Interpretation of electron- and neutrino-nucleus scattering data

Interpretation of Electron- and Neutrino-NucleusScattering Data

Omar Benhar

INFN and Department of PhysicsUniversita “La Sapienza”

I-00185 Roma, Italy

NUINT11Dehradun, Uttarakhand, India. March 6th, 2011

Outline

Preamble: Conclusions of my talk on the same subject at NUINT04

∗a philosophical or theoretical framework of any kind (Merriam-Webster)Omar Benhar (INFN, Roma) NUINT11 Dehradun 06/03/2011 2/ 18

Outline


Bottom line: theparadigm∗ of electron-nucleus scattering


Outline



Neutrino-nucleus scattering: impact of the flux average


Outline




Inclusion of reaction mechanisms beyond the impulse approximation


Outline





Learning form electron scattering again: a numerical experiment


Outline





Learning form electron scattering again: a numerical experiment

Outlook


Preamble: recollections of NUINT04

Omar Benhar (INFN, Roma) NUINT11 Dehradun 06/03/2011 3/ 18

Theparadigmof electron-nucleus scattering

Thanks to the availability of a large body of precise data, theoreticalmodels of electron-nucleus scattering have reached a high level ofaccuracy




The paradigm

⊲ Lepton kinematics fully determined⊲ Elementary interaction vertex (dσN ) determined by electron-protonand

electron-deuterondata (nuclear dynamics largely decoupled)




The paradigm

⊲ Lepton kinematics fully determined⊲ Elementary interaction vertex (dσN ) determined by electron-protonand

electron-deuterondata (nuclear dynamics largely decoupled)

A simple implementation: the impulse approximation (IA) scheme:

⊲ At large momentum transfer electron-nucleus scattering reduces to theincoherent sum of scattering processes involving individual nucleons

Σi

2 2q,ω q,ω

i

x


The electron-nucleus x-section in the IA regime

dσA =

∫

d3kdE dσN P(k,E)

Electron-nucleon cross section from proton and deuteron data

Nucleon spectral function

P(k,E) =∑

n

|〈n |ak|0〉|2 δ(E + E0 − En)

describes the momentumandenergy distribution of the knocked outnucleon. It can be obtained combining the available (e, e′p) data and theresults of accurate many-body calculations, based on highly realisticnuclear hamiltonians


Comparing quasi elastic (QE)e-A & ν-A x-sections

QE electron scattering is usually analyzed at fixed beam energy Ee andelectron scattering angleiθe, as a function of the energy transferω = Ee− Ee′ , |q| being nearly constant




The data set of MiniBooNE Charged Current Quasi Elastic (CCQE)events provides an unprecedented opportunity to perform a similaranalysis and carry out a systematic study of the (flux averaged) doubledifferential cross section

dσA

dTµdcosθµ=

1N

∫

dEνΦ(Eν)dσA

dEνdTµdcosθµ




The data set of MiniBooNE Charged Current Quasi Elastic (CCQE)events provides an unprecedented opportunity to perform a similaranalysis and carry out a systematic study of the (flux averaged) doubledifferential cross section

dσA

dTµdcosθµ=

1N

∫

dEνΦ(Eν)dσA

dEνdTµdcosθµ

Extending the paradigm of electron scattering to the analysis of theCCQE neutrino data amounts to using the nucleon axial form factorobtained from deuteron data, i.e. to setting the axial mass toMA = 1.03 GeV


Quasi elastic (QE) electron- & neutrino-nucleus x-sections

Recall: Calculations (PRL 105 (2010) 132301) involveno adjustableparameters

⊲ Data: J.S. O’Connellet al, PRC35, 1063 (1987)





⊲ Data: MiniBooNe, PRD 79 (2009) 072002





⊲ Data: MiniBooNe, PRD 79 (2009) 072002

The paradigm fails to explain theflux-averagedcross section


Impact of neutrino flux average

In neutrino interations the lepton kinematics isnot fully determined. Theflux-averaged double differential cross sections picks up contributions iatdifferent neutrino energies, corresponding to a variety of kinematicalregimes in which different reaction mechanisms dominate


Impact of neutrino flux average

In neutrino interations the lepton kinematics isnot fully determined. Theflux-averaged double differential cross sections picks up contributions iatdifferent neutrino energies, corresponding to a variety of kinematicalregimes in which different reaction mechanisms dominate

Schematic view of thee-A x-section atEe in the few GeV region


Contribution of different reaction mechanisms

consider the muon energy bin corresponding to the maximum oftheMiniBooNE CCQE cross section at 37 < θµ < 46

⊲ xBJ = 1→ Eν .788 GeV , xBJ = 0.5→ Eν .975 GeV⊲ Φ(.975)/Φ(.788)= 0.83


Reaction mechanisms beyond the IA scheme:Meson Exchange Currents (MEC)

The electroweak nuclear current involves two-nucleon contributions,arising from nucleon-nucleon interactions and nucleon excitations

J µA =A

∑

i=1

j µ1 (i) +A

∑

j>1=1

j µ2 (i, j)u (a) oooooooooo 0(b) (c)In electron nucleus scattering MEC are known to produce a significantenhancement of the3Heand4He inclusive x-section in the transversechannel


MEC effect on the transverse electromagnetic responseL/T separation of the the inclusiveeAx-section

d2σ

dΩe′dEe′=

(

dσdΩe′

)

M

[

Q4

|q|4RL(|q|, ω) +

(

12

Q2

|q|2+ tan2 θ

2

)

RT(|q|, ω)

]

Calculations by M.J. Dekkeret alPLB 266 ( 1991 ) 249.


Dynamically Consistent Treatment of MEC

The nuclear electromagnetic current must satisfy the continuity equation

∂µJµ = ∇ · J + i[H, J0] = 0 ,

whereH is the nuclear hamiltonian




∂µJµ = ∇ · J + i[H, J0] = 0 ,


The two-body current can be separated into a model-independent term,fully determined from the interaction, and a model-dependent oneassociated with theρπγ andωπγ electromagnetic couplings




∂µJµ = ∇ · J + i[H, J0] = 0 ,



A fully consistent treatment of the contribution of two particle-teo-holefinal states requires the inclusion of initial state nucleon-nucleoncorrelations, final state interactions and MEC




∂µJµ = ∇ · J + i[H, J0] = 0 ,



A fully consistent treatment of the contribution of two particle-teo-holefinal states requires the inclusion of initial state nucleon-nucleoncorrelations, final state interactions and MEC

ab initio calculations based on realistic nuclear hamiltonians and wavefunctions provide a very good description of the electron scatteringx-sections of light nuclei


May MEC contributions be the source of the disagreementbetween theory and CCQE data?

A piece of circumstantial evidence: the disagreement decreases at smallθµ


“Flux averaged” electron-nucleus x-section

The electron scattering x-section off Carbon atθe= 37 has beenmeasured for a number of beam energies

MIT-Bates data compared to theoretical calculations including QEscattering only


A numerical experiment

Consider the cross section atθ=37 and550≤ Te′ ≤ 650 MeV(corresponding to the QE peak at 730 MeV)

Data are available atEe = 730, 961, 1108, 1299 and 1501 MeV





Compute the flux averaged cross section using experimental data andassuming that the electron beam energies be distributed according to theMiniBooNE neutrino flux (Σexp)

Compute the flux averaged cross section using the results of theoreticalcalculations including QE scattering only (Σth)







The above procedure yields

Σexp

Σth∼> 1.20







The above procedure yields

Σexp

Σth∼> 1.20

The theoretical model that explains the QE x-sections at fixed beamenergy fails to reproduce the flux averaged x-section


Summary and outlook

Due to flux average, different reaction mechanism contribute to thedifferential neutrino cross section at fixed values of the measuredkinematical variables


Summary and outlook


The theoretical description of the flux averaged cross section requiresthat all the relevant mechanisms be taken into account within aconsistentframework


Summary and outlook



Electron scattering data suggest that a significant contribution may comefrom processes involving the meson exchenge currents


Summary and outlook



Electron scattering data suggest that a significant contribution may comefrom processes involving the meson exchenge currents

Quantitative studies of the flux averaged neutrino-nucleuscross sectioncarried out including meson exchange currents are needed inorder toclarify the controversial issue of the nucleon axial mass inthe nuclearmedium.


Oxygen spectral function

shell model states account for∼ 80% of the strenghtthe remaining∼ 20%, lies in the region of high momentumand largeremoval energy


MEC model of Dekkeret al (A.D. 1991)

Nuclear structure described according to the RFG model.


Interpretation of electron- and neutrino-nucleus scattering data

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