We propose a factorized approach to QED radiative corrections for inclusive and semi-inclusive deep-inelastic scattering to systematically account for QED and QCD radiation contributions to both processes on equal footing. This is achieved by utilizing factorization to resum logarithmically enhanced QED radiation into universal lepton distribution and fragmentation (or jet) functions. Numerical simulations suggest that the QED effects induced by the rotational distortion of the hadron transverse momentum, arising from the mismatch between the experimental Breit frame and the true photon-hadron frame, can be as large as 50\% for moderate $Q$, and become increasingly important for large transverse momenta. Our framework provides a uniform treatment of radiative effects for extracting three-dimensional hadron structure from high-energy lepton-hadron scattering at current and future facilities, such as the Electron-Ion Collider.
QED radiative effects in semi-inclusive deep-inelastic scattering: traditional and factorized approaches
Duke University（杜克大学）；Triangle Universities Nuclear Laboratory（三角大学核实验室）；Institute for Nuclear Problems of Belorussian State University（白俄罗斯国立大学核问题研究所）；Mississippi State University（密西西比州立大学）；Indiana University（印第安纳大学）；Shandong University（山东大学）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；Jefferson Lab（杰斐逊实验室）
We present the details of a new factorized approach to semi-inclusive deep-inelastic scattering which treats QED and QCD radiation on equal footing, and provides a systematically improvable approximation to the extraction of transverse momentum dependent parton distributions. We demonstrate how the QED contributions can be well approximated by collinear factorization, and illustrate the application of the factorized approach to QED radiation in inclusive scattering. For semi-inclusive processes, we show how radiation effects prevent a well-defined "photon-nucleon" frame, forcing one to use a t…
We apply the soft-collinear effective theory (SCET) to deep inelastic scattering near the endpoint region. The forward scattering amplitude, and the structure functions are shown to factorize as a convolution of the Wilson coefficients, the jet functions, the parton distribution functions. The behavior of the parton distribution functions near the endpoint region is considered. It turns out that it evolves with the Altarelli-Parisi kernel even in the endpoint region, and the parton distribution function can be factorized further into a collinear part and the soft Wilson line. The factorized fo…
We propose the lepton-jet correlation in deep inelastic scattering as a unique tool for nucleon/nucleus tomography at the electron-ion collider. The azimuthal angular correlation between the final state lepton and jet depends on the transverse momentum dependent quark distributions. We take the example of single transverse spin asymmetries to show the sensitivity to the quark Sivers function. When the correlation is studied in lepton-nucleus collisions, transverse momentum broadening effects can be used to explore cold nuclear matter effects. These features make lepton-jet correlations an impo…
Predictions for semi-inclusive deep inelastic lepton-nucleus scattering are presented. Both the effects of gluon radiation by the struck quark and the absorption of the produced hadron are considered. The gluon radiation covers a larger window in virtuality $Q^2$ because of the increased deconfinement of quarks inside nuclei. The absorption of hadrons formed inside the nucleus is described with a flavor dependent cross section. Calculations for rescaled fragmentation functions and nuclear absorption are compared with the EMC and HERMES data for N, Cu and Kr targets with respect to the deuteron…
We study the lepton-jet correlation in deep inelastic scattering. We perform one-loop calculations for the spin averaged and transverse spin dependent differential cross sections depending on the total transverse momentum of the final state lepton and the jet. The transverse momentum dependent (TMD) factorization formalism is applied to describe the relevant observables. To show the physics reach of this process, we perform a phenomenological study for HERA kinematics and comment on an ongoing analysis of experimental data. In addition, we highlight the potential of this process to constrain s…
We study charged lepton flavor violation (CLFV) associated with heavy quark pair production in lepton-nucleon deep-inelastic scattering $\ell_i N \to \ell_j q\bar{q} X$. Here $\ell_i$ and $\ell_j$ denote the initial and final leptons; $N$ and $X$ are respectively the initial nucleon and arbitrary final hadronic system. We employ a model Lagrangian in which a scalar and pseudoscalar mediator generates the CLFV. We derive heavy quark structure functions for scalar and pseudoscalar currents and compute momentum distributions of the final lepton for the process. Our focus is on the heavy quark mas…
We have made a thorough investigation of the nuclear structure function W_2A in the region of 0.8 < x < 1.5 and Q^2 < 20 GeV^2, separating the quasielastic and inelastic plus deep inelastic contributions. The agreement with present experimental data is good giving support to the results for both channels. Predictions are made in yet unexplored regions of x and Q^2 to assert the weight of the quasielastic or inelastic channels. We find that at Q^2 < 4 GeV^2 the structure function is dominated by the quasielastic contributions for x < 1.5, while for values of Q^2 > 15 GeV^2 and the range of x st…
We consider the spin polarization of leptons produced in neutrino and antineutrino nucleon deep inelastic scattering, via charged currents, and we study the positivity constraints on the spin components in a model independent way. These results are very important, in particular in the case of $τ^{\pm}$ leptons, because the polarization information is crucial in all future neutrino oscillation experiments.
This review outlines our present experimental knowledge and theoretical understanding of deep-inelastic scattering on nuclear targets. The emphasis is primarily on nuclear coherence phenomena, such as shadowing, where the key physics issue is the exploration of hadronic and quark-gluon fluctuations of a high-energy virtual photon and their passage through the nuclear medium. New developments in polarized deep-inelastic scattering on nuclei are also discussed, and more conventional binding and Fermi motion effects are summarized. The report closes with a brief outlook on vector meson electropro…
Based on the requirement in the simulation of lepton-nucleus deep inelastic scattering (DIS), we construct a fortran program LDCS 1.0 calculating the differential and total cross sections for the unpolarized charged lepton-unpolarized nucleon and neutrino-unpolarized nucleon neutral current (charged current) DIS at leading order. Any set of the experimentally fitted parton distribution functions could be employed directly. The mass of incident and scattered leptons is taken into account and the boundary conditions calculating the single differential and total cross section are studied. The cal…
Semi-inclusive deep inelastic lepton scattering off few-nucleon systems is investigated assuming that virtual boson absorption occurs on a hadronic cluster which can be either a two-nucleon correlated pair or a six-quark bag. In both cases the relevance of nuclear effects on forward and backward nucleon emissions is illustrated and the differences expected in the energy distribution of the emitted nucleons are analyzed both at x>1 and x<1.
The $O(α)$ leptonic QED corrections to neutral current polarized deep inelastic lepton-nucleon scattering are calculated in leptonic variables both for the case of longitudinal and transverse nucleon polarization. The results of the complete calculation are compared with the corresponding leading log expressions. Numerical results are presented for the corrections in the kinematic range of the HERMES experiment and possible future polarized proton beam experiments at HERA.
The one-loop electroweak radiative correction of the lowest order to lepton current for deep inelastic scattering of longitudinally polarized leptons by polarized nucleons is obtained in model independent way. The detailed numerical analysis within kinematical requirements of future polarization collider experiments is performed. The possibility to reduce radiative effects by detection of hard photons is studied.
The contribution of the radiative tail from the quasielastic peak to low order radiative correction to deep inelastic scattering of polarized leptons by polarized $^3$He was calculated within the sum rules formalism and $y$-scaling hypothesis. Numerical analysis was carried out under the conditions of HERMES experiment.
We investigate hadron formation in deep inelastic lepton scattering on N, Kr and Xe nuclei in the kinematic regime of the HERMES experiment. The elementary electron-nucleon interaction is described within the event generator PYTHIA while a full coupled-channel treatment of the final state interactions is included by means of a BUU transport model. We find a good agreement with the measured charged hadron multiplicity ratio $R_M^h$ for N and Kr targets by accounting for the deceleration and absorption of the primarily produced particles as well as for the creation of secondary hadrons in the fi…
The perturbative QCD predictions concerning deep inelastic scattering at low $x$ are summarized. The theoretical framework based on the leading log $1/x$ resummation and $k_t$ factorization theorem is described. The role of studying final states in deep inelastic scattering for revealing the details of the underlying dynamics at low $x$ is emphasised and some dedicated measurements, like deep inelastic scattering accompanied by an energetic jet, the measurement of the transverse energy flow and deep inelastic diffraction, are briefly discussed.
We calculate the O(α_s) corrections to the production of a hard and isolated photon accompanied by one or two jets in deep inelastic lepton nucleon scattering at HERA. Numerical results are presented and the potential of this process for studies of parton distribution functions is discussed.
Main nuclear corrections for inelastic scattering of charged leptons on nuclei, namely shadowing, EMC-effect and Fermi motion have been investigated. Simple formulas describing these effects for different x-regions have been proposed, and unified expression for any transferred energy and momentum as well as for different nuclei has been obtained. Results of calculations of the ratio of nucleus structure function (per nucleon) and free nucleon structure function are in a good agreement with SLAC data.
We discuss the close relation between shadowing in deep-inelastic lepton-nucleus scattering and diffractive photo- and leptoproduction of hadrons from free nucleons. We show that the magnitude of nuclear shadowing at small Bjorken-x, as measured by the E665 and NMC collaborations, is directly related to HERA data on the amount of diffraction in the scattering from free nucleons.
In this paper we extend the calculation of the QED corrections to deep inelastic lepton-proton scattering with a tagged photon, taking into account the full corrections on the lepton side. Comparing to previous results that were obtained by considering only large logarithmic terms at leading and next-to-leading accuray, we find that the difference is in general quite small, however, it may be significant in the region of large $y$ and small $x$.
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.
We calculate the polarization of Lambda and Anti-Lambda particles produced in deep inelastic polarized lepton scattering. We use two models: the naive quark model and a model in which SU(3)$_F$ symmetry is used to deduce the spin structure of SU(3) octet hyperons from that of the proton. We perform the calculations for Lambda and Anti-Lambda produced directly or as decay products of $Σ^0$ and $Σ^*$.
We calculate shadowing in the process of deep inelastic interactions of leptons with nuclei in the perturbative regime of QCD. We find appreciable shadowing for heavy nuclei (e.g. Pb) in the region of small Bjorken scaling variable $10^{-5}\leq x \leq 10^{-3}$. This shadowing depends weakly on $Q^2$, but it may be strongly influenced, especially at $x \geq 10^{-3}$, by the existence of real parts of the forward scattering amplitudes.
We perform a χ^2-analysis of Nuclear Parton Distribution Functions (NPDFs) using neutral current charged-lepton Deeply Inelastic Scattering (DIS) and Drell-Yan data for several nuclear targets. The nuclear A dependence of the NPDFs is extracted in a next-to-leading order fit. We compare the nuclear corrections factors F2(Fe)/F2(D) for this charged-lepton data with other results from the literature. In particular, we compare and contrast fits based upon the charged-lepton DIS data with those using neutrino-nucleon DIS data.
It is shown that in semi-inclusive deep inelastic scattering (DIS) of electrons off a complex nucleus A, the detection, in coincidence with the scattered electron, of a nucleus (A-1) in the ground state, as well as of a nucleon and a nucleus (A-2), also in the ground state, may provide unique information on several long standing problems, such as : i) the nature and the relevance of the final state interaction in DIS; ii) validity of the spectator mechanism in DIS; iii) the medium induced modifications of the nucleon structure function; iv) the origin of the EMC effect.
The flavor and helicity distributions of the $Λ$ and $\barΛ$ hyperons for both valence and sea quarks are calculated in a perturbative QCD (pQCD) based model. We relate these quark distributions to the fragmentation functions of the $Λ$ and $\barΛ$, and calculate the $z$-dependence of the longitudinal spin transfer to the $Λ$ and $\barΛ$ in lepton deep-inelastic scattering (DIS). It is shown that the spin transfer to the $Λ$ is compatible with the first HERMES results at DESY and further tests are suggested. We also make predictions for the $z$-dependence of the $Λ$ and $\barΛ$ longitudinal po…
We extend the calculations of the spin alignments of vector mesons in $e^+e^-$ annihilation in a recent Rapid Communication to deeply inelastic lepton-nucleon scatterings. We present the results for different mesons in the current fragmentation regions of $μ^- N$$ \to$$ μ^- VX$ at high energies and $ν_μN $$\to$$ μ^- VX$ at both high and low energies. We also present the predictions for $ν_μN$$ \to$$ μ^- VX$ at NOMAD energies in the target fragmentation region using a valence quark model.
We present a compact form of the leptonic currents for the computation of the processes involving an initial virtual boson (photon, $W^{\pm}$ or $Z_0$). For deeply inelastic scattering, once the azimuthal angle of the plane expanded by the initial- and final-state leptons are integrated over in the boson-proton rest frame, the azimuthal-asymmetric terms vanish, which, however, is NOT true when some physical quantities (such as the transverse momentum of the observed particle) are specified in laboratory frame. The abuse of the symmetry may lead to wrong results.
It is shown that new data from the HERMES collaboration, as well as all of the earlier improved data from experiments concerning the EMC effect and shadowing in deep-inelastic scattering of leptons from nuclei, provide strong evidence for an explicit dynamical role played by exchanged quarks and nuclear gluons in the basic, tightly-bound systems of three and four nucleons, He3 and He4. This opens the way for specific quark-gluon dynamics instigating multinucleon correlations in nuclei.
The off-shell behaviors of bound nucleons in deep inelastic lepton nucleus scattering are discussed in two scenarios with the basic constituents chosen to be baryon-mesons and quark-gluons respectively in light-cone formalism. It is found that when taking into account the effect due to internal quark structure of nucleons, the derived scaling variable for bound nucleons and the calculated nuclear structure functions are different from those in considering the baryon-mesons as the effective elementary constituents. This implies that the pure baryon-meson descriptions of nuclei give the inaccura…
The deep inelastic scattering cross section in the endpoint region, $x \sim 1$, has been subjected to extensive analysis. We revisit this process, and show that in the endpoint individual factors in the factorized hadronic tensor have rapidity divergences. We regulate these divergences using a recently introduced rapidity regulator, and find that each factor requires a different scale to minimize large rapidity logarithms. Interestingly, in this case running in rapidity is non-perturbative. In addition, we give an operator definition of the parton distribution function in the endpoint region, …
The processes of lepton-nucleon scattering, including ones with both polarized beams, at high energy provide relevant information about interaction and particles structure, allowing to analyze nucleon spin structure. As energy and experimental accuracy rise, necessity to improve Born cross sections and polarized asymmetries with higher order radiative corrections becomes substantial. In this report we stress on lowest order bremsstrahlung corrections treatment using helicity amplitudes method as applied to actual nowadays charged current lepton-nucleon deep inelastic processes, that allows to …
We present a detailed description of high-energy neutrino and antineutrino inelastic inclusive scattering off nuclei in terms of nuclear structure functions. In our approach we take into account a QCD description of the nucleon structure functions as well as a number of basic nuclear effects including nuclear shadowing, Fermi motion and binding, nuclear pion excess and off-shell correction to bound nucleon structure functions. These effects prove to be important in the studies of charged-lepton deep-inelastic scattering. We discuss similarities and dissimilarities in the calculation of nuclear…
Physics and programming aspects are discussed for a Fortran 77 Monte Carlo program to simulate complete events in deep inelastic lepton-nucleon scattering. The parton level interaction is based on the standard model electroweak cross sections, which are fully implemented in leading order for any lepton of arbitrary polarization, and different parametrizations of parton density functions can be used. First order QCD matrix elements for gluon radiation and boson-gluon fusion are implemented and higher order QCD radiation is treated using parton showers. Hadronization is performed using the Lund …
In inclusive deep-inelastic lepton-hadron scattering multi-photon exchange between the leptonic and the hadronic part of the process causes single spin asymmetries. The asymmetries exist for a polarized target as well as a polarized incoming or outgoing lepton, if the polarization vector has a component transverse with respect to the reaction plane. The spin dependent parts of the single polarized cross sections are suppressed like $α_{em} m_{pol}/Q$ - where $m_{pol}$ denotes the mass of the polarized particle - compared to the leading terms of the cross section for unpolarized or double-polar…
Deep inelastic scattering of leptons off nuclear targets is analized within the convolution model taking into account nucleon-nucleon correlations. We show that in the nuclear medium nucleons are distributed according to a function that exhibits a sizeable Q**2-dependence and reduces to the ordinary light-cone distribution in the Bjorken limit. At Q**2 < 50 (GeV/c)**2 and x > 1 this Q**2-dependence turns out to be stronger than the one associated with the nucleon structure function, predicted by pertubative quantum chromodynamics.
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 …
Inclusive e^\pm p single and double differential cross sections for neutral (NC) and charged current (CC) deep inelastic scattering processes are measured with the H1 detector at HERA. The data were taken at a centre-of-mass energy of \sqrt{s} = 319 GeV with a total integrated luminosity of 327.8 pb^{-1} shared between two lepton beam charges and two longitudinal lepton polarisation modes. The differential cross sections are measured in the range of negative four-momentum transfer squared, Q2, between 60 and 50 000 GeV2, and Bjorken x between 0.0008 and 0.65. The measurements are combined with…
We calculate the polarizations for different octet hyperons produced in the current fragmentation regions of the deeply inelastic lepton-nucleon scatterings $μ^-N \to μ^- HX$ and $ν_μ N \to μ^- HX$ at high energy using different models for spin transfer in fragmentation processes. The results show that measurements of those hyperon polarizations should provide useful information to distinguish between different models in particular the SU(6) and the DIS pictures used frequently in the literature. We found, in particular, that measuring the polarization of $Σ^+$ produced in these processes can …
The composite model is constructed to describe inelastic high-energy scattering of muons and taus in standard rock. It involves photonuclear interactions at low $Q^2$ as well as moderate $Q^2$ processes and the deep inelastic scattering (DIS). In the DIS region the neutral current contribution is taken into consideration. Approximation formulas both for the muons and tau energy loss in standard rock are presented for wide energy range.
We study the perturbative QCD corrections to 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 dist…
A leading order QCD analysis of spin asymmetries in polarized deep inelastic lepton nucleon scattering is presented within the framework of the radiative parton model. Two resulting sets of plausible leading order spin dependent parton distributions are presented, respecting the fundamental positivity constraints down to the low resolution scale $Q^2=μ_{LO}^2=0.23$ GeV$^2$. The $Q^2$ dependence of the spin asymmetries $A_1^{p,n,d}(x,Q^2)$ is investigated in the range $1 \leq Q^2 \leq 20$ GeV$^2$ and shown to be non-negligible for $x$-values relevant for the analysis of present data and possibl…
The three well-known forms of relativistic dynamics are unitarily equivalent and the problem of constructing the current operators can be solved in any form. However the notion of the impulse approximation is reasonable only in the point form. In particular, the parton model which is the consequence of the impulse approximation in the front form is incompatible with Lorentz invariance, P invariance and T invariance. The results for deep inelastic scattering based on the impulse approximation in the point form give natural qualitative explanation of the fact that the values given by the parton …
We discuss nuclear effects on neutrino-nuclear interactions in a wide kinematical range from shallow to deep inelastic scattering (DIS) region. There is necessity from neutrino communities to have precise neutrino-nucleus cross sections for future measurements on neutrino oscillations and leptonic CP violation. We try to create a model to calculate neutrino cross sections in the wide kinematical range, from quasi-elastic scattering and resonance productions to the DIS. In this article, nuclear modifications of structure functions are mainly discussed, and a possible extension to the $Q^2 \to 0…
The results for one-loop correction to deep inelastic scattering of longitudinal polarized leptons on longitudinal polarized hadrons are obtained withing the framework of the standard theory of electroweak interactions and ordinary quark-parton model. The on-shell renormalization scheme in t'Hooft-Feynman gauge is applied. The numerical analysis is carried out under conditions of modern particle physics experiments.Particular emphasis is laid on contributions usually ignored at RC procedure --- electroweak corrections to electromagnetic asymmetry and RC to hadronic current. The structure of RC…
Hadron production in lepton-nucleus deep inelastic scattering is studied in a quark energy loss model. The leading-order computations for hadron multiplicity ratios are presented and compared with the selected HERMES pions production data with the quark hadronization occurring outside the nucleus by means of the hadron formation time. It is found that the obtained energy loss per unit length is $0.440 \pm 0.013$ GeV/fm for an outgoing quark by the global fit. It is confirmed that the atomic mass number dependence of hadron attenuation is theoretically and experimentally in good agreement with …
We present the basic aspects of deep inelastic phenomena in the framework of the QCD parton model. After recalling briefly the standard kinematics, we discuss the physical interpretation of unpolarized and polarized structure functions in terms of parton distributions together with several important sum rules. We also make a rapid survey of the experimental situation together with phenomenological tests, in particular concerning various QCD predictions. In the summary, we try to identify some significant open questions, to clarify where we stand and to see what we expect to learn in the future…
Hadron production in lepton-nucleus deep inelastic scattering is studied in a model including quark energy loss and nuclear absorption. The leading-order computations for hadron multiplicity ratios are presented and compared with the selected HERMES experimental data with the quark hadronization occurring inside the nucleus by means of the hadron formation time. It is shown that with increase of the energy fraction carried by the hadron, the nuclear suppression on hadron multiplicity ratio from nuclear absorption gets bigger. It is found that when hadronization occurs inside the nucleus, the n…
It is proposed, that ``the colorless objects'' which manifest themselves in large-rapidity-gap events are color-singlet gluon-clusters due to self-organized criticality (SOC), and that optical-geometrical concepts and methods are useful in examing the space-time properties of such objects. A simple analytical expression for the $t$-dependence of the inelastic single diffractive cross section $dσ/dt$ ($t$ is the four-momentum transfer squared) is derived. Comparison with the existing data and predictions for future experiments are presented. The main differences and similarities between the SOC…
A review is given of the QCD corrections to charm quark production in deep inelastic electron-proton scattering. An outline of the computation of the virtual photon-parton subprocesses, from which one obtains the heavy quark coefficient functions, is given. The dominant production mechanisms are discussed. Further we show that the asymptotic heavy quark coefficient functions, computed in the limit Q^2 >> m^2, can be derived using the operator product expansion technique. Further we present the various schemes proposed in the literature to describe the charm component of the structure function …
It is suggested to determine the $A$ dependence of distortions of the nucleon structure function $F_2(x)$ by summing the distortions over an interval ($x_1, x_2$). It was found from the analysis of data on deep--inelastic scattering of muons and electrons from nuclei that the $A$ dependence of distortion magnitudes obtained in each of three regions under study, namely shadowing, antishadowing and the EMC effect region, follow the same functional form, being different in the normalizing factor only. All the available data give evidence for the saturation of the distortion magnitude with rising …
We study roles of quark-quark correlations in the baryons for the deep inelastic structure function and the $ΔI=1/2$ rule of the non-leptonic weak hyperon decay. The quark-quark correlation is incorporated phenomenologically as diquarks within the Nambu and Jona-Lasinio model. The strong diquark correlations in the spin-0 channel enhance the $ΔI=1/2$ weak matrix elements, and account for the $ΔI=1/2$ rule. The ratio of the nucleon structure functions $F_2^{n}(x)/F_2^{p}(x)$ also comes to agree with experiment due to the diquark correlations.
