Semi-inclusive deep inelastic scattering at small-x

We study the semi-inclusive hadron production in deep inelastic scattering at small-x. A transverse-momentum-dependent factorization is found consistent with the results calculated in the small-x approaches, such as the color-dipole framework and the color glass condensate, in the appropriate kinematic region at the lowest order. The transverse-momentum-dependent quark distribution can be studied in this process as a probe for the small-x saturation physics. Especially, the ratio of quark distributions as a function of transverse momentum at different x   demonstrates strong dependence on the saturation scale. The Q²$Q^2$ dependence of the same ratio is also studied by applying the Collins–Soper–Sterman resummation method.     

Higher order QCD corrections to charged-lepton deep-inelastic scattering and global fits of parton distributions

We study the perturbative QCD corrections to the heavy-quark structure functions of charged-lepton deep-inelastic scattering and their impact on global fits of parton distributions. We include the logarithmically enhanced terms near threshold due to soft gluon resummation in the QCD corrections at next-to-next-to-leading order. We demonstrate that this approximation is sufficient to describe the available HERA data in most parts of the kinematic region. The threshold-enhanced next-to-next-to-leading order corrections improve the agreement between predictions based on global fits of the parton distribution functions and the HERA collider data even in the small-x region.     

Evidence for the discrete asymptotically-free BFKL Pomeron from HERA data

We show that the next-to-leading-order renormalization-group-improved asymptotically-free BFKL Pomeron provides a good fit to HERA data on virtual photoproduction at small x   and large Q²$Q^2$. The leading discrete Pomeron pole reproduces qualitatively the Q²$Q^2$ dependence of the HERA data for x∼¹⁰⁻³$x\sim {10}^{\mathrm{-3}}$, and a fit using the three leading discrete singularities reproduces quantitatively the Q²$Q^2$ and x   dependence of the HERA data for x<¹⁰⁻²$x<{10}^{\mathrm{-2}}$. This fit fixes the phase for all the BFKL wavefunctions at a chosen infrared scale.     

Could saturation effects be visible in a future electron–ion collider?

We expect to observe parton saturation in a future electron–ion collider. In this Letter we discuss this expectation in more detail considering two different models which are in good agreement with the existing experimental data on nuclear structure functions. In particular, we study the predictions of saturation effects in electron–ion collisions at high energies, using a generalization for nuclear targets of the b-CGC model, which describes the ep HERA quite well. We estimate the total, longitudinal and charm structure functions in the dipole picture and compare them with the predictions obtained using collinear factorization and modern sets of nuclear parton distributions. Our results show that inclusive observables are not very useful in the search for saturation effects. In the small x region they are very difficult to disentangle from the predictions of the collinear approaches. This happens mainly because of the large uncertainties in the determination of the nuclear parton distribution functions. On the other hand, our results indicate that the contribution of diffractive processes to the total cross section is about 20% at large A   and small Q²$Q^2$, allowing for a detailed study of diffractive observables. The study of diffractive processes becomes essential to observe parton saturation.     

New gauge anomalies and topological invariants in various dimensions

The very precise combined HERA data provides a testing ground in which the relevance of novel QCD regimes, other than the successful linear DGLAP evolution, in small-x inclusive DIS data can be ascertained. We present a study of the dependence of the AAMQS fits, based on the running coupling BK non-linear evolution equations (rcBK), on the fitted dataset. This allows for the identification of the kinematical region where rcBK accurately describes the data, and thus for the determination of its applicability boundary. We compare the rcBK results with NNLO DGLAP fits, obtained with the NNPDF methodology with analogous kinematical cuts. Further, we explore the impact on LHC phenomenology of applying stringent kinematical cuts to the low-x HERA data in a DGLAP fit.     

Resummation of large logarithms in the heavy-quark effects on the parton distributions inside the virtual photon

We discuss the resummation of the large logarithmic terms appearing in the heavy-quark effects on parton distribution functions inside the virtual photon. We incorporate heavy-quark mass effects by changing the initial condition of the leading-order DGLAP evolution equation. In a certain kinematical limit, we recover the logarithmic terms of the next-to-leading order heavy-quark effects obtained in the previous work. This method enables us to resum the large logarithmic terms due to heavy-quark mass effects on the parton distributions in the virtual photon. We numerically calculate parton distributions using the formulae derived in this work, and we discuss the property of the resummed heavy-quark effects.     

On the next-to-next-to-leading order QCD corrections to heavy-quark production in deep-inelastic scattering

The contribution of quarks with masses m?_ΛQCD$m?{\Lambda }_{\mathrm{QCD}}$ is the only part of the structure functions in deep-inelastic scattering (DIS) which is not yet known at the next-to-next-to-leading order (NNLO) of perturbative QCD. We present improved partial NNLO results for the most important structure function _F2(x,Q²)$F_2(x,Q^2)$ near the partonic threshold, in the high-energy (small-x  ) limit and at high scales Q²?m²$Q^2?m^2$; and employ these results to construct approximations for the gluon and quark coefficient functions which cover the full kinematic plane. The approximation uncertainties are carefully investigated, and found to be large only at very small values, x?10⁻³$x?{10}^{-3}$, of the Bjorken variable.     

Dynamical parton distributions of the proton and small-x physics

The perturbative properties of parton distributions generated radiatively from a valence-like input at some low resolution scale are discussed with the aim of explaining the physical aspects underlying the reliability of the predicted distributions in the small-x region. Aspects of higher-twist (shadowing) effects as well as small-x resummations are discussed. Utilizing recent improved data atx?10^?2 and a factorization scheme in which the heavy quarksc, b, ..., arenot entailed among the intrinsic (massless) parton distributions, we readjust our valencelike input and provide parametrizations of the slightly modified dynamical LO and NLO $(\overline {MS} ,DIS)$ predictions for parton distributions.     

Probing the perturbative NLO parton evolution in the small-<Emphasis Type="Italic">x</Emphasis> region

A dedicated test of the perturbative QCD NLO parton evolution in the very small-x region is performed. We find a good agreement with recent precision HERA data for F ₂ ^p(x,Q ²), as well as with the present determination of the curvature of F ₂ ^p. Characteristically, perturbative QCD evolutions result in a positive curvature which increases as x decreases. Future precision measurements in the very small x-region, x < 10^-4, could provide a sensitive test of the range of validity of perturbative QCD.Received: 6 December 2004, Revised: 1 February 2005, Published online: 9 March 2005     

Interacting partons

By analysing the asymptotic form of Feynman diagrams in quantum field theory a modified parton model is proposed, which takes into account the parton interaction leading to the breaking of the Bjorken scaling for $\text{Q}{}^2\text{? 20?30 (}\text{GeV}\text{/c)}{}^2$.     

Large perturbative corrections to the Drell-Yan process in QCD

The total cross section $\text{d}\text{σ}\text{d}\text{Q}{}^2$ for the production of a muon pair of invariant mass Q²via the Drell-Yan mechanism and the Feynman x_F differential cross section $\text{d}{}^2\text{σ}\text{d}\text{Q}{}^2\text{d}\text{x}{}_{\mathrm{<mtext>F</mtext>}}$ are calculated in QCD retaining all terms up to order α_s(Q². The calculations are performed using dimensional regularisation of the intermediary infrared and collinear singularities, but we present our results in a form independent of such details. The corrections to both these cross sections coming from radiative corrections to the lowest-order $\text{q}\text{q}$ annihilation diagram are found to be large at present values of Q² and S when the cross section is expressed in terms of parton densities derived from leptonproduction, for all Drell-Yan processes of practical interest. Numerical calculations are presented which show, for any reasonable parametrisation of the parton densities, that the neglect of higher-order terms in α_s(Q²) is not justifiable. The quark-gluon diagrams on the other hand give small corrections in this order and are only important for PP scattering.     

Transverse momentum distribution of partons in QCD

The renormalization group approach is applied to the study of transverse momentum distribution of partons in QCD. We generalize the method of Altarelli and Parisi to obtain a formula for the mean squared average transverse momentum as a function of Q² and x, the virtual photon mass squared and the longitudinal momentum fraction of the parton. For large Q², it decreases with x in addition to the expected increase with Q². This x-dependence reduces substantially the transverse momentum of massive μ-pairs produced by hadronic collisions from its linear dependence on $\text{(}\text{Q}{}^2\text{ln}\text{Q}{}^2\text{)}\text{1}\text{2}$.     

Determination of parton sea from μ pair production data

We describe a determination of the parton sea from pN → μ⁺μ^?X via the Drell-Yan formula, making a minimum of theoretical assumptions. The method requires deep inelastic eN, μN structure functions to be extrapolated to suitable values of x, Q². We determine the non-strange sea component $\text{u}\text{(x, Q}{}^2\text{) +}\text{d}\text{(x, Q}{}^2\text{)}$ between x = 0.2 and 0.5 with Q² = x²s, and s = 750 GeV².     

Does leading ln x resummation predict the rise of g 1 at small x?

We numerically analyse the evolution of the flavor non-singlet g ₁ structure function taking into account the all-order resummation of α_s ln² × terms which is expected to have much stronger effects than the DGLAP evolution in the small x region. We include a part of the next-to-leading logarithmic corrections coming from the resummed “coefficient function” which are not considered in the calculation of Blümlein and Vogt to respect the factorization scheme independence. It is pointed out that the resummed coefficient function gives unexpectedly large suppression factor over the experimentally accessible range of x and Q ². This fact implies that the next-to-leading logarithmic contributions are very important for the g ₁ structure function.     

Preliminary evidence for UA(1) breaking in QCD from lattice calculations

We suggest a simple definition of the topological charge density Q(x) in the lattice Yang-Mills theory and evaluate A≡∝d⁴x〈Q(x)Q(0)〉 in SU(2) by Monte Carlo simulation. The “data” interpolate well between the strong and weak coupling expansions, which we compute to order g^?12 and g⁶, respectively. After subtraction of the perturbative tail, our points exhibit the expected asymptotic freedom behaviour giving $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{≌(0.11±0.02)K}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, K being the SU(2) quarkless string tension. Although a larger value for $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{K}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ would be preferable, we are led to conclude (at least tentatively) that the U_A(1) problem of QCD is indeed solved perturbatively in the quark loop expansion.     

Dynamical parton distributions revisited

Dynamical parton densities, generated radiatively from valence-like inputs at some low resolution scale, are confronted with recent small-x data on deep inelastic and other hard scattering processes. It is shown that within theoretical uncertainties our previous (1994) dynamical/radiative parton distributions are compatible with most recent data and still applicable within the restricted accuracy margins of the presently available next-to-leading order calculations. Due to recent high precision measurements we also present an updated, more accurate, version of our (valence-like) dynamical input distributions. Furthermore, our perturbatively stable parameter-free dynamical predictions are extended to the extremely small-x region, , relevant to questions concerning ultra-high-energy cosmic ray and neutrino astronomy. Received: 22 June 1998 / Published online: 21 August 1998