Deep Inelastic Structure Functions Research Articles

Deep inelastic scattering from gauge string duality in D3-D7 brane model

We calculate deep inelastic structure functions for mesons in the D3-D7 brane model, that incorporates flavour to the AdS/CFT correspondence. We consider two different prescriptions for the hadronic current dual: a gauge field in the AdS bulk and a gauge field on the D7 brane. We also calculate elastic form factors in both cases. We compare our results with other holographic models.

Exclusive photoproduction of ϒ: From HERA to Tevatron

The forward photoproduction amplitude for γp→ϒp is calculated in a pQCD k⊥-factorization approach with an unintegrated gluon distribution constrained by inclusive deep-inelastic structure functions. The total cross section for diffractive ϒs is compared with recent HERA data. We also discuss the 2S/1S ratio in diffractive ϒ-production. The amplitude is used to predict the cross section for exclusive ϒ production in hadronic reactions. Differential distributions for the exclusive pp¯→pϒp¯ process are calculated for Tevatron energies. We also show predictions for LHC. Absorption effects are included.

On the range of validity of the dipole picture

We derive correlated bounds on ratios of deep inelastic structure functions from the dipole picture of photon-hadron scattering at high energies. In particular we consider ratios of the longitudinal structure function, the total structure function, and the charm part of the latter. We also consider ratios of total structure functions taken at the same energy but at three different photon virtualities. It is shown that by confronting these bounds with experimental data we can significantly constrain the range of validity of the dipole picture.

Deep inelastic scattering from gauge string duality in the soft wall model

Deep inelastic structure functions have been calculated by Polchinski and Strassler in gauge/string duality introducing a hard infrared (IR) cut off in AdS space. Here we investigate this problem using a soft IR cut off that leads to linear Regge trajectories for mesons. We calculate the structure functions for scalar particles in the large x regime where supergravity approximation holds and the small x regime where massive string states contribute. We also propose a hybrid model to calculate structure functions for fermions in the supergravity approximation. In the deep inelastic limit our results are in agreement with those obtained using a hard cut off.

A dispersive approach to Sudakov resummation

We present a general all-order formulation of Sudakov resummation in QCD in terms of dispersion integrals. We show that the Sudakov exponent can be written as a dispersion integral over spectral density functions, weighted by characteristic functions that encode information on power corrections. The characteristic functions are defined and computed analytically in the large- β 0 limit. The spectral density functions encapsulate the non-Abelian nature of the interaction. They are defined by the time-like discontinuity of specific effective charges (couplings) that are directly related to the familiar Sudakov anomalous dimensions and can be computed order-by-order in perturbation theory. The dispersive approach provides a realization of dressed gluon exponentiation, where Sudakov resummation is enhanced by an internal resummation of running-coupling corrections. We establish all-order relations between the scheme-invariant Borel formulation and the dispersive one, and address the difference in the treatment of power corrections. We find that in the context of Sudakov resummation the infrared-finite-coupling hypothesis is of special interest because the relevant coupling can be uniquely identified to any order, and may have an infrared fixed point already at the perturbative level. We prove that this infrared limit is universal: it is determined by the cusp anomalous dimension. To illustrate the formalism we discuss a few examples including B-meson decay spectra, deep inelastic structure functions and Drell–Yan or Higgs production.

Analytic Expression for the JointxandQ2Dependences of the Deep-Inelastic Structure Functions

We obtain a good analytic fit to the joint Bjorken-$x$ and ${Q}^{2}$ dependences of ZEUS data on the deep-inelastic structure function ${F}_{2}^{p}(x,{Q}^{2})$. At fixed virtuality ${Q}^{2}$, as we showed previously, our expression is an expansion in powers of $\mathrm{ln}(1/x)$ that satisfies the Froissart bound. Here we show that for each $x$, the ${Q}^{2}$ dependence of the data is well described by an expansion in powers of $\mathrm{ln}{Q}^{2}$. The resulting analytic expression allows us to predict the logarithmic derivatives $\mathbf{(}{\ensuremath{\partial}}^{n}{F}_{2}^{p}/(\ensuremath{\partial}\mathrm{ln}{Q}^{2}{)}^{n}{\mathbf{)}}_{x}$ for $n=1,2$ and to compare the results successfully with other data. We extrapolate the proton structure function ${F}_{2}^{p}(x,{Q}^{2})$ to the very large ${Q}^{2}$ and the very small $x$ regions that are inaccessible to present-day experiments and contrast our expectations with those of conventional global fits of parton distribution functions.

Generalized parton distributions from hadronic observables: Zero skewness

We propose a physically motivated parametrization for the unpolarized generalized parton distributions. At zero value of the skewness variable, $\ensuremath{\zeta}$, the parametrization is constrained by simultaneously fitting the experimental data on both the nucleon elastic form factors and the deep inelastic structure functions. A rich phenomenology can be addressed based on this parametrization. In particular, we track the behavior of the average: (i) interparton distances as a function of the momentum fraction, $X$, (ii) $X$ as a function of the four-momentum transfer, $t$; and (iii) the intrinsic transverse momentum ${k}_{\ensuremath{\perp}}$ as a function of $X$. We discuss the extension of our parametrization to $\ensuremath{\zeta}\ensuremath{\ne}0$ where additional constraints are provided by higher moments of the generalized parton distributions obtained from ab initio lattice QCD calculations.

Threshold Resummation in Momentum Space from Effective Field Theory

Methods from soft-collinear effective theory are used to perform the threshold resummation of Sudakov logarithms for the deep-inelastic structure function F2(x,Q2) in the end-point region x-->1 directly in momentum space. An explicit all-order formula is derived, which expresses the short-distance coefficient function C in the convolution F2 = C multiply sign in circle phi q in terms of Wilson coefficients and anomalous dimensions defined in the effective theory. Contributions associated with the physical scales Q2 and Q2(1-x) are separated from nonperturbative hadronic physics in a transparent way. A crucial ingredient to the momentum-space resummation is the exact solution to the integro-differential evolution equation for the jet function, which is derived. The methods developed in this Letter can be applied to many other hard QCD processes.

Model independent method for determination of the DIS structure of free neutron

We present a model independent procedure for extracting deep-inelastic structure function of “free” neutron from the electron–deuteron scattering with protons produced in the target fragmentation region of the reaction. This procedure is based on the extrapolation of t, which describes the invariant momentum transfered to the proton, to the unphysical region corresponding to the mass of the struck neutron. We demonstrate that the impulse approximation diagram of the reaction has a pole at this limit with a residue being proportional to the “free” neutron structure function. The method is analogous to that of Chew and Low for extraction of the “free” pion–pion and neutron–neutron cross sections from p(π,p)X and d(n,n)pn reactions, respectively. We demonstrate that in the extrapolation the final state interaction amplitudes are smooth functions of t and have negligible contribution in the extracted “free” nucleon structure function. We also estimate the range of the recoil nucleon momenta which could be used for successful extrapolation procedure.

Next-to-next-to-leading order evolution of non-singlet fragmentation functions

Abstract We have investigated the next-to-next-to-leading order (NNLO) corrections to inclusive hadron production in e + e − annihilation and the related parton fragmentation distributions, the ‘time-like’ counterparts of the ‘space-like’ deep-inelastic structure functions and parton densities. We have re-derived the corresponding second-order coefficient functions in massless perturbative QCD, which so far had been calculated only by one group. Moreover we present, for the first time, the third-order splitting functions governing the NNLO evolution of flavour non-singlet fragmentation distributions. These results have been obtained by two independent methods relating time-like quantities to calculations performed in deep-inelastic scattering. We briefly illustrate the numerical size of the NNLO corrections, and make a prediction for the difference of the yet unknown time-like and space-like splitting functions at the fourth order in the strong coupling constant.

Renormalization scale-fixing for complex scattering amplitudes

We show how to fix the renormalization scale for hard-scattering exclusive processes such as deeply virtual meson electroproduction by applying the BLM prescription to the imaginary part of the scattering amplitude and employing a fixed-t dispersion relation to obtain the scale-fixed real part. In this way, we resolve the ambiguity in BLM renormalization scale-setting for complex scattering amplitudes. We illustrate this by computing the H generalized parton distribution at leading twist in an analytic quark-diquark model for the parton-proton scattering amplitude that can incorporate Regge exchange contributions characteristic of the deep inelastic structure functions.

Soft-gluon resummation effects on parton distributions

We gauge the impact of soft-gluon resummation on quark distributions by performing a simple fit of Deep Inelastic Scattering structure function data using next-to-leading order (NLO) and next-to-leading-logarithmic (NLL)-resummed coefficient functions. We make use of NuTeV charged-current data, as well as New Muon Collaboration (NMC) and Bologna-CERN-Dubna-Munich-Saclay (BCDMS) neutral-current results, which probe large values of x. Our results suggest that the inclusion of resummation effects in global fits of parton distributions is both feasible and desirable, in order to achieve at large x the accuracy goals of the LHC physics program.

Structure Functions and Parton Distributions

I review recent progress in the determination of the parton structure of the nucleon, in particular from deep-inelastic structure functions. I explain how the needs of current and future precision phenomenology, specifically at the LHC, have turned the determination of parton distributions into a quantitative problem. I describe the results and difficulties of current approaches and ideas to go beyond them.

Colour Dipole Phenomenology

Recent, precise HERA data are analysed in the context of colour dipole models, both with and without gluon saturation. The data on the deep inelastic structure function F2 seem to prefer parameterisations which include saturation effects. That is they indicate that the strong rise with energy of the dipole cross-section, which holds for small dipoles, pertains only for r r s ( x ) where r s ( x ) decreases monotonically as x decreases. The corresponding predictions for the diffractive structure function F 2 D ( 3 ) also hint at saturation, although the data are not accurate enough to be decisive.

Unbiased determination of the proton structure functionF2pwith faithful uncertainty estimation

We construct a parametrization of the deep-inelastic structure function of the proton F_2 based on all available experimental information from charged lepton deep-inelastic scattering experiments. The parametrization effectively provides a bias-free determination of the probability measure in the space of structure functions, which retains information on experimental errors and correlations. The result is obtained in the form of a Monte Carlo sample of neural networks trained on an ensemble of replicas of the experimental data. We discuss in detail the techniques required for the construction of bias-free parameterizations of large amounts of structure function data, in view of future applications to the determination of parton distributions based on the same method.

Gluon Saturation in the Colour Dipole Model?

We use data on the deep inelastic structure function F_2 in order to constrain the cross-section for scattering a colour dipole off a proton. The data seem to prefer parameterisations which include saturation effects. That is they indicate that the strong rise with energy of the dipole cross-section, which holds for small dipoles, pertains only for r < r_s(x) where r_s(x) decreases monotonically as x decreases. Subsequent predicitions for the diffractive structure function F_2^{D(3)} also hint at saturation, although the data are not really sufficiently accurate.

Mellin representation for the heavy flavor contributions to deep inelastic structure functions

We derive semi-analytic expressions for the analytic continuation of the Mellin transforms of the heavy flavor QCD coefficient functions for neutral current deep inelastic scattering in leading and next-to-leading order to complex values of the Mellin variable N. These representations are used in Mellin-space QCD evolution programs to provide fast evaluations of the heavy flavor contributions to the structure functions F2(x,Q2), FL(x,Q2) and g1(x,Q2).

Deep inelastic scattering asx→1using soft-collinear effective theory

Soft-collinear effective theory (SCET) is used to sum Sudakov double-logarithms in the x ->1 endpoint region for the deep inelastic scattering structure function. The calculations are done in both the target rest frame and the Breit frame. The separation of scales in the effective theory implies that the anomalous dimension of the SCET current is linear in ln mu, and the anomalous dimension for the Nth moment of the structure function is linear in ln N, to all orders in perturbation theory. The SCET formulation is shown to be free of Landau pole singularities. Some important differences between the deep inelastic structure function and the shape function in B decay are discussed.

First results for three-loop deep-inelastic structure functions in QCD

As a first step towards the complete calculation of deep-inelastic scattering at third order of massless perturbative QCD, we have computed the fermionic ( n f ) contributions to the flavour non-singlet structure functions in unpolarized electromagnetic scattering. We briefly discuss the approach chosen for this calculation, the problems we encountered and the status of the project. We show the results for the corresponding anomalous dimension in both Mellin- N and Bjorken-ξ. Together with the n f part of A 3, our calculation facilitates the complete determination of the threshold-resummation coefficients B 2 and D 2 DIS. The latter quantity vanishes in the MS scheme.

Uncertainties of predictions from parton distributions I: Experimental errors

We determine the uncertainties on observables arising from the errors on the experimental data that are fitted in the global MRST2001 parton analysis. By diagonalizing the error matrix we produce sets of partons suitable for use within the framework of linear propagation of errors, which is the most convenient method for calculating the uncertainties. Despite the potential limitations of this approach we find that it can be made to work well in practice. This is confirmed by our alternative approach of using the more rigorous Lagrange multiplier method to determine the errors on physical quantities directly. As particular examples we determine the uncertainties on the predictions of the charged-current deep-inelastic structure functions, on the cross-sections for W production and for Higgs boson production via gluon--gluon fusion at the Tevatron and the LHC, on the ratio of W-minus to W-plus production at the LHC and on the moments of the non-singlet quark distributions. We discuss the corresponding uncertainties on the parton distributions in the relevant x,Q^2 domains. Finally, we briefly look at uncertainties related to the fit procedure, stressing their importance and using sigma_W, sigma_H and extractions of alpha_S(M_Z^2) as examples. As a by-product of this last point we present a slightly updated set of parton distributions, MRST2002.