Charged current inclusive neutrino cross sections ... · Charged current inclusive neutrino cross...

Charged current inclusive neutrino cross sections:Superscaling extension to the pion production andrealistic spectral function for quasielastic region

M.V. Ivanov1,2 A.N. Antonov1 M.B. Barbaro3 J.A. Caballero4

G.D. Megias4 R. Gonzalez-Jimenez4 E. Moya de Guerra2

J.M. Udias2

1Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy ofSciences, Sofia, Bulgaria

2Grupo de Fısica Nuclear, Departamento de Fısica Atomica, Molecular y Nuclear,Universidad Complutense de Madrid, Madrid, Spain

3Dipartimento di Fisica, Universita di Torino and INFN, Sezione di Torino,Torino, Italy

4Departamento de Fısica Atomica, Molecular y Nuclear, Universidad de Sevilla,Sevilla, Spain

June 8, 201514th International Conference on Nuclear Reaction Mechanisms, Varenna, Italy, June 15–19, 2015 1/37

1 Theoretical scheme

2 Test versus electron scattering

3 Neutrino scattering

Charged current inclusive neutrino cross sections: Superscaling extension to the pion production and . . . 2/37

In most neutrino experiments, the interactions of the neutrinosoccur with nucleons bound in nuclei. The influence of nucleoninteractions on the response of nuclei to neutrino probes must thenbe considered, ideally in a model independent way. Modelpredictions for these reactions involve many different effects(nuclear correlations, interactions in the final state, possiblemodification of the nucleon and nucleon resonances propertiesinside the nuclear medium) that presently cannot be computed in aunambiguous and precise way. This is particularly true for thechannels where neutrino interactions take place by means ofexcitation of a nucleon resonance and ulterior production ofmesons.


One way of avoiding model-dependencies is to use the nuclearresponse to other leptonic probes, such as electrons, under similarconditions than the neutrino experiments. In this work we havecompared the predictions for neutrino-induced CC π+ productioncross sections on mineral oil (CH2) obtained using the superscalinganalyses with the MiniBooNE data

A.A. Aguilar-Arevalo et al. (MiniBooNE Collaboration),Phys. Rev. D 83, 052007 (2011).

and for νµ-12C inclusive charged current double differential crosssections with T2K data

K. Abe et al. (T2K Collaboration), Phys. Rev. D 87, 092003(2013).

This is justified on the success of the scaling ideas and theobservation of superscaling in electron-nucleus scattering.


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F(en)

/ F

tot [G

eV

-1]

en [GeV]

T2K - nmT2K - ne

MiniBooNE - nm


The method relies on the superscaling properties of the electronscattering data: at sufficiently high momentum transfer theinclusive differential (e, e ′) cross sections, divided by a suitablefunction which takes into account the single nucleon content of theproblem, depends only upon one kinematical variable, the scalingvariable (this behavior is called scaling of first kind) and theresulting function is roughly the same for all nuclei (scaling ofsecond kind). When both kinds of scaling are fulfilled the crosssection is said to superscale.


More specifically the scaling function

f =d2σ/dΩdk ′

S(q, ω), (1)

being S related to the single nucleon cross section, becomes, forlarge q, a function only of the scaling variable

ψQE = ±

√√√√ 1

2TF

(q

√1 +

1

τ− ω − 1

), (2)

where TF is the Fermi kinetic energy, 4m2Nτ = q2 − ω2 and

the − (+) sign corresponds to energy transfers lower (higher) thanthe QEP (ψ = 0).


Indeed the analyses of the world data on inclusiveelectron-nucleus scattering confirmed the observation of thisphenomenon and thus allowed to extract a universal nuclearresponse to weak interacting probes.


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-2 -1 0 1 2 3

fQE(y

)

y


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-2 -1 0 1 2 3

fQE(y

)

y

RFG


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-2 -1 0 1 2 3

fQE(y

)

y

RFGNO+FSI


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-2 -1 0 1 2 3

fQE(y

)

y

RFGSuSA

NO+FSI


The superscaling analysis has been extended to the first resonancepeak in

J. E. Amaro et al., Phys. Rev. C 71, 015501 (2005).

where the contribution of the ∆ has been (approximately) isolatedin the experimental data by subtracting the quasielastic scalingcontribution from the total experimental cross sections; thereduced cross section has been studied as a function of a newscaling variable

ψ∆ = ±

√√√√ 1

2TF

(q

√ρ+

1

τ− ωρ− 1

), (3)

which accounts for the inelasticity through the quantityρ = 1 + (m2

∆ −m2N)/(4τm2

N).


The results show that also in this region superscaling is workingquite well and therefore a second superscaling function, f ∆(ψ∆),can be extracted from the data to account for the nucleardynamics. Clearly this approach can work only at ψ∆ < 0, since atψ∆ > 0 other resonances and the tail of the deep-inelasticscattering start contributing.


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12C, ee = 1108 MeV, qe = 37.500o, qQE » 674.6 MeV

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12C, ee = 1930 MeV, qe = 16.000

o, qQE » 536.3 MeV

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12C, ee = 680 MeV, qe = 36.000

o, qQE » 402.5 MeV

QE(NO+FSI)D(SuSA)

QE(NO+FSI)+D(SuSA)

ds

/dw

dW

(nb/M

eV

/sr)

w(MeV) w(MeV)


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12C, ee = 3595 MeV, qe = 16.020

o, qQE » 1044.3 MeV

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12C, ee = 560 MeV, qe = 145.000

o, qQE » 795.0 MeV

QE(NO+FSI)D(SuSA)

QE(NO+FSI)+D(SuSA)

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12C, ee = 1299 MeV, qe = 37.500

o, qQE » 791.0 MeV

ds

/dw

dW

(n

b/M

eV

/sr)

w(MeV) w(MeV)


To obtain of the results of applying the SuSA and RFG ∆-scalingfunction to the calculations of neutrino-induced charged-currentcharged pion production, we follow the formalism given in


The charge-changing neutrino cross section in the target laboratoryframe is given in the form[

d2σ

dΩdk ′

]χ

≡ σ0F2χ; σ0 ≡

(G cos θc)2

2π2

[k ′ cos θ/2

]2(4)

where χ = + for neutrino-induced reactions (for example,νl + n→ `− + p, where ` = e, µ, τ) and χ = − forantineutrino-induced reactions (for example, νl + p → `+ + n),G = 1.16639× 10−5 GeV−2 is the Fermi constant and θc is theCabibbo angle (cos θc = 0.9741),

tan2 θ/2 ≡ |Q2|

v0, v0 ≡ (ε+ ε′)2 − q2 = 4εε′ − |Q2|.


The function F2χ depends on the nuclear structure and can be

written as:

F2χ = [VCCRCC + 2VCLRCL + VLLRLL + VTRT] + χ[2VT′RT′ ]

that is, as a generalized Rosenbluth decomposition havingcharge-charge (CC), charge-longitudinal (CL),longitudinal-longitudinal (LL) and two types of transverse (T,T′)responses (R’s) with the corresponding leptonic kinematical factors(V ’s). The nuclear response functions in ∆-region are expressed interms of the nuclear tensor W µν in the corresponding region timesthe single-nucleon response.


The nuclear response functions Ri can be expressed in terms of thenuclear tensor W µν . For the excitation of a stable ∆ resonance theRFG hadronic tensor turns out to be:

[W µν ]∆ =1

2

3N4mNη

3Fκ

fRFG (ψ∆)Uµν∆ , (5)

where κ = q/2mN and ηF =√ξF (ξF + 2) = kF/mN are the

dimensionless transferred and Fermi momentum, respectively, andthe “single-nucleon” tensor Uµν

∆ embeds the information about theN −∆ transition1.

The basic expressions used to calculate the “single-nucleon” tensorUµν

∆ are given in


1Actually in a fully relativistic framework the single nucleon physics cannotbe exactly disentangled from the many-body part of the problem and the tensorUµν

∆ contains corrections due to the medium.Charged current inclusive neutrino cross sections: Superscaling extension to the pion production and . . . 25/37

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 four axial (CA3,4,5,6) ones. Vector form factors have been

determined from the analysis of photo and electro-production data,mostly on a deuteron target, considered as a good approximationto free nucleons to these purposes. Among the axial form factorsthe most important contribution comes from CA

5 . The form factorCA

6 , whose contribution to the differential cross section vanishesfor massless leptons, can be related to CA

5 due to the partialconservation of the axial current. Since there are no othertheoretical constraints for CA

3,4,5(q2), they have to be fitted to data.


In our calculations we use for vector and axial form-factors twodifferent parameterizations: the one given in

L. Alvarez-Ruso, S. K. Singh and M. J. Vicente Vacas,Phys. Rev. C 59, 3386 (1999),

where deuteron effects were evaluated (authors estimated that thelatter reduce the cross section by 10%), we call it “PR1”, and theone from

E. A. Paschos, J.-Y. Yu and M. Sakuda,Phys. Rev. D 69, 014013 (2004),

called by us“PR2”.


With these ingredients, we obtain the cross section for CC ∆++

and ∆+ production on proton and neutron, respectively. Onceproduced, the ∆ decays into πN pairs. For the amplitudes A ofpion production the following isospin decomposition applies

A(νl p → l−p π+) = A3,

A(νl n→ l−n π+) =1

3A3 +

2√

2

3A1,

A(νl n→ l−p π0) = −√

2

3A3 +

2

3A1,

with A3 being the amplitude for the isospin 3/2 state of the πNsystem, predominantly ∆, and A1, the amplitude for the isospin1/2 state which is not considered here.


π+ production from ∆ resonance region of neutrino-inducedcharged-current νµ–CH2

(MiniBooNE experiment)


Firstly, I will show the results for the double-differential crosssection results of the π+ production from ∆ resonance region ofneutrino-induced charged-current νµ–CH2 reaction averaged overthe neutrino flux Φ(εν), namely

d2σ

dTµd cos θ=

1

Φtot

∫ [d2σ

dTµd cos θ

]εν

Φ(εν)dεν , (1)

where Tµ and θ are correspondingly the kinetic energy andscattering angle of the outgoing muon, εν is the neutrino energyand Φtot is the total integrated νµ flux factor for the MiniBooNEexperiment. In each figure the results have been averaged over thecorresponding angular bin of cos θ.


d2s

/d(c

osq

)/dTm [1

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m2/M

eV

]

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0.95 < cosq < 1.00

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Tm [GeV]

0.35 < cosq < 0.40

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0.75 < cosq < 0.80

RFG, PR1RFG, PR2

SuSA, PR1SuSA, PR2MiniBooNE

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Tm [GeV]

0.55 < cosq < 0.60


d2s

/d(c

osq

)/dTm [1

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2 c

m2/M

eV

]

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Tm [GeV]

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RFG, PR1RFG, PR2

SuSA, PR1SuSA, PR2MiniBooNE

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0.15 < cosq < 0.20


The SuSA approach provides neutrino-nucleus cross-sectionpredictions, based on the observed nuclear response to electronprojectiles under similar kinematics as the neutrinos considered inthis work. In this way, the SuSA scaling function andcorresponding cross-section predictions, incorporate effect of finalstate interaction, the properties of the ∆ resonance in the nuclearmedium, etc. SUSA predictions are in good agreement with theMiniBooNE experimental data for pionic cross-section.


νµ inclusive charged current double differential cross sections

(T2K experiment)


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pm [MeV/c]

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QE(NO+FSI)1p

QE(NO+FSI)+1p


So, we can conclude that the idea of the SuSA approach forthe ∆-region (extracted from electron scatteringexperiments) and natural orbitals (NO+FSI) scaling functionincluding final state interaction for the QE-region and theirextension to neutrino processes can be very useful inpredicting of νµ inclusive charged current cross sections.


THANK YOU VERY MUCH FOR YOUR ATTENTION !!!


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