Proton Spin Structure Function Research Articles

Chiral perturbation theory of the hyperfine splitting in (muonic) hydrogen

The ongoing experimental efforts to measure the hyperfine transition in muonic hydrogen prompt an accurate evaluation of the proton-structure effects. At the leading order in alpha , which is O(alpha ^5) in the hyperfine splitting (hfs), these effects are usually evaluated in a data-driven fashion, using the empirical information on the proton electromagnetic form factors and spin structure functions. Here we perform a first calculation based on the baryon chiral perturbation theory (Bchi PT). At leading orders it provides a prediction for the proton polarizability effects in hydrogen (H) and muonic hydrogen (mu H). We find large cancellations among the various contributions leading to, within the uncertainties, a zero polarizability effect at leading order in the Bchi PT expansion. This result is in significant disagreement with the current data-driven evaluations. The small polarizability effect implies a smaller Zemach radius R_textrm{Z}, if one uses the well-known experimental 1S hfs in H or the 2S hfs in mu H. We, respectively, obtain R_textrm{Z}(textrm{H}) = 1.010(9) fm, R_textrm{Z}(mu textrm{H}) = 1.040(33) fm. The total proton-structure effect to the hfs at O(alpha ^5) is then consistent with previous evaluations; the discrepancy in the polarizability is compensated by the smaller Zemach radius. Our recommended value for the 1S hfs in mu text {H} is 182.640(18),textrm{meV}.

Transverse proton gluon anisotropy points behind the Standard Model

The present work focuses on transverse gluon densities in the proton and derives exemplar distributions showing azimuthal anisotropies. Such anomalies relative to the Standard Model may be visible in scattering experiments involving protons. I describe baryons as mass eigenstates of a Hamiltonian structure on an intrinsic U(3) configuration space. This has yielded the neutral flavour baryon spectrum and given a rather accurate value for the neutron mass 939.9(5) MeV from first principles. Quark and gluon fields are shaped by the momentum form of the intrinsic wave function. This has led to parton distribution functions for the u and d valence quarks for the proton and to a proton spin structure function agreeing with experiments over four orders of magnitude in the parton momentum fraction.

On quarks and the origin of QCD: Partons and baryons from intrinsic states

We create quarks from baryons in stead of constituting baryons from quarks. The quantum fields of QCD are generated via the exterior derivative (momentum form) of baryon wave functions on an intrinsic configuration space, the Lie group U(3). Local gauge transformations correspond to coordinate translations in the intrinsic space. A proton spin structure function and a proton magnetic moment are derived. We show how the spectrum of unflavoured baryons, the N and Delta resonances, can be understood from a mass Hamiltonian on the intrinsic space and note how our model resolves the problem of colour confinement. We calculate an approximate value for the relative neutron-to-proton mass shift and give an exact value for the neutron mass. We predict neutral charge singlets that may be interpreted as neutral pentaquarks at LHCb.

Impact of recent COMPASS data on polarized parton distributions and structure functions

We perform a new extraction of polarized parton distribution functions (PPDFs) from the spin structure function experimental data in the fixed-flavor number scheme (FFNS). In this analysis, we include recent proton and deuteron spin structure functions obtained by the \texttt{COMPASS} collaboration. We examine the impact of the \texttt{new COMPASS} proton and deuteron data on the polarized parton densities and compare with results from our previous study (KATAO PPDFs), which used the Jacobi polynomial approach. We find the extracted PPDFs of the proton, neutron, and deuteron structure functions are in very good agreement with the experimental data. The results for extracted PPDFs are also compared with available theoretical models from the literature.

Final COMPASS results on the deuteron spin-dependent structure function [formula omitted] and the Bjorken sum rule

Final results are presented from the inclusive measurement of deep-inelastic polarised-muon scattering on longitudinally polarised deuterons using a 6LiD target. The data were taken at 160 GeV beam energy and the results are shown for the kinematic range 1(GeV/c)2<Q2<100(GeV/c)2 in photon virtuality, 0.004<x<0.7 in the Bjorken scaling variable and W>4GeV/c2 in the mass of the hadronic final state. The deuteron double-spin asymmetry A1d and the deuteron longitudinal-spin structure function g1d are presented in bins of x and Q2. Towards lowest accessible values of x, g1d decreases and becomes consistent with zero within uncertainties. The presented final g1d values together with the recently published final g1p values of COMPASS are used to again evaluate the Bjorken sum rule and perform the QCD fit to the g1 world data at next-to-leading order of the strong coupling constant. In both cases, changes in central values of the resulting numbers are well within statistical uncertainties. The flavour-singlet axial charge a0, which is identified in the MS‾ renormalisation scheme with the total contribution of quark helicities to the nucleon spin, is extracted at next-to-leading order accuracy from only the COMPASS deuteron data: a0(Q2=3(GeV/c)2)=0.32±0.02stat±0.04syst±0.05evol. Together with the recent results on the proton spin structure function g1p, the results on g1d constitute the COMPASS legacy on the measurements of g1 through inclusive spin-dependent deep inelastic scattering.

COMPASS results on proton longitudinal spin structure function g1and quark fragmentation functions

We present a few recent highlights from the COMPASS experiment at CERN, related to the nucleon spin and structure: the proton spin structure function g1 p (x) measured using 200 GeV polarized muons, together with a QCD fit of g1 world data; pion and kaon multiplicities in DIS in view of constraining quark fragmentation functions.The statistical precision on g1 p is improved by a factor of ~2 at low x. A reevaluation of the Bjorken sum rule based on COMPASS data alone confirms its validation within 9% accuracy. An NLO QCD fit to g1 world data leads to a value of the quark spin contribution to the nucleon spin ΔΣ, between 0.26 and 0.36 at Q2 = 3 (GeV/c)2 , the size of the uncertainty being driven by the unknown shape of the polarized parton distributions.The results on pion and kaon multiplicities produced in DIS of muons off an isoscalar target constitute an impressive data set of more than 400 points in π and 400 in K, covering a large kinematical domain in (x, z, Q2 ), which will be used in future NLO QCD fits to extract quark fragmentation functions into π and K. A LO fit is performed to extract the favoured and unfavoured quark fragmentation functions into pions.

Compass Measurement of g1 and QCD Fits

We present the latest COMPASS results on the proton spin structure function g[Formula: see text](x) at 200[Formula: see text]GeV. The data improve the statistical precision by a factor of [Formula: see text]2 at low x. A reevaluation of the Bjorken sum rule based on COMPASS proton and deuteron data confirms its validation to a 9% accuracy. Finally, results from a global NLO QCD fit of g1 world data are shown. The extracted spin singlet distribution leads to an integrated value of [Formula: see text] at Q[Formula: see text] (GeV/c)2. The large uncertainty is mainly driven by the unknown shape of the distribution.

New analysis concerning the strange quark polarization puzzle

The fact that analyses of semi-inclusive deep inelastic scattering suggest that the polarized strange quark density $\mathrm{\ensuremath{\Delta}}s(x)+\mathrm{\ensuremath{\Delta}}\overline{s}(x)$ is positive in the measured region of Bjorken $x$, whereas all analyses of inclusive deep inelastic scattering yield significantly negative values of this quantity, is known as the ``strange quark polarization puzzle.'' We have analyzed the world data on inclusive deep inelastic scattering, including the COMPASS 2010 proton data on the spin asymmetries, and for the first time, the new extremely precise JLab CLAS data on the proton and deuteron spin structure functions. Despite allowing, in our parametrization, for a possible sign change, our results confirm that the inclusive data yield significantly negative values for the polarized strange quark density.

FLAVOR AND SPIN DEPENDENT STRUCTURE OF THE NUCLEON AND MESON

We employ the polarized chiral constituent quarks to extract the polarized structure function of the nucleon. The polarized valon model is used to calculate the spin dependence of parton distribution functions of meson. The connection between the polarized structure of the proton and the Goldstone bosons, using the chiral quark model (χQM) is analyzed and the spin dependence of the parton distribution functions for pion and kaon, is obtained thoroughly. These functions are evolved to high Q2 values, using the singlet, nonsinglet and quark–gluon moments (ΔMS, ΔMNS, ΔMgq) which are convoluted with the polarized valon distributions. The polarized valon distributions for meson are computed, based on a phenomenological method and a comparison between polarized and unpolarized parton distribution functions for pion and kaon are performed. As a consequence of the χQM, the SU (3)f symmetry breaking for the spin dependent of the nucleon sea distributions is achieved. The required polarized parton distributions of the proton will be obtained from the parton distribution functions of the polarized meson via the related convolution integral which are existed in the χQM. Following that the analytical result for the proton's spin structure function, [Formula: see text], is obtained and compared with experimental data. Finally, the parton orbital angular momentum of meson are introduced and the total spin of the meson, based on this quantity and the first moment of distributions for gluon and singlet sectors, are obtained.

Erratum: Polarized structure of nucleon in the valon representation

We have utilized the concept of valon model to calculate the spin structure functions of proton, neutron and deuteron. The valon structure itself is universal and arises from the perturbative dressing of the valence quark in QCD. Our results agree rather well with all the relevant experimental data on $g_{1}^{p, n, d}$ and $g_{A}/g_{v}$, and suggests that the sea quark contribution to the spin of proton is consistent with zero. It also reveals that while the total quark contribution to the spin of valon is almost constant at $Q^{2}>=1$ the gluon contribution grows with the increase of $Q^2$ and hence requiring a sizable negative orbital angular momentum component $L_z$. This component along with the singlet and non-singlet parts are calculated in the Next-to-Leading order in QCD. We speculate that gluon contribution to the spin content of the proton is about 60% for all $Q^2$ values. Finally, we show that the size of gluon polarization and hence, $L_{z}$, is sensitive to the initial scale$Q_{0}^{2}$.

Polarized structure of nucleon in the valon representation

We have utilized the concept of valon model to calculate the spin structure functions of proton, neutron, and deuteron. The valon structure itself is universal and arises from the perturbative dressing of the valence quark in QCD. Our results agree rather well with all of the relevant experimental data on g1p,n,d and gA/gV, and suggests that the sea quark contribution to the spin of proton is consistent with zero. It also reveals that while the total quark contribution to the spin of a valon, ΔΣvalon, is almost constant at Q2 ≥ 1 the gluon contribution grows with the increase of Q2 and hence requiring a sizable negative orbital angular momentum component Lz. This component along with the singlet and non-singlet parts are calculated in the Next-to-Leading order in QCD . We speculate that gluon contribution to the spin content of the proton is about 60% for all Q2 values. Finally, we show that the size of gluon polarization and hence, Lz, is sensitive to the initial scale Q02.

Target mass corrections to proton spin structure functions and quark–hadron duality

Target mass corrections to proton spin structure functions in deep inelastic scattering region are analysed. Moreover, Bloom–Gilman quark–hadron dualities of proton spin structure functions g 1 and g 2 , in inelastic resonance region, are studied. The onsets of the dualities are discussed.

Proton Spin Structure Functions and Quark–Hadron Duality

Quark–hadron duality of three proton spin structure functions g1,g2 and gT are discussed simultaneously. It is found that theonsets of the quark–hadron dualities of g1p, g2p and gTp aresimilar and they are expected to be at about Q2~2 GeV2. Inaddition, our results show that the elastic peak remarkably breaks localquark–hadron duality.

An analysis of quark–hadron dualities in proton spin structure functions

Bloom–Gilman quark–hadron dualities of proton spin structure functions g 1 , g 2 and g T , in inelastic resonance region, are analyzed. The contribution of the nucleon elastic peak to the local duality and the local duality of each resonance region are also discussed. It is found that the occurrences of the quark–hadron dualities of g 1 p and g 2 p are similar and are expected at about 2 GeV 2. Moreover, our results show that the nucleon elastic peak and Δ ( 1232 ) resonance remarkably break the quark–hadron dualities.

Proton spin structure function, g1, with the unified evolution equations including NLO DGLAP terms and double logarithms, ln(1/x)

Theoretical predictions show that at low values of the Bjorken parameter x the spin structure function, g1, is influenced by large logarithmic corrections, $\ln^2(1/x)$ , which may be predominant in this region. These corrections are also partially contained in the NLO part of the standard DGLAP evolution. Here we calculate the nucleon structure function, g1, and the gluon distribution, $\Delta g$ , using the unified evolution equations written for the singlet and the non-singlet parton distributions. These equations include (i) the terms which describe the NLO DGLAP evolution and (ii) the ladder and non-ladder terms which contribute to the resummation of $\ln^2(1/x)$ . Subtractions of singularities from the evolution kernels are performed so as to avoid double counting the double logarithmic contributions coming from the NLO DGLAP and the ladder and non-ladder terms. The sensitivity of the results to the factorization scheme applied is tested by introducing the DGLAP terms into the evolution equations at two different factorization schemes.

1- Results from the SMC experiment at CERN. 2- The COMPASS experiment at CERN

SMC : The SMC collaboration has measured the proton and deuteron spin structure function g 1 in the kinematical range 0.00006 < x < 0.8 and 0.02 < Q 2 < 100 GeV 2. A brief summary of the NLO pQCD global analysis of all g 1 world data available in 1998 is given. The first moments of the proton, deuteron and neutron structure function were calculated in two factorization schemes ( MS and AB). They lead to a value of a 0 close to 0.2, which corresponds to ΔΣ= 0.19 in the MS scheme, and 0.38 in the AB one. The Bjorken sum rule is tested and found to agree with the theoretical predictions at the level of 10 %. COMPASS : The first goal of the COMPASS experiment at CERN is the measurement of the contribution of the gluon polarization Δ g to the nucleon spin. The measurement will be done by scattering high energy polarized muons on a polarized proton or deuteron target. The photon gluon fusion process, which is sensitive to the gluon density distribution, will be signed by the presence of charmed particles ( D 0, D 0) or of high p t hadrons pairs of opposite charge. In addition to Δ g, the longitudinal and transversely polarized parton distributions will be measured for the different flavors. A new spectrometer with large acceptance, high rate capability and identification of particles is being commissioned.

Resonances and higher twist in polarized lepton–nucleon scattering

We present a detailed analysis of resonance contributions in the context of higher twist effects in the moments of the proton spin structure function g 1. For each of these moments, it is found that there exists a characteristic Q 2 region in which (perturbative) higher twist corrections coexist with (non-perturbative) resonance contribution of comparable magnitude.

Physics results from HERMES

The Hermes experiment at the Desy laboratory in Hamburg, Germany, studies the spin structure of the nucleon. Its unique feature is the combination of a polarized internal gas target with the longitudinally polarized 27.5 GeV electron/positron beam of the Hera accelerator. Recent Hermes measurements include the proton spin structure function g1p, the flavor decomposition of the polarized quark distributions in the nucleon, the DIS contribution to the generalized GDH sum rule, the first observation of a spin asymmetry in exclusive vector meson production and the first observation of a single-spin azimuthal asymmetry in semi-inclusive pion production. Additionally, the possibility of using various unpolarized gases as target material broadens the spectrum of physics measurements with Hermes.

Measurement of the proton spin structure function g1p with a pure hydrogen target

A measurement of the proton spin structure function g 1 p( x, Q 2) in deep-inelastic scattering is presented. The data were taken with the 27.6 GeV longitudinally polarised positron beam at HERA incident on a longitudinally polarised pure hydrogen gas target internal to the storage ring. The kinematic range is 0.021< x<0.85 and 0.8 GeV 2< Q 2<20 GeV 2. The integral ∫ 0.021 0.85 g 1 p (x) dx evaluated at Q 0 2 of 2.5 GeV 2 is 0.122±0.003(stat.)±0.010(syst.).

The spin content of the proton in full QCD

We present preliminary results on the proton spin structure function in full QCD. The measurement has been done using 4 flavours of staggered fermions and an improved definition of the lattice topological charge density.