# Posts Tagged structure function

## Recent Postings from structure function

### 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.

### Phase Characteristics of the ALMA 3 km Baseline Data

We present the phase characteristics study of the Atacama Large Millimeter/submillimeter Array (ALMA) long (up to 3 km) baseline, which is the longest baseline tested so far using ALMA. The data consist of long time-scale (10 – 20 minutes) measurements on a strong point source (i.e., bright quasar) at various frequency bands (bands 3, 6, and 7, which correspond to the frequencies of about 88 GHz, 232 GHz, and 336 GHz). Water vapor radiometer (WVR) phase correction works well even at long baselines, and the efficiency is better at higher PWV (>1 mm) condition, consistent with the past studies. We calculate the spatial structure function of phase fluctuation, and display that the phase fluctuation (i.e., rms phase) increases as a function of baseline length, and some data sets show turn-over around several hundred meters to 1 km and being almost constant at longer baselines. This is the first millimeter/submillimeter structure function at this long baseline length, and to show the turn-over of the structure function. Furthermore, the observation of the turn-over indicates that even if the ALMA baseline length extends to the planned longest baseline of 15 km, fringes will be detected at a similar rms phase fluctuation as that at a few km baseline lengths. We also calculate the coherence time using the 3 km baseline data, and the results indicate that the coherence time for band 3 is longer than 400 seconds in most of the data (both in the raw and WVR-corrected data). For bands 6 and 7, WVR-corrected data have about twice longer coherence time, but it is better to use fast switching method to avoid the coherence loss.

### Polarizability sum rule across real and virtual Compton scattering processes [Cross-Listing]

We derive a sum rule relating various electromagnetic properties of a spin-1/2 particle and consider its empirical implications for the proton. Given the measured values of the proton anomalous magnetic moment, electric and magnetic charge radii, the slope of the first moment of the spin structure function $g_1$, and the recently determined proton spin polarizability $\gamma_{E1M2}$, the sum rule yields a constraint on the low-momentum behavior of a generalized polarizability appearing in virtual Compton scattering. With the help of the presently ongoing measurements of different electromagnetic observables at the MAMI, Jefferson Lab, and HI$\gamma$S facilities, the sum rule will provide a model-independent test of the low-energy spin structure of the nucleon.

### Polarizability sum rule across real and virtual Compton scattering processes [Cross-Listing]

We derive a sum rule relating various electromagnetic properties of a spin-1/2 particle and consider its empirical implications for the proton. Given the measured values of the proton anomalous magnetic moment, electric and magnetic charge radii, the slope of the first moment of the spin structure function $g_1$, and the recently determined proton spin polarizability $\gamma_{E1M2}$, the sum rule yields a constraint on the low-momentum behavior of a generalized polarizability appearing in virtual Compton scattering. With the help of the presently ongoing measurements of different electromagnetic observables at the MAMI, Jefferson Lab, and HI$\gamma$S facilities, the sum rule will provide a model-independent test of the low-energy spin structure of the nucleon.

### 3-loop heavy flavor Wilson coefficients in deep-inelastic scattering

We present our most recent results on the calculation of the heavy flavor contributions to deep-inelastic scattering at 3-loop order in the large $Q^2$ limit, where the heavy flavor Wilson coefficients are known to factorize into light flavor Wilson coefficients and massive operator matrix elements. We describe the different techniques employed for the calculation and show the results in the case of the heavy flavor non-singlet and pure singlet contributions to the structure function $F_2(x,Q^2)$.

### The 3-Loop Pure Singlet Heavy Flavor Contributions to the Structure Function $F_2(x,Q^2)$ and the Anomalous Dimension

The pure singlet asymptotic heavy flavor corrections to 3-loop order for the deep-inelastic scattering structure function $F_2(x,Q^2)$ and the corresponding transition matrix element $A_{Qq}^{(3), \sf PS}$ in the variable flavor number scheme are computed. In Mellin-$N$ space these inclusive quantities depend on generalized harmonic sums. We also recalculate the complete 3-loop pure singlet anomalous dimension for the first time. Numerical results for the Wilson coefficients, the operator matrix element and the contribution to the structure function $F_2(x,Q^2)$ are presented.

### The 3-Loop Pure Singlet Heavy Flavor Contributions to the Structure Function $F_2(x,Q^2)$ and the Anomalous Dimension [Cross-Listing]

The pure singlet asymptotic heavy flavor corrections to 3-loop order for the deep-inelastic scattering structure function $F_2(x,Q^2)$ and the corresponding transition matrix element $A_{Qq}^{(3), \sf PS}$ in the variable flavor number scheme are computed. In Mellin-$N$ space these inclusive quantities depend on generalized harmonic sums. We also recalculate the complete 3-loop pure singlet anomalous dimension for the first time. Numerical results for the Wilson coefficients, the operator matrix element and the contribution to the structure function $F_2(x,Q^2)$ are presented.

### The Nonperturbative Structure of Hadrons [Cross-Listing]

In this thesis we explore a diverse array of issues that strike at the inherently nonperturbative structure of hadrons at momenta below the QCD confinement scale. In so doing, we mainly seek a better control over the partonic substructure of strongly-interacting matter, especially as this relates to the nonperturbative effects that both motivate and complicate experiments — particularly DIS; among others, such considerations entail sub-leading corrections in $Q^2$, dynamical higher twist effects, and hadron mass corrections. We also present novel calculations of several examples of flavor symmetry violation, which also originates in the long-distance properties of QCD at low energy. Moreover, we outline a recently developed model, framed as a hadronic effective theory amenable to QCD global analysis, which provides new insights into the possibility of nonperturbative heavy quarks in the nucleon. This model can be extended to the scale of the lighter mesons, and we assess the accessibility of the structure function of the interacting pion in the resulting framework.

### The Nonperturbative Structure of Hadrons

In this thesis we explore a diverse array of issues that strike at the inherently nonperturbative structure of hadrons at momenta below the QCD confinement scale. In so doing, we mainly seek a better control over the partonic substructure of strongly-interacting matter, especially as this relates to the nonperturbative effects that both motivate and complicate experiments — particularly DIS; among others, such considerations entail sub-leading corrections in $Q^2$, dynamical higher twist effects, and hadron mass corrections. We also present novel calculations of several examples of flavor symmetry violation, which also originates in the long-distance properties of QCD at low energy. Moreover, we outline a recently developed model, framed as a hadronic effective theory amenable to QCD global analysis, which provides new insights into the possibility of nonperturbative heavy quarks in the nucleon. This model can be extended to the scale of the lighter mesons, and we assess the accessibility of the structure function of the interacting pion in the resulting framework.

### Geometrical scaling in charm structure function ratios

By using a Laplace-transform technique, we solve the next-to-leading-order master equation for charm production and derive a compact formula for the ratio $R^{c}=\frac{F^{^{c\overline{c}}}_L}{F^{^{c\overline{c}}}_2}$, which is useful for extracting the charm structure function from the reduced charm cross section, in particular, at DESY HERA, at small x. Our results show that this ratio is independent of xat small x. In this method of determining the ratios, we apply geometrical scaling in charm production in deep inelastic scattering (DIS). Our analysis shows that the renormalization scales have a sizable impact on the ratio Rcat high $Q^{2}$. Our results for the ratio of the charm structure functions are in a goodagreement with some phenomenological models.

### Clustering structure of nuclei in deep inelastic processes

A clustering aspect is explained for the $^9$Be nucleus in charged-lepton deep inelastic scattering. Nuclear modifications of the structure function $F_2$ are studied by the ratio $R_{\rm EMC} = F_2^A /F_2^D$, where $A$ and $D$ are a nucleus and the deuteron, respectively. In a JLab experiment, an unexpectedly large nuclear modification slope $|dR_{\rm EMC}/dx|$ was found for $^9$Be, which could be related to its clustering structure. We investigated a mean conventional part of a nuclear structure function $F_2^A$ by a convolution description with nucleon momentum distributions calculated by antisymmetrized (or fermionic) molecular dynamics (AMD) and also by a simple shell model. We found that clustering effects are small in the conventional part, so that the JLab result could be associated with an internal nucleon modification or a short-range nuclear correlation which is caused by high densities due to cluster formation.

### The QCD analysis of the combined set for the F_3 structure function data based on the analytic approach

We apply analytic perturbation theory to the QCD analysis of the xF_3(x,Q^2) structure function considering a combined set of deep inelastic scattering data presented by several collaborations, and extract values of the scale parameter Lambda_{QCD}, the parameters of the form of the xF_3 structure function, and the x-shape of the higher twist contribution. We study the difference between the results obtained within the standard perturbative and analytic approaches in comparison with the experimental errors and state that the greatest difference occurs for large x.

### The QCD analysis of the combined set for the F_3 structure function data based on the analytic approach [Replacement]

We apply analytic perturbation theory to the QCD analysis of the xF_3(x,Q^2) structure function considering a combined set of deep inelastic scattering data presented by several collaborations, and extract values of the scale parameter Lambda_{QCD}, the parameters of the form of the xF_3 structure function, and the x-shape of the higher twist contribution. We study the difference between the results obtained within the standard perturbative and analytic approaches in comparison with the experimental errors and state that the greatest difference occurs for large x.

### The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous Dimensions for the Structure Function $F_2(x,Q^2)$ and Transversity

We calculate the massive flavor non-singlet Wilson coefficient for the heavy flavor contributions to the structure function $F_2(x,Q^2)$ in the asymptotic region $Q^2 \gg m^2$ and the associated operator matrix element $A_{qq,Q}^{(3), \rm NS}(N)$ to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable $N$. This matrix element is associated to the vector current and axial vector current for the even and the odd moments $N$, respectively. We also calculate the corresponding operator matrix elements for transversity, compute the contributions to the 3-loop anomalous dimensions to $O(N_F)$ and compare to results in the literature. The 3-loop matching of the flavor non-singlet distribution in the variable flavor number scheme is derived. All results can be expressed in terms of nested harmonic sums in $N$ space and harmonic polylogarithms in $x$-space. Numerical results are presented for the non-singlet charm quark contribution to $F_2(x,Q^2)$.

### The ratio of the beauty structure functions $R^b = F^b_L/F^b_2$ at low x

We study the structure functions $F_{k}^{b}(x,Q^{2})$ ($k=2, L$) and the reduced cross section $\sigma_{r}^{b}(x,Q^{2})$ for small values of Bjorken$^{,}$s $x$ variable with respect to the hard (Lipatov) pomeron for the gluon distribution and provide a compact formula for the ratio $R^{b}$ that is useful to extract the beauty structure function from the beauty reduced cross section, in particular at DESY HERA. Also we show that the effects of the nonlinear corrections to the gluon distribution tame the behavior of the beauty structure function and the beauty reduced cross section at low $x$.

### Long-term optical and radio variability of BL Lacertae

Well-sampled optical and radio light curves of BL Lacertae in B, V, R, I bands and 4.8, 8.0, 14.5 GHz from 1968 to 2014 were presented in this paper. A possible $1.26 \pm 0.05$ yr period in optical bands and a $7.50 \pm 0.15$ yr period in radio bands were detected based on discrete correlation function, structure function as well as Jurkevich method. Correlations among different bands were also analyzed and no reliable time delay was found between optical bands. Very weak correlations were detected between V band and radio bands. However, in radio bands the variation at low frequency lagged that at high frequency obviously. The spectrum of BL Lacertae turned mildly bluer when the object turned brighter, and stronger bluer-when-brighter trends were found for short flares. A scenario including a precessing helical jet and periodic shocks was put forward to interpret the variation characteristics of BL Lacertae.

### The structure function of Galactic \HI opacity fluctuations on AU scales based on MERLIN, VLA and VLBA data

We use MERLIN, VLA and VLBA observations of Galactic \HI absorption towards 3C~138 to estimate the structure function of the \HI opacity fluctuations at AU scales. Using Monte Carlo simulations, we show that there is likely to be a significant bias in the estimated structure function at signal-to-noise ratios characteristic of our observations, if the structure function is constructed in the manner most commonly used in the literature. We develop a new estimator that is free from this bias and use it to estimate the true underlying structure function slope on length scales ranging $5$ to $40$~AU. From a power law fit to the structure function, we derive a slope of $0.81^{+0.14}_{-0.13}$, i.e. similar to the value observed at parsec scales. The estimated upper limit for the amplitude of the structure function is also consistent with the measurements carried out at parsec scales. Our measurements are hence consistent with the \HI opacity fluctuation in the Galaxy being characterized by a power law structure function over length scales that span six orders of magnitude. This result implies that the dissipation scale has to be smaller than a few AU if the fluctuations are produced by turbulence. This inferred smaller dissipation scale implies that the dissipation occurs either in (i) regions with densities $\gtrsim 10^3$cm$^-3$ (i.e. similar to that inferred for "tiny scale" atomic clouds or (ii) regions with a mix of ionized and atomic gas (i.e. the observed structure in the atomic gas has a magneto-hydrodynamic origin).

### Dynamical behavior connection of the gluon distribution and the proton structure function at small $x$

We make a critical study of the relationship between the singlet structure function $F_{2}^{S}$ and the gluon distribution $G(x,Q^{2})$ proposed in the past two decades, which is frequently used to extract the gluon distribution from the proton structure function. We show that a simple relation is not generally valid in the simplest state. We complete this relation by using a Laplace transform method and hard-pomeron behavior at LO and NLO at small $x$. Our study shows that this relation is dependent on the splitting functions and initial conditions at $Q^{2} = Q^{2}_{0}$ and running coupling constant at NLO. The resulting analytic expression allows us to predict the proton structure function with respect to the gluon distributions and to compare the results with H1 data and a QCD analysis fit. Comparisons with other results are made and predictions for the proposed best approach are also provided.

### Photon structure function revisited

The flux of papers from electron positron colliders containing data on the photon structure function ended naturally around 2005. It is thus timely to review the theoretical basis and confront the predictions with a summary of the experimental results. The discussion will focus on the increase of the structure function with x (for x away from the boundaries) and its rise with log Q**2, both characteristics beeing dramatically different from hadronic structure functions. Comparing the data with a specific QCD prediction a new determination of the QCD coupling coupling constant is presented. The agreement of the experimental observations with the theoretical calculations of the real and virtual photon structure is a striking success of QCD.

### A lower bound on the Longitudinal Structure Function at small x from a self-similarity based model of Proton

Self-similarity based model of proton structure function at small \textit{x} was reported in the literature sometime back. The phenomenological validity of the model is in the kinematical region $6.2\, \times \, 10^{-7} \leq x \leq 10^{-2}$ and $0.045 \leq Q^{2} \leq 120 \, \mathrm{GeV^{2}}$. We use momentum sum rule to pin down the corresponding self-similarity based gluon distribution function valid in the same kinematical region. The model is then used to compute bound on the longitudinal structure function $F_{L}\left(x,Q^{2} \right)$ for Altarelli-Martinelli equation in QCD and is compared with the recent HERA data.

### Color dipole cross section and inelastic structure function

Instead of starting from a theoretically motivated form of the color dipole cross section in the dipole picture of deep inelastic scattering, we start with a parametrization of the deep inelastic structure function for electromagnetic scattering with protons, and then extract the color dipole cross section. Using the Donnachie-Landshoff parametrization of $F_2(x,Q^2)$, we find the dipole cross section from an approximate form of the presumed dipole cross section convoluted with the perturbative photon wave function for virtual photon splitting into a color dipole with massless quarks. The color dipole cross section determined this way works quite well in the massive case, reproducing the original Donnachie-Landshoff structure function for $0.1$ GeV$^2\leq Q^2\leq 10$ GeV$^2$. We discuss the large and small form of the dipole cross section and compare with other parameterizations.

### Color dipole cross section and inelastic structure function [Replacement]

Instead of starting from a theoretically motivated form of the color dipole cross section in the dipole picture of deep inelastic scattering, we start with a parametrization of the deep inelastic structure function for electromagnetic scattering with protons, and then extract the color dipole cross section. Using the parametrizations of $F_2(\xi=x \ {\rm or}\ W^2,Q^2)$ by Donnachie-Landshoff and Block et al., we find the dipole cross section from an approximate form of the presumed dipole cross section convoluted with the perturbative photon wave function for virtual photon splitting into a color dipole with massless quarks. The color dipole cross section determined this way reproduces the original structure function within about 10\% for $0.1$ GeV$^2\leq Q^2\leq 10$ GeV$^2$. We discuss the large and small form of the dipole cross section and compare with other parameterizations.

### Q2-evolution of parton densities at small x values. Effective scale for combined H1 and ZEUS F2 data

We use the Bessel-inspired behavior of the structure function F2 at small x, obtained for a flat initial condition in the DGLAP evolution equations. We fix the scale of the coupling constant, which eliminates the singular part of anomalous dimesnions at the next-to-leading order of approximation. The approach together with the "frozen" and analytic modifications of the strong coupling constant is used to study the precise combined H1 and ZEUS data for the structure function F2 published recently.

### The effect on PDFs and $\alpha_S(M_Z^2)$ due to changes in flavour scheme and higher twist contributions

I consider the effect on MSTW partons distribution functions (PDFs) due to changes in the choices of theoretical procedure used in the fit. I first consider using the 3-flavour fixed flavour number scheme instead of the standard general mass variable flavour number scheme used in the MSTW analysis. This results in the light quarks increasing at all relatively small $x$ values, the gluon distribution becoming smaller at high values of $x$ and larger at small $x$, the preferred value of the coupling constant $\alpha_S(M_Z^2)$ falling, particularly at NNLO, and the fit quality deteriorates. I also consider lowering the kinematic cut on $W^2$ for DIS data and simultaneously introducing higher twist terms which are fit to data. This results in much smaller effects on both PDFs and $\alpha_S(M_Z^2)$ than the scheme change, except for quarks at very high $x$. I show that the structure function one obtains from a fixed input set of PDFs using the fixed flavour scheme and variable flavour scheme differ significantly for $x \sim 0.01$ at high $Q^2$, and that this is due to the fact that in the fixed flavour scheme there is a slow convergence of large logarithmic terms of the form $(\alpha_S\ln(Q^2/m_c^2))^n$ relevant for this regime. I conclude that some of the most significant differences in PDF sets are largely due to the choice of flavour scheme used.

### The effect on PDFs and $\alpha_S(M_Z^2)$ due to changes in flavour scheme and higher twist contributions [Replacement]

I consider the effect on MSTW partons distribution functions (PDFs) due to changes in the choices of theoretical procedure used in the fit. I first consider using the 3-flavour fixed flavour number scheme instead of the standard general mass variable flavour number scheme used in the MSTW analysis. This results in the light quarks increasing at all relatively small $x$ values, the gluon distribution becoming smaller at high values of $x$ and larger at small $x$, the preferred value of the coupling constant $\alpha_S(M_Z^2)$ falling, particularly at NNLO, and the fit quality deteriorates. I also consider lowering the kinematic cut on $W^2$ for DIS data and simultaneously introducing higher twist terms which are fit to data. This results in much smaller effects on both PDFs and $\alpha_S(M_Z^2)$ than the scheme change, except for quarks at very high $x$. I show that the structure function one obtains from a fixed input set of PDFs using the fixed flavour scheme and variable flavour scheme differ significantly for $x \sim 0.01$ at high $Q^2$, and that this is due to the fact that in the fixed flavour scheme there is a slow convergence of large logarithmic terms of the form $(\alpha_S\ln(Q^2/m_c^2))^n$ relevant for this regime. I conclude that some of the most significant differences in PDF sets are largely due to the choice of flavour scheme used.

### Nonlinear correction to the longitudinal structure function at small x

We computed the longitudinal proton structure function $F_{L}$, using the nonlinear Dokshitzer-Gribov-Lipatov-Altarelli-parisi (NLDGLAP) evolution equation approach at small $x$. For the gluon distribution, the nonlinear effects are related to the longitudinal structure function. As, the very small $x$ behavior of the gluon distribution is obtained by solving the Gribov, Levin, Ryskin, Mueller and Qiu (GLR-MQ) evolution equation with the nonlinear shadowing term incorporated. We show, the strong rise that is corresponding to the linear QCD evolution equations, can be tamed by screening effects. Consequently, the obtained longitudinal structure function shows a tamed growth at small $x$. We computed the predictions for all detail of the nonlinear longitudinal structure function in the kinematic range where it has been measured by $H1$ collaboration and compared with computation Moch, Vermaseren and Vogt at the second order with input data from MRST QCD fit.

### The approximation method for calculation of the exponent of the gluon distribution-$\lambda_{g}$ and the structure function-$\lambda_{S}$ at low $x$ [Replacement]

We present a set of formulae using the solution of the QCD Dokshitzer-Gribov-Lipatov-Altarelli-parisi (DGLAP) evolution equation to the extract of the exponent $\lambda_g$ gluon distribution and $\lambda_S$ structure function from the Regge- like behavior at low $x$. The exponents are found to be independent of $x$ and to increase linearly with ln$Q^{2}$ and compared with the most data from H1 Collaboration. We also calculated the structure function $F_{2}(x,Q^{2})$ and the gluon distribution $G(x,Q^{2})$ at low $x$ assuming the Regge- like behavior of the gluon distribution function at this limit and compared with NLO QCD fit to the H$1$ data, two Pomeron fit, multipole Pomeron exchange fit and MRST (A.D.Martin, R.G.Roberts, W.J.Stirling and R.S.Thorne), DL(A.Donnachie and P.V.Landshoff), NLO-GRV(M.Gluk, E.Reya and A.Vogt) fit results, respectively.

### The approximation method for calculation of the exponent of the gluon distribution-$\lambda_{g}$ and the structure function-$\lambda_{S}$ at low $x$

We present a set of formulae using the solution of the QCD Dokshitzer-Gribov-Lipatov-Altarelli-parisi (DGLAP) evolution equation to the extract of the exponent $\lambda_g$ gluon distribution and $\lambda_S$ structure function from the Regge- like behavior at low $x$. The exponents are found to be independent of $x$ and to increase linearly with ln$Q^{2}$ and compared with the most data from H1 Collaboration. We also calculated the structure function $F_{2}(x,Q^{2})$ and the gluon distribution $G(x,Q^{2})$ at low $x$ assuming the Regge- like behavior of the gluon distribution function at this limit and compared with NLO QCD fit to the H$1$ data, two Pomeron fit, multipole Pomeron exchange fit and MRST (A.D.Martin, R.G.Roberts, W.J.Stirling and R.S.Thorne), DL(A.Donnachie and P.V.Landshoff), NLO-GRV(M.Gluk, E.Reya and A.Vogt) fit results, respectively.

### Hard- Pomeron behavior of the Longitudinal Structure Function $F_{L}$ in the Next- to- Leading- Order at low $x$

We present an analytic formula to extract the longitudinal structure function in the next- to -leading order of the perturbation theory at low $x$, from the Regge- like behavior of the gluon distribution and the structure function at this limit. In this approach, the longitudinal structure function has the hard- Pomeron behavior. The determined values are compared with the $H1$ data and MRST model. All results can consistently be described within the framework of perturbative QCD which essentially show increases as $x$ decreases.

### Analytical approach for the approximate solution of the longitudinal structure function with respect to the GLR-MQ equation at small x [Replacement]

We show that the nonlinear corrections to the longitudinal structure function can be tamed the singularity behavior at low x values, with respect to GLR-MQ equations. This approach can determined the shadowing longitudinal structure function based on the shadowing corrections to the gluon and singlet quark structure functions. Comparing our results with HERA data show that at very low x this behavior completely tamed by these corrections.

### Analytical approach for the approximate solution of the longitudinal structure function with respect to the GLR-MQ equation at small x

We show that the nonlinear corrections to the longitudinal structure function can be tamed the singularity behavior at low x values, with respect to GLR-MQ equations. This approach can determined the shadowing longitudinal structure function based on the shadowing corrections to the gluon and singlet quark structure functions. Comparing our results with HERA data show that at very low x this behavior completely tamed by these corrections.

### Evolution of the longitudinal structure function at small x

We derive an approximation approach to evolution of the longitudinal structure function, by using a Laplace-transform method. We solve the master equation and derive the longitudinal structure function as a function of the initial condition $F_{L}(x,Q^{2}_{0})$ at small x. Our results are independent of the longitudinal coefficient functions and extend from the leading order (LO) up to next-to-next-to-leading order (NNLO). The comparisons with H1 data and other parameterizations are made and results show that they are in agreement with H1 data and some phenomenological models.

### Analysis of the logarithmic slope of $F_{2}$ from the Regge gluon density behavior at small $x$

We study of the accuracy of the Regge behavior of the gluon distribution function for obtain an approximation relation, which is frequently used to extract the logarithmic slopes of the structure function from the gluon distribution at small $x$. We show that the Regge behavior analysis results are comparable with HERA data and also are better than other methods that expand of the gluon density at distinct points of expansion. Also we show that for $Q^{2}=22.4 GeV^{2}$, the $x$ dependence of the data is well described by gluon shadowing corrections to GLR-MQ equation. The resulting analytic expression allow us to predict the logarithmic derivative $\frac{{\partial}F_{2}(x,Q^{2})}{{\partial}lnQ^{2}}$ and to compare the results with H1 data and a QCD analysis fit with MRST parametrization input.

### Analytical solution of the longitudinal structure function $F_{L}$ in the leading and next-to-leading-order analysis at low x with respect to Laguerre polynomials method

The aim of the present paper is to apply the Laguerre polynomials method for the analytical solution of the Altarelli- Martinelli equation. We use this method of the low $x$ gluon distribution to the longitudinal structure function using MRST partons as input. Having checked that this model gives a good description of the data to predict of the longitudinal structure function at leading and next to leading order analysis at low $x$

### The Ratio of the Charm Structure Functions $F^{c}_{k}(k = 2, L)$ at Low x in Deep Inelastic Scattering with Respect to the Expansion Method

We study the expansion method for the gluon distribution function at low x values and calculate the charm structure functions in the LO and NLO analysis. Our results provide a compact formula for the ratio $R^{c} =F^{c}_{L}/F^{c}_{2}$, which is approximately independent of x and the details of the parton distribution function at low x values. This ratio could be a good probe of the charm structure function $F^{c}_{2}$ in the proton deduced from the reduced charm cross sections at DESY HERA. These results show that the charm structure functions obtained are in agreement with HERA experimental data and other theoretical models.

### The predictions of the charm structure function exponents behaviour at low x in deep inelastic scattering

We use the hard (Lipatov) pomeron for the low-x gluon distribution and provide a compact formula for the ratio $R^{c} =F_{L}^{c}/F_{2}^{c}$ that is useful to extract the charm structure function from the reduced charm cross-section, in particular at DESY HERA. Our results show that this ratio is independent of x and independent of the DGLAP evolution of the gluon PDF. As a result, we show that the charm structure function and the reduced charm cross-section exponents do not have the same behaviour at very low x. This difference is independent of the input gluon distribution functions and predicts the non-linear effects and some evidence for shadowing and antishadowing at HERA and RHIC.

### Longitudinal Structure Function $F_{L}$ from Charm Structure Function $F^{c}_{2}$

We predict the effect of the charm structure function on the longitudinal structure function at small x. In NLO analysis we find that the hard Pomeron behavior gives a good description of $F_{L}$ and $F^{c}_{k}$ (k = 2,L) at small x values. We conclude that a direct relation between $F_{L}/F^{c}_{2}$ would provide useful information on how to measure longitudinal structure function at high $Q^{2}$ values. Having checked that this model gives a good description of the data, when compared with other models.

### Analysis of the proton longitudinal structure function from the gluon distribution function

We make a critical, next-to-leading order, study of the relationship between the longitudinal structure function FL and the gluon distribution proposed in Cooper- Sarkar et al. (Z. Phys. C 39:281, 1988; Acta Phys. Pol. B 34:2911 2003), which is frequently used to extract the gluon distribution from the proton longitudinal structure function at small x. The gluon density is obtained by expanding at particular choices of the point of expansion and compared with the hard Pomeron behavior for the gluon density. Comparisons with H1 data are made and predictions for the proposed best approach are also provided.

### OH Maser Sources in W49N: Probing Magnetic Field and Differential Anisotropic Scattering with Zeeman pairs using the VLBA

Our analysis of a VLBA 12-hour synthesis observation of the OH masers in a well-known star-forming region W49N has yielded valuable data that enables us to probe distributions of magnetic fields in both the maser columns and the intervening interstellar medium (ISM). The data consisting of detailed high angular-resolution images (with beam-width ~20 milli-arc-seconds) of several dozen OH maser sources or "spots", at 1612, 1665 and 1667 MHz, reveal anisotropic scatter broadening, with typical sizes of a few tens of milli-arc-seconds and axial ratios between 1.5 to 3. Such anisotropies have been reported earlier by Desai, Gwinn & Diamond (1994) and interpreted as induced by the local magnetic field parallel to the Galactic plane. However, we find a) the apparent angular sizes on the average a factor of ~2.5 less than those reported by Desai et al. (1994), indicating significantly less scattering than inferred earlier, and b) a significant deviation in the average orientation of the scatter-broadened images (by ~10 degrees) from that implied by the magnetic field in the Galactic plane. More intriguingly, for a few Zeeman pairs in our set, significant differences (up to 6 sigma) are apparent in the scatter broadened images for the two hands of circular polarization, even when apparent velocity separation is less than 0.1 km/s. This may possibly be the first example of a Faraday rotation contribution to the diffractive effects in the ISM. Using the Zeeman pairs, we also study the distribution of magnetic field in the W49N complex, finding no significant trend in the spatial structure function. In this paper, we present the details of our observations and analysis leading to these findings, discuss implications of our results for the intervening anisotropic magneto-ionic medium, and suggest the possible implications for the structure of magnetic fields within this star-forming region.

### Modeling Statistical Properties of Solar Active Regions through DNS of 3D-MHD Turbulence

Statistical properties of the Sun’s photospheric turbulent magnetic field, especially those of the Active Regions (ARs), have been studied using the line-of-sight data from magnetograms taken by SOHO and several other instruments (see e.g. Abramenko et al (2002, 2003),Abramenko and Yurchyshyn (2010)). This includes structure functions and their exponents, flatness curves and correlation functions. In these works, the dependence of structure function exponents ($\zeta_p$) of the order of the structure functions ($\it{p}$) was modeled using a non-intermittent K41 model. It is now well known that the ARs are highly turbulent and are associated with strong intermittent events. In this paper we compare some of the observations from Abramenko et al (2003) with the log-Poisson model (Biskamp 2003) used for modeling intermittent MHD turbulent flows. Next, we analyze the structure function data obtained from the direct numerical simulations (DNS) of homogeneous, incompressible 3D-MHD turbulence in three cases: sustained by forcing, freely decaying and a flow initially driven and later allowed to decay (case 3). The respective DNS replicate the properties seen in the plots of $\zeta_p$ against $\it{p}$ of ARs. We also reproduce the trends and changes observed in intermittency in flatness [Abramenko and Yurchyshyn (2010)] and correlation functions [Abramenko et al (2003)] of ARs. It is suggested from this analysis that an AR in the onset phase of a flare can be treated as a forced 3D-MHD turbulent system in its simplest form and that the flaring stage is representative of decaying 3D-MHD turbulence. It is also inferred that significant changes in intermittency from the initial onset phase of a flare to its final peak flaring phase, are related to the time taken by the system to reach the initial onset phase.

### A multi-epoch spectroscopic study of the BAL quasar APM 08279+5255: I. C IV absorption variability

Broad Absorption Lines indicate gas outflows with velocities from thousands km/s to about 0.2 the speed of light, which may be present in all quasars and may play a major role in the evolution of the host galaxy. The variability of absorption patterns can provide informations on changes of the density and velocity distributions of the absorbing gas and its ionization status. We collected 23 photometrical and spectro-photometrical observations at the 1.82m Telescope of the Asiago Observatory since 2003, plus other 5 spectra from the literature. We analysed the evolution in time of the equivalent width of the broad absorption feature and two narrow absorption systems, the correlation among them and with the R band magnitude. We performed a structure function analysis of the equivalent width variations. We present an unprecedented monitoring of a broad absorption line quasar based on 28 epochs in 14 years. The shape of broad absorption feature shows a relative stability, while its equivalent width slowly declines until it sharply increases during 2011. In the same time the R magnitude stays almost constant until it sharply increases during 2011. The equivalent width of the narrow absorption redwards of the systemic redshift only shows a decline. The broad absorption behaviour suggests changes of the ionisation status as the main cause of variability. We show for the first time a correlation of this variability with the R band flux. The different behaviour of the narrow absorption system might be due to recombination time delay. The structure function of the absorption variability has a slope comparable with typical optical variability of quasars. This is consistent with variations of the 200 A ionising flux originating in the inner part of the accretion disk.

### The Perils of Analytic Continuation [Cross-Listing]

A nice paper by Morrison demonstrates the recent convergence of opinion that has taken place concerning the graviton propagator on de Sitter background. We here discuss the few points which remain under dispute. First, the inevitable decay of tachyonic scalars really does result in their 2-point functions breaking de Sitter invariance. This is obscured by analytic continuation techniques which produce formal solutions to the propagator equation that are not propagators. Second, Morrison’s de Sitter invariant solution for the spin two sector of the graviton propagator involves derivatives of the scalar propagator at $M^2 = 0$, where it is not meromorphic unless de Sitter breaking is permitted. Third, de Sitter breaking does not require zero modes. Fourth, the ambiguity Morrison claims in the equation for the spin two structure function is fixed by requiring it to derive from a mode sum. Fifth, Morrison’s spin two sector is not "physically equivalent" to ours because their coincidence limits differ. Finally, it is only the noninvariant propagator that gets the time independence and scale invariance of the tensor power spectrum correctly.

### Principal Component Analysis of Spectral Line Data: Analytic Formulation

Principal component analysis is a powerful statistical system to investigate the structure and dynamics of the molecular interstellar medium, with particular emphasis on the study of turbulence, as revealed by spectroscopic imaging of molecular line emission. To-date, the method to retrieve the power law index of the velocity structure function or power spectrum has relied on an empirical calibration and testing with model turbulent velocity fields, while lacking a firm theoretical basis. In this paper, we present an analytic formulation that reveals the detailed mechanics of the method and confirms previous empirical calibrations of its recovery of the scale dependence of turbulent velocity fluctuations.

### A Study of starless dark cloud LDN 1570: Distance, Dust properties and Magnetic field geometry

We wish to map the magnetic field geometry and to study the dust properties of the starless cloud, L1570, using multi-wavelength optical polarimetry and photometry of the stars projected on the cloud. We made R-band imaging polarimetry of the stars projected on a cloud, L1570, to trace the magnetic field orientation. We also made multi-wavelength polarimetric and photometric observations to constrain the properties of dust in L1570. We estimated a distance of 394 +/- 70 pc to the cloud using 2MASS JHKs colours. Using the values of the Serkowski parameters namely $\sigma_{1}$, $\bar \epsilon$, {\lambda}max and the position of the stars on near infrared color-color diagram, we identified 13 stars that could possibly have intrinsic polarization and/or rotation in their polarization angles. One star, 2MASS J06075075+1934177, which is a B4Ve spectral type, show the presence of diffuse interstellar bands in the spectrum apart from showing H{\alpha} line in emission. There is an indication for the presence of slightly bigger dust grains towards L1570 on the basis of the dust grain size-indicators such as {\lambda}max and Rv values. The magnetic field lines are found to be parallel to the cloud structures seen in the 250{\mu}m images (also in 8{\mu}m and 12{\mu}m shadow images) of L1570. Based on the magnetic field geometry, the cloud structure and the complex velocity structure, we believe that L1570 is in the process of formation due to the converging flow material mediated by the magnetic field lines. Structure function analysis showed that in the L1570 cloud region the large scale magnetic fields are stronger when compared with the turbulent component of magnetic fields. The estimated magnetic field strengths suggest that the L1570 cloud region is sub-critical and hence could be strongly supported by the magnetic field lines.

### Complementarity of direct and indirect Dark Matter detection experiments [Cross-Listing]

We investigate the prospects for reconstructing the mass, spin-independent and spin-dependent cross-sections of Dark Matter particles with a combination of a future direct detection experiments such as XENON1T, and the IceCube neutrino telescope in the 86-string configuration including the DeepCore array. We quantify the degree of complementarity between the two experiments by adopting realistic values for their exposure, energy threshold and resolution. Starting from benchmark models arising from a supersymmetric model with 25 free parameters, we show that despite the stringent constraints set by the run with 79 strings, IceCube can help break the degeneracies in the Dark Matter cross-section parameter space, even in the unfortunate case where it fails to discover high energy neutrinos from the Sun. We also discuss how the uncertainties associated with the nuclear structure function and with astrophysical quantities such as the Dark Matter density and velocity distribution affect the reconstruction of the Dark Matter particle parameters from the combined datasets.

### Yaglom law in the expanding solar wind

We study the Yaglom law, which relates the mixed third order structure function to the average dissipation rate of turbulence, in a uniformly expanding solar wind by using the two scales expansion model of magnetohydrodynamic (MHD) turbulence. We show that due to the expansion of the solar wind two new terms appear in the Yaglom law. The first term is related to the decay of the turbulent energy by nonlinear interactions, whereas the second term is related to the non-zero cross-correlation of the Els\"asser fields. Using magnetic field and plasma data from WIND and Helios 2 spacecrafts, we show that at lower frequencies in the inertial range of MHD turbulence the new terms become comparable to Yaglom’s third order mixed moment, and therefore they cannot be neglected in the evaluation of the energy cascade rate in the solar wind.