# Posts Tagged structure function

## Recent Postings from structure function

### Transverse Momentum Dependent Parton Distributions with self-similarity at small $x$ and models of proton structure function

In this paper we make re-analysis of a self-similarity based model of the proton structure function at small $x$ pursued in recent years. The additional assumption is that it should be singularity free in the entire kinematic range $0\leq \textit{x}\leq 1$. Our analysis indicates that the singularity free version of the model is valid in a more restrictive range of $Q^{2}$. We then analyse the defining Transverse Momentum Dependent Parton Distributions (TMD) occurred in the models and show that the proper generalizations and initial conditions on them not only remove the undesired singularity but also results in a QCD compatible structure function with logarithmic growth in $Q^2$. The phenomenological range of validity is then found to be much larger than the earlier versions. We also extrapolate the models to large $x$ in a parameter free way.

### Interpretation of the structure function of rotation measure in the interstellar medium

The observed structure function (SF) of rotation measure (RM) varies as a broken power-law function of angular scales. The systematic shallowness of its spectral slope is inconsistent with the standard Kolmogorov scaling. This motivates us to examine the statistical analysis on RM fluctuations. The correlations of RM constructed by Lazarian & Pogosyan (2016) are demonstrated to be adequate in explaining the observed features of RM SFs through a direct comparison between the theoretically obtained and observationally measured SF results. By segregating the density and magnetic field fluctuations and adopting arbitrary indices for their respective power spectra, we find that when the SFs of RM and emission measure have a similar form over the same range of angular scales, the statistics of the RM fluctuations reflect the properties of density fluctuations. RM SFs can be used to evaluate the mean magnetic field along the line of sight, but cannot serve as an informative source on the properties of turbulent magnetic field in the interstellar medium. We identify the spectral break of RM SFs as the inner scale of a shallow spectrum of electron density fluctuations, which characterizes the typical size of discrete electron density structures in the observed region.

### Study of HERA ep Data at Low Q^2 and Low x_Bj and the Need for Higher-Twist Corrections to Standard pQCD Evolution

A detailed comparison of HERA data at low Bjorken-$x$ and low four-momentum-transfer squared, $Q^2$, with predictions based on $\ln{Q^2}$ evolution (DGLAP) in perturbative Quantum Chromo Dynamics suggests inadequacies of this framework. The standard DGLAP evolution was augmented by including an additional higher-twist term in the description of the longitudinal structure function, $F_{\rm L}$. This additional term, $F_{\rm L}~A_{\rm L}^{\rm HT}/Q^2$, improves the description of the reduced cross sections significantly. The resulting predictions for $F_{\rm L}$ suggest that further corrections are required for $Q^2$ less than about 2 GeV$^2$.

### Study of HERA ep Data at Low Q^2 and Low x_Bj and the Need for Higher-Twist Corrections to Standard pQCD Evolution [Cross-Listing]

A detailed comparison of HERA data at low Bjorken-$x$ and low four-momentum-transfer squared, $Q^2$, with predictions based on $\ln{Q^2}$ evolution (DGLAP) in perturbative Quantum Chromo Dynamics suggests inadequacies of this framework. The standard DGLAP evolution was augmented by including an additional higher-twist term in the description of the longitudinal structure function, $F_{\rm L}$. This additional term, $F_{\rm L}~A_{\rm L}^{\rm HT}/Q^2$, improves the description of the reduced cross sections significantly. The resulting predictions for $F_{\rm L}$ suggest that further corrections are required for $Q^2$ less than about 2 GeV$^2$.

### Exploring the nature of broadband variability in the FSRQ 3C 273

Detailed investigation of broadband flux variability in the blazar 3C 273 allows us to probe the location and size of emission regions and their physical conditions. We report the results on correlation studies of the flaring activity observed between 2008 and 2012. The observed broadband variations were investigated using the structure function and the discrete correlation function, and power spectral density analysis (PSD) methods. The PSD analysis showed that the optical/IR light curve slopes are consistent with the slope of white noise processes, while, the PSD slopes at radio, X-ray and gamma-ray energies are consistent with red-noise processes. The flux variations at gamma-ray and mm-radio bands are found to be significantly correlated. Using the estimated time lag of (110\pm27) days between gamma-ray and radio light curves, we constrained the location of the gamma-ray emission region at a de-projected distance of 1.2\pm0.9 pc from the jet apex. Flux variations at X-ray bands were found to have a significant correlation with variations at both radio and \gamma-rays energies. The correlation between X-rays and gamma-rays light curves suggests presence of two components responsible for the X-ray emission. A negative time lag of -(50\pm20) days, where the X-rays are leading the emission, suggests X-rays are emitted closer to the jet apex from a compact region at a distance of ~(0.5\pm0.4) pc from the jet apex. A positive time lag of (110\pm20) days suggests jet-base origin of the other X-ray component at ~(4--5)~pc from the jet apex. The flux variations at radio frequencies were found to be well correlated with each other such that the variations at higher frequencies are leading the lower frequencies, which could be expected in the standard shock-in-jet model.

### Nuclear medium effects in $F_{2A}^{EM}(x,Q^2)$ and $F_{2A}^{Weak}(x,Q^2)$ structure functions

Recent phenomenological analysis of experimental data on DIS processes induced by charged leptons and neutrinos/antineutrinos beams on nuclear targets by CTEQ collaboration has confirmed the observation of CCFR and NuTeV collaborations, that weak structure function $F_{2A}^{Weak} (x,Q^2)$ is different from electromagnetic structure function $F_{2A}^{EM} (x,Q^2)$ in a nucleus like iron, specially in the region of low $x$ and $Q^2$. In view of this observation we have made a study of nuclear medium effects on $F_{2A}^{Weak} (x,Q^2)$ and $F_{2A}^{EM} (x,Q^2)$ for a wide range of $x$ and $Q^2$ using a microscopic nuclear model. We have considered Fermi motion, binding energy, nucleon correlations, mesonic contributions from pion and rho mesons and shadowing effects to incorporate nuclear medium effects. The calculations are performed in a local density approximation using a relativistic nucleon spectral function which includes nucleon correlations. The numerical results in the case of iron nucleus are compared with the experimental data.

### Investigation of pionic contribution in the lepton and anti-lepton production cross section in p-Cu and p-Pt collision [Cross-Listing]

For detailed explanation of the experimental results of lepton production cross section in hadronic collisions such as nucleon-nucleon or nucleon-nuclei, it is of great importance to use quarks and sea quarks distribution function inside free and bound nucleons. In this paper the role of pion cloud inside the nucleus in the structure function of Cu and Pt nuclei and the EMC ratio of these nuclei were investigated by using harmonic oscillator model.

### Investigation of pionic contribution in the lepton and anti-lepton production cross section in p-Cu and p-Pt collision

For detailed explanation of the experimental results of lepton production cross section in hadronic collisions such as nucleon-nucleon or nucleon-nuclei, it is of great importance to use quarks and sea quarks distribution function inside free and bound nucleons. In this paper the role of pion cloud inside the nucleus in the structure function of Cu and Pt nuclei and the EMC ratio of these nuclei were investigated by using harmonic oscillator model.

### Progress on nuclear modifications of structure functions [Cross-Listing]

We report progress on nuclear structure functions, especially on their nuclear modifications and a new tensor structure function for the deuteron. To understand nuclear structure functions is an important step toward describing nuclei and QCD matters from low to high densities and from low to high energies in terms of fundamental quark and gluon degrees of freedom beyond conventional hadron and nuclear physics. It is also practically important for understanding new phenomena in high-energy heavy-ion collisions at RHIC and LHC. Furthermore, since systematic errors of current neutrino-oscillation experiments are dominated by uncertainties of neutrino-nucleus interactions, such studies are valuable for finding new physics beyond current framework. Next, a new tensor-polarized structure function $b_1$ is discussed for the deuteron. There was a measurement by HERMES; however, its data are inconsistent with the conventional convolution estimate based on the standard deuteron model with D-state admixture. This fact suggests that a new hadronic phenomenon should exist in the tensor-polarized deuteron at high energies, and it will be experimentally investigated at JLab from the end of 2010's.

### Progress on nuclear modifications of structure functions

We report progress on nuclear structure functions, especially on their nuclear modifications and a new tensor structure function for the deuteron. To understand nuclear structure functions is an important step toward describing nuclei and QCD matters from low to high densities and from low to high energies in terms of fundamental quark and gluon degrees of freedom beyond conventional hadron and nuclear physics. It is also practically important for understanding new phenomena in high-energy heavy-ion collisions at RHIC and LHC. Furthermore, since systematic errors of current neutrino-oscillation experiments are dominated by uncertainties of neutrino-nucleus interactions, such studies are valuable for finding new physics beyond current framework. Next, a new tensor-polarized structure function $b_1$ is discussed for the deuteron. There was a measurement by HERMES; however, its data are inconsistent with the conventional convolution estimate based on the standard deuteron model with D-state admixture. This fact suggests that a new hadronic phenomenon should exist in the tensor-polarized deuteron at high energies, and it will be experimentally investigated at JLab from the end of 2010's.

### Progress on nuclear modifications of structure functions [Cross-Listing]

We report progress on nuclear structure functions, especially on their nuclear modifications and a new tensor structure function for the deuteron. To understand nuclear structure functions is an important step toward describing nuclei and QCD matters from low to high densities and from low to high energies in terms of fundamental quark and gluon degrees of freedom beyond conventional hadron and nuclear physics. It is also practically important for understanding new phenomena in high-energy heavy-ion collisions at RHIC and LHC. Furthermore, since systematic errors of current neutrino-oscillation experiments are dominated by uncertainties of neutrino-nucleus interactions, such studies are valuable for finding new physics beyond current framework. Next, a new tensor-polarized structure function $b_1$ is discussed for the deuteron. There was a measurement by HERMES; however, its data are inconsistent with the conventional convolution estimate based on the standard deuteron model with D-state admixture. This fact suggests that a new hadronic phenomenon should exist in the tensor-polarized deuteron at high energies, and it will be experimentally investigated at JLab from the end of 2010's.

### Progress on nuclear modifications of structure functions [Cross-Listing]

We report progress on nuclear structure functions, especially on their nuclear modifications and a new tensor structure function for the deuteron. To understand nuclear structure functions is an important step toward describing nuclei and QCD matters from low to high densities and from low to high energies in terms of fundamental quark and gluon degrees of freedom beyond conventional hadron and nuclear physics. It is also practically important for understanding new phenomena in high-energy heavy-ion collisions at RHIC and LHC. Furthermore, since systematic errors of current neutrino-oscillation experiments are dominated by uncertainties of neutrino-nucleus interactions, such studies are valuable for finding new physics beyond current framework. Next, a new tensor-polarized structure function $b_1$ is discussed for the deuteron. There was a measurement by HERMES; however, its data are inconsistent with the conventional convolution estimate based on the standard deuteron model with D-state admixture. This fact suggests that a new hadronic phenomenon should exist in the tensor-polarized deuteron at high energies, and it will be experimentally investigated at JLab from the end of 2010's.

### A new approach to the variability characterization of active galactic nuclei

The normalized excess variance is a popular method used by many authors to estimate the variability of active galactic nuclei (AGNs), especially in the X-ray band. We show that this estimator is affected by the cosmological time dilation, so that it should be appropriately corrected when applied to AGN samples distributed in wide redshift intervals. We propose a formula to modify this estimator, based on the use of the structure function. To verify the presence of the cosmological effect and the reliability of the proposed correction, we use data extracted from the XMM-Newton Serendipitous Source Catalogue, data release 5 (XMMSSC-DR5), and cross-matched with the Sloan Digital Sky Survey quasar catalogue, of data release 7 and 12.

### Pion structure function from leading neutron electroproduction and SU(2) flavor asymmetry

We examine the efficacy of pion exchange models to simultaneously describe leading neutron electroproduction at HERA and the $\bar{d}-\bar{u}$ flavor asymmetry in the proton. A detailed $\chi^2$ analysis of the ZEUS and H1 cross sections, when combined with constraints on the pion flux from Drell-Yan data, allows regions of applicability of one-pion exchange to be delineated. The analysis disfavors several models of the pion flux used in the literature, and yields an improved extraction of the pion structure function and its uncertainties at parton momentum fractions in the pion of $4 \times 10^{-4} \lesssim x_\pi \lesssim 0.05$ at a scale of $Q^2$=10 GeV$^2$. Based on the fit results, we provide estimates for leading proton structure functions in upcoming tagged deep-inelastic scattering experiments at Jefferson Lab on the deuteron with forward protons.

### Pion structure function from leading neutron electroproduction and SU(2) flavor asymmetry [Cross-Listing]

We examine the efficacy of pion exchange models to simultaneously describe leading neutron electroproduction at HERA and the $\bar{d}-\bar{u}$ flavor asymmetry in the proton. A detailed $\chi^2$ analysis of the ZEUS and H1 cross sections, when combined with constraints on the pion flux from Drell-Yan data, allows regions of applicability of one-pion exchange to be delineated. The analysis disfavors several models of the pion flux used in the literature, and yields an improved extraction of the pion structure function and its uncertainties at parton momentum fractions in the pion of $4 \times 10^{-4} \lesssim x_\pi \lesssim 0.05$ at a scale of $Q^2$=10 GeV$^2$. Based on the fit results, we provide estimates for leading proton structure functions in upcoming tagged deep-inelastic scattering experiments at Jefferson Lab on the deuteron with forward protons.

### Recent progress in some exclusive and semi-exclusive processes in proton-proton collisions

We present the main results of our recent analyses of exclusive production of vector charmonia ($J/\psi$ and $\psi'$) in $k_t$-factorization approach and for $\gamma \gamma$ production of charged dilepton pairs in exclusive and semiinclusive processes in a new approach, similar in spirit to $k_t$-factorization. The results for charmonia are compared with recent results of the LHCb collaboration. We include some helicity flip contributions and quantify the effect of absorption correction. The effect of $c \bar c$ wave function is illustrated. We present uncertainties related to $F_2$ structure function which are the main ingredient of the approach. Our results are compared with recent CMS data for dilepton production with lepton isolation cuts imposed.

### Helicity Evolution at Small-x [Replacement]

We construct small-x evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the $g_1$ structure function. These evolution equations resum powers of $\alpha_s \, \ln^2 (1/x)$ in the polarization-dependent evolution along with the powers of $\alpha_s \, \ln (1/x)$ in the unpolarized evolution which includes saturation effects. The equations are written in an operator form in terms of polarization-dependent Wilson line-like operators. While the equations do not close in general, they become closed and self-contained systems of non-linear equations in the large-$N_c$ and large-$N_c \, \& \, N_f$ limits. As a cross-check, in the ladder approximation, our equations map onto the same ladder limit of the infrared evolution equations for $g_1$ structure function derived previously by Bartels, Ermolaev and Ryskin.

### Helicity Evolution at Small-x

We construct small-x evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the $g_1$ structure function. These evolution equations resum powers of $\alpha_s \, \ln^2 (1/x)$ in the polarization-dependent evolution along with the powers of $\alpha_s \, \ln (1/x)$ in the unpolarized evolution which includes saturation effects. The equations are written in an operator form in terms of polarization-dependent Wilson line-like operators. While the equations do not close in general, they become closed and self-contained systems of non-linear equations in the large-$N_c$ and large-$N_c \, \& \, N_f$ limits. As a cross-check, in the ladder approximation, our equations map onto the same ladder limit of the infrared evolution equations for $g_1$ structure function derived previously by Bartels, Ermolaev and Ryskin.

### Helicity Evolution at Small-x [Cross-Listing]

We construct small-x evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the $g_1$ structure function. These evolution equations resum powers of $\alpha_s \, \ln^2 (1/x)$ in the polarization-dependent evolution along with the powers of $\alpha_s \, \ln (1/x)$ in the unpolarized evolution which includes saturation effects. The equations are written in an operator form in terms of polarization-dependent Wilson line-like operators. While the equations do not close in general, they become closed and self-contained systems of non-linear equations in the large-$N_c$ and large-$N_c \, \& \, N_f$ limits. As a cross-check, in the ladder approximation, our equations map onto the same ladder limit of the infrared evolution equations for $g_1$ structure function derived previously by Bartels, Ermolaev and Ryskin.

### Helicity Evolution at Small-x [Replacement]

We construct small-x evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the $g_1$ structure function. These evolution equations resum powers of $\alpha_s \, \ln^2 (1/x)$ in the polarization-dependent evolution along with the powers of $\alpha_s \, \ln (1/x)$ in the unpolarized evolution which includes saturation effects. The equations are written in an operator form in terms of polarization-dependent Wilson line-like operators. While the equations do not close in general, they become closed and self-contained systems of non-linear equations in the large-$N_c$ and large-$N_c \, \& \, N_f$ limits. As a cross-check, in the ladder approximation, our equations map onto the same ladder limit of the infrared evolution equations for $g_1$ structure function derived previously by Bartels, Ermolaev and Ryskin.

### Helicity Evolution at Small-x [Replacement]

We construct small-x evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the $g_1$ structure function. These evolution equations resum powers of $\alpha_s \, \ln^2 (1/x)$ in the polarization-dependent evolution along with the powers of $\alpha_s \, \ln (1/x)$ in the unpolarized evolution which includes saturation effects. The equations are written in an operator form in terms of polarization-dependent Wilson line-like operators. While the equations do not close in general, they become closed and self-contained systems of non-linear equations in the large-$N_c$ and large-$N_c \, \& \, N_f$ limits. As a cross-check, in the ladder approximation, our equations map onto the same ladder limit of the infrared evolution equations for $g_1$ structure function derived previously by Bartels, Ermolaev and Ryskin.

### Novel QCD Phenomena at JLab

The $12~$GeV electron beam energy at Jefferson Laboratory provides ideal electroproduction kinematics for many novel tests of QCD in both the perturbative and nonperturbative domains. These include tests of the quark flavor dependence of the nuclear structure functions; measurements of the QCD running coupling at soft scales; measurements of the diffractive deep inelastic structure function; measurements of exclusive contributions to the $T-$ odd Sivers function; the identification of odderon" contributions; tests of the spectroscopic and dynamic features of light-front holography, as well as meson-nucleon supersymmetry"; the production of open and hidden charm states in the heavy-quark threshold domain; and the production of exotic hadronic states such as pentaquarks, tetraquarks and even octoquarks containing charm quarks. One can also study fundamental features of QCD at JLab$12$ such as the hidden color" of nuclear wavefunctions, the color transparency" of hard exclusive processes, and the intrinsic strangeness and charm" content of the proton wavefunction. I will also discuss evidence that the antishadowing of nuclear structure functions is non-universal; i.e., flavor dependent. I will also present arguments why shadowing and antishadowing phenomena may be incompatible with the momentum and other sum rules for the nuclear parton distribution functions. I will also briefly review new insights into the hadron mass scale, the hadron mass spectrum, the functional form of the QCD coupling in the nonperturbative domain predicted by light-front holography, and how superconformal algebra leads to remarkable supersymmetric relations between mesons and baryons.

### Mapping optically variable quasars towards the galactic plane

We present preliminary results of the CIDA Equatorial Variability Survey (CEVS), looking for quasar (hereafter QSO) candidates near the Galactic plane. The CEVS contains photometric data from extended and adjacent regions of the Milky Way disk ($\sim$ 500 sq. deg.). In this work 2.5 square degrees with moderately high temporal sampling in the CEVS were analyzed. The selection of QSO candidates was based on the study of intrinsic optical photometric variability of 14,719 light curves. We studied samples defined by cuts in the variability index (Vindex $>$ 66.5), periodicity index (Q $>$ 2), and the distribution of these sources in the plane (AT , ${\gamma}$), using a slight modification of the first-order of the structure function for the temporal sampling of the survey. Finally, 288 sources were selected as QSO candidates. The results shown in this work are a first attempt to develop a robust method to detect QSO towards the Galactic plane in the era of massive surveys such as VISTA and Gaia.

### The O(\alpha_s^3) Heavy Flavor Contributions to the Charged Current Structure Function xF_3(x,Q^2) at Large Momentum Transfer

We calculate the massive Wilson coefficients for the heavy flavor contributions to the non-singlet charged current deep-inelastic scattering structure function $xF_3^{W^+}(x,Q^2)+xF_3^{W^-}(x,Q^2)$ in the asymptotic region $Q^2 \gg m^2$ to 3-loop order in Quantum Chromodynamics (QCD) at general values of the Mellin variable $N$ and the momentum fraction $x$. Besides the heavy quark pair production also the single heavy flavor excitation $s \rightarrow c$ contributes. Numerical results are presented for the charm quark contributions and consequences on the Gross-Llewellyn Smith sum rule are discussed.

### The O(\alpha_s^3) Heavy Flavor Contributions to the Charged Current Structure Function xF_3(x,Q^2) at Large Momentum Transfer [Cross-Listing]

We calculate the massive Wilson coefficients for the heavy flavor contributions to the non-singlet charged current deep-inelastic scattering structure function $xF_3^{W^+}(x,Q^2)+xF_3^{W^-}(x,Q^2)$ in the asymptotic region $Q^2 \gg m^2$ to 3-loop order in Quantum Chromodynamics (QCD) at general values of the Mellin variable $N$ and the momentum fraction $x$. Besides the heavy quark pair production also the single heavy flavor excitation $s \rightarrow c$ contributes. Numerical results are presented for the charm quark contributions and consequences on the Gross-Llewellyn Smith sum rule are discussed.

### Active Galactic Nuclei Discovered in the Kepler Mission

We report on candidate active galactic nuclei (AGN) discovered during the monitoring of $\sim$500 bright (r < 18 mag) galaxies over several years with the Kepler Mission. Most of the targets were sampled every 30 minutes nearly continuously for a year or more. Variations of 0.001 mag and often less could be detected reliably. About 4.0% (19) of our random sample continuously fluctuated with amplitudes increasing with longer timescales, but the majority are close to the limits of detectability with Kepler. We discuss our techniques to mitigate the long term instrumental trends in Kepler light curves and our resulting structure function curves. The amplitudes of variability over four month periods, as seen in the structure functions and PSDs, can dramatically change for many of these AGN candidates. Four of the candidates have features in their Structure Functions that may indicate quasi-periodic behavior, although other possibilities are discussed.

### Do the Kepler AGN Light Curves Need Re-processing?

We gauge the impact of spacecraft-induced effects on the inferred variability properties of the light curve of the Seyfert 1 AGN Zw 229-15 observed by \Kepler. We compare the light curve of Zw 229-15 obtained from the Kepler MAST database with a re-processed light curve constructed from raw pixel data (Williams & Carini, 2015). We use the first-order structure function, $SF(\delta t)$, to fit both light curves to the damped power-law PSD of Kasliwal, Vogeley & Richards, 2015. On short timescales, we find a steeper log-PSD slope ($\gamma = 2.90$ to within $10$ percent) for the re-processed light curve as compared to the light curve found on MAST ($\gamma = 2.65$ to within $10$ percent)---both inconsistent with a damped random walk which requires $\gamma = 2$. The log-PSD slope inferred for the re-processed light curve is consistent with previous results (Carini & Ryle, 2012, Williams & Carini, 2015) that study the same re-processed light curve. The turnover timescale is almost identical for both light curves ($27.1$ and $27.5$~d for the reprocessed and MAST database light curves). Based on the obvious visual difference between the two versions of the light curve and on the PSD model fits, we conclude that there remain significant levels of spacecraft-induced effects in the standard pipeline reduction of the Kepler data. Re-processing the light curves will change the model inferenced from the data but is unlikely to change the overall scientific conclusion reached by Kasliwal et al. 2015---not all AGN light curves are consistent with the DRW.

### High x Structure Function of the Virtually Free Neutron

The pole extrapolation method is applied for the first time to data on semi-inclusive deep-inelastic scattering off the deuteron with tagged spectator protons to extract the high Bjorken x structure function of the neutron. This approach is based on the extrapolation of the measured cross sections at different momenta of the detected spectator proton to the non-physical pole of the bound neutron in the deuteron. The advantage of the method is that it makes it possible to suppress nuclear effects in a maximally model independent way. The neutron structure functions obtained in this way demonstrate surprising x dependence at x> 0.6, indicating the possibility of a rise in the neutron to proton structure function ratio. Such a rise may indicate new dynamics in the generation of high x quarks in the nucleon. One such mechanism we discuss is the possible dominance of short-range isosinglet quark-quark correlations that can enhance the d-quark distribution in the proton resulting in d/u -> 1.

### High x Structure Function of the Virtually Free Neutron [Replacement]

The pole extrapolation method is applied for the first time to the data on semi-inclusive inelastic scattering off the deuteron with tagged spectator protons to extract the high Bjorken x structure function of the neutron. This approach is based on the extrapolation of the measured cross sections at different momenta of the spectator proton to the non-physical pole of the bound neutron in the deuteron. The advantage of the method is that it makes it possible to suppress nuclear effects in a maximally model independent way. The neutron structure functions obtained in this way demonstrate a surprising $x$ dependence at x\ge 0.6, indicating a possible rise of the neutron to proton structure function ratio. Such a rise may indicate new dynamics in the generation of high-x quarks in the nucleon. One such mechanism we discuss is the possible dominance of short-range isosinglet quark-quark correlations that can enhance the d-quark distribution in the proton.

### Mapping the Gas Turbulence in the Coma Cluster: Predictions for Astro-H

Astro-H will be able for the first time to map gas velocities and detect turbulence in galaxy clusters. One of the best targets for turbulence studies is the Coma cluster, due to its proximity, absence of a cool core, and lack of a central active galactic nucleus. To determine what constraints Astro-H will be able to place on the Coma velocity field, we construct simulated maps of the projected gas velocity and compute the second-order structure function, an analog of the velocity power spectrum. We vary the injection scale, dissipation scale, slope, and normalization of the turbulent power spectrum, and apply measurement errors and finite sampling to the velocity field. We find that even with sparse coverage of the cluster, Astro-H will be able to measure the Mach number and the injection scale of the turbulent power spectrum--the quantities determining the energy flux down the turbulent cascade and the diffusion rate for everything that is advected by the gas (metals, cosmic rays, etc). Astro-H will not be sensitive to the dissipation scale or the slope of the power spectrum in its inertial range, unless they are outside physically-motivated intervals. We give the expected confidence intervals for the injection scale and the normalization of the power spectrum for a number of possible pointing configurations, combining the structure function and velocity dispersion data. Importantly, we also determine that measurement errors on the line shift will bias the velocity structure function upward, and show how to correct this bias.

### Mapping the Gas Turbulence in the Coma Cluster: Predictions for Astro-H [Replacement]

Astro-H will be able for the first time to map gas velocities and detect turbulence in galaxy clusters. One of the best targets for turbulence studies is the Coma cluster, due to its proximity, absence of a cool core, and lack of a central active galactic nucleus. To determine what constraints Astro-H will be able to place on the Coma velocity field, we construct simulated maps of the projected gas velocity and compute the second-order structure function, an analog of the velocity power spectrum. We vary the injection scale, dissipation scale, slope, and normalization of the turbulent power spectrum, and apply measurement errors and finite sampling to the velocity field. We find that even with sparse coverage of the cluster, Astro-H will be able to measure the Mach number and the injection scale of the turbulent power spectrum--the quantities determining the energy flux down the turbulent cascade and the diffusion rate for everything that is advected by the gas (metals, cosmic rays, etc.). Astro-H will not be sensitive to the dissipation scale or the slope of the power spectrum in its inertial range, unless they are outside physically motivated intervals. We give the expected confidence intervals for the injection scale and the normalization of the power spectrum for a number of possible pointing configurations, combining the structure function and velocity dispersion data. Importantly, we also determine that measurement errors on the line shift will bias the velocity structure function upward, and show how to correct this bias.

### The 3-Loop Non-Singlet Heavy Flavor Contributions to the Structure Function g_1(x,Q^2) at Large Momentum Transfer

We calculate the massive flavor non-singlet Wilson coefficient for the heavy flavor contributions to the polarized structure function $g_1(x,Q^2)$ in the asymptotic region $Q^2 \gg m^2$ to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable $N$ and the momentum fraction $x$, and derive heavy flavor corrections to the Bjorken sum-rule. Numerical results are presented for the charm quark contribution. Results on the structure function $g_2(x,Q^2)$ in the twist-2 approximation are also given.

### The Spin Structure Function $g_1^{\rm p}$ of the Proton and a Test of the Bjorken Sum Rule [Cross-Listing]

New results for the double spin asymmetry $A_1^{\rm p}$ and the proton longitudinal spin structure function $g_1^{\rm p}$ are presented. They were obtained by the COMPASS collaboration using polarised 200 GeV muons scattered off a longitudinally polarised NH$_3$ target. The data were collected in 2011 and complement those recorded in 2007 at 160\,GeV, in particular at lower values of $x$. They improve the statistical precision of $g_1^{\rm p}(x)$ by about a factor of two in the region $x\lesssim 0.02$. A next-to-leading order QCD fit to the $g_1$ world data is performed. It leads to a new determination of the quark spin contribution to the nucleon spin, $\Delta \Sigma$ ranging from 0.26 to 0.36, and to a re-evaluation of the first moment of $g_1^{\rm p}$. The uncertainty of $\Delta \Sigma$ is mostly due to the large uncertainty in the present determinations of the gluon helicity distribution. A new evaluation of the Bjorken sum rule based on the COMPASS results for the non-singlet structure function $g_1^{\rm NS}(x,Q^2)$ yields as ratio of the axial and vector coupling constants $|g_{\rm A}/g_{\rm V}| = 1.22 \pm 0.05~({\rm stat.}) \pm 0.10~({\rm syst.})$, which validates the sum rule to an accuracy of about 9\%.

### Nucleon spin structure II: Spin structure function $g_1^p$ at small $x$

The spin structure function $g_1^p$ of the proton is studied in a two component framework, where the perturbative evolution of parton distributions and nonperturbative vector meson dominance model are used. We predict the $g_1^p$ asymmetric behavior at small $x$ from lower $Q^2$ to higher $Q^2$. We find that the contribution of the large gluon helicity dominates $g_1^p$ at $x>10^{-3}$ but mixed with nonperturbative component which complicates the asymptomatic behavior of $g_1^p$ at $x<10^{-3}$. The results are compatible with the data including the HERA early estimations and COMPASS new results. The predicted strong $Q^2$- and $x$-dependence of $g_1^p$ at $0.01<Q^2<3 GeV^2$ and $x<0.1$ can be checked on the next Electron-Ion Collider.

### Nucleon spin structure [Replacement]

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 QCD evolution equation-the DGLAP equation with the parton recombination corrections, where the nucleon is almost only consisted 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 a significant orbital angular momentum of the gluons is required to balance the gluon spin momentum; (ii) The spin structure function $g_1^p$ of the proton is studied, where the perturbative evolution of parton distributions and nonperturbative Vector Meson Dominance (VMD) model are used. We predict $g_1^p$ asymptotic behavior at small $x$ from lower $Q^2$ to higher $Q^2$. The results are compatible with the data including the HERA early 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 $\Gamma_1^p(Q^2)$. The results suggest a possible extended objects with size $0.2-0.3~ fm$ inside the proton.

### Quantum Monte Carlo calculations of the thermal conductivity of neutron star crusts [Replacement]

We use the quantum Monte Carlo (QMC) techniques to calculate the static structure function $S(q)$ of a one-component ion lattice and use it to calculate the thermal conductivity $\kappa$ of high-density solid matter expected in the neutron star crust. By making detailed comparisons with the results for the thermal conductivity obtained using standard techniques based on the one-phonon approximation (OPA) valid at low temperature, and the multi-phonon harmonic approximation expected to be valid over a wide range of temperatures, we asses the temperature regime where $S(q)$ from QMC can be used directly to calculate $\kappa$. We also compare the QMC results to those obtained using classical Monte Carlo to quantitatively asses the magnitude of the quantum corrections. We find that quantum effects became relevant for the calculation of $\kappa$ at temperature $T \lesssim 0.3 ~\Omega_\mathrm{P}$, where $\Omega_\mathrm{P}$ is the ion plasma frequency. At $T \simeq 0.1 ~\Omega_\mathrm{P}$ the quantum effects suppress $\kappa$ by about $30\%$. The comparison with the results of the OPA indicates that dynamical information beyond the static structure is needed when $T \lesssim 0.1~ \Omega_\mathrm{P}$. These quantitative comparisons help to establish QMC as a viable technique to calculate $\kappa$ at moderate temperatures in the range $T=0.1-1~\Omega_\mathrm{P}$ of relevance to the study of accreting neutron stars. This finding is especially important because QMC is the only viable technique so far for calculating $\kappa$ in multi-component systems at low-temperatures.

### Quantum Monte Carlo calculations of the thermal conductivity of neutron star crusts [Replacement]

We use the quantum Monte Carlo (QMC) techniques to calculate the static structure function $S(q)$ of a one-component ion lattice and use it to calculate the thermal conductivity $\kappa$ of high-density solid matter expected in the neutron star crust. By making detailed comparisons with the results for the thermal conductivity obtained using standard techniques based on the one-phonon approximation (OPA) valid at low temperature, and the multi-phonon harmonic approximation expected to be valid over a wide range of temperatures, we asses the temperature regime where $S(q)$ from QMC can be used directly to calculate $\kappa$. We also compare the QMC results to those obtained using classical Monte Carlo to quantitatively asses the magnitude of the quantum corrections. We find that quantum effects became relevant for the calculation of $\kappa$ at temperature $T \lesssim 0.3 ~\Omega_\mathrm{P}$, where $\Omega_\mathrm{P}$ is the ion plasma frequency. At $T \simeq 0.1 ~\Omega_\mathrm{P}$ the quantum effects suppress $\kappa$ by about $30\%$. The comparison with the results of the OPA indicates that dynamical information beyond the static structure is needed when $T \lesssim 0.1~ \Omega_\mathrm{P}$. These quantitative comparisons help to establish QMC as a viable technique to calculate $\kappa$ at moderate temperatures in the range $T=0.1-1~\Omega_\mathrm{P}$ of relevance to the study of accreting neutron stars. This finding is especially important because QMC is the only viable technique so far for calculating $\kappa$ in multi-component systems at low-temperatures.

### Thermal conductivity of the neutron star crust: A reappraisal

We use classical and quantum Monte Carlo techniques to study the static structure function $S(q)$ of a one-component ion lattice and use it to calculate the thermal conductivity $\kappa$ of high-density solid matter expected in the neutron star crust. We also calculate the phonon spectrum using the dynamic-matrix method and use it to obtain $\kappa$ in the one-phonon approximation. We compare the results obtained with these methods and assess the validity of some commonly used approximations in the literature. We find that quantum effects became relevant for the calculation of $\kappa$ when the temperature $T\lesssim 0.3~\Omega_\mathrm{P}$, where $\Omega_\mathrm{P}$ is the ion plasma frequency. Dynamical information beyond the static structure becomes relevant when $T\lesssim 0.1~\Omega_\mathrm{P}$. We discuss the implications of these findings for calculations of $\kappa$ in multi-component systems and identify strategies for using Monte Carlo techniques in future work.

### Geometrical scaling behavior of the top structure functions ratio at the LHeC

We consider the ratio of the top structure functions $R^{t}(\tau_{t})$ in top pair production as a probe of the top content of the proton at the LHeC project. We study the top structure functions with the geometrical scaling of gluon distribution at small $x$ and show that top reduced cross section exhibits geometrical scaling in a large range of photon vitualities. This analysis shows that top longitudinal structure function has sizeable impact on the top reduced cross section at $Q^{2}{\approx}~ 4m_{t}^{2}$.

### On the longitudinal structure function in the dipole model [Replacement]

We compare new HERA data for the longitudinal structure function $F_{\rm L}$ with the predictions of different variants of the dipole model. In particular we show that the ratio $F_{\rm L}/F_2$ is well described by the dipole models and is rather insensitive to the details of the fit. Fits to $F_2$ are performed with the help of geometrical scaling (GS). Using the property of GS we derive the bounds for $F_{\rm L}/F_2$ both for the different versions of the dipole model and in the general case. Finally we briefly discuss how the higher Fock components of the photon wave function may affect these bounds.

### On the longitudinal structure function in the dipole model

We compare new HERA data for the longitudinal structure function $F_{\rm L}$ with the predictions of different variants of the dipole model. In particular we show that the ratio $F_{\rm L}/F_2$ is well described by the dipole models and is rather insensitive to the details of the fit. Fits to $F_2$ are performed with the help of geometrical scaling (GS). Using the property of GS we derive the bounds for $F_{\rm L}/F_2$ both for the different versions of the dipole model and in the general case. Finally we briefly discuss how the higher Fock components of the photon wave function may affect these bounds.

### On the longitudinal structure function in the dipole model [Replacement]

We compare new HERA data for the longitudinal structure function $F_{\rm L}$ with the predictions of different variants of the dipole model. In particular we show that the ratio $F_{\rm L}/F_2$ is well described by the dipole models and is rather insensitive to the details of the fit. Fits to $F_2$ are performed with the help of geometrical scaling (GS). Using the property of GS we derive the bounds for $F_{\rm L}/F_2$ both for the different versions of the dipole model and in the general case. Finally we briefly discuss how the higher Fock components of the photon wave function may affect these bounds.

### Forward Compton Scattering with weak neutral current: constraints from sum rules [Cross-Listing]

We generalize forward real Compton amplitude to the case of the interference of the electromagnetic and weak neutral current, formulate a low-energy theorem, relate the new amplitudes to the interference structure functions and obtain a new set of sum rules. We address a possible new sum rule that relates the product of the axial charge and magnetic moment of the nucleon to the 0th moment of the structure function $g_5(\nu,0)$. We apply the GDH and the finite energy sum rule for constraining the dispersive $\gamma Z$-box correction to the proton's weak charge.

### Coronal turbulence and the angular broadening of radio sources - the role of the structure function

The amplitude of density turbulence in the extended solar corona, especially near the dissipation scale, impinges on several problems of current interest. Radio sources observed through the turbulent solar wind are broadened due to refraction by and scattering off density inhomogeneities, and observations of scatter broadening are often employed to constrain the turbulence amplitude. The extent of such scatter broadening is usually computed using the structure function, which gives a measure of the spatial correlation measured by an interferometer. Most such treatments have employed analytical approximations to the structure function that are valid in the asymptotic limits $s \gg l_{i}$ or $s \ll l_{i}$, where $s$ is the interferometer spacing and $l_{i}$ is the inner scale of the density turbulence spectrum. We instead use a general structure function (GSF) that straddles these regimes, and quantify the errors introduced by the use of these approximations. We have included the effects of anisotropic scattering for distant cosmic sources viewed through the solar wind at small elongations. We show that the regimes where the GSF predictions are more accurate than those of the asymptotic expressions are not only of practical relevance, but are where inner scale effects influence estimates of scatter broadening. Taken together, we argue that the GSF should henceforth be used for scatter broadening calculations and estimates of turbulence amplitudes in the solar corona and solar wind.

### An Unobscured type II quasar candidate: SDSS J012032.19-005501.9

We report the finding of an unobscured type II Active Galactic Nuclei (AGN) candidate, SDSS J012032.19-005501.9 at a relatively high redshift of 0.601,which shows a number of unusual properties. It varies significantly on timescales of years as typical type I AGNs and marginally on timescales of weeks. The color-magnitude relation and the structure function are also consistent with that of type I AGNs, which imply that its variability likely originates from the black hole accretion system .However, no broad emission line is detected in the SDSS spectrum, and the upper limit of the equivalent width of the H$\rm \beta$ broad emission line is much less than that of type I AGNs. These properties suggest that SDSS J012032.19-005501.9 may be an unobscured quasar without broad emission lines intrinsically, namely an unobscured type II AGN or "true" type II AGN. Furthermore, its continuum luminosity is at least one order of magnitude fainter than the average value of thepast century expected from the [OIII] emission line. It indicates that SDSS J012032.19-005501.9 may be switching off. Additional possible scenarios to explain this intriguing source are also discussed. Future deep observations at multi-wavelengths are needed to reveal the nature of this peculiar and intriguing AGN.

### Hidden Color and the $b_1$ structure function of the deuteron [Cross-Listing]

The $b_1$ structure function is an observable feature of a spin-1 system sensitive to non-nucleonic components of the target nuclear wave function. A simple model for hidden-color, six-quark configurations is proposed and found to give substantial contributions for values of $x>0.2$. Good agreement with Hermes data is obtained. Predictions are made for an upcoming JLab experiment.

### Top structure function at the LHeC

The proposed linear and nonlinear behavior for the top structure function at the LHeC is considered. We present the conditions necessary to prediction the top structure function $F_{2}^{t}(x,Q^{2})$ with respect to the different predictions for the bahavior of the gluon at low $x$.

### Top structure function at the LHeC

The proposed linear and nonlinear behavior for the top structure function at the LHeC is considered. We present the conditions necessary to prediction the top structure function $F_{2}^{t}(x,Q^{2})$ with respect to the different predictions for the bahavior of the gluon at low $x$.

### Improved nonsinglet QCD analysis of the fixed-target DIS data

Deep inelastic scattering data on $F_2$ structure function obtained by BCDMS, SLAC and NMC collaborations in fixed-target experiments were analyzed in the non-singlet approximation with next-to-next-to-leading-order accuracy. The strong coupling constant is found to be $\alpha_s(M_Z^2) = 0.1157 \pm 0.0022 {(total exp.error)} + \biggl\{\begin{array}{l} +0.0028 \\ -0.0016 \end{array} {(theor)}$, which is seen to be well compatible with the average world value. Results obtained in the present paper confirm those derived in \cite{KKPS} by carrying out similar fits but with systematic errors in BCDMS data taken into account in a different way.

### Improved nonsinglet QCD analysis of the fixed-target DIS data [Replacement]

Deep inelastic scattering data on $F_2$ structure function obtained by BCDMS, SLAC and NMC collaborations in fixed-target experiments were analyzed in the non-singlet approximation with next-to-next-to-leading-order accuracy. The strong coupling constant is found to be $\alpha_s(M_Z^2) = 0.1157 \pm 0.0022 (total\,\,\,exp.error) + \biggl\{\begin{array}{l} +0.0028 \\ -0.0016 \end{array} (theor)$, which is seen to be well compatible with the average world value. Results obtained in the present paper by carrying out fits similar to those done in our earlier study, with the exception for systematic errors in BCDMS data taken into account in a different way, confirm those which were derived in that same paper.

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