Antonov, An

Barbaro, Maria Benedetta

Caballero, Ja

Ivanov, Mv

Moya De Guerra, E

Udias, Jm

English

Institutional Research Information System University of Turin

NUCLEAR THEORY, Vol. 32 (2013)eds. A.I. Georgieva, N. Minkov, Heron Press, SofiaSuperscaling Analysis and Neutrino-InducedCharged-Current Pion Production atMiniBooNE KinematicsM.V. Ivanov1,2, A.N. Antonov2, J.A. Caballero3, M.B. Barbaro4,E. Moya de Guerra1, J.M. Udias11Grupo de Fı´sica Nuclear, Departamento de Fı´sica Ato´mica, Molecular yNuclear, Facultad de Ciencias Fı´sicas, Universidad Complutense de Madrid,CEI Moncloa, Madrid E-28040, Spain2Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy ofSciences, Sofia 1784, Bulgaria3Departamento de Fı´sica Ato´mica, Molecular y Nuclear, Universidad de Sevilla,41080 Sevilla, Spain4Dipartimento di Fisica, Universita` di Torino and INFN, Sezione di Torino,Via P. Giuria 1, 10125 Torino, ItalyAbstract. Superscaling approximation (SuSA) predictions to neutrino-inducedcharged-current pion production in the Δ-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 scat-tering angle, the cross sections averaged over the angle, the total cross sectionfor the pion production, as well as CC1π+ to CCQE cross section ratio arecompared with the corresponding MiniBooNE experimental data. The SuSAcharged-current π+ predictions are in good agreement with data on neutrinoflux average cross-sections, but a somewhat different dependence on the neu-trino energy (for charged-current π+ and π0 production) is predicted than theone resulting from the experimental analysis.The studies of the neutrino oscillations are of particular importance beingrelated to the information on the limits of the Standard Model. In most neu-trino experiments, the interactions of the neutrinos occur with nucleons boundin nuclei. The influence of nucleon-nucleon interactions on the response of nu-clei to neutrino probes must then be considered, ideally in a model independentway. Model predictions for these reactions involve many different effects suchas nuclear correlations, interactions in the final state, possible modification ofthe nucleon properties inside the nuclear medium, that presently cannot be com-puted in an unambiguous and precise way. This is particularly true for the chan-nels where neutrino interactions take place by means of excitation of a nucleonresonance and ulterior production of mesons. The data set of neutrino-induced82Superscaling Analysis and Neutrino-Induced Charged-Current Pion Production ...charged-current (CC) charged and neutral pion production cross sections on min-eral oil recently released by the MiniBooNE collaboration [1] provides an un-precedented opportunity to carry out a systematic study of double differentialcross section of the processes:ν(k) + p(p) → μ−(k′) + Δ++(p′)↪→ p(p′′) + π+(pπ). (1)orν(k) + n(p)→ μ−(k′) + Δ+(p′)↪→ n(p′′) + π+(pπ) (2)or↪→ p(p′′) + π0(pπ). (3)averaged over the neutrino flux (k and p being the corresponding four-momentum).The momentum transfer will be denoted by q = k − k′.The extensive analyses of scaling [2–4] and superscaling [5–10] phenomenaobserved in electron-nucleus scattering lead to the use of the scaling function di-rectly extracted from (e, e′) data to predict neutrino (antineutrino)-nucleus crosssections [11], (not relying on a particular nuclear structure model). Within SuSAa “superscaling function” f(ψ) is built by factoring-out the single-nucleon con-tent off the double-differential cross section and plotting the remaining nuclearresponse versus a scaling variable ψ(q, ω). Approximate scaling of the first kind,i.e., no explicit dependence of f(ψ) on the momentum transfer q, can be seen attransfer energies below the quasielastic (QE) peak. Scaling of second kind,i.e.,no dependence of f(ψ) on the mass number, turns out to be excellent in thesame region. When scaling of both first and second types occur, one says thatsuperscaling takes place.The analyses of the world data on inclusive electron-nucleus scattering [7]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) [5, 6], the nuclear response theypredict departs from the one derived from the experimental data. The point isthat the scaling function in the RFG model is fQERFG(ψ) = 0 for ψ ≤ −1, whereasthe experimental scaling function extracted from (e, e′) data extends to largenegative values of the scaling variable ψ up to ψ ≈ −2 where effects beyond themean-field approximation are important. This showed the necessity to considermore complex dynamical pictures of finite nuclear systems -beyond the RFG- inorder to describe the nuclear response at intermediate energies.The SuSA model is based on the phenomenological superscaling functionextracted from the world data on quasielastic electron scattering [12]. Themodel has been extended to the Δ-resonance region [11] and to neutral cur-rent scattering [13]. It has been already employed to describe the non pionic83M.V. Ivanov et al.Figure 1. The SuSA scaling function in the Δ-region fΔ(ψΔ) (solid line) extracted fromthe world data on electron scattering [11]. The dotted line shows the scaling functionsfΔ(ψΔ) in the RFG model.(QE) cross-section of the MiniBooNE ν- and ν-nucleus cross-section [14–16]and in Ref. [17] it has been applied to neutrino (antineutrino) CCQE on 12C forenergy range up to 100 GeV with a comparison with the MiniBooNE and NO-MAD [18] data. Here and in [19] we extend the analysis to CC pion productioncross-section measured at MiniBooNE. As a reference, we also show results ob-tained within the RFG where the scaling function in the Δ-domain is simplygiven asfΔRFG(ψΔ) =34(1− ψΔ2)θ(1 − ψΔ2), (4)with ψΔ the dimensionless scaling variable extracted from the RFG analysis thatincorporates the typical momentum scale for the selected nucleus [8, 11].In Figure 1 we compare the Δ-region SuSA [11] and RFG scaling functions,which we use in our study. We present the results of applying the SuSA andRFG Δ-scaling function to neutrino-induced CC charged pion production. Wefollow the formalism given in [11]. The charged current neutrino cross sectionin the target laboratory frame is given in the formd2σdΩdk′=(G cos θck′)22π2(1− |Q2|4′)F2 (5)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 [11, 20]: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 factors84Superscaling Analysis and Neutrino-Induced Charged-Current Pion Production ...(V ’s). The nuclear response functions in Δ-region are expressed in terms ofthe nuclear tensor Wμν in the corresponding region. The basic expressionsused to calculate the single-nucleon cross sections are given in [11]. Theseinvolve the leptonic and hadronic tensors as well as the response and struc-ture functions for single nucleons. A convenient parametrization of the single-nucleon W+n → Δ+ vertex is given in terms of eight form-factors: four vec-tor (CV3,4,5,6) and four axial (CA3,4,5,6) ones. Vector form factors have been de-termined from the analysis of photo and electro-production data, mostly on adeuteron target. Among the axial form factors, the most important contributioncomes from CA5 . The factor CA6 , whose contribution to the differential cross sec-tion vanishes for massless leptons, can be related to CA5 by PCAC. Since thereare no other theoretical constraints for CA3,4,5(q2), they have to be fitted to data.We use two different parameterizations: the one given in [21] where deuteroneffects were evaluated, denoted as “PR1”, and the one from [22], called “PR2”.With these ingredients, we evaluate the cross section for CC Δ++ and Δ+production on proton and neutron, respectively. Once produced, the Δ decaysinto πN pairs. For the amplitudes A of pion production the following isospindecomposition applies:A(νl p→ l−p π+) = A3,A(νl n→ l−nπ+) = 13A3 +2√23A1,A(νl n→ l−p π0) = −√23A3 + 23A1,withA3 being the amplitude for the isospin 3/2 state of the πN system, predom-inantly Δ, and A1 the amplitude for the isospin 1/2 state that is not consideredhere.First we present the double-differential cross section for π+ production fromΔ resonance region of neutrino-induced CC νμ–CH2 reaction averaged over theneutrino flux Φ(ν), namelyd2σdTμd cos θ=1Φtot∫ [d2σdTμd cos θ]νΦ(ν)dν , (6)where Tμ and θ are correspondingly the kinetic energy and scattering angle ofthe outgoing muon, ν is the neutrino energy and Φtot is the total integrated νμflux factor for the MiniBooNE experiment (Φtot = 5.19×10−10 [νμ/cm2/POT]).The double-differential cross section averaged over the neutrino energy flux asa function of the muon kinetic energy Tμ is presented in Figure 2. Each panelcorresponds to a bin of cos θ. The “PR2” parametrization has been considered.Results with the PR1 parameterization are about 5% higher. We compare thepredictions of SuSA and RFG with the MiniBooNE data [1]. The nuclear targethas been considered as carbon and hydrogen in the mineral oil target. Figure 285M.V. Ivanov et al.Figure 2. The double-differential cross section averaged over the neutrino energy flux asa function of the muon kinetic energy Tμ obtained by SuSA (solid line) and RFG (dottedline) Δ-region scaling functions. In each subfigure the results have been averaged overthe corresponding angular bin of cos θ. “PR2” parametrization [22] is used. The resultsare compared with the MiniBooNE data [1].shows a good agreement between data and the SuSA predictions for the flux-averaged double-differential cross sections. This applies to both parameteriza-tions of the vector and axial form factors. As expected, RFG results have similarshape as SuSA ones, but they overestimate the data to a large extent.In Figure 3 are shown the results for π+ and π0 production obtained byintegrating the flux-averaged double-differential cross sections over angle:〈dσdTμ〉=1Φtot∫Φ(ν)∫ (d2σdTμd cos θ)νd(cos θ)dν . (7)The total cross section for π+ and π0 production as a function of the neutrinoenergy along with the MiniBooNE data are displayed in Figure 4. Poorer agree-ment with data than for the flux-averaged cross sections presented in Figures 286Superscaling Analysis and Neutrino-Induced Charged-Current Pion Production ...Figure 3. The dσ/dTμ results for π+ (left panel) and π0 (right panel) production obtainedby integrating the flux-averaged double-differential cross sections over cos θ [Eqs. (7)]are compared with the MiniBooNE data [1]. For vector and axial form-factors two pa-rameterizations, “PR1” [21] and “PR2” [22], are used.and 3 is clearly observed in the case of π+ production. The data seems to followa more linear dependence with the energy up to 2 GeV than the theory. However,before drawing definite conclusions, one has to consider that the unfolding pro-cedure used to extract the data of Figure 4 is model dependent, while the directcomparison with the data of Figures 2 and 3 is more significant. In the case ofπ0 production the RFG results are closer to the experimental MiniBooNE datawhile the SuSA results clearly underpredict the data.Figure 5 shows the ratio of CC1π+ (CC single-pion production) to CCQE(CC quasielastic scattering) cross sections from SuSA, SuSA+MEC (2p–2h me-son–exchange current) [14], and RFG approaches in comparison with theMiniBooNE data corrected for final state interactions. All these ratios have beenrescaled to an isoscalar target [23]. The results are obtained on the basis of totalcross sections for CC1π+ (given in Figure 4) and CCQE [14]. A similar conclu-sion as the one in the previous figure could be drawn here. It seems that thereFigure 4. The total cross section for π+ (left panel) and π0 (right panel) production arecompared with the MiniBooNE data [1]. For vector and axial form-factors two parame-terizations, “PR1” [21] and “PR2” [22], are used.87M.V. Ivanov et al.Figure 5. The results for CC1π+ to CCQE cross section ratio are compared withMiniBooNE data (corrected for final state interactions and rescaled for an isoscalar tar-get) [23].is too much π+ production strength below 1.2 GeV, and too little beyond that,compared to data.Summarizing, in this work we present results for the cross sections of neutri-no–induced CC π+ and π0 production obtained with the SuSA and RFG (shownas reference) models. The SuSA approach provides nuclear-model-independentneutrino-nucleus cross-section predictions, based on the observed nuclear re-sponse to electron projectile and the universal character of the scaling function.Notice that SuSA predictions incorporate effects of final state interaction (FSI),the properties of the Δ resonance in the nuclear medium, etc. The role of the FSIon the one-pion production has been considered for instance within the GIBUUtransport model [24], where it was shown that in order to reproduce the data,the total π+ cross section obtained with FSI included has to be multiplied by afactor of 1.5. SuSA predictions are in good agreement with the MiniBooNE ex-perimental data for charged pionic cross-section in the case of the flux averageddata, while some disagreement remains in the comparison to unfolded neutrinoenergy data. Notice that the accordance between SuSA and data here is betterthan the one for the non-pionic case, where the model was found to underpredictthe data unless meson exchange currents were explicitly included [14]. SuSApredictions underpredict the data in the case of neutral pion production, this re-sult is in agreement with other theoretical calculations [25–27]. We concludethat the SuSA approach for the Δ-region (extracted from electron scattering ex-periments) and its extension to neutrino processes is very useful in predictinghighly-model-independent cross sections for neutrino-induced CC π+ produc-tion.88Superscaling Analysis and Neutrino-Induced Charged-Current Pion Production ...AcknowledgementsThis work was partially supported by Spanish DGI and FEDER funds (FIS2011-28738-C02-01, FPA2010-17142), by the Junta de Andalucia, by the SpanishConsolider-Ingenio 2000 program CPAN (CSD2007-00042), by the Campusof Excellence International (CEI) of Moncloa project (Madrid) and AndaluciaTech, by the Istituto Nazionale di Fisica Nucleare under Contract MB31, bythe INFN-MICINN collaboration agreement (AIC-D-2011-0704), as well as bythe Bulgarian National Science Fund under contracts No. DO-02-285 and DID-02/16-17.12.2009. 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Superscaling analysis and neutrino-induced charged-current pion production at MiniBooNE kinematics

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Superscaling analysis and neutrino-induced charged-current pion production at MiniBooNE kinematics

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