Measurement of the 12C(e,e′) Cross Sections at Q2=0.8GeV2/c2

Few-Body Sys (2024) 65:78 h ps://doi.o g/10.1007/s00601-024-01944-y M. Miho ilo iˇc·L. Do ia ·P. Achenbach · A. M. Ankowski ·S. Bacca · D. Bosna ·A. Denig ·M.O. Dis le · A. Esse ·I. F išˇci´c·C. Gius i ·M. Hoek ·S. Kegel · M. Li ich ·G.D. Megias ·H. Me kel ·U. Mülle · J. Pochodzalla ·B. S. Schlimme ·M. Scho h ·C. S ien i · S. Ši ca ·J. E. Sobczyk ·Y. S ö inge ·M. Thiel Measu emen o he 12C(e,e)C oss Sec ions a Q2=0.8GeV2/c2 Recei ed: 20 June 2024 / Accep ed: 1 July 2024 / Published online: 1 Augus 2024 © The Au ho (s) 2024 Abs ac We p esen he indings o a s udy based on a new inelas ic elec on-sca e ing expe imen on he 12C nucleus ocusing on he kinema ic egion o Q2=0.8GeV2/c2. The measu ed c oss sec ion is sensi i e o he ans e se esponse unc ion and p o ides a s ingen es o heo e ical models, as well as o he heo e ical assump ions made in Mon e-Ca lo e en -gene a o codes de eloped o he in e p e a ion o neu ino-nucleus expe imen s,suchasDUNEandHype K.We ind ha mode ngene a o ssuchasGENIEandGiBUU ep oduce ou new expe imen al da a wi hin 10%. M. Miho ilo iˇc·S. Ši ca Jože S e an Ins i u e, 1000 Ljubljana, Slo enia M. Miho ilo iˇc·S. Ši ca Facul y o Ma hema ics and Physics, Uni e si y o Ljubljana, 1000 Ljubljana, Slo enia L. Do ia ·S. Bacca ·A. Denig ·M. O. Dis le ·A. Esse ·M. Hoek ·S. Kegel ·M. Li ich ·H. Me kel·U. Mülle · J. Pochodzalla ·B. S. Schlimme ·M. Scho h ·C. S ien i ·J. E. Sobczyk ·Y. S ö inge ·M. Thiel Ins i u ü Ke nphysik, Johannes Gu enbe g-Uni e si ä Mainz, 55128 Mainz, Ge many P. Achenbach Thomas Je e son Na ional Accele a o Facili y, Newpo News, VA 23606, USA A. M. Ankowski Ins i u e o Theo e ical Physics, Uni e si y o W ocław, pl. Maxa Bo na 9, 50-204 W ocław, Poland L. Do ia ·S. Bacca ·A. Denig ·H. Me kel (B )·B. S. Schlimme ·C. S ien i ·J. E. Sobczyk ·M. Thiel PRISMA+ Clus e o Excellence, Johannes Gu enbe g-Uni e si ä Mainz, 55128 Mainz, Ge many E-mail: [email p o ec ed] D. Bosna ·I. F išˇci´c Depa men o Physics, Uni e si y o Zag eb, HR-10002 Zag eb, C oa ia C. Gius i INFN, Sezione di Pa ia, 27100 Pa ia, I aly G. D. Megias Depa amen o de Física A ómica, Molecula y Nuclea , Uni e sidad de Se illa, 41080 Se ille, Spain 78 Page 2 o 9 M. Miho ilo iˇce al. 1 In oduc ion Elec ons ep esen a e y p ecise p obe o he in es iga ion o he a omic nucleus [1]. In he pas decades, expe imen s wi h elec ons ha e p o ided inc easingly accu a e in o ma ion on he s uc u e o nuclei and hei cons i uen s [2–9]. A he hea o his e o a e he inelas ic sca e ing expe imen s on nuclea a ge s a ene gies below 1 GeV, which gi e insigh in o he p ope ies and dynamics o nucleons embedded in he nuclea medium. In such sca e ing p ocesses, an elec on wi h ene gy E0in e ac s wi h he nucleus a es by exchanging a i ual pho on ans e ing ene gy ωand momen um q, such ha Q2=q2−ω2>0. Using he nucleon mass mNas a scale, he ene gy and momen um ans e a iables can be ew i en in dimensionless o m as λ=ω 2mN ,κ=q 2mN ,τ=Q2 4m2 N=κ2−λ2. The di e en ial c oss sec ion desc ibing he inclusi ein e ac ion o he elec on wi h he nucleus can be w i en as d2σ ddω=σM[ LRL(ω, q)+ TRT(ω, q)],(1) whe e σMis he Mo c oss Sec . [1], while Land Ta e kinema ic ac o s gi en by L=τ κ22 , T=τ 2κ2+ an2θe 2, and θeis he angle o he sca e ed elec on. The c oss sec ion depends on wo nuclea esponses, he longi- udinal and he ans e se esponse unc ions, which a e bo h unc ions o ωand q=|q|. The longi udinal esponse unc ion, RL(ω, q), depends on he cha ge ope a o and ca ies in o ma ion on he nucleon-nucleon co ela ions, while he ans e se esponse unc ion, RT(ω, q), is d i en by he magne ic cu en s [1]. Va ious c oss sec ion measu emen s we e pe o med, mos ly be o e 2000, bu he acqui ed da a we e domina ed by he longi udinal (cha ge) pa o nuclea esponse. His o ically, he mos ex ensi ely s udied nucleus has been ca bon. Fo his nucleus, he iches sample o (e,e)da a exis s. I consis s o almos 3500 da a poin s om 12 expe imen s [10,11] o ene gies be ween 0.12 and 17.3 GeV and sca e ing angles up o 145◦. These da a ha e been used o s udy he s uc u e o his nucleus and o de elop models desc ibing i s elec omagne ic esponse. In he pas , heo e ical calcula ions o 12C we e o en limi ed o he quasi-elas ic (QE) egion, and he mos demanding pa was he desc ip ion o he ans e se esponse, which has been o a long ime incomple e [1]. A mo e comp ehensi e desc ip ion o he 12C(e,e)c oss sec ion was de eloped in he mic oscopic calcula ion byGile al. [12], and mo e ecen ly Megias e al. [13] p oposed a supe scaling model, called SuSA 2-MEC, which conside s he comple e inelas ic spec um. The model shows qui e good ag eemen wi h da a o e a b oad ange o ene gy ans e . Howe e , he desc ip ion o he c oss sec ions a la ge sca e ing angles emains incomple e. An impo an mo i a ion o new s udies o inclusi e c oss sec ions comes also om he neu ino physics communi y [14,15]. Sho - and long-baseline neu ino expe imen s de ec neu inos h ough hei in e ac ions wi hnucleiandaima hep ecisemeasu emen o neu inomasses,mixingangles,andCP- iola ingphasein he lep on sec o . These measu emen s ep esen one o he highes p io i ies o con empo a y undamen al physics and hinge on he abili y o he expe imen s o econs uc he neu ino ene gy and on he p ecise knowledge o he neu ino-nucleus c oss sec ions. Al hough a igo ous expe imen al p og am o he measu emen o such c oss sec ions is in p og ess [16–20], neu ino expe imen s a e mos ly limi ed by s a is ical unce ain ies and he lack o knowledge o he neu ino lux. Elec on sca e ing expe imen s, wi h a p ecisely de e mined beam ene gy and he possibili y o pe o m inclusi e as well as exclusi e measu emen s wi h di e en inal s a es, ha e he po en ial o p o ide e y p ecise da a o es ing he nuclea models employed in neu ino expe imen s. Indeed, i has been demons a ed ha he in e p e a ion o he measu ed neu ino oscilla ions equi es ex en- si e heo e ical and expe imen al suppo om he nuclea physics communi y. In his con ex he 12C(e,e) eac ion has played an impo an ole in he de elopmen o eliable models desc ibing c oss Sec . [13,21]in expe imen s like MiniBooNE [22], MINER A [23], and T2K [24] ha use ca bon-based ma e ials (mine al Measu emen o he 12C(e,e)C oss Sec ions Page 3 o 9 78 oils, plas ic scin illa o s) as de ec o medium. To ensu e u he in ol emen o mode n neu ino e en gene a- o s like GENIE [25]andGiBUU[26], he ad ances in he buil -in heo e ical models mus be complemen ed by he new expe imen al da a on ele an nuclea a ge s and in ele an kinema ics [27,28]. In his pape we ocus on 12C and p esen new da a a Q2=0.8GeV2/c2 o wo easons. On he one hand ca bon is an in e es ing a ge o neu ino expe imen s as men ioned abo e, and on he o he hand new da a a la ge Q2in a kinema ic domina ed by he ans e se esponse will boos u he heo e ical p og ess [29–38]. 2 Expe imen The measu emen o he inclusi e c oss sec ion on 12C was pe o med a he Mainz Mic o on (MAMI) acili y using he spec ome e se up o he A1 Collabo a ion [39]. In he expe imen , an elec on beam wi h ene gy E0=855MeV was used in combina ion wi h a 43 mg/cm2 hick ca bon oil a ge . Fo measu ing he c oss sec ion as a unc ion o ene gy o sca e ed elec on Ewe employed a magne ic spec ome e (spec ome e A) wi h 20% momen um accep ance and 28 ms angula accep ance. The spec ome e was posi ioned a a ixed angle o 70◦, while i s momen um se ings we e adjus ed o measu e he c oss sec ion as a unc ion o ω=E0−E. The measu emen s we e made o se en di e en momen um se ings be ween 310 MeV/c and 650 MeV/cin o de o collec da a in he egion o he QE peak and he - esonance. Fo each se ing we collec ed 1.8 million e en s. The cen al momen um o each se ing was measu ed o a ela i e accu acy o 8 ×10−5. The spec ome e was equipped wi h a de ec o package consis ing o wo laye s o e ical d i chambe s (VDCs) o acking, wo laye s o plas ic scin illa ion de ec o s o igge ing, and a h eshold Che enko de ec o o elec on iden i ica ion. The beam cu en was be ween 2 and 3 μA and was limi ed by he maximum da a acquisi ion a e, esul ing in a aw a e o abou 500 Hz. The cu en was de e mined by a non-in asi e luxga e-magne ome e wi h an accu acy o <0.2%. The expe imen p o ided new c oss sec ions measu emen s in he egion o beam ene gies and sca e ing angles, whe e he exis ing measu emen s a e e y spa se, see Fig. 1. The quasi-elas ic peak is cen e ed a |q|=0.84 GeV/c, hus nicely complemen ing p e ious measu emen s a |q|≈0.8GeV/cpe o med a 560 MeV and 1299 MeV [40,41]. The expe imen al c oss sec ions o he 12C(e,e) eac ion we e ex ac ed om he da a by di iding he measu ed dis ibu ions o coun s by he in eg a ed luminosi y and he solid angle accep ed by he spec ome e . The accep ed solid angle was simula ed using a dedica ed simula ion o he h ee spec ome e s acili y o he A1 Collabo a ion [39], Simul++. To ensu e a eliable compa ison wi h he da a, he simula ion included ealis ic momen um and spa ial esolu ions o he spec ome e . The ela i e momen um, angula , and e ex esolu ions (FWHM) we e 2.4×10−4,4.7m ad,and9.4 mm, espec i ely. The simula ion also conside ed he This wo k Sealock e al. 1989 Ba eau e al. 1983 Exis ing da a q [ GeV / c ] ω[GeV] 10.80.60.40.20 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Fig. 1 Kinema ic con igu a ions o he 12C(e,e)c oss sec ion da a in e ms o ene gy and momen um ans e s ωand |q|. Black poin s ep esen a ailable c oss sec ion measu emen s wi h ela i e unce ain ies smalle han 10%. The kinema ics co e ed by his wo k a e p esen ed wi h ed ci cles. The complemen a y measu emen s o Ba eau e al. [40], and Sealock e al. [41], also a |q|∼0.8GeV/c, a e shown wi h blue diamonds and g een squa es, espec i ely 78 Page 4 o 9 M. Miho ilo iˇce al. Table 1 De ec ion e iciencies o he se up Con ibu ion E iciency ac o Unce ain y Scin illa o e iciency 0.990 0.003 Che enko e iciency 0.999 0.001 VDC e iciency 0.999 0.001 Pa icle iden i ica ion 0.983 0.017 The co ec ion ac o s o he c oss sec ions a e gi en by hei in e ses Fig. 2 Le : Measu ed c oss sec ion compa ed o he QE calcula ions o Megias e al. [13], Gius i e al. [45,46], Sobczyk e al. [47] and Benha e al. [10]. The g ay band shows he en elope o he quasi-elas ic c oss-sec ion calcula ions and ep esen s a measu e o he di e ences be ween di e en models. Cen e : Measu ed c oss sec ion compa ed o he ull heo e ical calcula ions o Megias e al. [13] based on he SuSA 2-MEC model and p edic ions o Ankowski [48] based on he global Fe mi gas model (FG) and local Fe mi gas model (LFG). Righ : Compa ison o he new da a wi h he esul s o he Mon e-Ca lo gene a o s GiBUU [26] and GENIE ( e sion 3.4) [25] employing LFG and SuSA 2-MEC [21] nuclea c oss-sec ion models elec on ene gy co ec ions due o mul iple sca e ing and adia ion losses. The in e nal and ex e nal adia i e co ec ions we e included using he o malism o Mo and Tsai [42]. The accompanying mul iple sca e ing co ec ions in he a ge and su ounding ma e ial we e app oxima ed by a Landau dis ibu ion [43]. Al oge he , he ene gy co ec ions ha e less han 4% e ec on he measu ed c oss sec ion. The in eg a ed luminosi y was de e mined om he p oduc o he accumula ed cha ge and he su ace densi yo he a ge ma e ial,co ec ed o dead- imeandDAQp escale ac o s.Theluminosi ywasde e mined sepa a ely o each collec ed da a-sample o ensu e ha dead- ime and p escale co ec ions we e consis en ly conside ed when weigh ing he measu ed spec a. The measu ed spec a we e co ec ed o he ine iciencies o he de ec ion sys em, see Table 1.The e iciencies o he scin illa ion de ec o and he Che enko de ec o we e e alua ed in a pas expe imen [44] and we e de e mined o be 99.0% and 99.85 %, espec i ely. The e iciency o he ack econs uc ion in he VDCs was de e mined o be (99.98 ±0.05)%. All h ee co ec ions we e conside ed as mul iplica i e co ec ion ac o s. Se e al cu s we e applied o bo h da a and simula ion. Fi s , a cu on he Che enko signal was applied o iden i y elec ons and minimize he backg ound a ising om cosmic pa icles and by nega i ely cha ged pions om he 12C(e,π−) eac ion. This cu was ollowed by cu s on he nominal momen um and angula accep ance o he spec ome e in o de o emo e he a e ac s a i s edges, caused by he ine icien pa s o he de ec o s, inge ields in he spec ome e s, and seconda y pa icles esca e ed om pa s o he collima o . The ex ac ed c oss sec ions a e p esen ed in Fig. 2. The sys ema ic unce ain ies o he ex ac ed c oss sec ions a e a combina ion o a ious con ibu ions. The unce ain ies ela ed o he de ec o e iciencies a e collec ed in Table 1. The unce ain y o he luminosi y is gi en by he unce ain y o he absolu e beam cu en calib a ion, which amoun s o 3.3 nA a 855 MeV and he luc ua ions o he beam cu en we e ela ed o he ins abili ies o accele a o ope a ion. The la e we e smalle han 5 nA, esul ing in he o al sys ema ic unce ain y smalle han 0.16 %. The dominan con ibu ion Measu emen o he 12C(e,e)C oss Sec ions Page 5 o 9 78 o he sys ema ic unce ain y is ela ed o he misiden i ica ion o pa icles in he Che enko de ec o and cu s applied o dis inguish elec ons om pions and muons. This unce ain y was es ima ed o be 1.7%.Thelas ele an con ibu ion o he sys ema ic unce ain y can be e alua ed by he o malism o Mo and Tsai [42], employed o desc ibe adia i e and mul iple sca e ing co ec ions o he c oss sec ion. These co ec ions add 0.2 % o he o al unce ain y o he measu ed c oss sec ions. Finally, he unce ain y o he posi ion o he ex ac ed c oss sec ions on he ene gy scale is ela ed o he ambigui ies in he absolu e ene gy calib a ion o he accele a o and spec ome e and amoun s o 2.7 MeV, which is less han 1/3 o he employed ene gy bin size. 3 Compa ison o Models and E en Gene a o s The ex ac ed c oss sec ion is i s compa ed o QE calcula ions o Gius i e al. [45,46], Sobczyk e al. [47], Megias e al. [13] and Benha e al. [10]. Figu e 2(Le ) shows ha he calcula ions ag ee wi h each o he a he le el o 4 % a he op o he QE peak. The compa ison o he expe imen al esul s o he comp ehensi e calcula ions o Megias e al. [13], which a e based on he SuSA 2-MEC model, a e shown in Fig. 2(Cen e ). The model exhibi s e y good o e all ag eemen wi h he da a, on a e age a he le el o 7%. Su p isingly he la ges inconsis ency be ween he da a and he calcula ions appea s a he op o he QE peak, whe e he disc epancyis 9 %. Since heQEcalcula ionsshow aconsis en pic u e he e, heobse ed disc epancybe ween he da a and he SuSA 2-MEC model is mos likely ela ed o he incomple e o inconsis en desc ip ion o he p ocesses in he “dip" egion, which a e he only emaining ele an con ibu ions o he c oss sec ion a ω≤400 MeV. An ag eemen a a simila le el has been achie ed by Ankowski [48] who calcula ed c oss sec ions by using bo h he global Fe mi gas model (FG) and he local Fe mi gas model (LFG) in combina ion wi h he Bos ed-Ch is y [49,50] app oach o desc ibing pion p oduc ion p ocesses in he “dip” and in he - esonance egion. The ela i e de ia ion o he FG calcula ion om he da a is on a e age 10%, while he p edic ion o he LFG model ag ees wi h he da a a he le el o 8%. Bo h calcula ions exhibi a isible inconsis ency a he op o he QE peak and in he “dip" egion, whe e he calcula ed c oss-sec ion do no ollow he co ec end o he da a. Finally, he ex ac ed c oss-sec ions we e compa ed also o he esul s o he Mon e-Ca lo gene a o s GiBUU [26] and GENIE [11,25]. Figu e2(Righ ) shows ha a he selec ed kinema ic se ing he gene a o s desc ibe he da a easonably well. GiBUU ag ees wi h he da a a he le el o 9%. The accu acy o he GENIE gene a o depends on he model used o calcula ing nuclea c oss sec ions. When he local Fe mi gas model is used, he calcula ed c oss sec ion ag ees on a e age wi h he da a a he le el o 22%. Simila ly o he esul s o Ankowski’s LFG model, he simula ed c oss sec ion o e es ima es he QE c oss sec ion. Addi ionally, he GENIE simula ion lacks s eng h in he - egion, whe e he calcula ed c oss sec ion is 17% smalle han he da a. The simula ed esul s imp o e when GENIE uses he SuSA 2 model o desc ibing QE sca e ing and p ocesses in he “dip" egion. In his case we obse e much be e ag eemen be ween he da a and simula ion a he QE peak. No e ha GENIE s ill uses i s de aul model o desc ibing he c oss sec ion in he - esonance egion, which is he sou ce o di e ence wi h espec o he Megias e al. esul shown in he cen e panel. Fo a mo e insigh ul analysis o he measu ed c oss sec ion and compa ison wi h he exis ing esul s ob ained unde di e en kinema ic condi ions, he scaling o malism [51] can be employed. The o malism was i s de eloped wi hin he amewo k o he ela i is ic Fe mi gas model whe e he cha ac e is ic momen um is he Fe mi momen um kF, which can be exp essed as a dimensionless scale pa ame e ξF=1+k2 F/m2 N−1. Building on his o malism, wo dimensionless scaling a iables ψand ψwe e p oposed [52]: ψ≡1 √ξF λ−τ (1+λ)τ +κ√τ(τ +1) , ψ≡1 √ξF λ−τ (1+λ)τ+κ√τ(τ+1) .(2) The a iable ψis co ec ed o an empi ical ene gy shi Eshi co esponding o he a e age o he sepa a ion ene gies o he a ious shells con ibu ing o he nuclea g ound s a e [51]. Wi h he shi one achie es he cen e o he QE peak o be a ψ=0. Thenecessa y shi is achie ed by subs i u ing λand τwi h λ=λ−Eshi /2mN and τ=κ2−λ2. 78 Page 6 o 9 M. Miho ilo iˇce al. The idea o he scaling o malism is o ac o ize he elas ic c oss sec ion on a single nucleon, ob aining in his way a uni e sal scaling unc ion which con ains in o ma ion abou he nuclea s uc u e. Fo ha pu pose, educed longi udinal and ans e se esponse unc ions a e in oduced as [52]: L=kF RL GL(κ, λ), T=kF RT GT(κ, λ). The unc ions GLand GTa e exp essed as: GL(κ, λ) =(κ2/τ)[˜ G2 E+˜ W2] 2κ[1+ξF(1+ψ2)/2], GT(κ, λ) =2τ˜ G2 M+˜ W2 2κ[1+ξF(1+ψ2)/2], whe e =ξF(1−ψ2)√τ(1+τ κ+1 3ξF(1−ψ2)τ κ2, ˜ W1=τ˜ G2 M, ˜ W2=1 1+τ˜ G2 E+τ˜ G2 M, ˜ G2 E=ZG p E 2+NG n E 2, ˜ G2 M=ZG p M 2+NG n M 2. He e Zand N ep esen he numbe o p o ons and neu ons in he nucleus, espec i ely, Gp,n Eand Gp,n M a e nucleon elec ic and magne ic o m ac o s [53]. Using hese unc ions a dimensionless scaling unc ion o he o al c oss sec ion can be w i en as: =kF d2σ/dedω σM[ LGL(κ, λ) + TGT(κ, λ)]. = Lsin2χTL + Tcos2χTL,(3) whe e he angle χTL is de ined as an2χTL = LGL TGT .(4) This angle cha ac e izes he a io be ween he longi udinal and ans e se con ibu ions o he c oss sec ion. A χTL ≈0 he inclusi e c oss sec ion is domina ed by he ans e se esponse, while a χTL ≈90◦ he c oss sec ion is go e ned by he longi udinal esponse [51]. Using he scaling a iables in Eqs. (2), (3), and (4), he measu ed c oss sec ions could be compa ed o he p e ious measu emen s a |q|≈0.8GeV/co Ba eau e al. [40] and Sealock e al. [41]. The ex ac ed alues o he dimensionless scaling unc ion (ψ)a e shown in Fig. 3. This igu e shows he app oxima e scaling o he measu ed c oss sec ions which s a s o b eak o ψ>0 when he ans e se con ibu ions o he - esonance begin o domina e he c oss Sec . [51,52]. A he QE peak he expe imen al alues o his wo k and Sealock e al. collec ed a sca e ing angles θ<90◦, which co esponds o χTL =36◦and 46◦, espec i ely, ag ee e y well wi h each o he . On he o he hand, he scaling unc ion econs uc ed om da a o Ba eau e al. a θ=145◦is o e 20 % highe a he op o he QE peak. These da a coincide wi h a much smalle alue o χTL =12◦, and a e hus domina ed by he ans e se esponse RTwhich is known o b eak scaling due o a ious nonelas ic con ibu ions anging om inal-s a e-in e ac ion (FSI) e ec s o con ibu ions om he meson-exchange cu en s (MEC) [51]. Expe imen al alues we e compa ed also o he ull calcula ions o Megias e al.. In e es ingly, a he op o he QE peak he heo y is consis en wi h he da a o Ba eau e al., bu o e shoo s he expe imen al alues o his wo k and ha o Sealock e al.. The analysis o he QE c oss sec ions has e ealed ha o hese wo da a se s he QE pa ma ches he s eng h o he measu ed c oss sec ion, indica ing ha he disc epancy migh be due o he o e es ima ed MEC con ibu ions. Measu emen o he 12C(e,e)C oss Sec ions Page 7 o 9 78 SuSA 2 QE (1299 MeV) SuSA 2 QE (855 MeV) SuSA 2 QE (560 MeV) SuSA 2 (1299 MeV) SuSA 2 (855 MeV) SuSA 2 (560 MeV) Sealock e al. Ba eau e al. This wo k ψ (ψ) 3210−1−2 1.5 1 0.5 0 Fig. 3 The scaling unc ion (ψ)a |q|≈0.8GeV/c. The expe imen al alues o his wo k, Ba eau e al. [40], and Sealock e al. [41] a e shown oge he wi h he esul s o he SuSA 2-MEC model a co esponding beam ene gies o 560MeV (Ba eau e al.), 855 MeV ( his wo k) and 1299 MeV (Sealock e al.) and p esen ed wi h he ull lines. The dash-do ed lines a e used o p esen con ibu ions o he QE p ocesses o he calcula ed scaling unc ions [13] 4 Conclusions We p esen ed he expe imen al c oss sec ion o he inclusi e eac ion 12C(e,e)a Q2=0.8GeV2/c2.The measu emen was made a he kinema ics ha is ele an o he accele a o based neu ino expe imen s, bu whe e he a ailable da a a e sca ce. Since he new da a se has no been conside ed in any o he heo e ical models, we could use hem o challenge he calcula ions and gene a o s employed in he in e p e a ion o he expe imen s wi h neu inos. We ha e demons a ed ha he e en gene a o s in combina ion wi h selec ed nuclea models a e capable o desc ibing da a a he le el o 10 %. Fo e en highe p ecision o he gene a o s in he u u e, he buil -i nuclea models need o be u he e ined, especially he desc ip ion o he ans e se pa o he in e ac ion, which go e ns he inclusi e c oss sec ion in he egion o he “dip" and - esonance. To achie e his goal, u he heo e ical and expe imen al in es iga ions o c oss sec ions a Q2≈1GeV2/c2 a e needed. Kinema ics a lowe Q2would also be use ul o es MEC models. In pa icula , he p ospec o ha ing ab-ini io calcula ions in he ligh and mid-mass sec o wi h MEC [30,35,54–57] will mo i a e u he expe imen al ac i i ies in he u u e on a ious a ge s. Acknowledgemen s The au ho s would like o hank he MAMI accele a o g oup o he excellen beam quali y which made his expe imen possible. We also hank U. Mosel o use ul discussions. This wo k is suppo ed by he Fede al S a e o Rhineland- Pala ina e, by he Deu sche Fo schungsgemeinscha (DFG) h ough he Clus e o Excellence “P ecision Physics, Fundamen al In e ac ions, and S uc u e o Ma e " (PRISMA+EXC 2118/1) unded by he DFG wi hin he Ge man Excellence S a egy (P ojec ID 390831469), by he DFG g an "Elec on Sca e ing on Nuclei o Neu ino Physics" (P ojec ID 521414474), by he Slo enian Resea ch Agency unde G an s P1-0102 and J1-4383, by he Eu opean Union’s Ho izon 2020 esea ch and inno a ion p og amme unde he Ma ie Skłodowska-Cu ie g an ag eemen No. 101026014, by C oa ian Science Founda ion unde he p ojec IP-2018-01-8570 and by he Uni e si y o Tokyo ICRR’s In e Uni e si y Resea ch P og am FY2024 (Re . 2024i-J-001), Japan; he Spanish Minis e io de Ciencia, Inno ación y Uni e sidades and ERDF (Eu opean Regional De elopmen Fund) unde con ac PID2020-114687GB100 and by he Jun a de Andalucía g an No. FQM160. Au ho Con ibu ions M.M. and L.D. w o e he main manusc ip ex . S.B., A.A., C.G., G.M. and J.S. p o ided he heo e ical in e p e a ion o he da a, all o he au ho s we e in ol ed in he da a aking. All au ho s e iewed he manusc ip . Da a A ailabili y Da a can be ob ained om M. Miho ilo ic <miha.miho ilo [email protected] >. Open Access This a icle is licensed unde a C ea i e Commons A ibu ion 4.0 In e na ional License, which pe mi s use, sha ing, adap a ion, dis ibu ion and ep oduc ion in any medium o o ma , as long as you gi e app op ia e c edi o he o iginal au ho (s) and he sou ce, p o ide a link o he C ea i e Commons licence, and indica e i changes we e made. The images o o he hi d pa y ma e ial in his a icle a e included in he a icle’s C ea i e Commons licence, unless indica ed o he wise in a c edi line o he ma e ial. I ma e ial is no included in he a icle’s C ea i e Commons licence and you in ended use is no pe mi ed by s a u o y egula ion o exceeds he pe mi ed use, you will need o ob ain pe mission di ec ly om he copy igh holde . 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