Target Mass Corrections Research Articles

Structure functions at low [formula omitted]: higher twists and target mass effects

We review the physics of structure functions at low Q 2 , focusing on the phenomenon of quark-hadron duality and the resonance–scaling transition, both phenomenologically and in the context of quark models. We also present a new implementation of target mass corrections to nucleon structure functions which, unlike existing treatments, has the correct kinematic threshold behavior at finite Q 2 in the x → 1 limit.

Target mass corrections to proton spin structure functions and quark–hadron duality

Target mass corrections to proton spin structure functions in deep inelastic scattering region are analysed. Moreover, Bloom–Gilman quark–hadron dualities of proton spin structure functions g 1 and g 2 , in inelastic resonance region, are studied. The onsets of the dualities are discussed.

TARGET MASS EFFECTS IN POLARIZED DEEP INELASTIC SCATTERING

The target mass effects in polarized DIS have been studied. It was demonstrated that taking into account the first-order target mass corrections to g1 a very good approximation of the exact formula is achieved. It was also shown that their magnitude in the pre-asymptotic DIS region is small except for x > 0.65, where their large effect is partially suppressed by the large values of Q2 due to the cut W2 > 4 GeV 2. The difference between the size of the target mass and higher twist corrections is illustrated.

Target mass and finite momentum transfer corrections to unpolarized and polarized diffractive scattering

A quantum field theoretic treatment of inclusive deep-inelastic diffractive scattering is given. The process can be described in the general framework of non-forward scattering processes using the light-cone expansion in the generalized Bjorken region. Target mass and finite t corrections of the diffractive hadronic tensor are derived at the level of the twist-2 contributions both for the unpolarized and the polarized case. They modify the expressions contributing in the limit t, M 2 → 0 for larger values of β or/and t in the region of low Q 2 . The different diffractive structure functions are expressed through integrals over the relative momentum of non-perturbative t-dependent 2-particle distribution functions. In the limit t, M 2 → 0 these distribution functions are the diffractive parton distribution. Relations between the different diffractive structure functions are derived.

Target mass corrections revisited

We propose a new implementation of target mass corrections to nucleon structure functions which, unlike existing treatments, has the correct kinematic threshold behavior at finite Q^2 in the x -> 1 limit. We illustrate the differences between the new approach and existing prescriptions by considering specific examples for the F_2 and F_L structure functions, and discuss the broader implications of our results, which call into question the notion of universal parton distribution at finite Q^2.

Formula omitted], NLO Perturbative QCD and O(1 GeV) Mass Corrections

The deep-inelastic neutrino-nucleon cross section is one of the components of few GeV neutrino interactions. We present here our results for neutrino-isoscalar nucleon charged current scattering including perturbative next-to-leading order QCD corrections, target mass corrections, charm mass and lepton mass corrections.

Target mass corrections for virtual Compton scattering at twist-2 and generalized, nonforward Wandzura–Wilczek and Callan–Gross relations

The off-cone Compton operator of twist-2 is Fourier transformed using a general procedure which is applicable, in principle, to any QCD tensor operator of definite (geometric) twist. That method allows, after taking the nonforward matrix elements, to separate quite effectively their imaginary part and to reveal some hidden structure in terms of appropriately defined variables, including generalized Nachtmann variables. In this way, without using the equations of motion, generalizations of the Wandzura–Wilczek relation and of the mass-corrected Callan–Gross relation to the nonforward scattering, having the same shape as in the forward case, are obtained. In addition, new relations for those structure functions which vanish in the forward case are derived. All the structure functions are expressed in terms of iterated generalized parton distributions of nth order. In addition, we showed that the absorptive part of twist-2 virtual Compton amplitude is determined by the nonforward extensions of g 1 , W 1 and W 2 only.

Study of target mass effects on the moments of [formula omitted] and Bloom–Gilman quark–hadron duality

We study the Nachtmann moments and Bloom–Gilman quark–hadron duality of nucleon spin structure function. The target mass corrections to the moments of g 1 are discussed. Moreover, the onset of Bloom–Gilman quark–hadron duality of g 1 is estimated to be ∼ 2 GeV 2 .

Target mass corrections to electroweak structure functions and perturbative neutrino cross sections

We provide a complete and consistent framework to include subasymptotic perturbative as well as mass corrections to the leading twist (tau=2) evaluation of charged and neutral current weak structure functions and the perturbative neutrino cross sections. We revisit previous calculations in a modern language and fill in the gaps that we find missing for a complete and ready-to-use "NLO xi-scaling" formulary. In particular, as a new result we formulate the mixing of the partonic and hadronic structure function tensor basis in the operator approach to deep inelastic scattering. As an underlying framework we follow the operator product expansion a la Georgi & Politzer that allows the inclusion of target mass corrections at arbitrary order in QCD and we provide explicit analytical and numerical results at NLO. We compare this approach with a simpler collinear parton model approach to xi-scaling. Along with target mass corrections we include heavy quark mass effects as a calculable leading twist power suppressed correction. The complete corrections have been implemented into a Monte Carlo integration program to evaluate structure functions and/or integrated cross sections. As applications, we compare the operator approach with the collinear approximation numerically and we investigate the NLO and mass corrections to observables that are related to the extraction of the weak mixing angle from a Paschos-Wolfenstein-like relation in neutrino-iron scattering. We expect that the interpretation of neutrino scattering events in terms of oscillation physics and electroweak precision physics will benefit from our results.

Parton-hadron duality in unpolarized and polarized structure functions

We study the phenomenon of parton-hadron duality in both polarised and unpolarised electron proton scattering using the HERMES and the Jefferson Lab data, respectively. In both cases we extend a systematic perturbative QCD based analysis to the integrals of the structure functions in the resonance region. After subtracting target mass corrections and large x resummation effects, we extract the remaining power corrections up to order 1/Q^2. We find a sizeable suppression of these terms with respect to analyses using deep inelastic scattering data. The suppression appears consistently in both polarised and unpolarised data, except for the low Q^2 polarised data, where a large negative higher twist contribution remains. Possible scenarios generating this behavior are discussed.

Direct extraction of QCD [formula omitted] from moments of structure functions in neutrino–nucleon scattering, using the CORGI approach

We use recently calculated next-to-next-to-leading (NNLO) anomalous dimension coefficients for the n=1,3,5,…,13 moments of the xF 3 structure function in νN scattering, together with the corresponding three-loop Wilson coefficients, to obtain improved QCD predictions for the moments. The Complete Renormalization Group Improvement (CORGI) approach is used, in which all dependence on renormalization or factorization scales is avoided by a complete resummation of ultraviolet logarithms. The Bernstein Polynomial method is used to compare these QCD predictions to the xF 3 data of the CCFR Collaboration, and direct fits for Λ MS (5) , with N f =5 effective quark flavours, over the range 20< Q 2<125.9 GeV 2, were performed. We obtain Λ MS (5)=202 +54 −45 MeV, corresponding to the three-loop running coupling α s ( M Z )=0.1174 +0.0043 −0.0043. Including target mass corrections as well we obtain Λ MS (5)=228 +35 −36 MeV, corresponding to α s ( M Z )=0.1196 +0.0027 −0.0031.

Twist cut-off for scalar off-cone operators in q-space

We show that the twist decomposition of non-local scalar off-cone QCD-operators, which in x-space is infinite, after Fourier transformation with the singular functions 1/(x2−iϵ)λ for λ=1 and 2 terminates at leading and sub-leading twist, respectively. Therefore, only a finite number of twists contribute to the target mass corrections of light-cone dominated scattering processes. Their explicit expressions may be read off directly from the twist decomposition in x-space.

Heavy-quarkonium hadron cross section inQCDat leading twist

We compute the total cross section of a heavy quarkonium on a hadron target in leading twist QCD, including target mass corrections. Our method relies on the analytical continuation of the operator product expansion of the scattering amplitude, obtained long ago by Bhanot and Peskin. The cross section has a simple partonic form, which allows us to investigate the phenomenology of $J/\ensuremath{\psi}$ and $\ensuremath{\Upsilon}$ dissociation by both pions and protons.

Resummation of target mass corrections in two-photon processes: twist-two sector

We develop a formalism for the resummation of target mass corrections in off-forward two-photon amplitudes given by a chronological product of electromagnetic currents, arising in, e.g., deeply virtual Compton scattering. The method is based on a relation of composite operators with a definite twist to harmonic tensors, which form an irreducible representation of the Lorentz group. We give an application of the framework for the matrix elements of twist-two operators.

Target-mass corrections and the Bloom-Gilman duality of the nucleon structure function

The occurrence of the Bloom-Gilman local duality in the low-order moments of the nucleon structure function is investigated for values of the squared four-momentum transfer Q 2 between ∼0.5 and 10 ( GeV/c) 2 . At variance with previous analyses truncated Cornwall-Norton moments, limited to the nucleon-resonance production regions, are considered. The role played by target-mass corrections is illustrated, showing that target-mass effects are necessary (but not sufficient) for producing the observed Bloom-Gilman duality of the nucleon structure function. The possibility of a local duality between the unphysical region at large values of the Nachtmann variable and the nucleon elastic peak contribution is analyzed. It is found that the proton magnetic form factor extracted assuming local duality is significantly below the experimental data at low and intermediate values of Q 2.

Studies of higher twist and higher order effects in NLO and NNLO QCD analysis of lepton-nucleon scattering data on $F_2$ and $R ={\sigma_L}/{\sigma_T}$

We report on the extraction of the higher twist contributions to F_2 and R = sigma_L/sigma_T from the global NLO and NNLO QCD fits to lepton nucleon scattering data over a wide range of Q^2. The NLO fits require both target mass and higher twist contributions at low Q^2. However, in the NNLO analysis, the data are described by the NNLO QCD predictions (with target mass corrections) without the need for any significant contributions from higher twist effects. An estimate of the difference between NLO and NNLO parton distribution functions is obtained.

Calculation of electroproduction to NNLO and precision determination of αs

We use the known values of the two-loop Wilson coefficients and the three-loop anomalous dimension matrix γ( n) to perform a next-to-next-to leading order (NNLO) calculation of ep deep inelastic scattering. Because γ( n) is only known for a few values of n, the method of average reconstruction has to be used, which leaves 102 effective experimental points, for 12 parameters: the QCD mass Λ, and 11 initial values for the moments of the structure functions. The data points spread in the range of momenta 2.5 GeV 2⩽Q 2⩽230 GeV 2 . The χ 2/d.o.f. decreases substantially when going from LO to NLO, and also from NLO to NNLO (although only a little now) to χ 2/d.o.f.=79.2/(102−12). The favoured value of Λ is Λ(n f=4,3 loop)=282.7±35.1 MeV , corresponding to the value of the coupling at the Z mass of α ( 3 loop) s(M Z 2)=0.1172±0.0024 . The calculation, which constitutes a very precise test of QCD, includes target mass corrections; the error takes into account experimental errors and higher twist effects among other estimated theoretical errors.

Nucleon mass corrections to spin dependent structure functions and relations between their twist-3 contributions

The nucleon mass corrections are calculated to all polarized structure functions for neutral and charged current deep inelastic scattering in lowest order in the coupling constant. The impact of the target mass corrections on the general relations between the twist-2 and twist-3 parts of the structure functions is studied and three new relations between the twist-3 contributions are derived. The size of nucleon mass corrections for the g 1 and g 2 structure functions are estimated.

Target mass corrections for polarized structure functions and new sum rules

The target mass corrections are calculated for all structure functions of neutral and charged current deep inelastic scattering in lowest order in the coupling constant. Representations of the correction to the twist-2 and twist-3 contributions are derived both in Mellin- n and x-space. The impact of the target mass corrections on the general relations between the twist-2 and twist-3 parts of the structure functions is studied and three new relations between the twist-3 contributions are derived.

Parton Distributions,d/u, and Higher Twist Effects at Highx

A re-analysis of the NMC and SLAC data leads to a great improvement in our knowledge of the valence d and u parton distribution functions at high x. Standard parton distributions with our modifications are in good agreement with QCD predictions for d/u at x=1, and with the CDHSW nu p and nubar p data, the HERA charged current cross section data, the collider high-P_t jet data, and the CDF W asymmetry data. With the inclusion of target mass and higher twist corrections, the modified PDF's also describe all DIS data up to x = 0.98 and down to Q^2 = 1 GeV^2.