Nuclear effects in deep inelastic scattering and transition region
S. Kumano
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8 pages, LaTeX, 2 style files, 6 eps files, JPS Conference Proceedings in press, International workshop on Neutrino-Nucleus Interactions in the Few-GeV Region (NuInt15), Osaka, Japan, November 16-21, 2015
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 $Q^2 \to 0$ region is explained. We also comment on the transition region between baryon resonances and the DIS. There are ongoing experimental efforts on nuclear modifications of structure functions or parton distribution functions such as by pA reactions at RHIC and LHC, Drell-Yan measurements at Fermilab, Miner$ν$a neutrino DIS, and charged-lepton DIS at JLab.
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…
We use several diverse parameterizations of diffractive parton distributions, extracted in leading twist QCD analyses of the HERA diffractive deep inelastic scattering (DIS) data, to make predictions for leading twist nuclear shadowing of nuclear quark and gluon distributions in DIS on nuclei. We find that the HERA diffractive data are sufficiently precise to allow us to predict large nuclear shadowing for gluons and quarks, unambiguously. We performed detailed studies of nuclear shadowing for up and charm sea quarks and gluons within several scenarios of shadowing and diffractive slopes, as w…
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…
Highly inelastic electron scattering is analyzed within the context of the unified relativistic approach previously considered in the case of quasielastic kinematics. Inelastic relativistic Fermi gas modeling that includes the complete inelastic spectrum - resonant, non-resonant and Deep Inelastic Scattering - is elaborated and compared with experimental data. A phenomenological extension of the model based on direct fits to data is also introduced. Within both models, cross sections and response functions are evaluated and binding energy effects are analyzed. Finally, an investigation of the …
Hadronization, the process by which energetic quarks evolve into hadrons, has been studied phenomenologically for decades. However, little experimental insight has been gained into the space-time features of this fundamentally non-perturbative process. New experiments at Jefferson Lab, in combination with HERMES data, will provide significant new insights into the phenomena connected with hadron formation in deep inelastic scattering, such as quark energy loss in-medium, gluon emission, and color field restoration.
A light front treatment of the nuclear wave function is developed and applied, using the mean field approximation, to infinite nuclear matter. The nuclear mesons are shown to carry about a third of the nuclear plus momentum, p+; but their momentum distribution has support only at p+ =0, and the mesons do not contribute to nuclear deep inelastic scattering. This zero mode effect occurs because the meson fields are independent of space-time position.
By considering the $x$-dependence of $π^+$, $π^-$, $K^+$, $K^-$, $Λ$, $\barΛ$, $p$, $\bar{p}$ hadron productions in charged lepton semi-inclusive deep inelastic scattering off nuclear target (using Fe as an example) and deuteron D target, % at $Q^2=5$ GeV$^2$, we find that $(\barΛ^A/Λ^A)/(\barΛ^D/Λ^D)$ and $({\bar{p}}^A/{p}^A)/({\bar{p}}^A/p^A)$ are ideal to figure out the nuclear sea content, which is predicted to be different by different models accounting for the nuclear EMC effect.
We propose simple Monte Carlo method for calculating parton distribution in nuclei. The EMC effect is automatically included by means of two parameters, which characterize the change of nuclear pion field. Good agreement with experimental data in the broad range of variable x is obtained.
We set tight constraints on the energy loss of hard quarks in nuclear matter from NA3 Drell-Yan measurements. Our estimate then allows for the description of HERMES preliminary deep inelastic scattering data on hadron production.
A light front treatment of the nuclear wave function is developed and applied, using the mean field approximation, to infinite nuclear matter. The nuclear mesons are shown to carry about a third of the nuclear plus momentum; but their momentum distribution has support only at for vanishingly small values of the plus momentum, so the mesons do not contribute to nuclear deep inelastic scattering. This zero mode effect occurs because the meson fields are independent of space-time position.
We consider the potential benefits of searching for supersymmetric dark-matter through its inelastic excitation, via the "scalar current", of low-lying collective nuclear states in a detector. If such states live long enough so that the gamma radiation from their decay can be separated from the signal due to nuclear recoil, then background can be dramatically reduced. We show how the kinematics of neutralino-nucleus scattering is modified when the nucleus is excited and derive expressions for the form factors associated with exciting collective states. We apply these results to two specific ca…
Nuclear structure functions at small x and small or moderate $Q^2$ are studied using the relation with diffraction on nucleons which arises from Gribov's Reggeon Calculus. A reasonable description of experimental data is obtained with no fitted parameters. A comparison with other models and predictions for future lepton-ion colliders are provided. Consequences for the reduction of multiplicities in nucleus-nucleus collisions at energies of RHIC and LHC are examined.
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 high-energy dependencies of diffractive and non-diffractive inelastic cross-sections in view of the recent LHC data which revealed a presence of the reflective scattering mode.
We discuss effect of nuclear shadowing in neutrino deep-inelastic scattering in terms of non perturbative parton model. We found that for small Bjorken $x$ and large $Q^2$ the structure function $F_3$ is shadowed in nuclei about two times as stronger as $F_2$. The underlying reason and phenomenological aspects of this observation are discussed.
Nuclear effect in the neutrino-nucleus charged-Current inelastic scattering process is studied by analyzing the CCFR and NuTeV data. Structure functions $F_2(x,Q^2)$ and $xF_3(x,Q^2)$ as well as differential cross sections are calculated by using CTEQ parton distribution functions and EKRS and HKN nuclear parton distribution functions, and compared with the CCFR and NuTeV data. It is found that the corrections of nuclear effect to the differential cross section for the charged-current anti-neutrino scattering on nucleus are negligible, the EMC effect exists in the neutrino structure function $…
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.
We calculate the inclusive spectra of secondaries produced in soft (minimum bias) p+Pb collisions in the framework of Quark-Gluon String Model at LHC energy, by taking into account the inelastic screening corrections (percolation effects). The role of these effects is expected to be very large at the very high energies, and they should decrease the spectra more than 2 times in the midrapidity region at sqrt(s)_(NN) = 5 TeV. The experimental data confirm such a picture, which means that the nuclear screening effects are connected with the Pomeron interaction rather than with the interactions of…
We estimate the magnitude of charge symmetry breaking effects in deep inelastic scattering from nuclei. The resulting contribution to systematic uncertainties in hadronic determinations of $sin^2θ_W$ are found to be less than the current experimental accuracy, but may be important in the analyses of more precise future experiments. We expect the largest nuclear charge symmetry breaking effects in the Paschos-Wolfenstein ratio $R^-$, where the resulting uncertainty in the determination of $sin^2 θ_W$ reaches $10^{-3}$.
We discuss shadowing corrections to the structure function $F_2$ in neutrino deep-inelastic scattering on heavy nuclear targets. In particular, we examine the role played by shadowing in the comparison of the structure functions $F_2$ measured in neutrino and muon deep inelastic scattering. The importance of shadowing corrections in the determination of the strange quark distributions is explained.
The current status of deep inelastic scattering is briefly reviewed. We discuss future theoretical developments desired and measurements needed to further complete our understanding of the picture of nucleons at short distances.
It is shown that the combination of the structure functions $F_2$ predicted by the CKMT model at low and moderate values of $Q^2$ and MRS99 parton distribution functions at high $Q^2$ gives a good description of the data over complete measured region of $x$ and $Q^2$. Using these structure functions the main characteristics of the muon-nucleus inelastic scattering are calculated. Nuclear effects and contributions of the neutral current and $γ- Z$ interference are taken into account.
Nuclear shadowing corrections to the structure functions of deep inelastic scattering of intermediate-mass nuclei are calculated at very low values of Bjorken x and small values of Q^2 (Q^2<5 GeV^2). The two-component approach (generalized VMD plus hard pomeron) is used for a description of the underlying virtual photon - nucleon interaction. The hard component of the nucleon structure function is calculated in a framework of the colour dipole model with dipole cross section having Regge-type energy dependence. Numerical results for nuclear shadowing corrections are compared with available dat…
We propose extended version of stationary string model to describe the nuclear attenuation. This model takes into account flavour content of particles and allows to include into consideration all hadrons created from string. The predictions of the model are compared with experimental results obtained by HERMES collaboration (DESY) on different nuclei (N and Kr).
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.
The proton structure function is re-deduced from the data of deep inelastic electron-proton scattering after enhanced correction that is made due to the multiple scattering effect. The Glauber approach is used to account for the multiple scattering of electron with the quark constituents of the proton. The results are compared with the prediction of the parton model. Appreciable deviation is observed only at low values of the Bjorken scaling, which correspond to the extremely deep inelastic scattering.
The leptonic QED radiative corrections are calculated in the next-to-leading log approximation ${\cal O}[α^2 \ln(Q^2/m_e^2)]$ for unpolarized deeply inelastic $ep$--scattering in the case of mixed variables. The corrections are determined using mass factorization in the OMS--scheme for the double--differential scattering cross sections.
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.
Neutrinos with energy of order 10~MeV, such as from pion decay-at-rest sources, are an invaluable tool for studying low-energy neutrino interactions with nuclei -- previously enabling the first measurement of coherent elastic neutrino-nucleus scattering. Beyond elastic scattering, neutrinos and dark matter in this energy range also excite nuclei to its low-lying nuclear states, providing an additional physics channel. Here, we consider neutral-current inelastic neutrino-nucleus and dark matter(DM)-nucleus scattering off $^{40}$Ar, $^{133}$Cs, and $^{127}$I nuclei that are relevant to a number …
We calculate the multiple scattering effect on single hadron production in semi-inclusive lepton-nucleus deeply inelastic scattering. We show that the quantum interference of multiple scattering amplitudes leads to suppression in hadron productions. At the leading power in medium length, the suppression can be approximately expressed in terms of a shift in $z$ of the fragmentation function $D(z)$, and could be therefore interpreted as the collisional energy loss. We compare our calculation with existing experimental data. We also discuss the effect of quark mass on the suppression. Our approac…
We review recent developments in the study of deep inelastic scattering from light nuclei, focusing in particular on deuterium, helium, and lithium. Understanding the nuclear effects in these systems is essential for the extraction of information on the neutron structure function.
We study the scaling properties in deep inelastic scattering using the most recent combined structure function data $F_2$ from the H1 and ZEUS collaborations. We also perform a direct fit to the $F_2$ data inspired by the scaling properties. Our analysis favours the QCD saturation mechanism from the Balitski Kovchegiv equation wuth running coupling.
We present an improved method for handling off-shell effects in deep inelastic nuclear scattering. With a firm understanding of the effects of the nuclear wave function, including these off-shell corrections as well as binding and nucleon-nucleon correlations, we can begin to examine the role of QCD in nuclei through an analysis of the moments of the nuclear structure function. Our analysis is aimed at extracting the Q^2 dependence of the moments of the nucleon structure function by using the recent high x world Iron data and by properly removing nuclear effects from the perturbative contribut…
A survey is given on the new 2- and 3-loop results for the heavy flavor contributions to deep-inelastic scattering in the unpolarized and the polarized case. We also discuss related new mathematical aspects applied in these calculations.
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 have modelled parton distribution in nuclei using a suitably modified nuclear Fermi motion. The modifications concern the nucleon rest energy which changes the Björken x in nuclear medium. We also introduce final state interactions between the scattered nucleon and the rest of the nucleus. The energy-momentum sum rule is saturated. Good agreement with experimental data of the EMC effect for $x> 0.15$ and nuclear lepton pair production data has been obtained.
Considering the high-energy limit of the QCD gluon distribution inside a nucleus, we calculate the proton-nucleus total inelastic cross section using a simplified dipole model. We show that, if gluon saturation occurs in the nuclear surface region, the total cross section of proton-nucleus collisions increases more rapidly as a function of the incident energy compared to that of a Glauber-type estimate. We discuss the implications of this with respect to recent ultra-high-energy cosmic ray experiments.
A model for shadowing in nuclear structure functions at small $x$ and small or moderate $Q^2$ is presented using the relation with diffraction that arises from Gribov's reggeon calculus. A reasonable description of the experimental data is obtained with no fitted parameters. A comparison with predictions from other models is performed.
Using a recent parametrization of nuclear effects in parton distribution functions we calculate the neutrino-nucleon cross section at energies relevant for ultra high energy neutrino telescopes. The modification of the cross section in comparison with the calculation using parton densities in free nucleons is of the order of few per cent for the parameter range of interest in neutrino telescopes (A=10 and E=10$^6$ GeV) and it reaches 20 % at the highest energies (E=10$^{12}$ GeV) and for the largest nuclear size (A=190) considered.
We consider deep inelastic scattering (DIS) on a nucleus described using a density expansion. In leading order, the scattering is dominated by the incoherent scattering on individual nucleons distributed using the Thomas-Fermi approximation. We use the holographic structure functions for DIS scattering on single nucleons to make a non-perturbative estimate of the nuclear structure function in leading order in the density. Our results are compared to the data in the large-x regime.
In the framework of the collinear factorized pQCD approach we calculate the small-$x_B$ process-dependent nuclear modification to the structure functions measured in neutrino-nucleus deeply inelastic scattering. We include both heavy quark mass corrections $(M^2/Q^2)$ and resummed nuclear-enhanced dynamical power corrections in the quantity $(ξ^2/Q^2)(A^{1/3}-1)$ with $ξ^2$ evaluated to leading order in $α_s$. Our formalism predicts a measurable difference in the shadowing pattern of the structure functions $F_2^A(x_B,Q^2)$ and $F_3^A(x_B,Q^2)$ and a significant low- and moderate-$Q^2$ modific…
We present recent results on newly calculated 2- and 3-loop contributions to the heavy quark parts of the structure functions in deep-inelastic scattering due to charm and bottom.
We study nuclear effects in charged current deep inelastic neutrino-iron scattering in the frame-work of a chi^2 analysis of parton distribution functions. We extract a set of iron PDFs and show that under reasonable assumptions it is possible to constrain the valence, light sea and strange quark distributions. Our iron PDFs are used to compute x_{Bj}-dependent and Q^2-dependent nuclear correction factors for iron structure functions which are required in global analyses of free nucleon PDFs. We compare our results with nuclear correction factors from neutrino-nucleus scattering models and cor…
Recent measurement of the structure function $F_2^ν$ in neutrino deep inelastic scattering allows us to compare structure function measured in neutrino and charged lepton scattering for the first time with reasonable precision. The comparison between neutrino and muon structure functions made by the CCFR Collaboration indicates that there is a discrepancy between these structure functions at small Bjorken x values. In this talk I examine two effects which might account for the experimental discrepancy: nuclear shadowing corrections for neutrinos and contributions from strange and anti strange …
The $O(α^2\log(Q^2/m_e^2))$ leptonic QED corrections to unpolarized deeply inelastic electron-nucleon scattering are calculated in the mixed variables.
Using the "Quality Factor" (QF) method, we analyse the scaling properties of deep-inelastic processes at HERA and fixed target experiments for x<10^{-2}.
