Spin Structure Of Nucleon Research Articles

Status of the NICA project at JINR

The NICA (Nuclotron-based Ion Collider fAcility) is the new international research facility under construction at the Joint Institute for Nuclear Research (JINR) in Dubna. The main targets of the facility are the following: 1) study of hot and dense baryonic matter at the energy range of the maximum baryonic density; 2) investigation of nucleon spin structure and polarization phenomena; 3) development of JINR accelerator facility for high energy physics research based on the new collider of relativistic ions from protons to gold and polarized protons and deuterons as well with the maximum collision energy of √SNN ~11GeV (Au79+ +Au79+) and ~ 27 GeV (p+p). Two collider detector setups MPD and SPD are foreseen. The setup BM@N (Baryonic Matter at Nuclotron) is commissioned for data taken at the existing Nuclotron beam fixed target area. The MPD construction is in progress whereas the SPD is still at the beginning design stage. An average luminosity of the collider is expected at the level of 1027 cm-2 s-1 for Au79+ and 1032 cm-2 s-1 for polarized protons at 27 GeV. The status of NICA design and construction work is briefly described below.

Status of NICA

The NICA (Nuclotron-based Ion Collider fAcility) is the new international research facility under construction at the Joint Institute for Nuclear Research (JINR) in Dubna. The main targets of the facility are the following: 1) study of hot and dense baryonic matter at the energy range of the maximum baryonic density; 2) investigation of nucleon spin structure and polarization phenomena; 3) development of JINR accelerator facility for high energy physics research based on the new collider of relativistic ions from protons to gold and polarized protons and deuterons as well with the maximum collision energy of sqrt(sNN) ~11GeV (Au79+ +Au79+) and ~ 27 GeV (p+p). Two collider detector setups MPD and SPD are foreseen. The setup BM@N (Baryonic Matter at Nuclotron) is commissioned for data taken at the existing Nuclotron beam fixed target area. The MPD construction is in progress whereas the SPD is still at the beginning design stage. An average luminosity of the collider is expected at the level of 1027 cm-2 s-1 for Au (79+) and 1032 cm-2 s-1 for polarized protons at 27 GeV. The status of NICA design and construction work is briefly described below.

A possible layout of the Spin Physics Detector with toroid magnet.

The Spin Physics Detector project for carrying out experiments at the 2-nd interaction point of the NICA collider is under preparation. The design of the collider allows reaching collision energy in the c.m.s. as high as √s = 26 GeV for polarized proton-proton collisions and √s = 12 GeV for polarized deuteron-deuteron collisons with a luminosity of up to 1032 cm2 s-1 (for protons) and 1031cm2s-1 for deuterons. Such a high luminosity of polarized beams interactions opens unique possibilities to investigate a variety of polarization phenomena including those related to the nucleon spin structure. A proposal for the experimental set-up based on a toroid type magnet is presented.

Process-independent strong running coupling

We unify two widely different approaches to understanding the infrared behaviour of quantum chromodynamics (QCD), one essentially phenomenological, based on data, and the other computational, realised via quantum field equations in the continuum theory. Using the latter, we explain and calculate a process-independent running-coupling for QCD, a new type of effective charge that is an analogue of the Gell-Mann--Low effective coupling in quantum electrodynamics. The result is almost identical to the process-dependent effective charge defined via the Bjorken sum rule, which provides one of the most basic constraints on our knowledge of nucleon spin structure. This reveals the Bjorken sum to be a near direct means by which to gain empirical insight into QCD's Gell-Mann--Low effective charge.

NICA project at JINR: status and prospects

The project NICA (Nuclotron-based Ion Collider fAcility) is aimed to study hot and dense baryonic matter in heavy-ion collisions in the energy range up to 11.0 AGeV . The plan of NICA accelerator block development includes an upgrade of the existing superconducting (SC) synchrotron Nuclotron and construction of the new injection complex, SC Booster, and SC Collider with two interaction points (IP). The heavy-ion collision program will be performed with the fixed target experiment Baryonic Matter at Nuclotron (BM@N) at the beam extracted from the Nuclotron, and with Multi-Purpose Detector (MPD) at the first IP of NICA Collider. Investigation of nucleon spin structure and polarization phenomena is foreseen with the Spin Physics Detector (SPC) at the second IP of the Collider.

Nucleon spin structure functions at NNLO in the presence of target mass corrections and higher twist effects

We extract polarized parton distribution functions (PPDFs), referred to as "KTA17," together with the highly correlated strong coupling $\alpha_s$ from recent and up-to-date $g_1$ and $g_2$ polarized structure functions world data at next-to-next-to-leading order in perturbative QCD. The stability and reliability of the results are ensured by including nonperturbative target mass corrections as well as higher-twist terms which are particularly important at the large-$x$ region at low Q$^2$. Their role in extracting the PPDFs in the nucleon is studied. Sum rules are discussed and compared with other results from the literature. This analysis is made by means of the Jacobi polynomials expansion technique to the DGLAP evolution. The uncertainties on the observables and on the PPDFs throughout this paper are computed using standard Hessian error propagation which served to provide a more realistic estimate of the PPDFs uncertainties.

Spin-dependent sum rules connecting real and virtual Compton scattering verified

We present a detailed derivation of the two sum rules relating the spin polarizabilities measured in real, virtual, and doubly-virtual Compton scattering. For example, the polarizability $\delta_{LT}$, accessed in inclusive electron scattering, is related to the spin polarizability $\gamma_{E1E1}$ and the slope of generalized polarizabilities $P^{(M1,M1)1}-P^{(L1,L1)1}$, measured in, respectively, the real and the virtual Compton scattering. We verify these sum rules in different variants of chiral perturbation theory, discuss their empirical verification for the proton, and prospect their use in studies of the nucleon spin structure.

Investigation of the dp Breakup and dp Elastic Reactions at Intermediate Energies at Nuclotron

The main goal of the deuteron spin structure project is to investigate the spin structure of nucleon–nucleon and three nucleon short-range correlations via the measurements of the polarization observables in the deuteron induced reactions at intermediate energies at Nuclotron (Dubna, Russia). In this framework, dp nonmesonic breakup and dp elastic reactions are investigated using internal target station. The dp breakup data are obtained with the detection of two outgoing protons at the angles of $$19^{\circ }$$ – $$54^{\circ }$$ in lab. frame at the deuteron energies of 300–500 MeV. The data of dp elastic scattering for the deuteron energies up to 2000 MeV are obtained in angular range $$70^{\circ }$$ – $$120^{\circ }$$ in cm. The further perspectives of the investigations using polarized deuteron beam as well as the studies of the $${}^3{\mathrm{He}}(d,p){}^4{\mathrm{He}}$$ reaction are discussed.

Spin Physics Experiments at NICA-SPD

Nuclotron based Ion Collider fAcility (NICA) is a flagship project of the Joint Institute for Nuclear Research which is expected to be operational by 2021. Main tasks of “NICA Facility” are study of hot and dense baryonic matter, investigation the polarisation phenomena and the nucleon spin structure. The material presented here based on the Letter of Intent (LoI) dedicated to nucleon spin structure studies at NICA. Measurements of asymmetries in the lepton pair (Drell-Yan) production in collisions of non-polarised, longitudinally and transversely polarised proton and deuteron beams to be performed using the specialized Spin Physics Detector (SPD). These measurements can provide an access to all leading twist collinear and Transverse Momentum Dependent Parton Distribution Functions (TMD PDFs) in nucleons. The measurements of asymmetries in production of J/ψ and direct photons, which supply complimentary information on the nucleon structure, will be performed simultaneously. The set of these measurements permits to tests the quark-parton model of nucleons at the QCD twist-2 level with minimal systematic errors.

Gravitational form factors and nucleon spin structure

Nucleon scattering by the classical gravitational field is described by the gravitational (energy-momentum tensor) form factors (GFFs), which also control the partition of nucleon spin between the total angular momenta of quarks and gluons. The equivalence principle (EP) for spin dynamics results in the identically zero anomalous gravitomagnetic moment, which is the straightforward analog of its electromagnetic counterpart. The extended EP (ExEP) describes its (approximate) validity separately for quarks and gluons and, in turn, results in equal partition of the momentum and total angular momentum. It is violated in quantum electrodynamics and perturbative quantum chromodynamics (QCD), but may be restored in nonperturbative QCD because of confinement and spontaneous chiral symmetry breaking, which is supported by models and lattice QCD calculations. It may, in principle, be checked by extracting the generalized parton distributions from hard exclusive processes. The EP for spin-1 hadrons is also manifested in inclusive processes (deep inelastic scattering and the Drell–Yan process) in sum rules for tensor structure functions and parton distributions. The ExEP may originate in either gravity-proof confinement or in the closeness of the GFF to its asymptotic values in relation to the mediocrity principle. The GFFs in time-like regions reveal some similarity between inflation and annihilation.

Spin Physics at NICA

The NICA-SPD project is under preparation at the 2nd interaction point of the NICA collider. The main purpose of this experiment is the study of the nucleon spin structure with high intensity polarized proton and deuteron beams. The design of the collider can allow us to reach a very high collision proton (deuteron) energy up to [Formula: see text]s [Formula: see text][Formula: see text]26 (12) GeV with the average luminosity up to 10[Formula: see text] (10[Formula: see text] cm[Formula: see text] Both proton and deuteron beams will be effectively polarized. The one gives us unique possibilities to investigate the polarized phenomena and nucleon spin structure at NICA. The comprehensive program of these studies is presented.

The RHIC Spin Program Overview

After more than a decade of RHIC running as a polarized proton collider, we summarize recent achievements of the RHIC spin program and their impact on our understanding of the nucleon's spin structure, i.e. the individual parton (quarks and gluons) contributions to the helicity structure of the nucleon, and to understand the origin of the transverse spin phenomena. Open questions are identified and a suite of future measurements with polarized beams at RHIC to address them is laid out.

J/ψ Longitudinal Double Spin Asymmetry Measurement at Forward Rapidity in p + p Collisions at s = 510 GeV

The polarized gluon distribution, as described by the polarized parton distribution function [Formula: see text], is an important part of the spin structure of the nucleon; however the current data have very limited constraints on [Formula: see text] for [Formula: see text]. During the 2013 RHIC run, the PHENIX experiment collected 146 pb[Formula: see text] of longitudinally polarized [Formula: see text] data at [Formula: see text] GeV with an average beam polarization of 52%. At this energy, [Formula: see text] particles are predominantly produced through gluon-gluon interactions and thus the longitudinal double spin asymmetry, [Formula: see text], is sensitive to the gluon polarization inside the proton. We measure the [Formula: see text] [Formula: see text] in the rapidity range [Formula: see text] by detecting the decay [Formula: see text] pairs using the PHENIX muon detector arms. In this kinematic range, [Formula: see text] is sensitive to the polarized gluon distribution at small [Formula: see text] as well as at moderate [Formula: see text] where recent RHIC data on jet and [Formula: see text] production show possible evidence for significant gluon polarization. Compared to previous measurements in 2005 and 2006, the Run 2013 data set has roughly twenty times more statistics and will allow us to measure [Formula: see text] with a statistical uncertainty at [Formula: see text]% level. In these preceedings, the latest status of this analysis will be presented.

Recent results on nucleon spin structure study at RHIC

Both the PHENIX and STAR experiments at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory are running polarized proton–proton collisions at $$\sqrt s $$ = 200 and 500 GeV. The main goal of the RHIC spin physics program is to gain deeper insight into the spin structure of the nucleon. We will give an overview of recent spin results from RHIC, particularly the study of gluon polarization via jet/hadron production and sea quark polarization via W boson production in longitudinally polarized proton–proton collisions.

Nucleon spin structure

This paper contains three parts relating to the nucleon spin structure in a simple picture of the nucleon: (i) The polarized gluon distribution in the proton is dynamically predicted starting from a low scale by using a nonlinear quantum chromodynamics (QCD) evolution equation — the Dokshitzer–Gribov–Lipatov–Altarelli–Paris (DGLAP) equation with the parton recombination corrections, where the nucleon is almost consisted only of valence quarks. We find that the contribution of the gluon polarization to the nucleon spin structure is much larger than the predictions of most other theories. This result suggests that a significant orbital angular momentum of the gluons is required to balance the gluon spin momentum. (ii) The spin structure function [Formula: see text] of the proton is studied, where the perturbative evolution of parton distributions and nonperturbative vector meson dominance (VMD) model are used. We predict [Formula: see text] asymptotic behavior at small x from lower Q2to higher Q2. The results are compatible with the data including the early HERA estimations and COMPASS new results. (iii) The generalized Gerasimov–Drell–Hearn (GDH) sum rule is understood based on the polarized parton distributions of the proton with the higher twist contributions. A simple parameterized formula is proposed to clearly present the contributions of different components in the proton to [Formula: see text]. The results suggest a possible extended objects with size 0.2–0.3 fm inside the proton.

Neutrino-pair bremsstrahlung from nucleon-αversus nucleon-nucleon scattering

We study the impact of the nucleon-$\alpha$ P-wave resonances on neutrino-pair bremsstrahlung. Because of the non-central spin-orbit interaction, these resonances lead to an enhanced contribution to the nucleon spin structure factor for temperatures $T \lesssim 4$ MeV. If the $\alpha$-particle fraction is significant and the temperature is in this range, this contribution is competitive with neutron-neutron bremsstrahlung. This may be relevant for neutrino production in core-collapse supernovae or other dense astrophysical environments. Similar enhancements are expected for resonant non-central nucleon-nucleus interactions.

Small- and large-x nucleon spin structure from a global QCD analysis of polarized parton distribution functions

I investigate the behavior of spin-dependent parton distribution functions in the regions of small and large momentum fractions x. I present a systematic comparison between predictions for relevant observables obtained with various models of nucleon spin structure and a recent global analysis of spin-dependent distributions, NNPDFpol1.1. Together with its unpolarized counterpart, NNPDF2.3, they form a mutually consistent set of parton distributions. Because they include most of the available experimental information, and are determined with a minimally biased methodology, these are especially suited for such a study. I show how NNPDFpol1.1 can discriminate between different theoretical models, even though NNPDF uncertainties remain large near the endpoints x→0 and x→1, due to the lack of experimental information. I discuss how our knowledge of nucleon spin structure may be improved at small x by future measurements at an Electron–Ion Collider, and at large x by recent measurements at Jefferson Lab, also in view of its 12 GeV upgrade.

New results on transverse spin asymmetries from COMPASS

One of the important objectives of the COMPASS experiment is the exploration of transverse spin structure of nucleon via spin (in)dependent azimuthal asymmetries in semi-inclusive deep inelastic scattering (SIDIS) of polarized leptons (and soon also Drell-Yan (DY) reactions with $\pi^-$) off transversely polarized target. For this purpose a series of measurements were made in COMPASS, using 160 GeV/c longitudinally polarized muon beam and polarized $^6LiD$ and $NH_3$ targets and are foreseen with 190 GeV/c $\pi^-$ beam on polarized $NH_3$. The experimental results obtained by COMPASS for azimuthal effects in SIDIS play an important role in the general understanding of the three-dimensional nature of the nucleon and are widely used in theoretical analyses and global data fits. Future first ever polarized DY-data from COMPASS compared with SIDIS results will open a new chapter probing general principles of QCD TMD-formalism. In this review main focus will be given to the very recent COMPASS results obtained for SIDIS transverse spin asymmetries from four "Drell-Yan" $Q^2$-ranges.

Status of the NICA project at JINR

The NICA (Nuclotron-based Ion Collider fAcility) project is now under active realization at the Joint Institute for Nuclear Research (JINR, Dubna). The main goal of the project is a study of hot and dense strongly interacting matter in heavy ion (up to Au) collisions at the centre-of-mass energies up to 11 GeV per nucleon. Two modes of operation are foreseen, collider mode and extracted beams, with two detectors: MPD and BM@N. The both experiments are in preparation stage. An average luminosity in the collider mode is expected as 10E27 cm-2 s-1 for Au (79+). Extracted beams of various nucleus species with maximum momenta of 13 GeV/c (for protons) will be available. A study of spin physics with extracted and colliding beams of polarized deuterons and protons at the energies up to 27 GeV (for protons) is foreseen with the NICA facility. The proposed program allows one to search for possible signs of phase transitions and critical phenomena as well as to shed light on the problem of the nucleon spin structure.

Chiral Odd GPDs

Nucleon spin structure, transversity and the tensor charge are of central importance to understanding the role of QCD in hadronic physics. A new approach to measuring orbital angular momenta of quarks in the proton via twist 3 GPDs is shown. The “flexible parametrization” of chiral even GPDs is reviewed and its transformation into the chiral odd sector is discussed. The resulting parametrization is applied to recent data on π 0 and η electroproduction.