Parton Momentum Distribution Research Articles

Mass distributions of dijet resonances from excited quarks at proton-proton colliders

We study the expected experimental mass distributions of dijet resonances from excited quarks in proton-proton collisions at energies s = 13, 14, 27, 100, 300, and 500 TeV. We explore in detail the expected shapes at both the generator and experimental levels, and identify within the distributions the effects of the excited quark natural width, parton momentum distributions of the proton, radiation, and experimental resolution. We present both differential and cumulative probability distributions as a function of dijet mass, and the signal acceptance of a window in dijet mass centered on each resonance. We find that for a range of resonance masses, between 10% and 50% of s, the dijet mass distributions and window acceptance are practically universal, approximately invariant under changes in resonance mass and s. This universality is violated when the resonance mass reaches 60% of s, because the steepness of the parton momentum distributions of the proton produces a significant tail at low dijet mass. This work supports our Snowmass 2021 study on the sensitivity to dijet resonances at proton-proton colliders.

Simulation of multiple hadron production and transition to quark-gluon plasmas based on nonlinear dynamics

A dynamics of quark-gluon plasmas has been defined by the evolution parameter, which at high energies depends on collision energy of atomic nuclei for appropriate multiplicities of secondary hadrons. The paper is based on the solution of evolution equation for patrons momentum distribution. A transition from regular propagation to irregular chaotic is an indicator of the quark-gluon plasma emerging. Nonlinear renormalization group equation has been solved by the method of Poincaré mappings. The equation is a model of the evolution of the momentum distribution of partons due to competing processes of their creation and fusion. As the energy increases, sequential bifurcation (doubling) of phase trajectories occurs, and scale-invariant fractal structures are to create. At sufficiently high energies of quarks and gluons, a dynamically determined quark-gluon system, corresponding to QGP, arises in space. There are also hadron-like structures. Quantum coherence effects follow by dynamic chaos. As a result, quarks and gluons merge into stable attractor structures with their subsequent decay into hadrons. The nonlinear equation introduced for quark-gluon cascade, which comprises dynamical chaos, has include effects of parton recombination. The chaotic dynamics has been connected specifically to the transverse momenta of partons. Clearly, the formation of dynamically determined stable structures should be unknown before, attractor mechanism of quark hadronization.

Imaging the nucleus with high-energy photons

In the 1930's, nuclear physicists developed the first realistic atomic models, showing that nuclei were made up of protons and neutrons. In the 1960's, Deep Inelastic Scattering experiments showed that protons and neutrons had internal structure: quarks and gluons (collectively, partons), and later experiments showed that the parton momentum distributions are different in heavy nuclei, compared to those in free nucleons. This difference is not surprising; partons are sensitive to their environment, and two gluons from different nucleons may fuse together, for example. Understanding how quarks and gluons behave in the nuclear environment is a significant focus of modern nuclear physics. Recent measurements have provided us with an improved understanding of how quark and gluon densities are altered in heavy nuclei. We have also begun to make multi-dimensional pictures of the nucleus, exploring how these alterations are distributed within heavy nuclei. We naturally expect these modifications to be largest in the core of a nucleus, and smaller near its periphery; this can change the effective shape of the nucleus. We have also started to explore the transverse momentum distribution of the partons in the nuclei, and, using incoherent photoproduction as a probe, study event-by-event fluctuations in nucleon and nuclei parton densities. This article will explore recent progress in measurements of nuclear structure at high energy, with some emphasis on these multi-dimensional pictures. We will also discuss how a future electron-ion collider (EIC) with high luminosity and center-of-mass energy will make exquisitely detailed images of partons in a nucleus.

Triple Differential Dijet Cross Section at the LHC.

The measurement of the triple-differential dijet production cross section as a function of the average transverse momentum p_{T,avg}, half the rapidity separation y^{*}, and the boost y_{b} of the two leading jets in the event enables a kinematical scan of the underlying parton momentum distributions. We compute for the first time the second-order perturbative QCD corrections to this triple-differential dijet cross section, at leading color in all partonic channels, thereby enabling precision studies with LHC dijet data. A detailed comparison with experimental CMS 8TeV data is performed, demonstrating how the shape of this differential cross section probes the parton densities in different kinematical ranges.

Nucleon parton distributions from hadronic quantum fluctuations

A physical model is presented for the nonperturbative parton distributions in the nucleon. This is based on quantum fluctuations of the nucleon into baryon-meson pairs convoluted with Gaussian momentum distributions of partons in hadrons. The hadronic fluctuations, here developed in terms of hadronic chiral perturbation theory, occur with high probability and generate sea quarks as well as dynamical effects also for valence quarks and gluons. The resulting parton momentum distributions $f(x,{Q}_{0}^{2})$ at low momentum transfers are evolved with conventional Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equations from perturbative QCD to larger scales. This provides parton density functions $f(x,{Q}^{2})$ for the gluon and all quark flavors with only five physics-motivated parameters. By tuning these parameters, experimental data on deep-inelastic structure functions can be reproduced and interpreted. The contribution to sea quarks from hadronic fluctuations explains the observed asymmetry between $\overline{u}$ and $\overline{d}$ in the proton. The strange-quark sea is strongly suppressed at low ${Q}^{2}$, as observed.

The Bethe-Salpeter approach to bound states: from Euclidean to Minkowski space

The challenge to obtain from the Euclidean Bethe–Salpeter amplitude the amplitude in Minkowski is solved by resorting to un-Wick rotating the Euclidean homogeneous integral equation. The results obtained with this new practical method for the amputated Bethe–Salpeter amplitude for a two-boson bound state reveals a rich analytic structure of this amplitude, which can be traced back to the Minkowski space Bethe–Salpeter equation using the Nakanishi integral representation. The method can be extended to small rotation angles bringing the Euclidean solution closer to the Minkowski one and could allow in principle the extraction of the longitudinal parton density functions and momentum distribution amplitude, for example.

Quasi-parton distribution functions, momentum distributions, and pseudo-parton distribution functions

We show that quasi-PDFs may be treated as hybrids of PDFs and primordial rest-frame momentum distributions of partons. This results in a complicated convolution nature of quasi-PDFs that necessitates using large $p_3 \sim 3$ GeV momenta to get reasonably close to the PDF limit. As an alternative approach, we propose to use pseudo-PDFs $P(x, z_3^2)$ that generalize the light-front PDFs onto spacelike intervals and are related to Ioffe-time distributions $M (\nu, z_3^2)$, the functions of the Ioffe time $\nu = p_3 z_3$ and the distance parameter $z_3^2$ with respect to which it displays perturbative evolution for small $z_3$. In this form, one may divide out the $z_3^2$ dependence coming from the primordial rest-frame distribution and from the problematic factor due to lattice renormalization of the gauge link. The $\nu$-dependence remains intact and determines the shape of PDFs.

Spinodal instabilities of baryon-rich quark matter in heavy ion collisions

Using the test-particle method to solve the transport equation derived from the Nambu-Jona-Lasino (NJL) model, we study how phase separation occurs in expanding quark matter like that in a heavy ion collision. To test our method, we first investigate the growth rates of unstable modes of quark matter in a static cubic box and find them to agree with the analytical results that were previously obtained using the linear response theory. In this case, we also study the higher-order scaled density moments in the quark matter, which have values of 1 for a uniform density distribution or a distribution where the nonzero density regions all have same value, and they are found to increase with time and saturate at values significantly larger than 1 after the phase separation. The skewness of the quark number event-by-event distribution in a small subvolume of the system is also found to increase, but this feature disappears if the subvolume is large. For the expanding quark matter, two cases are considered: one using a blast-wave model for the initial conditions and the other using initial conditions from a multiphase transport (AMPT) model. In both cases, we find that the expansion of the quark matter is slowed down by the presence of a first-order phase transition. Also, density clumps appear in the system and the momentum distribution of partons becomes anisotropic, which can be characterized by large scale density moments and nonvanishing anisotropic elliptic and quadrupolar flows, respectively. The large density fluctuations further lead to an enhancement in the dilepton yield. In the case with the AMPT initial conditions, the presence of a first-order phase transition also results in a narrower distribution of partons in rapidity. These effects of density fluctuations can be regarded as possible signals for a first-order phase transition that occurs in the baryon-rich quark matter formed in relativistic heavy ion collisions.

Two-particle correlation via Bremsstrahlung

Ridge is the well-known structure in two-particle angular correlations at highenergy heavy-ion collisions. This structure is physically understood through elliptic and higher-order flows at nucleus-nucleus collisions. This behavior is also found in small systems, such as proton-proton collisions, recently. However, Ridge structure in small system is hard to be understood using hydrodynamics, since small systems are not dense enough to produce the Quark-Gluon plasma. Thus, we try to describe this phenomena through kinematic interaction between jets and medium partons. In high-energy heavy-ion collision, the energetic particles called jets go out in specific direction and lose their energy while passing through the medium. During such process, photons/gluons are emitted from interaction between jets and medium partons. We concentrate on energy loss via photon radiations, known as Bremsstrahlung. Recently, two symmetric double scattering processes between jet particle and medium parton are reported to be able to produce certain constructive interference, which gives collective motion and medium partons are aligned along incoming jet particles. We conjecture that similar behavior might happen in Bremsstrahlung processes, and therefore we consider the two symmetric diagrams of photon emission and medium parton scattering. We expect these two amplitudes to give constructive interference leading to the collective motion of medium. We check the correlation between emitted photon and final jet, and those between medium parton and final jet for high-energy jet. To describe parton momentum distribution in medium, we use the Maxwell-Boltzmann distribution. We discover collective motion in both angular correlations. We also check the tendency of the angular correlation for two particles according to the incident angle of jet particle, energy of emitted photon and temperature of systems, respectively. We can conclude that collective motion is able to be understood through kinematic description.

Studying the information content of TMDs using Monte Carlo generators

Theoretical advances in studies of the nucleon structure have been spurred by recent measurements of spin and/or azimuthal asymmetries worldwide. One of the main challenges still remaining is the extraction of the parton distribution functions, generalized to describe transverse momentum and spatial distributions of partons from these observables with no or minimal model dependence. In this review we present the latest developments in the field with emphasis on requirements for Monte Carlo event generators, indispensable for studies of the complex 3D nucleon structure, and discuss examples of possible applications.

Monte Carlo Generators for Studies of the 3D Structure of the Nucleon

In this study, extraction of transverse momentum and space distributions of partons from measurements of spin and azimuthal asymmetries requires development of a self consistent analysis framework, accounting for evolution effects, and allowing control of systematic uncertainties due to variations of input parameters and models. Development of realistic Monte-Carlo generators, accounting for TMD evolution effects, spin-orbit and quark-gluon correlations will be crucial for future studies of quark-gluon dynamics in general and 3D structure of the nucleon in particular.

Jet-induced collective modes in an anisotropic quark-gluon plasma

We discuss the characteristics of collective modes induced by relativistic jets in a collisionless anisotropic quark-gluon plasma (AQGP) assuming a colorless Tsunami-like momentum distribution of the jet partons. Within the framework of the transport equation, we derive and discuss the dispersion relations for both the stable and unstable modes of the composite system in the Vlasov approximation. We consider the case when the wave vector is parallel to the anisotropy direction as the growth rate of the unstable mode is maximum in this scenario. When the wave vector ($\mathbf{k}$) is perpendicular to the jet velocity (${\mathbf{v}}_{\text{jet}}$), two stable modes are found (referred to as mode I and mode II hereafter) of which one is independent of the jet velocity. In case of $\mathbf{k}\ensuremath{\parallel}{\mathbf{v}}_{\text{jet}}$, we obtain two identical modes (mode I) and one distinct mode (referred to as mode III hereafter). In all of the cases it is found that stable modes shift toward the light cone for nonzero values of the anisotropy parameter ($\ensuremath{\xi}$) and the jet strength ($\ensuremath{\eta}$). In case of unstable mode I, the growth rate increases with $\ensuremath{\xi}$ for fixed $\ensuremath{\eta}$. The growth rate in case of modes II and III increases with $\ensuremath{\xi}$ and $\ensuremath{\eta}$, and the nature of the increase depends on the jet velocity.

Tomography of exotic hadrons in high-energy exclusive processes

We investigated the possibility of determining internal structure of exotic hadrons by using high-energy reaction processes, where quarks and gluons are appropriate degrees of freedom. In particular, it should be valuable to investigate the high-energy exclusive processes which include generalized parton distributions (GPDs) and generalized distribution amplitudes (GDAs). The GPDs and GDAs contain momentum distributions of partons and form factors. We found that the exotic nature appears in momentum distributions of quarks as suggested by the constituent-counting rule and in the form factors associated with exotic hadron sizes and the number of constituents. Transition GPDs to exotic hadrons could probe such exotic signatures. We also propose that these exotic signatures should be found in exclusive production processes of exotic hadrons from gamma^* gamma in electron-positron annihilation. For example, the GDAs contain information on a time-like form factor of the energy-momentum tensor of a hadron h. We show that the cross section of e gamma -> e+hbar h is sensitive to the exotic signature by looking at the hbar h invariant-mass dependence by taking light hadrons, h=f_0 (980) and a_0 (980). From such GDA measurements, the tomography of exotic hadrons becomes possible, for example, by Belle and BaBar experiments and by future linear collider.

Studies of the 3D structure of the proton at Jlab

In recent years parton distributions, describing longitudinal momentum, helicity and transversity distributions of quarks and gluons, have been generalized to account also for transverse degrees of freedom. Two new sets of more general distributions, Transverse Momentum Distributions (TMDs) and Generalized Parton Distributions (GPDs) were introduced to describe transverse momentum and spatial distributions of partons. Great progress has been made since then in measurements of different Single Spin Asymmetries (SSAs) in semi-inclusive and hard exclusive processes, providing access to TMDs and GPDs, respectively. Studies of TMDs and GPDs are also among the main driving forces of the JLab 12 GeV upgrade project.

Structure and spin of the nucleon

Parton distribution functions, describing longitudinal momentum, helicity and transversity distributions of quarks and gluons, have been recently generalized to account also for transverse degrees of freedom. Two new sets of more general distributions, Transverse Momentum Distributions and Generalized Parton Distributions, were introduced to describe transverse momentum and space distributions of partons. Great progress has been made since then in measurements of different Single Spin Asymmetries (SSAs) in semi-inclusive and hard exclusive processes providing access to TMDs and GPDs, respectively. Facilities world-wide involved in studies of the 3D structure of nucleon include HERMES, COMPASS, BELLE, BaBar, Halls A, B, and C at JLab, and PHENIX and STAR at RHIC (BNL). TMD studies in the Drell-Yan process are also becoming an important part of the program of hadron scattering experiments. Studies of TMDs are also among the main driving forces of the JLab 12-GeV upgrade project, several of the forward upgrade proposals of STAR and PHENIX at RHIC, and future facilities, such as the Electron Ion Collider (EIC), FAIR in Germany, and NICA in Russia. In this contribution we present an overview of the latest developments in studies of parton distributions and discuss newly released results, ongoing activities, as well as some future measurements.

Jets, Bulk Matter, and their Interaction in Heavy Ion Collisions at the LHC

We discuss a theoretical scheme that accounts for bulk matter, jets, and the interaction between the two. The physical picture of our approach is the following: Initial hard scatterings result in mainly longitudinal flux tubes, with transversely moving pieces carrying the pt of the partons from hard scatterings. These flux tubes constitute eventually both bulk matter (which thermalizes, flows, and finally hadronizes) and jets, according to some criteria based on partonic energy loss. High energy flux tube segments will leave the fluid, providing jet hadrons via the usual Schwinger mechanism of flux-tube breaking caused by quark-antiquark production. But the jets may also be produced at the freeze-out surface. Here we assume that the quark-antiquark needed for the flux tube breaking is provided by the fluid, with properties (momentum, flavor) determined by the fluid rather than the Schwinger mechanism. Considering transverse fluid velocities up to 0.7c, and thermal parton momentum distributions, one may get a "push" of a couple of GeV to be added to the transverse momentum of the string segment. This will be a crucial effect for intermediate pt jet hadrons.

Parton transport via transverse and longitudinal scattering in dense media

The effect of multiple scatterings on the propagation of hard partonic jets in a dense nuclear medium is studied in the framework of deep-inelastic scattering (DIS) off a large nucleus. Power counting arguments based on the Glauber improved soft collinear effective theory are used to identify the class of leading power corrections to the process of a single parton traversing the extended medium without emission. It turns out that the effect of longitudinal drag and diffusion (often referred to as straggling) is as important as transverse scattering, when relying solely on power counting arguments. With the inclusion of momentum exchanges in both transverse and longitudinal directions between the traversing hard parton and the constituents of the medium, we derive a differential equation for the time (or distance) evolution of the hard parton momentum distribution. Keeping up to the second order in a momentum gradient expansion, this equation describes in-medium evolution of hard jets which experience longitudinal drag and diffusion plus the transverse broadening caused by multiple scatterings from the medium.

Intrinsic transverse momentum and parton correlations from dynamical chiral symmetry breaking

The dynamical breaking of chiral symmetry in QCD is caused by nonperturbative interactions on a scale rho ~ 0.3 fm, much smaller than the hadronic size R ~ 1 fm. These short-distance interactions influence the intrinsic transverse momentum distributions of partons and their correlations at a low normalization point. We study this phenomenon in an effective description of low-energy dynamics based on chiral constituent quark degrees of freedom, which refers to the large-N_c limit of QCD. The nucleon is obtained as a system of constituent quarks and antiquarks moving in a self-consistent classical chiral field (chiral quark-soliton model). The calculated distributions of constituent quarks/antiquarks are matched with QCD partons at the scale rho^{-2}. The p_T distribution of valence quarks is localized at p_T^2 ~ R^{-2} and roughly of Gaussian shape. The sea quark distribution exhibits a would-be power-like tail ~1/p_T^2 extending up to the chiral symmetry-breaking scale. Such behavior is seen in the flavor-singlet unpolarized and nonsinglet polarized sea. The high-momentum tails are the result of short-range correlations between sea quarks in the nucleon's light-cone wave function, analogous to NN correlations in nuclei. The nucleon wave function contains correlated pairs of transverse size rho << R with sigma- and pi-like quantum numbers, whose internal wave functions become identical at p_T^2 ~ rho^{-2} (restoration of chiral symmetry). These features are model-independent and represent an effect of dynamical chiral symmetry breaking on the nucleon's partonic structure. Our results have numerous implications for the P_T distributions of particles produced in hard scattering processes. The nonperturbative parton correlations predicted here could be observed in particle correlations between the current and target fragmentation regions of DIS.

Separating jets from bulk matter in heavy ion collisions at the LHC

We discuss a theoretical scheme that accounts for bulk matter, jets, and the interaction between the two. The physical picture of our approach is the following: Initial hard scatterings result in mainly longitudinal flux tubes, with transversely moving pieces carrying the pt of the partons from hard scatterings. These flux tubes constitute eventually both bulk matter (which thermalizes, flows, and finally hadronizes) and jets, according to some criteria based on partonic energy loss. High energy flux tube segments will leave the fluid, providing jet hadrons via the usual Schwinger mechanism of flux-tube breaking caused by quark-antiquark production. But the jets may also be produced at the freeze-out surface. Here we assume that the quark-antiquark needed for the flux tube breaking is provided by the fluid, with properties (momentum, flavor) determined by the fluid rather than the Schwinger mechanism. Considering transverse fluid velocities up to 0.7c, and thermal parton momentum distributions, one may get a "push" of a couple of GeV to be added to the transverse momentum of the string segment. This will be a crucial effect for intermediate pt jet hadrons.

Elliptic and triangular flow and their correlation in ultrarelativistic high multiplicity proton–proton collisions at 14 TeV

The spatial configuration of initial partons in high multiplicity proton–proton scatterings at 14 TeV is assumed as three randomly positioned “hot spots”. The parton momentum distribution in the hot spots is calculated by HIJING2.0 with some modifications. This initial condition causes not only large eccentricity ϵ2 but also triangularity ϵ3 and the correlation of ϵ2−ϵ3 event-plane angles. The final elliptic flow v2, triangular flow v3, and the correlation of v2−v3 event-plane angles are calculated by using the parton cascade model BAMPS to simulate the space–time parton evolution. Our results show that the v2−v3 correlation is different from that of ϵ2−ϵ3. This finding indicates that translations of different Fourier components of the initial spatial asymmetry to the final flow components are not independent. A dynamical correlation between the elliptic and triangular flow appears during the collective expansion.