Parton Distributions In QCD Research Articles

Proof of sum rules for double parton distributions in QCD

Double hard scattering can play an important role for producing multiparticle final states in hadron-hadron collisions. The associated cross sections depend on double parton distributions, which at present are only weakly constrained by theory or measurements. A set of sum rules for these distributions has been proposed by Gaunt and Stirling some time ago. We give a proof for these sum rules at all orders in perturbation theory, including a detailed analysis of the renormalisation of ultraviolet divergences. As a by-product of our study, we obtain the form of the inhomogeneous evolution equation for double parton distributions at arbitrary perturbative order.

Ultrahigh energy neutrino scattering: An update

We update our estimates of charged and neutral current neutrino total cross sections on isoscalar nucleons at ultrahigh energies using a global (x, Q^2) fit, motivated by the Froissart bound, to the F_2 (electron-proton) structure function utilizing the most recent analysis of the complete ZEUS and H1 data sets from HERA I. Using the large Q^2, small Bjorken-x limits of the "wee" parton model, we connect the ultrahigh energy neutrino cross sections directly to the large Q^2, small-x extrapolation of our new fit, which we assume saturates the Froissart bound. We compare both to our previous work, which utilized only the smaller ZEUS data set, as well as to recent results of a calculation using the ZEUS-S based global perturbative QCD parton distributions using the combined HERA I results as input. Our new results substantiate our previous conclusions, again predicting significantly smaller cross sections than those predicted by extrapolating pQCD calculations to neutrino energies above 10^9 GeV.

The Role of Logarithmic Expansions for Nonsinglet QCD Analysis of [formula omitted

In this paper the analysis of certain logarithmic expansions, which developed for precision studies of the evolution of the QCD parton distributions (pdf) at the Large Hadron Collider, is used. The x F 3 data of the CCFR collaboration is used to parameterize the non-singlet parton distributions in this order. In the fitting procedure, Bernstein polynomial method is employed. The results of valence quark distributions in the NLO are compered with exact and truncated solutions for non-singlet case.

NNLO logarithmic expansions and exact solutions of the DGLAP equations from x-space: New algorithms for precision studies at the LHC

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 same accuracy of other methods, based on Mellin space, and of brute force methods, which solve the equations by finite differences. The implementation of our analysis allows to compare with existing benchmarks for the evolution of the pdf's, useful for applications at the LHC, and to extend them significantly in a systematic fashion, especially when solutions that retain logarithmic corrections only of a certain accuracy are searched for.

Calculation of the Gluon Distribution Function Using Alternative Method for the Proton Structure Function

A calculation of the proton structure function is reported with an approximation method that relates the reduced cross section derivative and the scaling violation at low x by using quadratic form for the structure function. This quadratic form approximation method can be used to determine the structure function from the HERA reduced cross section data taken at low x. This new approach can determine the structure functions with reasonable precision even for low x values which have not been investigated. We observe that the Q2 dependence is quadratic over the full kinematic covered range. To test the validity of our new determined structure functions, we find the gluon distribution function in the leading order approximation with our new calculation for the structure functions and compare them with the QCD parton distribution functions.

Violation of sum rules for twist-3 parton distributions in QCD

Sum rules for twist-3 distributions are reexamined. Integral relations between twist-3 and twist-2 parton distributions suggest the possibility for a δ-function at x=0. We confirm and clarify this result by constructing h L and h L 3 (quark–gluon interaction dependent part of h L ) explicitly from their moments for a one-loop dressed massive quark. The physics of these results is illustrated by calculating h L ( x, Q 2) using light-front time-ordered pQCD to O(α S) on a quark target. A δ( x) term is also found in e( x, Q 2), but not in g T ( x, Q 2), to this order in O(α S) .

Extraction of the structure function F2(x,Q2) at low-x from the cross section derivative

Abstract A method to obtain an approximate relation between the reduced cross section derivative and the F 2 ( x , Q 2 ) scaling violations at low- x is presented. The resulting formula can be used to determine the structure function F 2 from the HERA reduced cross section data taken at low- x . This new approach can determine the structure function F 2 with reasonable precision even for low value x which has not been investigated. To test the validity of our determined structure functions,the obtained F 2 data are used to find the gluon distribution function as well as the longitudinal structure function which have been found by leading order approximation and from which comparison are made to QCD parton distribution functions.

Progress in the calculation of parton distributions in QCD

The secondary-beam facility of GSI provided the technical equipment for a new kind of fission experiment. Fission properties of short-lived neutron-deficient nuclei have been investigated in inverse kinematics. The measured element distributions reveal new kinds of systematics on shell structure and even–odd effects and lead to an improved understanding of structure effects in nuclear fission. The relevance of these studies for some presently considered applications is described. Prospects for future experiments are discussed.

Evolution of twist-three parton distributions in QCD beyond the large- Nc limit

We formulate a consistent 1/ N c 2 expansion of the QCD evolution equations for the twist-three quark distributions g 2( x, Q 2), h L ( x, Q 2) and e( x, Q 2) based on the interpretation of the evolution as a three-particle quantum-mechanical problem with hermitian Hamiltonian. Each distribution amplitude can be decomposed in contributions of partonic components with DGLAP-type scale dependence. We calculate the 1/ N c 2 corrections to the evolution of the dominant component with the lowest anomalous dimension – the only one that survives in the large- N c limit – and observe a good agreement with the exact numerical results for N c =3. The 1/ N c 2 admixture of operators with higher anomalous dimensions is shown to be concentrated at a few lowest partonic components and in general is rather weak.

Positivity constraints for parton distributions in QCD

The status of positivity constraints in QCD and their stability against evolution in leading and next-to-leading orders, with the particular emphasis on the role of quantum anomalies, is discussed.

Higher-twist parton distributions in QCD 2

The higher-twist structure functions are calculated in QCD 1+1 and formal sum rules are derived. It is demonstrated that the sum rule for the first moment of ƒ 4 is violated if one restricts the integration to “experimental data” ( x > 0). However, the sum rule is valid if a δ-function at the origin is taken into account. The physical origin of this δ-function is clarified from the point of view of canonical light-cone quantization (“zero mode” for the “bad” component) as well as using dispersion relations (fixed pole). The coefficient of the δ-function can be calculated by means of these dispersion relations as well as by considering a slightly non-forward Compton amplitude instead of the usual forward amplitude.

Soft gluon resummation formulae for hard parton processes in QCD

We briefly review the treatment of leading logarithmic behaviour of the parton distributions in QCD within the Bethe-Salpeter framework by analysing directly parton hadron Green functions in the limit of parton four-momentum k 2 → − ∞ in a special light-like gauge involving a spectator vector. This technique allows us to derive the factorization of parton probabilities in leading logarithmic order in QCD in the various inclusive processes involving a single short-distance scale. The proof requires us to show that the use of planar gauges η = p A + p B + ⋯, where p A, p B ⋯ are the observed hadron momenta, reduces to choosing the appropriate light-like gauge for each hadron-parton BS channel, after demonstrating a Bloch-Nordsieck cancellation of the real and virtual soft left-over gluons. In the case where two large momentum scales appear, by restricting the transverse phase space into which the gluons are radiated, we derive the double logarithmic eikonal renormalization of the hard scattering formula of the type proposed recently by Parisi and Petronzio.