Spin-dependent Structure Function Research Articles

Factorization for azimuthal asymmetries in SIDIS at next-to-leading power

Differential measurements of the semi-inclusive deep inelastic scattering (SIDIS) process with polarized beams provide important information on the three-dimensional structure of hadrons. Among the various observables are azimuthal asymmetries that start at subleading power, and which give access to novel transverse momentum dependent distributions (TMDs). Theoretical predictions for these distributions are currently based on the parton model rather than a rigorous factorization based analysis. Working under the assumption that leading power Glauber interactions do not spoil factorization at this order, we use the Soft Collinear Effective Theory to derive a complete factorization formula for power suppressed hard scattering effects in SIDIS. This yields generalized definitions of the TMDs that depend on two longitudinal momentum fractions (one of them only relevant beyond tree level), and a complete proof that only the same leading power soft function appears and can be absorbed into the TMD distributions at this order. We also show that perturbative corrections can be accounted for with only one new hard coefficient. Factorization formulae are given for all spin dependent structure functions which start at next-to-leading power. Prospects for improved subleading power predictions that include resummation are discussed.

Probing gluon helicity with heavy flavor at the Electron-Ion Collider

We propose a new measurement of the heavy flavor hadron double spin asymmetry in deep-inelastic scattering at a future Electron-Ion Collider (EIC) to constrain the polarized gluon distribution function inside the proton. Statistical projection on $D^0$ meson double spin asymmetry is calculated with an EIC central detector using an all-silicon tracker and vertexing subsystem. A first impact study was done by interpreting pseudo-data at next-to-leading order in QCD. The sensitivity of the experimental observable in constraining gluon helicity distribution in a wide range of parton momentum fraction $x$ has been investigated considering different beam energy configurations. This measurement complements the inclusive spin-dependent structure function measurement and provides an opportunity to constrain the gluon helicity distribution in the moderate $x$ region.

Dispersion relation analysis of the radiative corrections to gA in the neutron \u03b2-decay

We present the first and complete dispersion relation analysis of the inner radiative corrections to the axial coupling constant gA in the neutron β-decay. Using experimental inputs from the elastic form factors and the spin-dependent structure function g1, we determine the contribution from the γW-box diagram to a precision better than 10−4. Our calculation indicates that the inner radiative corrections to the Fermi and the Gamow-Teller matrix element in the neutron β-decay are almost identical, i.e. the ratio λ = gA/gV is almost unrenormalized. With this result, we predict the bare axial coupling constant to be {overset{circ }{g}}_A=-1.2754{(13)}_{mathrm{exp}}{(2)}_{mathrm{RC}} based on the PDG average λ = −1.2756(13).

Spin Dependent Structure Function and Asymmetry of Neutron at Q 2 >1 Gev 2 Using Thermodynamical Bag Model

Spin Dependent Structure Function and Asymmetry of Neutron at Q 2 >1 Gev 2 Using Thermodynamical Bag Model

Analytical approaches to the determination of spin-dependent parton distribution functions at NNLO approximation

In this paper, we present {\tt SMKA18} analysis which is a first attempt to extract the set of next-to-next-leading-order (NNLO) spin-dependent parton distribution functions (spin-dependent PDFs) and their uncertainties determined through the Laplace transform technique and Jacobi polynomial approach. Using the Laplace transformations, we present an analytical solution for the spin-dependent Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NNLO approximation. The results are extracted using a wide range of proton $g_1^{p}(x, Q^2)$, neutron $g_1^{n}(x, Q^2)$ and deuteron $g_1^{d}(x, Q^2)$ spin-dependent structure functions dataset including the most recent high-precision measurements from {\tt COMPASS16} experiments at CERN which are playing an increasingly important role in global spin-dependent fits. The careful estimations of uncertainties have been done using the standard 'Hessian error' propagation. We will compare our results with the available spin-dependent inclusive deep inelastic scattering dataset and other results for the spin-dependent PDFs in literature. The results obtained for the spin-dependent PDFs as well as spin-dependent structure functions are clearly explained both in the small and large values of $x$.

Longitudinal double-spin asymmetry [formula omitted] and spin-dependent structure function [formula omitted] of the proton at small values of x and Q2

We present a precise measurement of the proton longitudinal double-spin asymmetry A1p and the proton spin-dependent structure function g1p at photon virtualities 0.006(GeV/c)2<Q2<1(GeV/c)2 in the Bjorken x range of 4×10−5<x<4×10−2. The results are based on data collected by the COMPASS Collaboration at CERN using muon beam energies of 160GeV and 200GeV. The statistical precision is more than tenfold better than that of the previous measurement in this region. In the whole range of x, the measured values of A1p and g1p are found to be positive. It is for the first time that spin effects are found at such low values of x.

OPE in Wilson lines with sub-eikonal spin corrections for TMDs and g1 structure function

Low-x evolution of spin-dependent TMDs and spin g1 structure function are relevant for the future Electron Ion Collider. To study spin-dynamics at high energies it is necessary to extend the eikonal approximation to include sub-eikonal corrections. I will discuss the Operator Product Expansion (OPE) in terms of Wilson lines with sub-eikonal corrections and derive the sub-eikonal quark propagator.

Study of spin-dependent structure functions of He3 and H3 at NNLO approximation and corresponding nuclear corrections

We determine polarized parton distribution functions (PPDFs) and structure functions from recent experimental data of polarized deep inelastic scattering (DIS) on nuleons at next-to-next-to-leading order (NNLO) approximation in perturbative quantum chromodynamic (pQCD). The nucleon polarized structure functions are computed using the Jacobi polynomial approach while target mass corrections (TMCs) are included in our fitting procedure. Having extracted the polarized spin structure functions, we extend our study to describe $^3{\mathrm He}$ and $^3{\mathrm H}$ polarized structure functions, as well as the Bjorken sum rule. We also explore the importance of the nuclear corrections on the polarized nuclear structure functions at small and large values of $x$. Our results are compared with the recent available and high precision polarized $^3{\mathrm He}$ and $^3{\mathrm H}$ experimental data.

Decoupling of the Leading Order DGLAP Evolution Equation with Spin Dependent Structure Functions

We propose an analytical solution for DGLAP evolution equations with polarized splitting functions at the Leading Order (LO) approximation based on the Laplace transform method. It is shown that the DGLAP evolution equations can be decoupled completely into two second order differential equations which then are solved analytically by using the initial conditions $\delta F^{\mathrm {S}}(x,Q^{2})=\mathcal {F}[\partial \delta F^{\mathrm {S}}_{0}(x), \delta F^{\mathrm {S}}_{0}(x)]$ and ${\delta G}(x,Q^{2})=\mathcal {G}[\partial \delta G_{0}(x), \delta G_{0}(x)]$ . We used this method to obtain the polarized structure function of the proton as well as the polarized gluon distribution function inside the proton and compared the numerical results with experimental data of COMPASS, HERMES, and AAC’08 Collaborations. It was found that there is a good agreement between our predictions and the experiments.

Small-x Behavior of Non-singlet Spin Structure Function and Bjorken Sum Rule with pQCD Correction up to NNLO and Higher Twist Correction

A calculation of the non-singlet part of spin dependent structure function, $xg_1^{NS}(x,Q^2)$ and associated sum rule, the Bjorken Sum rule up to next-next-to-leading order(NNLO) is presented. We use a unified approach incorporating Regge theory and the theoretical framework of perturbative Quantum Chromodynamics. Using a Regge behaved model with $Q^2$ dependent intercept as the initial input, we have solved the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equation up to NNLO at small-$x$ for $xg_1^{NS}(x,Q^2)$ and the solutions are utilised to calculate the polarised Bjorken sum rule(BSR). We have also extracted the higher twist contribution to BSR based on a simple parametrisation. These results for both of $xg_1^{NS}(x,Q^2)$ and BSR, along with higher twist corrections are observed to be consistent with the available data taken from SMC, E143, HERMES, COMPASS and JLab experiments. In addition, our results are also compared with that of other theoretical and phenomenological analysis based on different models and a very good agreement is also observed in this regard. Further a very good consistency between our calculated results and theoretical QCD predictions of BSR is also achieved.

Nucleon structure functions and longitudinal spin asymmetries

The chiral constituent quark model (χ CQM) has been used to analyse the phenomenological dependence of the spin independent (F 1 p, n and F 2 p, n ) and the spin dependent (g 2 p, n ) structure functions of the nucleon on the the Bjorken scaling variable x . The implication of the presence of the sea quarks has been discussed for the p and n longitudinal spin asymmetries (A 1 p (x ) and A 1 n (x ) ratio of polarized to unpolarized quark distribution functions for up and down quarks in the p and n , , , and . The results have been compared with the recent available experimental observations.

Effective field theories for muonic hydrogen

Experimental measurements of muonic hydrogen bound states have recently started to take place and provide a powerful setting in which to study the properties of QCD. We profit from the power of effective field theories (EFTs) to provide a theoretical framework in which to study muonic hydrogen in a model independent fashion. In particular, we compute expressions for the Lamb shift and the hyperfine splitting. These expressions include the leading logarithmic O (mμ α 6 ) terms, as well as the leading hadronic effects. Most remarkably, our analyses include the determination of the spin-dependent and spin-independent structure functions of the forward virtualphoton Compton tensor of the proton to O (p 3 ) in HBET and including the Delta particle. Using these results we obtain the leading hadronic contributions to the Wilson coeffcients of the lepton-proton four fermion operators in NRQED. The spin-independent coeffcient yields a pure prediction for the two-photon exchange contribution to the muonic hydrogen Lamb shift, which is the main source of uncertainty in our computation. The spindependent coeffcient yields the prediction of the hyperfine splitting. The use of EFTs crucially helps us organizing the computation, in such a way that we can clearly address the parametric accuracy of our result. Furthermore, we review in the context of NRQED all the contributions to the energy shift of O (mμ α 5 , as well as those that scale like mr α 6 × logarithms.

Polarized parton densities and spin dependent structure function of the nucleon

We study the polarized parton distribution functions (PPDFs) from recent experimental data at the next-to-leading order (NLO) approximation in the fixed-flavor number scheme. In this analysis, we can compare our results with experimental data such as very recent COMPASS data. It would be very worth to study the PPDFs parametrization form when we want to use this new COMPASS data in QCD analysis on polarized proton structure and parton distribution functions.

Nucleon structure functions and longitudinal spin asymmetries in the chiral quark constituent model

We have analysed the phenomenological dependence of the spin independent ($F_1^{p,n}$ and $F_2^{p,n}$) and the spin dependent ($g_1^{p,n}$) structure functions of the nucleon on the the Bjorken scaling variable $x$ using the unpolarized distribution functions of the quarks $q(x)$ and the polarized distribution functions of the quarks $\Delta q(x)$ respectively. The chiral constituent quark model ($\chi$CQM), which is known to provide a satisfactory explanation of the proton spin crisis and related issues in the nonperturbative regime, has been used to compute explicitly the valence and sea quark flavor distribution functions of $p$ and $n$. In light of the improved precision of the world data, the $p$ and $n$ longitudinal spin asymmetries ($A_1^p(x)$ and $A_1^n(x)$) have been calculated. The implication of the presence of the sea quarks has been discussed for ratio of polarized to unpolarized quark distribution functions for up and down quarks in the $p$ and $n$ $\frac{\Delta u^p(x)}{u^p(x)}$, $\frac{\Delta d^p(x)}{d^p(x)}$, $\frac{\Delta u^n(x)}{u^n(x)}$, and $\frac{\Delta d^n(x)}{d^n(x)}$. The ratio of the $n$ and $p$ structure functions $R^{np}(x)=\frac{F_2^n(x)}{F_2^p(x)}$ has also been presented. The results have been compared with the recent available experimental observations. The results on the spin sum rule have also been included and compared with data and other recent approaches.

The nonsinglet spin-dependent structure function evolution by Laplace and characteristics methods

We evaluate the non-singlet spin-dependent structure function g1NS at leading order (LO) and next-to-leading order (NLO) by using the Laplace-transform technique and method of characteristics and also obtain its first moment at NLO. The polarized non-singlet structure function results are compared with the data from HERMES (A. Airapetian et al., Phys. Rev. D 75, 012007 (2007)) and E143 (K. Abe et al. (E143 Collab.), Phys. Rev. D 58, 112003 (1998)) at LO and NLO analyses and the first-moment the result at NLO is compared with the result of the NLO GRSV2000 fit. Considering the solution, this method is valid at low- and large-x regions.

Results on longitudinal spin physics at COMPASS

The COMPASS experiment at the CERN SPS has taken data on deep inelastic scattering of polarised muons on a polarised NH3 target in 2007 and 2011 and on a polarised LiD target in 2002–2004 and 2006. The new results on the longitudinal double spin asymmetry A 1 p and the spin-dependent structure function g 1 p obtained from the 2011 data set are presented. These results are used in a NLO QCD fit to the world data to obtain the polarised parton distributions. Also an update of the results on the Bjorken sum rule, connecting the integral of the non-singlet spin-dependent structure function with the ratio of the weak coupling constants, will be given.Direct access to the gluon polarisation is possible via the photon gluon fusion process in semi-inclusive deep inelastic scattering. This process is studied using the p T dependence of charged hadron asymmetries. The latest results indicate a positive gluon polarisation in the kinematic region of COMPASS

Results on longitudinal spin physics at COMPASS

The COMPASS experiment at the CERN SPS has taken data for deep inelastic scattering of polarised muons off a polarised NH3 target in 2007 and 2011 and off a polarised 6LiD target in 2002–2004 and 2006.We present our new results on the longitudinal double spin asymmetry A1p and the spin-dependent structure function g1p obtained from the 2011 data set. These results are used in a NLO QCD fit to the world data to obtain the polarised parton distributions. Also an update on our results on the Bjorken sum rule, connecting the integral of the non-singlet spin-dependent structure function with the ratio of the weak coupling constants, is given.The gluon polarisation can be accessed directly via the photon gluon fusion process in semi-inclusive deep inelastic scattering. This process is studied using the pT dependence of charged hadron asymmetries. The latest results indicate a positive gluon polarisation in the kinematic region of COMPASS.

A Measurement of g2p at Low Q2

Jefferson Lab has been at the forefront of a program to study the polarized structure of nucleons using electron scattering. Measurements of the spin dependent structure functions, [Formula: see text] and [Formula: see text], have proven to be powerful tools in testing and understanding QCD. The neutron structure function [Formula: see text] has been measured extensively in Hall A at Jefferson Lab over a wide range of [Formula: see text], but data for [Formula: see text] remains scarce. This docment will discuss the [Formula: see text] experiment, which ran in Hall A at Jefferson Lab in the spring of 2012, and will provide the first measurement of [Formula: see text] in the resonance region; covering [Formula: see text] GeV2. The 0[Formula: see text] moment of [Formula: see text] provides a test of the Burkhardt-Cottingham sum rule, which states that the integral of [Formula: see text] over the Bjorken scaling variable [Formula: see text] goes to zero. This sum rule, valid for all values of [Formula: see text], has been satisfied for the neutron, but a violation is suggested for the proton at high [Formula: see text]. The 2[Formula: see text] moment allows for a benchmark test of [Formula: see text]PT at low [Formula: see text]. Specifically, the behavior of the longitudinally-transverse spin polarizability ([Formula: see text]), as [Formula: see text]PT calculations of this quantity deviate significantly from the measured neutron data. This document will discuss the current status of the analysis along with preliminary results.

Deep inelastic scattering with the SPS muon beam

We review results from deep inelastic muon scattering experiments at the SPS which started in 1978, and are still actively pursued today. Key results include the precision measurement of scaling violations and of the strong coupling constant, spin-dependent structure functions, and studies of the internal spin structure of protons and neutrons. These experiments have revealed a wealth of details about the internal structure of nucleons in terms of quarks and gluons.

Transverse spin structure functiong2(x,Q2)in the valon model

The spin dependent structure function, g2ww(x,Q^2), is calculated in the valon model. A simple approach is given for the determination of the twist-3 part of the g2(x, Q^2) in Mellin space; thus, enabling us to obtain the full transverse structure function, g2(x, Q^2) for proton, neutron and the deuteron. In light of the new data, we have further calculated the transversely polarized structure function of g23He(x, Q^2). Our results are checked against the experimental data and nice agreements are observed.