Results for the two real parton differential distributions needed for implementing a next-to-leading order (NLO) parton shower Monte Carlo are presented. They are also integrated over the phase space in order to provide solid numerical control of the MC codes and for the discussion of the differences between the standard $\bar{MS}$ factorization and Monte Carlo implementation at the level of inclusive NLO evolution kernels. Presented results cover the class of non-singlet diagrams entering into NLO kernels. The classic work of Curci-Furmanski-Pertonzio was used as a guide in the calculations.
We show for a first time ever a prototype of a fully exclusive QCD NLO parton shower for the initial state (albeit for a limited set of diagrams). It is based on the rigorous theorems of the collinear factorisation, however the standard DGLAP evolution kernels are replaced by their exclusive versions. Contrary to the standard DGLAP approach, the constructed parton shower provides fully exclusive events, i.e. four-momenta of all emitted partons. At the inclusive level it is identical to the MS-bar scheme of the DGLAP evolution.
Polarised singlet DGLAP equations are solved by applying the method of characteristics. The singlet equations are first transformed into a pair of coupled partial differential equations by a Taylor series expansion valid to be at small x. The equations are then reduced to canonical forms and the resultant equations solved by applying the method of characteristics. Results are compared with some exact solutions of polarised DGLAP equations available in the literature.
The explicit expressions for the non-singlet DIS structure function g_1 at small $x$ are obtained by resumming the leading logarithmic contributions. The role played by the fits for the initial parton densities currently used in the DGLAP on the small-x behavior of the non-singlet g_1 is discussed. Explicit expressions combining DGLAP with our results are presented.
The explicit expressions for the non-singlet DIS structure functions obtained at small x by resumming the most singular logarithmic contributions are discussed and compared in detail with the DGLAP evolution for different values of x and Q^2. The role played by the initial conditions for the parton densities currently used in the DGLAP analysis, on the small-$x$ behavior of the non-singlet structure functions is discussed. Explicit expressions are presented which implement the NLO DGLAP contributions with our small-x results.
The non-singlet structure functions have been obtained by solving Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations in leading order (LO) and next-to-leading order (NLO) at the small-x limit. Here a Taylor series expansion has been used and then the method of characteristics has been applied to solve the evolution equations. Results are comopared with the Fermilab experiment E665 data and New Muon Collaboration (NMC) data.
Study of parton distribution function (PDF) is a topic of significant interest in QCD. To overcome the shortcomings of conventional PDFs, several alternative methods have been suggested in recent years. The present work reports the x distribution of the Non-singlet structure function in Leading order using the complete solution of Taylor-approximated DGLAP equation. The formalism is more general than the similar ones reported in recent literature. Our predictions are compared with the CCFR neutrino data as well as exact results.
The next-to-leading order (NLO) evolution of the parton distribution functions (PDFs) in QCD is a common tool in the lepton-hadron and hadron-hadron collider data analysis. The standard NLO DGLAP evolution is formulated for inclusive (integrated) PDFs and done using inclusive NLO kernels. We report here on the ongoing project, called KRKMC, in which NLO DGLAP evolution is performed for the exclusive multiparton (fully unintegrated) distributions (ePDFs) with the help of the exclusive kernels. These kernels are calculated within the two-parton phase space for the non-singlet evolution, using Cu…
In this paper, we solved the coupled Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for singlet and gluon structure functions in leading order (LO) at low-x assuming the Regge behaviour of quark and gluon structure functions at this limit, and t and x-evolutions of singlet and gluon structure functions are presented. We have compared our results of gluon structure function with global MRST 2004 and GRV 1998 gluon parameterizations and the results of deuteron structure function with New Muon Collaboration (NMC) data. We have shown that the solutions of coupled equations …
A semi-numerical solution to Dokshitzer- Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations at leading order (LO), next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) in the small-x limit is presented. Here we have used Taylor series expansion method to solve the evolution equations and, t- and x-evolutions of the singlet structure functions have been obtained with such solution. We have also calculated t- and x-evolutions of deuteron structure functions F_2^d, and the results are compared with the E665 data and NMC data. The results are also compared to those obtaine…
We show that it is possible to use hard-Pomeron behavior to the gluon distribution and singlet structure function at low $x$. We derive a second-order independent differential equation for the gluon distribution and the singlet structure function. In this approach, both singlet quarks and gluons have the same high-energy behavior at small $x$. These equations are derived from the next-to-leading order DGLAP evolution equations. All results can be consistently described in the framework of perturbative QCD, which shows an increase of gluon distribution and singlet structure functions as $x$ dec…
We present a set of independent formulae to extract the gluon distribution and singlet structure function from its derivatives with respect to $lnQ^{2}$ in the next- to- leading order of perturbation theory at low-$x$ based on a hard pomeron exchange. In this approach, both singlet quarks and gluons have the same high-energy behavior at small $x$. This approach needs the QCD input parameterizations for a independent DGLAP evolutions that we calculated numerically and compared with MRST, GRV and DL model- the Pomeron has a hard nature. Its evolution gives a good fit to the experimental data. Th…
Coupled DGLAP equations involving singlet quark and gluon distributions are explored by a Taylor expansion as two first order partial differential equations in two variables. The system of equations are then solved by the Lagrange's method and Method of Characteristics. We obtain the proton structure function by combining the corresponding non-singlet and singlet structure functions by both the methods. Analytical solutions for proton structure function thus obtained are compared with the data available and their compatibility is checked. Data favors the analytical solution by Lagrange's metho…
The explicit expressions for the non-singlet and singlet components of the DIS structure function g_1 comprising the DGLAP -expressions for the coefficient functions and the anomalous dimensions, and accounting for the total resummation of the most singular contributions to those are obtained.
Theoretical predictions show that at low values of Bjorken $x$ the spin structure function, $g_1$ is influenced by large logarithmic corrections, $ln^2(1/x)$, which may be predominant in this region. These corrections are also partially contained in the NLO part of the standard DGLAP evolution. Here we calculate the non-singlet component of the nucleon structure function, $g_1^{NS}=g_1^p-g_1^n$, and its first moment, using a unified evolution equation. This equation incorporates the terms describing the NLO DGLAP evolution and the terms contributing to the $ln^2(1/x)$ resummation. In order to …
We explain particular, unique, approximate solutions of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations and also solutions of DGLAP evolution equations by using regge behaviour of structure functions and method of characteristic for t and x-evolutions of singlet and non-singlet structure functions in leading order (LO) and next-to-leading order (NLO). Hence t-evolution of deuteron, proton, neutron and difference of proton and neutron and x-evolution of deuteron, proton and neutron structure functions in LO and NLO at low-x from DGLAP evolution equations. The results …
We present particular and unique solutions of singlet and non-singlet Dokshitzer-Gribov-Lipatov- Altarelli-Parisi (DGLAP) evolution equations in next-to-next-to-leading order (NNLO) at low-x. We obtain t-evolutions of deuteron, proton, neutron and difference and ratio of proton and neutron structure functions at low-x from DGLAP evolution equations. The results of t-evolutions are compared with HERA and NMC lox-x and low-Q2 data. We also compare our result of t-evolution of proton structure function with a recent global parameterization.
In this paper the singlet and non-singlet hadron structure functions have been obtained by solving Dokshitzer-Gribov-Lipatov-Alterelli-Parisi (DGLAP) evolution equations in leading order (LO) at the small-x limit. Here we have used a Taylor Series expansion and then the method of characteristics to solve the evolution equation. We have also calculated t and x-evolutions of deuteron structure function and the results are compared with the New Muon Collaboration (NMC) data.
We investigate the role of the choice of the upper phase space limit Q in the Curci-Furmanski-Petronzio (CFP) factorization scheme, which exploits dimensional regularization MS scheme. We examine how the choice of Q influences the evaluation of the standard DGLAP (inclusive) evolution kernels, gaining experience needed in the construction of the exclusive Monte Carlo modelling of the NLO DGLAP evolution. In particular, we uncover three types of mechanisms which assure the independence on Q of the inclusive DGLAP kernels calculated in the CFP scheme. We use the examples of three types of the Fe…
We present a set of formulas to extract two second-order independent differential equations for the gluon and singlet distribution functions. Our results extend from the LO up to NNLO DGLAP evolution equations with respect to the hard-Pomeron behavior at low-x. In this approach, both singlet quarks and gluons have the same high-energy behavior at low-x. We solve the independent DGLAP evolution equations for the functions $F^{s}_{2}(x,Q^{2})$ and $G(x,Q^{2})$ as a function of their initial parameterization at the starting scale $Q^{2}_{0}$ . The results not only give striking support to the har…
In this paper, we find the t and x-evolution of deuteron structure function from DGLAP evolution equation of singlet structure function in leading order at small-x assuming the Regge behaviour of the singlet structure function at this limit and we compare our result of deuteron structure function with New Muon Collaboration data to find the range of the intercept of Regge behaviour for deuteron structure function. We also discuss the limitations of Taylor series expansion method in the Regge behaviour of structure function.
In this paper the singlet and non-singlet structure functions have been obtained by solving Dokshitzer, Gribove, Lipatov, Alterelli, Parisi (DGLAP) evolution equations in leading order (LO) and next to leading order (NLO) at the small x limit. Here we have used a Taylor Series expansion and then the method of characteristics to solve the evolution equations. We have also calculated t and x-evolutions of deuteron structure function and the results are compared with the New Muon Collaboration (NMC) data.
Using Laplace transform techniques, along with newly-developed accurate numerical inverse Laplace transform algorithms, we decouple the solutions for the singlet structure function $F_s(x,Q^2)$ and $G(x,Q^2)$ of the two leading-order coupled singlet DGLAP equations, allowing us to write fully decoupled solutions: F_s(x,Q^2)={\cal F}_s(F_{s0}(x), G_0(x)), G(x,Q^2)={\cal G}(F_{s0}(x), G_0(x)). Here ${\cal F}_s$ and $\cal G$ are known functions---found using the DGLAP splitting functions---of the functions $F_{s0}(x) \equiv F_s(x,Q_0^2)$ and $G_{0}(x) \equiv G(x,Q_0^2)$, the chosen starting funct…
In this paper we present solutions of the coupled DGLAP equations for quark and gluon singlet by applying the method of characteristics. Solutions are presented both in analytic and semi-analytic forms, compared with the exact results and the validity range obtained.
A generalization of the leading-order DGLAP evolution at small x is performed for the non-singlet structure function by resumming the leading-order DGLAP anomalous dimension to all orders in the QCD coupling. Explicit expressions are obtained for the non-singlet structure function of the deep inelastic scattering, taking into account both the double-logarithmic and the single-logarithmic contributions, including the running alpha_s effects. It is shown that when these contributions are included, the asymptotic small-x behaviour is power-like, with an exponent of about 0.4.
In this paper, we derive two second- order of differential equation for the gluon and singlet distribution functions by using the Laplace transform method. We decoupled the solutions of the singlet and gluon distributions into the initial conditions (function and derivative of the function) at the virtuality $Q_{0}^{2}$ separately as these solutions are defined by: \begin{eqnarray} F_{2}^{s}(x,Q^{2}) &=& \mathcal{F}(F_{s0}, \partial F_{s0})\nonumber &&\mathrm{and} \nonumber G(x,Q^{2}) &=& \mathcal{G}(G_{0}, \partial G_{0}).\nonumber \end{eqnarray} We compared our results with the MSTW paramete…
Analytical solutions for the non-singlet polarized parton distribution are obtained by solving the DGLAP equation by two analytical methods: Lagranges Method and Method of Characteristics.The relative merits of the two methods are discussed while comparing with HERMES data in the small x region.We also calculate the partial spin fractions carried by small x, nonsinglet partons.
In the present paper we summarize our results on the structure function g_1 and present explicit expressions for the non-singlet and singlet components of g_1 which can be used at arbitrary x and Q^2. These expressions combine the well-known DGLAP-results for the anomalous dimensions and coefficient functions with the total resummation of the leading logarithmic contributions and the shift of Q^2 -> Q^2 + μ^2, with μ/Λ_{QCD} approx 10 (approx 55) for the non-singlet (singlet) components of g_1 respectively. In contrast to DGLAP, these expressions do not require the introduction of singular par…
In this work, we present an analytical solution for QCD$\otimes$QED coupled Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations at the leading order (LO) accuracy in QED and next-to-leading order (NLO) accuracy in perturbative QCD using double Laplace transform. This technique is applied to obtain the singlet, gluon and photon distribution functions and also the proton structure function. We also obtain contribution of photon in proton at LO and NLO at high energy and successfully compare the proton structure function with HERA data \cite{12} and APFEL results \cite{7}. Some…
Using repeated Laplace transform techniques, along with newly-developed accurate numerical inverse Laplace transform algorithms, we transform the coupled, integral-differential NLO singlet DGLAP equations first into coupled differential equations, then into coupled algebraic equations, which we can solve iteratively. After Laplace inverting the algebraic solution analytically, we numerically invert the solutions of the decoupled differential equations. Finally, we arrive at the decoupled NLO evolved solutions F_s(x,Q^2)=calF_s(F_{s0}(x),G_0(x)) and G(x,Q^2)=calG(F_{s0}(x),G_0(x)), where calF_s…
We have analytically solved the LO pQCD singlet DGLAP equations using Laplace transform techniques. Newly-developed highly accurate numerical inverse Laplace transform algorithms allow us to write fully decoupled solutions for the singlet structure function F_s(x,Q^2)and G(x,Q^2) as F_s(x,Q^2)={\cal F}_s(F_{s0}(x), G_0(x)) and G(x,Q^2)={\cal G}(F_{s0}(x), G_0(x)). Here {\cal F}_s and \cal G are known functions of the initial boundary conditions F_{s0}(x) = F_s(x,Q_0^2) and G_{0}(x) = G(x,Q_0^2), i.e., the chosen starting functions at the virtuality Q_0^2. For both G and F_s, we are able to eit…
We are reporting on the ongoing effort of the Monte Carlo (MC) modelling of NLO DGLAP QCD evolution in the fully unintegrated form. The resulting parton shower MC is performing on its own the NLO QCD evolution, contrary to all known programs of this kind which are limited to LO level only. We overview this new MC scheme, for the non-singlet subset of the gluonstrahlung diagrams. Precision numerical tests of this new scheme are also shown.
Explicit expressions for the non-singlet and singlet structure functions g_1 in the small-x region are obtained. They include the total resummation of the double- and single- logarithms of x and account for the running QCD coupling effects. Both the non-singlet and singlet structure functions are Regge behavied asymptotically, with the intercepts predicted in agreement with experiments. A detailed comparison with the DGLAP evolution equations for different values of x and Q^2 is performed. Finally, the role played by singular terms in DGLAP fits is discussed and explicitly shown to mimic the r…
We summarize the theoretical approach to the solution of the NNLO DGLAP equations using methods based on the logarithmic expansions in x-space and their implementation into the C program Candia 1.0. We present the various options implemented in the program and discuss the different solutions. The user can choose the order of the evolution, the type of the solution, which can be either exact or truncated, and the evolution either with a fixed or a varying flavor number, implemented in the varying-flavour-number scheme (VFNS). The renormalization and factorization scale dependences are treated s…
We obtain a pair of second order differential equations in two variables $x$ and $t$ from the coupled DGLAP QCD evolution equations at small $x$ using the standard Taylor series expansion method.To that end we keep terms upto $O(x^2 )$.We use the standard assumption about the relationship between the singlet Structure Function and the gluon distributions available in current literature. We solve the taylor approximated $O(x)$ DGLAP equations by Lagrange's auxiliary method and $O(x^2)$ equation by Method of Separation of Variables and then show that the two solutions obtained in each for $O(x)$…
We study a parton shower description, based on a dipole picture, of the final state in electron-positron annihilation. In such a shower, the distribution function describing the inclusive probability to find a quark with a given energy depends on the shower evolution time. Starting from the exclusive evolution equation for the shower, we derive an equation for the evolution of the inclusive quark energy distribution in the limit of strong ordering in shower evolution time of the successive parton splittings. We find that, as expected, this is the DGLAP equation. This paper is a response to a r…
Presently available perturbative QCD calculations combining hard process matrix element with the Parton Shower Monte Carlo programs feature hard process matrix element calculated often beyond the leading order (LO), that is including complete next-to-leading-order (NLO), or even next-to-next-to-leading-order (NNLO) corrections, while Parton Shower is only at the leading order (LO). We report here on a work in progress which demonstrate feasibility of constructing Parton Shower Monte Carlo (PSMC) featuring complete NLO corrections to QCD evolution with respect to the logarithm of the factorizat…
We present particular and unique solutions of singlet and non-singlet Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations in leading order (LO) and next-to-leading order (NLO) and gluon, sea and valence quark Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations in leading order (LO) by applying Taylor expansion method at small-x. We obtain t-evolutions of deuteron, proton, neutron, difference and ratio of proton and neutron, gluon, light sea and valence quark structure functions and x-evolution of deuteron,gluon and light sea quark structure functions at sm…
The next-to-leading order (NLO) evolution of the parton distribution functions (PDF's) in QCD is the "industry standard" in the lepton-hadron and hadron-hadron collider data analysis. The standard NLO DGLAP evolution is formulated for inclusive (integrated) PDFs and is done using inclusive NLO kernels. We report here on the ongoing project, called KRKMC, in which NLO DGLAP evolution is performed for the exclusive multiparton (fully unintegrated) distributions (ePDF's) with the help of the exclusive kernels. These kernels are calculated within the two-parton phase space for bremsstrahlung subse…
Feynman diagrams with two real partons contributing to the next-to-leading-order singlet gluon-quark DGLAP kernel are analysed. The infra-red singularities of unintegrated distributions are examined numerically. The analytical formulae are also given in some cases. The role of the colour coherence effects is found to be crucial for cancellations of the double- and single-logarithmic infra-red singularities.
We propose a matrix evolution equation in (x,kt)-space for flavour singlet, unintegrated quark and gluon densities, which generalizes DGLAP and BFKL equations in the relevant limits. The matrix evolution kernel is constructed so as to satisfy renormalization group constraints in both the ordered and antiordered regions of exchanged momenta kt, and incorporates the known NLO anomalous dimensions in the MSbar scheme as well as the NLx BFKL kernel. We provide a hard Pomeron exponent and effective eigenvalue functions that include the n_f-dependence, and give also the matrix of resummed DGLAP spli…
We determine the UHE neutrino-nucleon cross-sections analytically both for charged and neutral current in the leading order by using the solutions of non-singlet DGLAP equation as well as singlet DGLAP equation respectively. Next we determine the cross-sections for both charged and neutral current at one loop level by carring out numerical integration of the double differential cross-section. For analytical solution, we take the standard MRST 2004 f4 LO parton distributions at $Q_0^2=1$ \,GeV$^2$ as input and for numerical solution (exact), we consider the GRV 94 parton distributions. Our anal…
Deuteron and proton structure functions are derived from Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations of singlet and non-singlet structure functions in next-to-leading order (NLO) at low-x assuming the Regge behaviour of singlet and non-singlet structure functions at this limit and results are compared with New Muon Collaboration (NMC) and E665 collaboration data sets.
A NNLO analysis of certain logarithmic expansions, developed for precision studies of the evolution of the QCD parton distributions (pdf) at the Large Hadron Collider, is presented. We elaborate on their relations to all the solutions of the DGLAP equations that have been hitherto obtained from Mellin space, to which are equivalent. Exact expansions, equivalent to exact solutions of the equations, are constructed in the non-singlet sector. The algorithmic features of our approach are also emphasized, since this method allows to obtain numerical solutions of the evolution equations with the sam…
In this paper, we compute the relativistic corrections to the fragmentation functions (FFs) of a heavy quark to $B_c$ and $B_c^*$ within the framework of non-relativistic QCD (NRQCD) factorization. The non-singlet and singlet DGLAP evolution are also presented.
Accounting for double-logarithms of x and running QCD coupling leads to expressions for both the non-singlet and singlet components of $g_1$. These expressions manifest the Regge asymptotics when x ->0 and differ considerably from the DGLAP expressions at small values of x.
Neutrino-nucleon scattering, which produces the parity violating term, xF3(x,Q2) the non-singlet hadron structure function in their weak interaction has significant contribution towards the understanding of valence quark distribution for low-Q2 and small-x region inside hadrons. Here x is the fractional momentum of partons and Q2 is the four momentum transfer in a deep inelastic scattering process. In this paper, the xF3(x,Q2) structure function has been obtained by solving the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equation in leading order and next-to-leading order at small-x l…
Closed expressions are presented for the contributions to QCD non-singlet forward evolution kernels $P(z)$ for the DGLAP equation and to $V(x,y)$ for non-forward (ER-BL) evolution equation for a certain class of diagrams which include renormalon chains. Calculations are performed in covariant $ξ$-gauge, in the \MSbar scheme. The assumption of "naive nonabelianization" approximation for kernel calculations is discussed, and a special choice of the gauge parameter $ξ=-3$ is analyzed in this context. Partial solutions to the ER-BL evolution equation are obtained.
Infrared evolution equations for small-$x$ behaviour of the non-singlet structure functions $f_1^{NS}$ and $g_1^{NS}$ are obtained and solved in the next-to-leading approximation, to all orders in $α_s$, and including running $α_s$ effects. The intercepts of these structure functions, i.e. the exponents of the power-like small-$x$ behaviour, are calculated. A detailed comparison with the leading logarithmic approximation (LLA) and DGLAP is made. We explain why the LLA predictions for the small-$x$ dependence of the structure functions may be more reliable than the prediction for the $Q^2$ depe…
Contributions to QCD non-singlet evolution kernels $P(z)$ for the DGLAP equation and $V(x,y)$ for the Brodsky-Lepage evolution equation are calculated for a certain class of diagrams which include renormalon chains. Closed expressions are presented for the sums of these contributions that dominate for a large number of flavors $N_f \gg 1$. Calculations are performed in covariant $ξ$-gauge, in the \MSbar scheme. The assumption of "naive nonabelianization" approximation for kernel calculations is discussed. The partial solution to the Brodsky-Lepage evolution equation is obtained.
We recently derived explicit solutions of the leading-order Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equations for the $Q^2$ evolution of the singlet structure function $F_s(x,Q^2)$ and the gluon distribution $G(x,Q^2)$ using very efficient Laplace transform techniques. We apply our results here to a study of the HERA data on deep inelastic $ep$ scattering as recently combined by the H1 and ZEUS groups. We use initial distributions $F_2^{γp}(x,Q_0^2)$ and $G(x,Q_0^2)$ fixed by a global fit to the HERA data. From $F_2^{γp}(x,Q_0^2)$ we obtain the singlet quark distribution $F_s(x,Q_0^…
The perturbative QCD expansion for $J/ψ$ photoproduction appears to be unstable: the NLO correction is large (and of opposite sign) to the LO contribution. Moreover, the predictions are very sensitive to the choice of factorization and renormalization scales. Here we show that perturbative stability is greatly improved by imposing a $`Q_0$ cut' on the NLO coefficient functions; a cut which is required to avoid double counting. $Q_0$ is the input scale used in the parton DGLAP evolution. This result opens the possibility of high precision exclusive $J/ψ$ data in the forward direction at the LHC…
The contributions to non-singlet evolution kernels $P(z)$ for the DGLAP equation and $V(x,y)$ for the Brodsky-Lepage evolution equation are calculated for certain classes of diagrams which include the renormalon chains. Closed expressions are obtained for the sums of contributions associated with these diagram classes. Calculations are performed in the $[ϕ^3]_6$ model and QCD in the \MSbar scheme. The contribution for one of the classes of diagrams dominates for a number of flavors $N_f \gg 1$. For the latter case, a simple solution to the Brodsky-Lepage evolution equation is obtained.
We introduce the physical factorisation scheme, which is necessary to describe observables which are `not completely inclusive'. We derive the formulae for NLO DGLAP evolution in this scheme, and also for the `rotation' of the conventional MSbar PDFs into the physical representation. Unlike, the MSbar prescription, where, for example, the gluon PDF at NLO obtains an admixture of the quark-singlet PDF, and vice-versa, the physical approach does not mix parton PDFs of different types. That is, the physical approach retains the precise quantum numbers of each PDF. The NLO corrections to DGLAP evo…
In the first chapter we give an introduction to hard diffractive scattering in QCD to introduce basic concepts and terminology. In the second chapter we make predictions for the evolution of skewed parton distributions in a proton in the LLA. We calculate the DGLAP-type evolution kernels in the LLA and solve the skewed GLAP evolution equations with a modified version of the CTEQ-package. In the third chapter, we discuss the algorithms used in the LO evolution program for skewed parton distributions in the DGLAP region, discuss the stability of the code and reproduce the LO diagonal evolution w…
We present a detailed study of the exclusive radiative decays $Z\toη^{(\prime)}γ$ employing the QCD factorization approach. We derive a factorization formula for the decay amplitudes valid at leading power in an expansion in $(Λ_{QCD}/m_Z)^2$, which includes convolutions of calculable hard-scattering kernels with the leading-twist quark and gluon light-cone distribution amplitudes of the mesons. Large logarithms arising in the evolution from the high scale $m_Z$ down to hadronic scales are resummed using the renormalization group, carefully accounting for the effects of the heavy bottom and ch…
We studied the effects of NLO $Q^2$ evolution of generalized parton distributions (GPDs) using the aligned-jet model for the singlet quark and gluon GPDs at an initial evolution scale. We found that the skewness ratio for quarks is a slow logarithmic function of $Q^2$ reaching $r^S=1.5-2$ at $Q^2=100$ GeV$^2$ and $r^g \approx 1$ for gluons in a wide range of $Q^2$. Using the resulting GPDs, we calculated the DVCS cross section on the proton in NLO pQCD and found that this model in conjunction with modern parameterizations of proton PDFs (CJ15 and CT14) provides a good description of the availa…
