Antonov, An

Barbaro, Maria Benedetta

Caballero, Ja

Gonzalez Jimenez, R

Ivanov, Mv

Megias, Gd

Moya De Guerra, E

Udias, Jm

English

Ivanov, M V

Antonov, A N

Barbaro, M B

Caballero, J A

Megias, G D

González-Jiménez, R

Moya de Guerra, E

Udías, J M

CERN Document Server

Charged-current inclusive neutrino cross sections: Superscaling extension to the pion production and realistic spectral function for quasielastic

Institutional Research Information System University of Turin

NUCLEAR THEORY, Vol. 34 (2015)eds. M. Gaidarov, N. Minkov, Heron Press, SofiaCharged-Current Inclusive Neutrino CrossSections: Superscaling Extension to the PionProduction and Realistic Spectral Function forQuasielastic RegionM.V. Ivanov1,2, A.N. Antonov1, M.B. Barbaro3, J.A. Caballero4,G.D. Megias4, R. Gonza´lez-Jime´nez5, E. Moya de Guerra2,J.M. Udı´as21Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy ofSciences, Sofia 1784, Bulgaria2Grupo de Fı´sica Nuclear, Departamento de Fı´sica Ato´mica, Molecular yNuclear, Facultad de Ciencias Fı´sicas, Universidad Complutense de Madrid,Madrid E-28040, Spain3Dipartimento di Fisica, Universita` di Torino and INFN, Sezione di Torino,Via P. Giuria 1, 10125 Torino, Italy4Departamento de Fı´sica Ato´mica, Molecular y Nuclear, Universidad de Sevilla,41080 Sevilla, Spain5Department of Physics and Astronomy, Ghent University, Proeftuinstraat 86,B-9000 Gent, BelgiumAbstract. Superscaling approximation (SuSA) predictions to neutrino-inducedcharged-current pion production in the ∆-resonance region are explored underMiniBooNE experimental conditions. The results obtained within SuSA for theflux-averaged double-differential cross sections of the pion production for theνµ+CH2 reaction as a function of the muon kinetic energy and of the scatteringangle, the cross sections averaged over the angle, the total cross section for thepion production are compared with the corresponding MiniBooNE experimentaldata. The SuSA charged-current pi+ predictions are in good agreement with dataon neutrino flux average cross-sections. The SuSA extension to the pion produc-tion region and the realistic spectral function S(p, E) for quasielastic scatteringare used for predictions of charged current inclusive neutrino-nucleus cross sec-tions. The results are compared with the inclusive neutrino-nucleus data fromthe T2K experiment.1 IntroductionNew measurements of inclusive charged current (CC) neutrino-nucleus scatter-ing cross sections, where only the outgoing lepton is detected, have been recentlyperformed by the T2K [1] collaboration. For neutrino energies around 1 GeV(T2K) the main contributions to the cross sections are associated with quasielas-tic (QE) scattering and one pion (1pi) production. In the present work we take55M.V. Ivanov et al.into account these contributions, while at higher neutrino energies multiple pionand kaon production, excitation of resonances other than the ∆ and deep inelas-tic channels should also be further considered.In most neutrino experiments, the interactions of the neutrinos occur with nu-cleons bound in nuclei. Model predictions for these reactions involve many dif-ferent effects such as nuclear correlations, interactions in the final state, possiblemodification of the nucleon properties inside the nuclear medium, that presentlycannot be computed in an unambiguous and precise way. This is particularlytrue for the channels where neutrino interactions take place by means of exci-tation of a nucleon resonance and ulterior production of mesons. The data onneutrino-induced CC charged pion production cross sections on mineral oil re-cently released by the MiniBooNE collaboration [2] provides an unprecedentedopportunity to carry out a systematic study of double differential cross section ofthe processes: νµ p→ µ−p pi+ and νµ n→ µ−npi+ averaged over the neutrinoflux.The analyses of the world data on inclusive electron-nucleus scattering [3]confirmed the observation of superscaling and thus justified the extraction of auniversal nuclear response to be also used for weak interacting probes. However,while there is a number of theoretical models that exhibit superscaling, such asfor instance the relativistic Fermi gas (RFG) [4, 5], the nuclear response departsfrom the one derived from the experimental data. This showed the necessity toconsider more complex dynamical pictures of finite nuclear systems – beyondthe RFG – in order to describe the nuclear response at intermediate energies.SuSA predictions are based on the phenomenological superscaling function ex-tracted from the world data on quasielastic electron scattering [6]. The model hasbeen extended to the ∆-resonance region [7] where the response of the nuclearsystem proceeds through excitation of internal nucleonic degrees of freedom. In-deed, a non-quasielastic cross section for the excitation region in which nucleonexcitations, particularly the ∆, play a major role was obtained by subtractingfrom the data QE-equivalent cross sections given by SuSA [8, 9]. This proce-dure has been possible due to the large amount of available high-quality data ofinelastic electron scattering cross sections on 12C, including also separate infor-mation on the longitudinal and transverse responses, the latter containing im-portant contributions introduced by effects beyond the impulse approximation(non-nucleonic).Here we extend the analysis to CC pion production cross-section measuredat MiniBooNe, that from the theoretical point of view can be seen as more chal-lenging. For instance, ∆ properties in the nuclear medium, as well as both co-herent and incoherent pion production for the nucleus should be considered inany theoretical approach, while in the SuSA procedure they are included phe-nomenologically extracted from the electron scattering data. All what is as-sumed within SuSA approach is the nuclear response to be factorized into asingle-nucleon part and a ‘nuclear function’ accounting for the overall interac-tion among nucleons. As mentioned before, the SuSA assumptions have been56Charged-Current Inclusive Neutrino Cross Sections: Superscaling Extension . . .Figure 1. The SuSA scaling function in the ∆-region f∆(ψ∆) (solid line) extracted fromthe world data on electron scattering [7]. The dotted line shows the scaling functionsf∆(ψ∆) in the RFG model.tested against a great deal of electron-nucleus scattering data with fair success(see Section 2.1). The factorization assumption allows to apply the same nu-clear responses derived from electron scattering to neutrino-induced reactions,with a mere use of the adequate single-nucleon terms for this case. To show theimportance of nuclear interaction effects as predicted within SuSA, as a refer-ence, we also show results obtained within the RFG, with no interactions amongnucleons, for which the scaling function in the ∆-domain is simply given asf∆RFG(ψ∆) =34(1− ψ∆2)θ(1− ψ∆2) with ψ∆ the dimensionless scaling vari-able extracted from the RFG analysis that incorporates the typical momentumscale for the selected nucleus [7, 10]. In Figure 1 we compare the ∆-regionSuSA [7] and RFG scaling functions, which we use in our study.2 Theoretical Scheme and Results2.1 Test versus Electron ScatteringIn Figure 2 we compare our theoretical predictions with inclusive electron scat-tering data on 12C. In the QE region we use natural orbitals scaling functionincluding final state interaction (NO+FSI), whereas for the ∆ region we makeuse e.g. the scaling function presented in Figure 1. Details in how the NO+FSIscaling function is obtained is given in Ref. [11] (see also A.N. Antonov in thisProceedings). Here we only show results for a few representative choices ofkinematics, similar to those involved in the neutrino experiments that we ad-dress in the following sections. As observed, results are in good agreement withthe data, while some disagreement remains in the comparison to the data in the“dip” region between the QE and ∆ peaks. Meson-exchange current (MEC)contribution, that is not accounted for in this work, plays a major role in fillingthe “dip” region.57M.V. Ivanov et al.Figure 2. Double-differential inclusive electron-carbon cross sections, dσ/dωdΩ. Thepanels are labeled according to beam energy, scattering angle, and value of qQE at thequasielastic peak. The results are compared with the experimental data from [12].2.2 pi+ Production in the MiniBooNE ExperimentIn what follows we present the results of applying the SuSA and RFG ∆-scalingfunction to neutrino-induced CC charged pion production. We follow the for-malism given in [7]. The charged-current neutrino cross section in the targetlaboratory frame is given in the formd2σdΩdk′=(G cos θck′)22pi2(1− |Q2|4′)F2, (1)where Ω, k′ and ′ are the scattering angle, momentum and energy of the out-going muon, G is the Fermi constant and θc is the Cabibbo angle. The functionF2 depends on the nuclear structure through the R responses and can be writtenas [7, 13]:F2 = V̂CCRCC + 2V̂CLRCL + V̂LLRLL + V̂TRT + 2V̂T′RT′that is, as a generalized Rosenbluth decomposition having charge-charge (CC),charge-longitudinal (CL), longitudinal-longitudinal (LL) and two types of trans-verse (T,T′) responses (R’s) with the corresponding leptonic kinematical factors(V ’s). The nuclear response functions in ∆-region are expressed in terms of thenuclear tensor Wµν in the corresponding region. The basic expressions used tocalculate the single-nucleon cross sections are given in [7]. These involve theleptonic and hadronic tensors as well as the response and structure functions forsingle nucleons. A convenient parametrization of the single-nucleon W+n →∆+ vertex is given in terms of eight form-factors: four vector (CV3,4,5,6) and fouraxial (CA3,4,5,6) ones. Vector form factors have been determined from the analy-sis of photo and electro-production data, mostly on a deuteron target. Among the58Charged-Current Inclusive Neutrino Cross Sections: Superscaling Extension . . .Figure 3. The double-differential cross section averaged over the neutrino energy flux asa function of the muon kinetic energy Tµ obtained by SuSA and RFG ∆-region scalingfunctions. In each subfigure the results have been averaged over the corresponding angu-lar bin of cos θ. For vector and axial form-factors two parameterizations, “PR1” [14] and“PR2” [15], are used.axial form factors, the most important contribution comes from CA5 . The factorCA6 , whose contribution to the differential cross section vanishes for masslessleptons, can be related to CA5 by PCAC. Since there are no other theoreticalconstraints for CA3,4,5(q2), they have to be fitted to data. We use two differentparameterizations: the one given in [14] where deuteron effects were evaluated(authors estimated that the latter reduce the cross section by 10%), denoted as“PR1”, and the one from [15], called “PR2”.With these ingredients, we evaluate the cross section for CC ∆++ and ∆+production on proton and neutron, respectively. Once produced, the ∆ decaysinto piN pairs. For the amplitudes A of pion production the following isospindecomposition applies: A(νl p→ l−p pi+) = A3,A(νl n→ l−npi+) = 13A3+2√23 A1, A(νl n→ l−p pi0) = −√23 A3 + 23A1, with A3 being the amplitude forthe isospin 3/2 state of the piN system, predominantly ∆, andA1 the amplitudefor the isospin 1/2 state that is not considered here.The double-differential cross section for CC neutrino-induced pi+ produc-tion averaged over the neutrino energy flux as a function of the muon kineticenergy Tµ is presented in Figure 3. Each panel corresponds to a bin of cos θ.PR1 and PR2 parametrizations have been considered. Results with the PR1 pa-rameterization are about 5% higher, that is a measure of the degree of uncertaintythat we expect from the choice of the single-nucleon response for this reaction.We compare the predictions of SuSA and RFG with the MiniBooNE data [2].The nuclear target has been considered as carbon and hydrogen in the mineraloil target. Here we show that SuSA predictions are in good agreement withthe MiniBooNE experimental data for pi+ cross-section in the case of the fluxaveraged data.59M.V. Ivanov et al. 0 2 4 6 8 10 0  200  400  600  800  10000.94 < cos qm < 1.00  0 2 4 6 8 10 12 0  200  400  600  800  10000.90 < cos qm < 0.94  0 2 4 6 8 10 12 14 0  200  400  600  800  10000.84 < cos qm < 0.90  0 1 2 3 4 5 6 7 8 9 0  200  400  600  800  10000.00 < cos qm < 0.84 QE(NO+FSI)1pQE(NO+FSI)+1pFigure 4. The CC inclusive T2K flux-folded νµ-12C double-differential cross sectionper nucleon evaluated using NO+FSI scaling function in the QE region [QE(NO+FSI)]and SuSA scaling function in the ∆-region [1pi] is displayed as a function of the muonmomentum for different bins in the muon angle. The separate contributions of the QEand 1pi are displayed. The data are from [1].2.3 Charged-Current Inclusive Neutrino Cross Sections inthe T2K ExperimentIn Figure 4 we show the CC inclusive νµ−12C double-differential cross sectionper nucleon versus the muon momentum, pµ, for different angular bins, foldedwith the T2K flux. The QE curve corresponds to the results obtained usingNO+FSI scaling function [11] (see also A.N. Antonov in this Proceedings). TheNO+FSI scaling function is obtained using realistic energy dependence of thespectral function S(p, E) and an account for the effects of short-range nucleon-nucleon correlations when natural orbitals (NOs) from the Jastrow method areincluded. The NO+FSI scaling function is accounting also for the role of thefinal-state interactions (FSI). The resonant pion production curve (1pi) is derivedwith the SuSA scaling function in the ∆-region f∆(ψ∆) (Figure 1). The bandcorresponds to the two different parametrizations, PR1 and PR2, described inSection 2.2. We observe that the model yields very good agreement with theT2K data.3 ConclusionsWe conclude that the idea of the SuSA approach for the ∆-region (extracted fromelectron scattering experiments) in addition with the use of natural orbitals scal-60Charged-Current Inclusive Neutrino Cross Sections: Superscaling Extension . . .ing function and including final state interaction (NO+FSI) for the QE-region,when being extended to neutrino processes, proves to be very successful in de-scribing νµ inclusive charged-current cross sections. Our model, after beingtested against electron scattering data, has been proved to explain with successneutrino scattering data taken at different kinematics and explaining several re-gions of great interest, such as the QE and ∆ ones.AcknowledgementsThis work was partially supported by INFN under project MANYBODY, bySpanish DGI and FEDER funds (FIS2011-28738-C02-01, FPA2013-41267), bythe Junta de Andalucia, by the Spanish Consolider-Ingenio 2000 program CPAN(CSD2007-00042), by the Campus of Excellence International (CEI) of Mon-cloa project (Madrid) and Andalucia Tech, by the Bulgarian National ScienceFund under contracts No. DFNI-T02/19 and DFNI-E02/6. R.G.J. acknowledgesfinancial help from the Interuniversity Attraction Poles Programme initiated bythe Belgian Science Policy Office.References[1] K. Abe et al. [T2K Collaboration], Phys. Rev. D 87 (2013) 092003.[2] A.A. Aguilar-Arevalo et al. (MiniBooNE Collaboration), Phys. Rev. D 83 (2011)052007.[3] T.W. Donnelly and I. Sick, Phys. Rev. Lett. 82 (1999) 3212; Phys. Rev. C 60 (1999)065502.[4] W.M. Alberico, A. Molinari, T.W. Donnelly, E.L. Kronenberg, and J.W. Van Orden,Phys. Rev. C 38 (1988) 1801.[5] M.B. Barbaro, R. Cenni, A. De Pace, T.W. Donnelly, and A. Molinari, Nucl. Phys.A 643 (1998) 137.[6] J. Jourdan, Nucl. Phys. A 603 (1996) 117.[7] J.E. Amaro, M.B. Barbaro, J.A. Caballero, T.W. Donnelly, A. Molinari and I. Sick,Phys. Rev. C 71 (2005) 015501.[8] M.B. Barbaro, J.A. Caballero, T.W. Donnelly, and C. Maieron, Phys. Rev. C 69(2004) 035502.[9] C. Maieron, J.E. Amaro, M.B. Barbaro, J.A. Caballero, T.W. Donnelly,C.F. Williamson, Phys. Rev. C 80 (2009) 035504.[10] C. Maieron, T.W. Donnelly, and I. Sick, Phys. Rev. C 65 (2002) 025502.[11] M.V. Ivanov, A.N. Antonov, J.A. Caballero, G.D. Megias, M.B. Barbaro, E. Moyade Guerra, J.M. Udı´as, Phys. Rev. C 89 (2014) 014607; M.V. Ivanov, A.N. Antonov,M.B. Barbaro, C. Giusti, A. Meucci, J.A. Caballero, R. Gonza´lez-Jime´nez, E. Moyade Guerra, and J.M. Udı´as, Phys. Rev. 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Charged-Current Inclusive Neutrino Cross
Sections: Superscaling Extension to the Pion
Production and Realistic Spectral Function for
Quasielastic Region

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Charged-Current Inclusive Neutrino Cross Sections: Superscaling Extension to the Pion Production and Realistic Spectral Function for Quasielastic Region

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