We report on a recently completed, first calculation of the full next-to-leading order QCD corrections for heavy flavor contributions to the inclusive structure function $g_1$ in longitudinally polarized deep-inelastic scattering. All results are derived with largely analytical methods and retain the full dependence on the heavy quark's mass. As a first phenomenological application, inclusive charm production at a future electron-ion collider and its sensitivity to the polarized gluon distribution is studied. Theoretical uncertainties due to the residual dependence on unphysical factorization and renormalization scales are estimated.
We propose new method which allows determination of the strange-sea quark spin distribution in the nucleon through measurement of various inclusive and semi-inclusive polarized deep inelastic electron- or muon-proton reactions. It is shown, that using combinations of inclusive data and semi-inclusive data containing neutral pions in the final state, it is possible to extract the strange-sea quark spin distribution. Similar result can be obtained for charged pions and some other hadrons also.
Recent measurements of inclusive deep inelastic scattering differential cross-section in the range 1.5 \gev2\le Q^2\le 30000 \gev2 and 5\cdot 10^{-6}\le x\le 0.65 are presented. Phenomenological analyses performed from these measurements are also described.
The non-valence spin-flavor structure of the nucleon extracted from semi-inclusive measurements of polarized deep inelastic scattering depends strongly on the transverse momentum of the detected hadrons which are used to determine the individual polarized sea distributions. This physics may explain the recent HERMES observation of a positively polarized strange sea through semi-inclusive scattering, in contrast to the negative strange sea polarization deduced from inclusive polarized deep inelastic scattering.
Within the framework of perturbative Quantum Chromodynamics we derive transverse momentum dependent distributions describing both current and target fragmentation in semi-inclusive Deep Inelastic Scattering. We present, to leading logarithmic accuracy, the corresponding crosssections describing final state hadrons on the whole phase space. Phenomenological implications and further developments are briefly discussed.
Cut vertices, a generalization of matrix elements of local operators, are revisited, and an expansion in terms of minimally subtracted cut vertices is formulated. An extension of the formalism to deal with semi-inclusive deep inelastic processes in the target fragmentation region is explicitly constructed. The problem of factorization is discussed in detail.
Within a perturbative approach to Quantum Chromodynamics (QCD), we show how to extend ordinary DGLAP longitudinal evolution equations to include the radiative transverse momentum generated in the collinear branching regime. Considering Semi-inclusive Deep Inelastic Scattering as a reference process, we perform such a generalization both in the current and in the target fragmentation region. These distributions are then used to predict semi-inclusive Deep Inelastic Scattering cross-sections onto the whole phase space of the detected hadron.
We present a method for extraction of detailed information on polarized quark densities from semi-inclusive deep inelastic scattering l+N -> l+h+X, in both LO and NLO QCD without any assumptions about fragmentation functions and polarized sea densities. The only symmetries utilised are charge conjugation and isotopic spin invariance of strong interactions.
The Sivers function is extracted from HERMES data on single spin asymmetries in semi-inclusive deeply inelastic scattering. The result is used for making predictions for the Sivers effect in the Drell-Yan process.
We explore the effects of the resummation of large logarithmic perturbative corrections to double-longitudinal spin asymmetries for inclusive and semi-inclusive deep inelastic scattering in fixed-target experiments. We find that the asymmetries are overall rather robust with respect to the inclusion of the resummed higher-order terms. Significant effects are observed at fairly high values of x, where resummation tends to decrease the spin asymmetries. This effect turns out to be more pronounced for semi-inclusive scattering. We also investigate the potential impact of resummation on the extrac…
The measurements of inclusive charm and beauty cross sections in deep-inelastic scattering $ep$ collisions at HERA are compared with the predictions of perturbative quantum chromodynamics from the CTEQ and MRST fitting groups, employing a range of theoretical schemes. The differences in the theoretical predictions are discussed and the theoretical uncertainties investigated.
New polarized fragmentation functions are introduced and justified, in addition to those conventional ones assumed to be independent of the helicity of the parent parton. It is demonstrated that due to our present ignorance concerning these new parton-spin dependent leading-twist fragmentation functions, it is impossible to utilize current experiments on spin-dependent semi-inclusive deep inelastic lepton nucleon scattering to disentangle the separate polarized parton distributions.
Miraculously, target mass corrections for inclusive deep inelastic scattering can be calculated exactly. On the contrary, there does not exist a consistent derivation of kinematic hadron mass corrections for semi-inclusive deep inelastic scattering (SIDIS). Recently this has become of topical interest, since there is a significant difference between the measured HERMES and COMPASS pion and kaon multiplicities, which cannot be explained as a consequence of evolution in $Q^2$, and it has been suggested that the difference can be understood if kinematic hadron mass corrections are taken into acco…
The contribution of lepton and photon pair production in ep-scattering to the cross section of semi-inclusive deep inelastic scattering ep-> e'p'X has been calculated. The numerical results showed a large contribution of this processes at $ϕ_h=180^o$, in a good agreement with preliminary experimental data.
The semi-inclusive deep inelastic scattering (SIDIS) process is considered. A theoretical procedure is proposed allowing the direct extraction from the SIDIS data of the first moments of the polarized valence distributions and of the first moment difference of the light sea quark polarized distributions in the next to leading QCD order. The validity of the procedure is confirmed by the respective simulations.
Following recent progresses in the understanding of high-energy scattering in QCD, we derive the first phenomenological consequences of Pomeron loops, in the context of both inclusive and diffractive deep inelastic scattering. In particular, we discuss diffusive scaling, a new scaling law that emerges for sufficiently high energies and up to very large values of $Q^2,$ well above the proton saturation momentum.
In this paper, we discuss the new hard pole contribution to the $P_{h\perp}$-weighted single-transverse spin asymmetry in semi-inclusive deep inelastic scattering. We perform the complete next-to-leading order calculation of the $P_{h\perp}$-weighted cross section and show that the new hard pole contribution is required in order to obtain the complete evolution equation for the Qiu-Sterman function derived by different approaches.
We demonstrate a factorization formula for semi-inclusive deep-inelastic scattering with hadrons in the current fragmentation region detected at low transverse momentum. To facilitate the factorization, we introduce the transverse-momentum dependent parton distributions and fragmentation functions with gauge links slightly off the light-cone, and with soft-gluon radiations subtracted. We verify the factorization to one-loop order in perturbative quantum chromodynamics and argue that it is valid to all orders in perturbation theory.
In the context of both inclusive and diffractive deep inelastic scattering, we derive the first phenomenological consequences of the inclusion of Pomeron loops in the QCD evolution equations towards high energy. We discuss the transition between the well-known geometric scaling regime and the new diffusive scaling, that emerges for sufficiently high energies and up to very large values of Q^2, well above the proton saturation momentum.
We study the beam single spin asymmetry in semi-inclusive hadron production in deep inelastic scattering in at order 1/Q. There are two competing contributions: the leading order transverse momentum dependent parton distribution $h_1^\perp(x,k_\perp)$ convoluted with chiral-odd fragmentation function $\hat e(z)$, and the chiral-odd distribution function $e(x)$ convoluted with Collins fragmentation function $H_1^\perp(z,k'_\perp)$. We estimate this asymmetry and compare with the experimental measurements from CLAS and HERMES collaborations.
We discuss resummation of large logarithmic terms that appear in the cross-section of semi-inclusive DIS in the case when the final-state hadron follows the direction of the incoming electroweak vector boson in the c.m. frame of the vector boson and the initial-state proton.
A study of inclusive production of single hadrons with finite transverse momentum in neutral current deep-inelastic scattering has been carried out. Cross sections have been calculated using perturbative Quantum Chromodynamics at next-to-leading order and compared to HERA data. Predictions for light charged hadron production data were also calculated for large values of Q^2 to show the possible effects of the Z-boson exchange.
The Sivers function is extracted from HERMES data on single spin asymmetries in semi-inclusive deeply inelastic scattering. Our analysis use a simple Gaussian model for the distribution of transverse parton momenta, together with the flavor dependence given by the leading 1/Nc approximation and a neglect of the Sivers antiquark distribution. We find that within the errors of the data these approximations are sufficient.
In the current region of semi-inclusive deep-inelastic scattering, most events are accompanied by intensive radiation of soft and collinear partons which cannot be reliably described at any fixed order of perturbative QCD. In this paper, a resummation formalism that describes such multiple parton radiation is compared to the HERA data on semi-inclusive DIS, including the distributions of energy flow and charged particle multiplicity. We show that the resummation of multiple parton radiation improves the agreement between the theory and the data. We make some suggestions on further experimental…
We calculate, in a model, the beam spin asymmetry in semi-inclusive jet production in deep inelastic scattering. This twist-3, $T$-odd observable is non-zero due to final state strong interactions. With reasonable choices for the parameters, one finds an asymmetry of several percent, about the size seen experimentally. We present the result both as an explicit asymmetry calculation and as a model calculation of the new transverse-momentum dependent distribution function $g^\perp$.
We analyse the role of partonic transverse motion in unpolarized Semi-Inclusive Deep Inelastic Scattering (SIDIS) processes. Imposing appropriate kinematical conditions, we find some constraints which fix an upper limit to the range of allowed kt values and lead to interesting results, particularly for some observables like the <cos phi_h> azimuthal modulation of the unpolarized SIDIS cross section and the average transverse momentum of the final, detected hadron.
We study the cross section for one-particle inclusive deep inelastic scattering off the nucleon for low transverse momentum of the detected hadron. We decompose the cross section in terms of structure functions and calculate them at tree level in terms of transverse-momentum-dependent parton distribution and fragmentation functions. Our results are complete in the one-photon exchange approximation at leading and first subleading twist accuracy, with both beam and target polarization.
We shortly review the various methods suggested for determining the transversity function. Among such methods, we consider especially those based on semi-inclusive deep inelastic scattering. In the framework of this kind of reactions, we propose to measure a double spin asymmetry, using a transversely polarized proton target and a longitudinally polarized lepton beam, and fixing the direction of the final pion. Under particular conditions, the asymmetry is sensitive to the transversity function.
We study the transverse-momentum distribution of hadrons produced in semi-inclusive deep-inelastic scattering. We consider cross sections for various combinations of the polarizations of the initial lepton and nucleon or the produced hadron, for which we perform the resummation of large double-logarithmic perturbative corrections arising at small transverse momentum. We present phenomenological results for the process $ep\to eπX$ for the typical kinematics in the COMPASS experiment. We discuss the impact of the perturbative resummation and of estimated non-perturbative contributions on the cor…
We present results for leading-twist azimuthal asymmetries in semi-inclusive lepton-nucleon deep-inelastic scattering due to naively time-reversal odd transverse-momentum dependent parton distribution functions from the light-cone constituent quark model. We carefully discuss the range of applicability of the model, especially with regard to positivity constraints and evolution effects. We find good agreement with available experimental data from COMPASS and HERMES, and present predictions to be tested in forthcoming experiments at Jefferson Lab.
We consider semi-inclusive deep inelastic scattering (SIDIS) and Drell-Yan events within transverse momentum dependent (TMD) factorization. Based on the simultaneous fit of multiple data points, we extract the unpolarized TMD distributions and the non-perturbative evolution kernel. The high quality of the fit confirms a complete universality of TMD non-perturbative distributions. The extraction is supplemented by phenomenological analyses of various parts of the TMD factorization, such as sensitivity to non-perturbative parameterizations, perturbative orders, collinear distributions, correlati…
We present a first attempt at a global fit of unpolarized quark transverse momentum dependent distribution and fragmentation functions from available data on semi-inclusive deep-inelastic scattering, Drell-Yan and $Z$ boson production processes. This analysis is performed in the low transverse momentum region, at leading order in perturbative QCD and with the inclusion of energy scale evolution effects at the next-to-leading logarithmic accuracy.
We calculate and analize the ${\cal{O}}(α_s)$ one-particle inclusive cross section in polarized deep inelastic lepton-hadron scattering, using dimensional regularization and the HVBM prescription for $γ_5$. We discuss the factorization of all the collinear singularities related to the process, particularly those which are absorbed in the redefinition of the spin dependent analogue of the recently introduced fracture functions. This is done in the usual $\overline{MS}$ scheme and in another one, called $\overline{MS_p}$, which factorizes soft contributions and guarantees the axial current (non)…
We study several azimuthal asymmetries in semi-inclusive deep inelastic scattering and in Drell-Yan, interpreting them in the framework of the formalism of the quark correlator, with a particular reference to T-odd functions. The correlator contains an undetermined energy scale, which we fix on the basis of a simple and rather general argument. We find a different value than the one assumed in previous treatments of T-odd functions. This implies different predictions on the Q^2 dependence of the above mentioned asymmetries. Our result about the azimuthal asymmetry of unpolarized Drell-Yan agre…
We present the calculation for single-inclusive jet production in (longitudinally) polarized deep-inelastic lepton-nucleon scattering at next-to-next-to leading order (NNLO) accuracy, based on the Projection-to-Born method. As a necessary ingredient to achieve the NNLO results, we also introduce the next-to-leading-order (NLO) calculation for the production of di-jets in polarized DIS. Our di-jet calculation is based on an extension of the dipole subtraction method to account for polarized initial-state partons. We analyze the phenomenological consequences of higher order QCD corrections for t…
We derive a general framework for describing semi-inclusive deep-inelastic lepton-nucleon scattering in terms of the unintegrated parton distributions and other higher twist parton correlations. Such a framework provides a consistent approach to the calculation of inclusive and semi-inclusive cross sections including higher twist effects. As an example, we calculate the azimuthal asymmetries to the order of 1/Q in semi-inclusive process with transversely polarized target. A non-vanishing single-spin asymmetry in the ``triggered inclusive process'' is predicted to be 1/Q suppressed with a part …
We investigate one-particle semi-inclusive processes in lepton-hadron scattering. In unpolarized scattering order $Q^{-1}$ corrections appear only when transverse momenta are detected. We consider the twist two and three matrix elements and calculate the semi-inclusive structure functions in terms of quark correlation functions. We find that at twist three level not only the standard quark distribution and fragmentation function contribute, but also two new transverse "profile functions". We demonstrate explicit gauge invariance of the hadronic tensor at the twist three level. The results of o…
We present an extraction of unpolarized partonic transverse momentum distributions (TMDs) from a simultaneous fit of available data measured in semi-inclusive deep-inelastic scattering, Drell-Yan and Z-boson production. To connect data at different scales, we use TMD evolution at next-to-leading logarithmic accuracy. The analysis is restricted to the low-transverse-momentum region, with no matching to fixed-order calculations at high transverse momentum. We introduce specific choices to deal with TMD evolution at low scales, of the order of 1 GeV$^2$. This could be considered as a first attemp…
A natural consequence of the composite operator propagator-vertex description of deep inelastic scattering developed by the authors is that the anomalous suppression observed in the flavour singlet contribution to the first moment of the polarised proton structure function $g_1^p$ (the `proton spin' problem) is not a special property of the proton structure but is a target independent effect which can be related to an anomalous suppression in the QCD topological susceptibility. In this paper, it is shown how this target independent mechanism can be tested in semi-inclusive deep inelastic scatt…
We consider the leading and sub-leading twist $T$-odd and even contributions to the $\cos 2ϕ$ azimuthal asymmetry in unpolarized dilepton production in Drell-Yan Scattering. We estimate the contributions' effects at $500 {\rm GeV}$, $ 50 {\rm GeV}$, and $25 {\rm GeV}$ energies in the framework of the parton model using a quark diquark-spectator model of the nucleon to approximate the soft contributions.
Analyzing recent ALICE data on inelastic pp scattering at the LHC energies we show that charged particle distributions exhibit geometrical scaling (GS). We show also that the inelastic cross-section is scaling as well and that in this case the quality of GS is better than for multiplicities. Moreover, exponent $λ$ characterizing the saturation scale is for the cross-section scaling compatible with the one found in deep inelastic ep scattering at HERA. Next, by parametrizing charged particles distributions by the Tsallis-like formula, we find a somewhat unexpected solution that still exhibits G…
We study the contribution of the twist-3 fragmentation function to the single-transverse spin asymmetry in semi-inclusive deep inelastic scattering within the framework of the collinear factorization. Making use of the Ward-Takahashi identity in QCD, we establish the formalism in the Feynman gauge to calculate the non-pole contribution of the twist-3 fragmentation function to the asymmetry and derive the complete cross-section formula in the leading order QCD perturbation theory. The obtained twist-3 hadronic tensor is shown to satisfy the electromagnetic gauge-invariance. The behavior in the …
The Collins fragmentation function is extracted from HERMES data on azimuthal single spin asymmetries in semi-inclusive deeply inelastic scattering, and BELLE data on azimuthal asymmetries in electron positron annihilations. A Gaussian model is assumed for the distribution of transverse parton momenta and predictions are used from the chiral quark-soliton model for the transversity distribution function. We find that the HERMES and BELLE data yield a consistent picture of the Collins fragmentation function which is compatible with COMPASS data and the information previously obtained from an an…
Establishing the twist-3 formalsim for the single transverse spin asymmetry, we present a complete single-spin-dependent cross section for SIDIS, $ep^\uparrow\to eπX$, associated with the twist-3 distribution for the transversely polarized nucleon. We emphasize that the consistency condition from the Ward identities for color gauge invariance is crucial to prove factorization property of the cross section.
The coefficient functions for heavy-flavour production in deeply inelastic electron-hadron scattering have been calculated previously. Analytic expressions are impossible to publish due to their length. Therefore we have tabulated them as two-dimensional arrays as is often done for the scale-dependent parton densities. Using this computer program we present event rates for charm production at HERA in bins of $x$ and $Q^2$. These rates are insensitive to variations in the factorization and renormalization scale $μ$.
We derive the twist-3 gluon fragmentation function (FF) contribution to the transversely polarized hyperon production in semi-inclusive deep inelastic scattering, $ep\to eΛ^\uparrow X$, in the leading order (LO) with respect to the QCD coupling in the framework of the collinear twist-3 factorization. Together with the known result for the contribution from the twist-3 distribution in the proton and the twist-3 quark FFs for the hyperon, this completes the LO cross section for this process. The constraint relations among the twist-3 FFs are taken into account. The formula is relevant to large-$…
We calculate the cross section for the inclusive production of B mesons in pp and ppbar collisions at next-to-leading order in the general-mass variable-flavor-number scheme and show that a suitable choice of factorization scales leads to a smooth transition to the fixed-flavor-number scheme. Our numerical results are in good agreement with data from the Tevatron and LHC experiments at small and at large transverse momenta.
The spin asymmetries in SIDIS associated with $T$-odd TMDs are presented in a light-front quark-diquark model of a proton. To incorporate the effects of the final state interaction, the light front wave functions are modified to have a phase factor which is essential to have Sivers or Boer-Mulders functions. The Sivers and Boer-Mulder asymmetries are compared with HERMES and COMPASS data.
We discuss a nonperturbative mechanism for one-spin asymmetries in inclusive hadron production. The main role in generation of this asymmetry belongs to the orbital angular momentum of quark-antiquark cloud in internal structure of constituent quarks.
As a possible source of the single transverse spin asymmetry, we study the contribution from purely gluonic correlation represented by the twist-3 ``three-gluon correlation" functions in the transversely polarized nucleon. We first define a complete set of the relevant three-gluon correlation functions, and then derive its contribution to the twist-3 single-spin-dependent cross section for the $D$-meson production in semi-inclusive deep inelastic scattering, which is relevant to determine the three-gluon correlations. Our cross-section formula differs from the corresponding result in the liter…
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 o…
Measurement of the distribution of hadronic energy in the final state in deeply inelastic electron scattering at HERA can provide a good test of our understanding of perturbative QCD. For this purpose, we consider the energy distribution function, which can be computed without needing final state parton fragmentation functions. We compute this distribution function for finite transverse momentum q_T at order alpha_s, and use the results to sum the perturbation series to obtain a result valid for both large and small values of transverse momentum.
In this paper, we compute the first set of ${\cal O}(α_s^2)$ corrections to semi-inclusive deep inelastic scattering structure functions. We start by studying the impact of the contribution of the partonic subprocesses that open at this order for the longitudinal structure function. We perform the full calculation analytically, and obtain the expression of the factorized cross section at this order. Special care is given to the study of their flavour decomposition structure. We analyze the phenomenological effect of the corrections finding that, even though expected to be small a priori, it tu…
We present a systematic calculation of the charged current semi-inclusive deeply inelastic scattering process at leading order twist-3 level in the parton model. We consider the general form of the negatively charged beam scattering off the polarized target which has spin-1. The calculations are carried out by applying the collinear expansion where multiple gluon scattering is taken into account and gauge links are obtained automatically. We first present the general form of the differential cross section in terms of the structure functions by kinematic analysis and then present the structure …
We present a strategy for the systematic extraction of a vast amount of detailed information on polarized parton densities and fragmentation functions from semi-inclusive deep inelastic scattering l+N -> l+h+X, in both LO and NLO QCD. A method is suggested for estimating the errors involved in the much simpler, and therefore much more attractive, LO analysis. The approach is based upon a novel interplay with data from inclusive DIS and from e+e- -> hX, and leads to a much simplified form of the NLO expressions. No assumptions are made about the equality of any parton densities and the only sym…
We study the single spin asymmetry (SSA) for the pion production with large transverse momentum p_T in semi-inclusive deep inelastic scattering $ep^\uparrow\to eπX$. We derive the twist-3 cross section formula for SSA, focussing on the soft-gluon-pole contributions associated with the twist-3 distribution for the nucleon and with the twist-3 fragmentation function for the pion. We present a simple estimate of the asymmetries due to each twist-3 effect from nucleon and pion, respectively, by fixing the overall strength of the relevant nonperturbative quantities by the data on the SSA A_N in $p^…
We study the single-transverse spin asymmetry in semi-inclusive hadron production in deep inelastic scattering. We derive the leading contribution to the asymmetry at moderate transverse momentum $P_{h\perp}$ of the produced hadron in terms of twist-three quark-gluon correlation functions, and compare with the approach based on the factorization at fixed transverse momentum involving the asymmetric transverse-momentum and spin-dependent quark distribution. We verify that the two approaches yield identical results in this regime. By a comparison with our earlier calculations for the single-spin…
We propose new formulas for extracting a difference of the polarized light sea-quark density, $Δ\bar d(x)-Δ\bar u(x)$, from polarized deep-inelastic semi-inclusive data. We have estimated the value of it from the present experimental data measured by SMC and HERMES groups. Although the data might suggest a violation of polarized light flavor sea-quark symmetry, the precision of the present data is not enough for confirming it.
We present a phenomenological analysis of the cos-phi and cos-2phi asymmetries in unpolarized semi-inclusive deep inelastic scattering, based on the recent multidimensional data released by the COMPASS and HERMES Collaborations. In the TMD framework, valid at relatively low transverse momenta, these asymmetries arise from intrinsic transverse momentum and transverse spin effects, and from their correlations. The role of the Cahn and Boer-Mulders effects in both azimuthal moments is explored up to order 1/Q. As the kinematics of the present experiments is dominated by the low-Q^2 region, higher…
