse momentum distribution of partons (``intrinsic k_T''). An energy dependent width of the transverse momentum distribution is extracted from pion and charged hadron production data in proton-proton/proton-antiproton collisions. Effects of multiscattering and shadowing in the strongly interacting medium are taken into account. Enhancement of the transverse momentum width is introduced and parameterized to explain the Cronin effect. In collisions between heavy nuclei, the model over-predicts central pion production cross sections (more significantly at higher energies), hinting at the presence of jet quenching. Predictions are made for proton-nucleus and nucleus-nucleus collisions at RHIC energies.

Effects of parton intrinsic transverse momentum on photon production in hard-scattering processes

We calculate the photon production cross section arising from the hard scattering of partons in nucleon-nucleon collisions by taking into account the intrinsic parton transverse momentum distribution and the next-to-leading-order contributions. As first pointed out by Owens, the inclusion of the intrinsic transverse momentum distribution of partons leads to an enhancement of photon production cross section in the region of photon transverse momenta of a few GeV/c for nucleon-nucleon collisions at a center-of-mass energy of a few tens of GeV. The enhancement increases as {radical} (s) decreases. Such an enhancement is an important consideration in the region of photon momenta under investigation in high-energy heavy-ion collisions. {copyright} {ital 1998} {ital The American Physical Society}

A quark model analysis of the transversity distribution

The feasibility of measuring chiral-odd parton distribution functions in polarized Drell-Yan and semi-inclusive experiments has renewed theoretical interest in their study. Models of hadron structure have proven succesful in describing the gross features of the chiral-even structure functions. Similar expectations support our study of the transversity parton distributions in the Isgur-Karl and MIT bag models. We confirm the diverse low x behavior of the transversity and spin structure functions at the experimental scale and show that it is fundamentally a consequence of the different behavior under evolution of these functions. The inequalities of Soffer establish constraints between data and model calculations of the chiral-odd transversity function. The approximate compatibility of our model calculations with these constraints conferes credibility to our estimates.

Charge radii of nucleons

Charge radii of nucleons are studied in the context of a quark parton model by using Sehgal's hypothesis of nonfactorizable transverse distribution of partons. It is shown that the observed negative sign and the finite magnitude of the squared neutron charge radius, =−(0.16÷0.11) fm2, can be reconciled if different, spatial distributions are assumed for the u and d quarks inside a nucleon.

Transverse momentum distribution of partons in QCD

The renormalization group approach is applied to the study of transverse momentum distribution of partons in QCD. We generalize the method of Altarelli and Parisi to obtain a formula for the mean squared average transverse momentum as a function of Q 2 and x, the virtual photon mass squared and the longitudinal momentum fraction of the parton. For large Q 2, it decreases with x in addition to the expected increase with Q 2. This x-dependence reduces substantially the transverse momentum of massive μ-pairs produced by hadronic collisions from its linear dependence on ( Q 2 ln Q 2 ) 1 2 .

The charge radius of the neutron and the quark-parton model

An attempt is made, within the framework of the quark parton model, to understand the negative sign of 〈 R 2〉 n , the mean square charge radius of the neutron. An hypothesis is made concerning the transverse momentum distribution of partons that is motivated by recent measurements on electroproduction. With this hypothesis, the result 〈 R 2〉 n < 0 implies the inequality σ υ N −σ υ N > 6 ∫ (F 2 ep −F 2 en ) dx ( σ's in units of G 2 ME π ) which appears to be in agreement with present data.