Inclusive Electron Scattering And The GENIE Neutrino Event Generator
A. Papadopoulou, A. Ashkenazi, S. Gardiner, M. Betancourt, S. Dytman, L.B. Weinstein, E. Piasetzky, F. Hauenstein, M. Khachatryan, S. Dolan, G. Megias, O. Hen
IInclusive Electron Scattering And The GENIE Neutrino Event Generator
A. Papadopolou, A. Ashkenazi, ∗ S. Gardiner, M. Betancourt, S. Dytman, L.B. Weinstein, E. Piasetzky, F. Hauenstein,
4, 1
M. Khachatryan, S. Dolan, G. Megias, and O. Hen Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA Fermi National Accelerator Laboratory, Batavia, IL University of Pittsburgh, Pittsburgh, PA Old Dominion University, Norfolk, Virginia 23529 School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel CERN, European Organization for Nuclear Research, Geneva, Switzerland Research Center for Cosmic Neutrinos, Institute for Cosmic RayResearch, University of Tokyo, Kashiwa, Chiba 277-8582, Japan (Dated: September 16, 2020)———————The extraction of neutrino mixing parameters from accelerator-based neutrino oscillation experi-ments relies on proper modeling of neutrino-nucleus scattering processes using neutrino interactionevent generators. Experimental tests of these generators are made more difficult by the broadrange of neutrino energies produced in accelerator-based beams and the low statistics of currentexperiments. Here we overcome this difficulty by exploiting the similarity of neutrino and electroninteractions with nuclei to test neutrino event generators using high-precision inclusive electronscattering data. To this end we revised the electron-scattering mode of the GENIE event generator( e -GENIE) to include electron-nucleus bremsstrahlung radiation effects and to use the exact samephysics models and, when relevant, model parameters, as the standard neutrino-scattering version.We also implemented new models for quasielastic (QE) scattering and meson exchange currents(MEC) based on the theory-inspired SuSAv2 approach. Comparing the new e -GENIE predictionswith inclusive electron scattering data, we find an overall adequate description of the data in theQE- and MEC-dominated lower energy transfer regime, especially when using the SuSAv2 models.Higher energy transfer-interactions, which are dominated by resonance production, are still not wellmodeled by e -GENIE. Introduction
The extraction of neutrino mixing parameters from neu-trino oscillation experiments relies on comparing theenergy-dependent neutrino flux Φ i ( E, L ) for neutrino fla-vor ν i near the neutrino production point ( L ≈
0) withthat at a significant distance L away. In practice, theflux is extracted from the measured neutrino-nucleus in-teractions in a detector, N i ( E rec , L ), where E rec is theincident neutrino energy, as reconstructed from the mea-sured particles ejected in the neutrino-nucleus interac-tion. Extracting Φ i ( E, L ) from N i ( E rec , L ) therefore re-quires knowledge of the ν -nucleus interaction processes.The measured interaction rate is related to the incidentneutrino flux via N ( E rec , L ) ∝ (cid:88) i (cid:90) Φ( E, L ) σ i ( E ) f σ i ( E, E rec ) dE, (1)where σ i ( E ) is the neutrino interaction cross-section forprocess i and f σ i ( E, E rec ) is a neutrino energy smear-ing matrix that relates the real and experimentally-reconstructed neutrino energies. The precision withwhich one can model σ i ( E ) and f σ i ( E, E rec ) determinesthe precision with which one can extract the neutrino flux. This in turn fixes the precision of the extractedoscillation parameters.Our knowledge of σ i ( E ) and f σ i ( E, E rec ) is encapsu-lated in event generators , computer programs which im-plement neutrino interaction models suitable for use inMonte Carlo simulations. Due to the critical role playedby neutrino event generators in the analysis and inter-pretation of data obtained by oscillation experiments,testing and improving generator physics models is es-sential for reducing systematic uncertainties in precisionneutrino experiments. However, due to the broadbandnature of accelerator-based neutrino beams (i.e., theirwide range of neutrino energies) and the limited statis-tics available from current experiments, it is very difficultto measure differential neutrino-nucleus cross sections forspecific neutrino energies and to test beam energy recon-struction techniques.Because neutrinos and electrons are both leptons, theyinteract with atomic nuclei in similar ways (see Fig. 1).Electrons interact via a vector current ( j µEM = ¯ uγ µ u )and neutrinos interact via vector and axial-vector ( j µCC =¯ uγ µ (1 − γ ) u − ig W √ ) currents.This gives an inclusive ( e, e (cid:48) ) electron-nucleon scatter-ing cross section that depends on only two structure func- a r X i v : . [ nu c l - t h ] S e p tions: d σ e dxdQ = 4 πα Q (cid:20) − yx F e ( x, Q ) + y F e ( x, Q ) (cid:21) . (2)Here F e and F e are the standard electromagnetic vectorstructure functions, Q = q − ω is the squared momen-tum transfer and q and ω are the three-momentum andenergy transfers, x = Q / (2 mω ) is the Bjorken scalingvariable, m is the nucleon mass, y = ω/E e is the elec-tron fractional energy loss, and α is the fine structureconstant. This formula is valid for Q (cid:29) m where theelectron-nucleon cross section is simplest. Cross sectionsat lower Q have more complicated factors multiplyingeach of the two structure functions.The corresponding inclusive charged current (CC)( ν, l ± ) neutrino-nucleon cross section (where l ± is theoutgoing charged lepton) has a similar form with the ad-dition of third, axial, structure function: d σ ν dxdQ = G F π (cid:20) − yx F ν ( x, Q ) + y F ν ( x, Q ) − y (1 − y/ F ν ( x, Q ) (cid:3) . (3)Here F ν and F ν are the neutrino-nucleus vector struc-ture functions, F ν is the axial structure function, and G F is the Fermi constant. The parity-conserving struc-ture functions, F ν and F ν , both include a vector-vectorterm identical to F e and F e , and an additional axial-axialterm. See Refs. [1–3] for more detail.These simple equations are very similar for lepton-nucleus scattering. In the limit of electron-nucleon elasticscattering ( x = 1), the two structure functions reduce tothe Dirac and Pauli form factors (which are linear combi-nations of the electric and magnetic form factors, G E ( Q )and G M ( Q )). Neutrino-nucleon elastic scattering has anadditional axial form factor. In the simplest case wherea lepton scatters quasielastically from a nucleon in thenucleus and the nucleon does not reinteract as it leavesthe nucleus, then the lepton-nucleus cross section is theintegral over all initial state nucleons: dσdEd Ω = (cid:90) p i (cid:90) E b d p i dE b KS ( p i , E b ) dσ free d Ω δ ( q − p f − p r ) δ ( ω − E b − T f − T r ) (4) FIG. 1. (left) electron-nucleus inclusive scattering via one-photon exchange and (right) charged current neutrino-nucleusinclusive scattering via W exchange with a final state chargedlepton. FIG. 2. Reaction mechanisms for lepton-nucleus scattering(a) quasielastic scattering (QE) where one nucleon is knockedout of the nucleus, (b) 2 p h where two nucleons are knockedout of the nucleus, (c) RES resonance production where anucleon is excited to a resonance which decays to a nucleonplus meson(s), and (d) DIS where the lepton interacts with aquark in the nucleon. where p i and p f are the initial and final momenta ofthe struck nucleon (in the absence of reinteraction, p f = q + p i ), p r = − p i is the momentum of the recoil A − E b is the nucleon binding energy, S ( p i , E b ) isthe probability of finding a nucleon in the nucleus withmomentum p i and binding energy E b , T f and T r arethe kinetic energies of the final state nucleon and A − dσ free /d Ω is the lepton-bound nucleon elasticcross section, and K is a known kinematic factor.This simple form is complicated for electrons and neu-trinos by nucleon reinteraction which changes the overlapintegral between the initial and final states (and thus thecross section), and changes the momentum and angle ofthe outgoing nucleon.Thus, to calculate even the simplest type of lepton-nucleus interaction, we need to know the momentum andbinding energy distribution of all nucleons in the nucleus,how the outgoing nucleon wave function is distorted bythe nucleon-nucleus potential, and how the outgoing nu-cleon kinematics is changed by final state interactions.In addition, the lepton can knock out two nucleonssimultaneously, either by interacting with a nucleon be-longing to a short range correlated (SRC) pair [4] or byinteracting with a meson being exchanged between twonucleons. And, of course, these two interactions add co-herently. The lepton can interact with a nucleon, excitingit to a resonance, which then deexcites resulting in emis-sion of a nucleon plus mesons or of two nucleons. Thelepton can also scatter inelastically from a quark in anucleon. All of these different reaction mechanisms arevery similar for electrons and for neutrinos. The out-going hadrons in all of these interactions will interactidentically with the residual nucleus, whether they areknocked out by an electron or by a neutrino.This correspondence provides a valuable opportunityfor rigorous tests of event generators: any generatormodel set which fails to accurately describe eA (vector)scattering data cannot be used with confidence to simu-late νA (vector + axial-vector) interactions.To demonstrate what can be learned by confronting aneutrino event generator with electron scattering data,we have created e -GENIE: a new electron-scatteringversion of the widely-used GENIE [5] event generator.Whenever possible e -GENIE uses the same code and thesame sets of physics models as the standard neutrino ver-sion.Here we focus specifically on testing our current knowl-edge of σ i ( E ) by benchmarking e -GENIE against exist-ing inclusive electron scattering data for different targetnuclei at several incident beam energies and scatteredelectron angles. We find that the new SuSAv2 modelsdescribe the inclusive data better than the older ones,but resonance production reactions are still not well de-scribed, especially at larger momentum transfer. Modeling
The most common lepton-nucleus interaction mecha-nisms include (Fig. 2): (a) quasielastic (QE) scatteringfrom individual moving nucleons in the nucleus; (b) two-nucleon knockout, due to interactions with a meson beingexchanged between two nucleons or to interactions withan SRC pair (refered to meson exchange current, MECor two-particle two-hole excitations, 2 p h ); (c) interac-tions which leave the struck nucleon in an excited state(resonance production or RES); and (d) non-resonant in-teractions with a quark within the nucleon (DIS).For fixed incident beam energy and scattered electronangle, the dominant process changes from QE at low en-ergy transfer ( ω ≈ Q / m ) through MEC to RES andto DIS at high energy transfer. Therefore, examiningthe agreement of e -GENIE with data as a function ofenergy transfer can provide valuable insight into the spe-cific shortcomings of the e -GENIE models and their im-plementations.The GENIE simulation framework offers several mod-els of the nuclear ground state, several models for eachof the eA or νA scattering mechanisms (each with var-ious tunable model parameters), and several models forhadronic final state interactions (FSI), i.e., intranuclearrescattering of the outgoing hadrons [5, 6]. In this sec-tion, we describe the different models relevant for thiswork and the electron-specific effects that we accountedfor during e -GENIE development.Since our goal is to use electron scattering data to val-idate neutrino interaction modeling in GENIE, we choseto unify the GENIE code for electron and neutrino scat-tering modes wherever possible. The neutrino interactswith a nucleus via the weak interaction and massive W or Z exchange, whereas the electron interacts mostly elec-tromagnetically via massless photon exchange, see Fig. 1.Both interactions probe the same nuclear ground stateand many of the nuclear reaction effects are similar oridentical. We thus constructed e -GENIE by setting theaxial part of the interaction to zero and using cross sec-tions that effectively differ by a factor of π α G F Q (see Eqs. 2and 3).When generating events for a beam of leptons with acontinuously-distributed energy spectrum, GENIE sam- ples an initial projectile energy E for each event using aprobability density function of the form P ( E ) ∝ Φ( E ) (cid:88) i σ i ( E ) (5)where Φ is the incident flux and the sum runs over thetotal cross sections σ i for each available interaction mode(QE, MEC, RES, etc.). A specific mode j is then sampledwith probability P j = σ j ( E ) (cid:80) i σ i ( E ) . (6)GENIE does not include interference between the am-plitudes of different reaction modes, i.e., the total crosssection is obtained by adding the individual cross sections σ i ( E ) incoherently.Many of the models reported in this work (except forSuSAv2) use the GENIE implementation of the localFermi gas (LFG) model to describe the nuclear groundstate. In a regular Fermi gas model, nucleons occupy allmomentum states up to the global Fermi momentum k F with equal probability. In the LFG model, the Fermi mo-mentum at a given radial position depends on the localnuclear density (obtained from measurements of nuclearcharge densities). To account for this radial dependence,GENIE selects an initial momentum for the struck nu-cleon by first sampling an interaction location r insidethe nucleus according to the nuclear density. The nu-cleon momentum is then drawn from a Fermi distributionusing the local Fermi momentum k F ( r ).We consider two distinct sets of GENIE models forQE and MEC: those used in the G18 10a 02 11a config-uration of GENIE v3.0.6 (referred to here as G2018) andchosen to describe data including mainly bubble chamberCCQE, CC1 π , CC2 π , CC inclusive and normalised topo-logical cross-section data [7], and those used in the newSuSAv2 model set [8] approved for inclusion in the near-future GENIE v3.2 release as the GTEST19 10b 00 000 configuration and referred to here as SuSAv2. In bothmodel sets, RES is modeled using the Berger-Sehgalmodel [9] and DIS reactions are modeled using Bodekand Yang[10]. These interactions are described in moredetail below.
Quasi Elastic (QE)
In QE interactions, a lepton scatters on a single nu-cleon, removing it from the spectator A − e -GENIE and modified the cross section as describedabove. This electron QE cross section differs in importantways (notably, the Rosenbluth treatment lacks mediumpolarization corrections) from the Valencia CCQE model[12] used in the G2018 configuration for neutrinos.A new QE model in GENIE, based on the SuSAv2 ap-proach [8, 13, 14], uses superscaling to write the inclusivecross section in terms of a universal function (i.e., inde-pendent of momentum transfer and nucleus). For EMscattering, the scaling function may be expressed in theform f ( ψ (cid:48) ) = k F d σd Ω e dν σ Mott ( v L G ee (cid:48) L + V T G ee (cid:48) T ) , (7)where ψ (cid:48) is a dimensionless scaling variable, k F is thenuclear Fermi momentum, the denominator is the single-nucleon elastic cross section, v L and v T are known func-tions of kinematic variables, and G ee (cid:48) L ( q, ω ) and G ee (cid:48) T ( q, ω )are the longitudinal and transverse nucleon structurefunctions (linearly related to F e and F e ) [15]. For e -GENIE, we extended the original implementation forneutrinos [8] to the electron case using a consistentphysics treatment.The original SuSAv2 QE cross section calculationsused a Relativistic Mean Field (RMF) model of the nu-clear ground state [16, 17]. This approach includes theeffects of the real part of the nucleon-nucleus potentialon the outgoing nucleons which creates a “distorted” nu-cleon momentum distribution.Although GENIE lacks the option to use an RMF nu-clear model directly, we achieve approximate consistencywith the RMF-based results by using a two-step strategyfor QE event generation. First, an energy and scatter-ing angle for the outgoing lepton are sampled accordingto the inclusive double-differential cross section. Thiscross section is computed by interpolating precomputedvalues of the nuclear responses G ee (cid:48) L ( q, ω ) and G ee (cid:48) L ( q, ω )which are tabulated on a two-dimensional grid in ( q, ω )space. The responses were obtained using the originalRMF-based SuSAv2 calculation.Second, the nucleon kinematics are determined bychoosing its initial momentum from an LFG distribution.The default nucleon binding energy used in GENIE forthe LFG model is replaced for SuSAv2 with an effectivevalue tuned to most closely duplicate the RMF distribu-tion. The outgoing nucleon kinematics are not neededfor the comparisons to inclusive ( e, e (cid:48) ) data shown in thiswork. Meson Exchange Current (MEC)
MEC describes an interaction that results in the ejec-tion of two nucleons from the nucleus (often referred to as2 p h ). It typically proceeds via lepton interaction witha pion being exchanged between two nucleons or by in- teraction with a nucleon in an SRC pair. GENIE hasseveral models for MEC.The G2018 configuration of e -GENIE uses the empiri-cal Dytman model [18], that is useable for both eA and νA scattering. It assumes that the MEC peak for inclu-sive scattering has a Gaussian distribution in W and islocated between the QE and first RES peaks. The ampli-tude of the MEC peak was tuned to electron scatteringdata. This model was developed in the context of empir-ically fitting GENIE to MiniBooNE inclusive neutrinoscattering data.For charged-current neutrino interactions, GENIEG2018 uses the very different Valencia 2 p h model[12, 19] instead of the empirical Dytman model, whichis still used for neutral-current interactions.Another MEC model, available for both eA and νA scattering, is the SuSAv2 MEC model [13, 20, 21]. Theevaluation of the 2 p h MEC contributions is performedwithin an exact RFG-based microscopic calculation thatenglobes the 2 p h states excited by the action of meson-exchange currents within a fully relativistic framework[14, 22–24], and considers the weak vector and axial com-ponents for neutrino-nucleus interactions in both longi-tudinal and transverse channels as well as a completeanalysis for electromagnetic reactions. As in the case forthe SuSAv2 QE model, we extend the original GENIEimplementation of SuSAv2 MEC for neutrinos [8] to theelectron case for e -GENIE. Resonance (RES) and Deep Inelastic Scattering (DIS)
Resonance production in GENIE is simulated using theBerger-Sehgal model [9], in which the lepton interactswith a single moving nucleon and excites it to one of 16resonances. The cross sections are calculated based onthe Feynman-Kislinger-Ravndal (FKR) model [25], with-out any interferences between them.The GENIE treatment of deep inelastic scattering usedin this work is based on that of Bodek and Yang [10].Hadronization is modeled using an approach which tran-sitions gradually between the AGKY model [26] and thePYTHIA 6 model [27]. At low values of the hadronicinvariant mass W , the Bodek-Yang differential cross sec-tion is scaled by tunable parameters that depend on themultiplicity of hadrons in the final-state [6].These parameters (together with a few others, such asthe axial masses for CCQE and CCRES) were recentlyretuned by the GENIE collaboration to measurements ofcharged-current ν µ and ¯ ν µ scattering on deuterium [7].The new tuning is included in the G2018 configurationbut not in SuSAv2. The modeling of RES and DIS isotherwise identical. [GeV] cal H(e,e'p) E e v e n t s · DataGENIE + radiative correctionGENIE default
FIG. 3. Number of events vs E cal = E e (cid:48) + T p the scat-tered electron energy plus proton kinetic energy for 4.32 GeVH( e, e (cid:48) p ). Black points are data [31] , red histogram showsthe unradiated GENIE prediction and blue histogram showsthe GENIE prediction with electron radiation. The GENIEcalculations have been scaled to have the same integral as thedata. Final State Interactions (FSIs)
The IntraNuclear Cascade (INC) model for FSIand hadronization is done in GENIE by the IN-TRANUKE [28, 29] package including two options. Thefirst, hA, an empirical data-driven method, uses thecross-section of pions and nucleons with nuclei as a func-tion of energy up to 1.2 GeV and the CEM03 [30] calcu-lation normalised to low energy data for higher energies.The second, hN, is a full INC calculation of pions, kaons,photons, and nucleon interactions with nuclei up to 1.2GeV.The e -GENIE G2018 configuration uses the hA FSImodel, while SuSAv2 uses hN. However, the choice ofFSI model has no effect on the inclusive cross sectionsconsidered in the present work. Radiative Corrections
When electrons scatter from nuclei, there are severalradiative effects that change the cross section. The in-coming and outgoing electrons can each radiate a realphoton, which changes the kinematics of the interactionor the detected particles, and there can be vertex or prop-agator corrections that change the cross section. Whencomparing electron scattering data to models, either thedata or the model needs to be corrected for radiativeeffects. Published electron scattering cross sections aretypically corrected for radiative effects, but this correc-tion is complicated and somewhat model-dependent.We implemented a framework for electron radiativecorrections in GENIE for the first time to allow compar-isons to non-radiatively corrected data. The framework · o = 60 q C, 0.24 GeV, · · o = 36 q C, 0.56 GeV, · · o = 60 q C, 0.56 GeV, · SuSav2 G2018 b / s r / G e V ] m [ d E W d s d Energy Transfer [GeV] Energy Transfer [GeV]
FIG. 4. Comparison of inclusive C( e, e (cid:48) ) scattering cross sec-tions for data and for GENIE. (left) data vs SuSAv2 and(right) data vs G2018. (top) E = 0 .
24 GeV, θ e = 60 ◦ and Q QE ≈ .
05 GeV [33], (middle) E = 0 .
56 GeV, θ e = 36 ◦ and Q QE ≈ .
11 GeV [33], and (bottom) E = 0 .
56 GeV, θ e = 60 ◦ and Q QE ≈ .
24 GeV [33]. Black points showthe data, solid black lines show the total GENIE prediction,colored lines show the contribution of the different reactionmechanisms: (blue) QE, (magenta) MEC, (red) RES and(green) DIS. allows electron radiation, which can change the kinemat-ics of the event by changing either the incident or scat-tered electron energy (through radiation of a real pho-ton). We modeled external radiation in the same way asthe Jefferson Lab SIMC event generator [32]. Future ver-sions of e -GENIE will incorporate cross section changesdue to vertex and propagator corrections.We validated the radiative correction procedure bycomparing a simulated sample to electron scattering fromprotons at Jefferson Lab. Figure 3 shows the data com-pared to the GENIE simulation with and without radia-tive corrections. The radiatively corrected calculation isclearly much closer to the data. The radiative tail of thedistribution is only significant for about 5 MeV below thepeak.This correction is used for comparisons with non-radiatively-corrected data. It was not used to comparewith the radiatively-corrected inclusive data shown be-low. e -GENIE comparisons to inclusive electronscattering data To test e -GENIE, we compare inclusive electron scatter-ing data to theoretical predictions made using two differ-ent program configurations which differ in their choice of · o = 37.5 q C, 0.961 GeV, · · o = 37.5 q C, 1.299 GeV, · · o = 15.54 q C, 2.222 GeV, · SuSav2 G2018 b / s r / G e V ] m [ d E W d s d Energy Transfer [GeV] Energy Transfer [GeV]
FIG. 5. Comparison of inclusive C( e, e (cid:48) ) scattering cross sec-tions for data and for GENIE. (left) data vs SuSAv2 and(right) data vs G2018. (top) E = 0 .
96 GeV, θ e = 37 . ◦ and Q QE ≈ .
32 GeV [34], (middle) E = 1 .
30 GeV, θ e = 37 . ◦ and Q QE ≈ .
54 GeV [34], and (bottom) E = 2 .
22 GeV, θ e = 15 . ◦ and Q QE ≈ .
33 GeV [35]. Black points showthe data, solid black lines show the total GENIE prediction,colored lines show the contribution of the different reactionmechanisms: (blue) QE, (magenta) MEC, (red) RES and(green) DIS. QE and MEC models: G2018 (which adopts the Rosen-bluth model for QE and the empirical Dytman model forMEC) and SuSAv2 (which adopts SuSAv2 for both QEand MEC).Figs. 4, 5 and 6 show the inclusive C( e, e (cid:48) ) cross sec-tions for a wide range of beam energies and scatter-ing angles compared to the G2018 and SuSAv2 mod-els. The QE peak is the one at lowest energy transfer( ν ≈ Q / m ) in each plot. The next peak at about 300MeV larger energy transfer corresponds to ∆(1232) ex-citation and the “dip region” is between the two peaks.SuSAv2 clearly describes the QE and dip regions muchbetter than G2018, especially at the three lowest momen-tum transfers (see Fig. 4). G2018 has particular difficultydescribing the data for E = 0 .
24 GeV and θ e = 60 ◦ ,where Q = 0 .
05 GeV at the quasielastic peak. G2018also predicts too small a width for the quasielastic peakand too small a 2p2h/MEC contribution for E = 0 . θ e = 60 ◦ . At higher incident energies, SuSAv2describes the data better than G2018, although it over-predicts the dip region cross section at E = 1 .
299 GeVand θ e = 37 . ◦ . Both model sets significantly disagreewith the data in the resonance region (where they usethe same RES and DIS models).Fig. 7 shows the inclusive Ar( e, e (cid:48) ) cross sections for · o = 37.5 q C, 1.501 GeV, · · o = 16 q C, 3.595 GeV, · o = 20 q C, 3.595 GeV, SuSav2 G2018 b / s r / G e V ] m [ d E W d s d Energy Transfer [GeV] Energy Transfer [GeV]
FIG. 6. Comparison of inclusive C( e, e (cid:48) ) scattering cross sec-tions for data and for GENIE. (left) data vs SuSAv2 and(right) data vs G2018. (top) E = 1 .
501 GeV, θ e = 37 . ◦ and Q QE ≈ .
92 GeV [34], (middle) E = 3 .
595 GeV, θ e = 16 ◦ and Q QE ≈ .
04 GeV [36], and (bottom) E = 3 .
595 GeV, θ e = 20 ◦ and Q QE ≈ . [36]. Black points showthe data, solid black lines show the total GENIE prediction,colored lines show the contribution of the different reactionmechanisms: (blue) QE, (magenta) MEC, (red) RES and(green) DIS. E = 2 .
222 GeV and θ e = 15 . ◦ [37] compared to theG2018 and SuSAv2 models. Both models reproduce thedata moderately well in the QE, dip and ∆-peak regions,but there is again significant disagreement at larger en-ergy transfers.Fig. 8 shows the inclusive Fe( e, e (cid:48) ) cross sections forseveral beam energies and scattering angles compared tothe G2018 and SuSAv2 models. The SuSAv2 model de-scribes the QE region better for all three data sets. TheSuSAv2 model describes the dip region significantly bet-ter for the two lower energies, but overpredicts the crosssection there at the highest energy. The disagreementnear the ∆ peak is a bit smaller for the Fe data than thecorresponding C data. Summary
We implemented an electron version of GENIE, the popu-lar neutrino-nucleus event generator. This new version ofGENIE is designed to use the same cross section modelsand the same event generation machinery as the neutrinoversion, in order to rigorously test the vector current partof the lepton-nucleus interaction. We also added partialradiative corrections for electron scattering.We compared two different GENIE model sets to in- · o = 15.54 q Ar, 2.222 GeV, · SuSav2 G2018 b / s r / G e V ] m [ d E W d s d Energy Transfer [GeV] Energy Transfer [GeV]
FIG. 7. Comparison of inclusive Ar( e, e (cid:48) ) scattering cross sec-tions for data and for GENIE at E = 2 .
22 GeV, θ e = 15 . ◦ and Q QE ≈ .
33 GeV [37]. (left) data vs SuSAv2 and (right)data vs G2018. Black points show the data, solid black linesshow the total GENIE prediction, colored lines show the con-tribution of the different reaction mechanisms: (blue) QE,(magenta) MEC, (red) RES and (green) DIS. · o = 60 q Fe, 0.56 GeV, · · o = 37.5 q Fe, 0.961 GeV, · · o = 37.5 q Fe, 1.299 GeV, · SuSav2 G2018 b / s r / G e V ] m [ d E W d s d Energy Transfer [GeV] Energy Transfer [GeV]
FIG. 8. Comparison of inclusive Fe( e, e (cid:48) ) scattering crosssections for data and for GENIE. (left) data vs SuSAv2and (right) data vs G2018. (a) Fe( e, e (cid:48) ), E = 0 .
96 GeV, θ e = 37 . ◦ and Q QE ≈ .
32 GeV [34], (b) Fe( e, e (cid:48) ), E = 1 . θ e = 37 . ◦ and Q QE ≈ .
54 GeV [34]. Black pointsshow the data, solid black lines show the total GENIE pre-diction, colored lines show the contribution of the differentreaction mechanisms: (blue) QE, (magenta) MEC, (red) RESand (green) DIS. clusive electron-scattering data for a wide range of tar-gets, beam energies and scattering angles. The G2018and SuSAv2 model sets differ in their description of QEand MEC scattering. Both models describe the data atleast moderately well in the QE and MEC regions. TheSuSAv2 model set describes the QE and MEC regionsin most of the data sets better than G2018. However,at the highest momentum transfers, e -GENIE dramati-cally overpredicts the data, indicating significant prob- lems with the momentum-transfer dependence of theRES and DIS models used.By developing an electron version of GENIE that usesthe same reaction mechanism models as the standardneutrino version, we have prepared the machinery to testthe vector current part of the lepton-nucleus interactionagainst more extensive, and more exclusive, electron scat-tering data sets. This should provide enough informationto allow us to improve the vector current interactions inneutrino event generators, which should improve the pre-cision of future neutrino oscillation experiments. ∗ Contact Author [email protected][1] L. Alvarez-Ruso et al. , Prog. Part. Nucl. Phys. , 1(2018), arXiv:1706.03621 [hep-ph].[2] T. Katori and M. Martini, J. Phys. G , 013001 (2018),arXiv:1611.07770 [hep-ph].[3] J. Amaro, M. Barbaro, J. Caballero, R. Gonzlez-Jimnez,G. Megias, and I. Ruiz Simo, (2019), arXiv:1912.10612[nucl-th].[4] O. Hen, G. A. Miller, E. Piasetzky, and L. B. Weinstein,Rev. Mod. Phys. , 045002 (2017).[5] C. Andreopoulos, A. Bell, D. Bhattacharya, F. Cavanna,J. Dobson, S. Dytman, H. Gallagher, P. Guzowski,R. Hatcher, P. Kehayias, A. Meregaglia, D. Naples,G. Pearce, A. Rubbia, M. Whalley, and T. Yang, Nucl.Inst. and Meth. A , 87 (2010), 0905.2517.[6] C. Andreopoulos, C. Barry, S. Dytman, H. Gallagher,T. Golan, R. Hatcher, G. Perdue, and J. Yarba, (2015),arXiv:1510.05494 [hep-ph].[7] J. Tena-Vidal, “Tuning the pion pro-duction with GENIE version 3,”https://indico.cern.ch/event/703880/contributions/3157410/,talk delivered at the 12th International Workshop onNeutrino-Nucleus Interactions in the Few-GeV Region(NuInt 18).[8] S. Dolan, G. D. Megias, and S. Bolognesi, Phys. Rev. D , 033003 (2020).[9] C. Berger and L. Sehgal, Phys. Rev. D , 113004 (2007),arXiv:0709.4378 [hep-ph].[10] A. Bodek and U. K. Yang, Journal of Physics G: Nuclearand Particle Physics , 1899 (2003), hep-ex/0210024.[11] R. Bradford, A. Bodek, H. S. Budd, and J. Arrington,Nucl. Phys. B Proc. Suppl. , 127 (2006), arXiv:hep-ex/0602017.[12] J. Nieves, I. R. Simo, and M. J. V. Vacas, Phys. Rev. C , 045501 (2011), 1102.2777.[13] G. D. Megias, J. E. Amaro, M. B. Barbaro, J. A. Ca-ballero, and T. W. Donnelly, Phys. Rev. D , 013012(2016).[14] G. Megias, J. Amaro, M. Barbaro, J. Caballero, T. Don-nelly, and I. Ruiz Simo, Phys. Rev. D , 093004 (2016),arXiv:1607.08565 [nucl-th].[15] J. Caballero, Phys. Rev. C , 015502 (2006), arXiv:nucl-th/0604020.[16] R. Gonzlez-Jimnez, A. Nikolakopoulos, N. Jachow-icz, and J. Udas, Phys. Rev. C , 045501 (2019),arXiv:1904.10696 [nucl-th].[17] R. Gonzlez-Jimnez, M. Barbaro, J. Caballero, T. Don- nelly, N. Jachowicz, G. Megias, K. Niewczas, A. Niko-lakopoulos, and J. Udas, Phys. Rev. C , 015503(2020), arXiv:1909.07497 [nucl-th].[18] T. Katori, AIP Conf. Proc. , 030001 (2015),arXiv:1304.6014 [nucl-th].[19] J. Schwehr, D. Cherdack, and R. Gran, (2017),1601.02038.[20] G. Megias et al. , Phys. Rev. D , 073004 (2015),arXiv:1412.1822 [nucl-th].[21] J. E. Amaro, M. B. Barbaro, J. A. Caballero, A. De Pace,T. W. Donnelly, G. D. Megias, and I. Ruiz Simo, Phys.Rev. C , 065502 (2017).[22] A. De Pace, M. Nardi, W. Alberico, T. Donnelly, andA. Molinari, Nucl. Phys. A , 249 (2004), arXiv:nucl-th/0403023.[23] I. Ruiz Simo, J. Amaro, M. Barbaro, A. De Pace, J. Ca-ballero, and T. Donnelly, J. Phys. G , 065105 (2017),arXiv:1604.08423 [nucl-th].[24] I. Ruiz Simo, C. Albertus, J. Amaro, M. Barbaro, J. Ca-ballero, and T. Donnelly, Phys. Rev. D , 033012(2014), arXiv:1405.4280 [nucl-th].[25] R. P. Feynman, M. Kislinger, and F. Ravndal, Phys.Rev. D , 2706 (1971).[26] T. Yang, C. Andreopoulos, H. Gallagher, K. Hofmann,and P. Kehayias, The European Physical Journal C , 1 (2009), 0904.4043.[27] T. Sj¨ostrand, S. Mrenna, and P. Skands, Journal of HighEnergy Physics , 026 (2006), hep-ph/0603175.[28] S. Dytman and A. Meyer, AIP Conference Proceedings , 213 (2011).[29] R. Merenyi, W. A. Mann, T. Kafka, W. Leeson, B. Saitta,J. Schneps, M. Derrick, and B. Musgrave, Phys. Rev. D , 743 (1992).[30] S. G. Mashnik, A. J. Sierk, K. K. Gudima, and M. I.Baznat, J. Phys. Conf. Ser. , 340 (2006).[31] R. Cruz-Torres et al. (Jefferson Lab Hall A Tritium),Phys. Lett. B , 134890 (2019), arXiv:1902.06358[nucl-ex].[32] “Simc monte carlo,” https://hallcweb.jlab.org/wiki/ in-dex.php/SIMC Monte Carlo (2020).[33] P. Barreau et al. , Nucl. Phys. A , 515 (1983).[34] R. M. Sealock, K. L. Giovanetti, S. T. Thornton, Z. E.Meziani, O. A. Rondon-Aramayo, S. Auffret, J.-P. Chen,D. G. Christian, D. B. Day, J. S. McCarthy, R. C. Mine-hart, L. C. Dennis, K. W. Kemper, B. A. Mecking, andJ. Morgenstern, Phys. Rev. Lett. , 1350 (1989).[35] H. Dai et al. (Jefferson Lab Hall A), Phys. Rev. C ,014617 (2018), arXiv:1803.01910 [nucl-ex].[36] D. Day et al. , Phys. Rev. C , 1849 (1993).[37] H. Dai et al. (The Jefferson Lab Hall A Collaboration),Phys. Rev. C99