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Neutrino Interactions with Nucleons and NucleiPowerPoint Presentation

Neutrino Interactions with Nucleons and Nuclei

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Neutrino InteractionswithNucleonsandNuclei

Tina Leitner, Oliver Buss,

Ulrich Mosel, Luis Alvarez-Ruso

Beijing 03/10

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Neutrino oscillationsearch

- neutrinooscillations: probabilityfor 2 flavors:
- Crucialparameter: neutrinoenergyE
Need to understand ‚classical‘ hadronicinteractions

Flux: obtained from Event-Generators

for hadronic production and subsequentweak decay

Energy must be reconstructed

from hadronic final state

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Oscillation Minium atMiniBooNE

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Motivation

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- Neutrino detectorsnowadays all contain (heavy) nuclei, haveto understand interactionsofneutrinoswith matter
- Interactions ofneutrinoswithnucleimaymaketheidentificationofelementaryprocesses, like knock-out, pion-productionorqescatteringdifficult.

Motivation

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- In-medium physics: vectorand axial form factors in medium havetobeextractedfromreactions on nuclei.
- NUTEV anomalyfor Weinberg angle
- Axial Mass: in MiniBooNEand K2K: 1.0 or 1.25 GeV?

- Neutrino-energy must bereconstructedfromdetectorresponse. NuclearPhysics Input isneeded

The Rebirth of Low Energy Nuclear Physics

Low-Energy Nuclear Physics

determines response

of nuclei to neutrinos

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Outline

l

n

W, Z

- neutrino-nucleusreaction: nlA l hadronsat ~ 0.5 – 1.5 GeVneutrinoenergy
- scattering off a singlenucleon
- freenucleon
- nucleonbound in a nucleus

- Total QE scattering off a nucleusandproduction
- final state interactions (FSI)
- GiBUUtransport model

- final state interactions (FSI)

- scattering off a singlenucleon
- Results:qe scattering,p production, nucleon knockout
- Conclusions

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Model Ingredients: ISI

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- Free primary interaction cross sections, cross sections boosted to restframe of moving nucleon in local Fermigas
- no off-shell dependence, but include spectral functions for baryons and mesons (binding + collision broadening)

- Cross sections taken from
- Electro- and Photoproduction for vector couplings
- Axial couplings modeled with PCAC

- Pauli-principle included
- Shadowing by geometrical factor (Q2,) included

Potential smoothes E-p distributions

Model Ingredients: ISI

- Hole spectralfunction (local TF)Local Thomas-Fermi Particles in mean-field potential!
- Particlespectralfunction: collisionalbroadening
- Inclusivecrosssection

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Neutrino nucleoncrosssection

QE

single ¼

R+

‚ DIS

¼

N

N'

note:

10-38 cm² = 10-11 mb

P. Lipari, Nucl. Phys. Proc. Suppl. 112, 274 (2002)

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Quasielasticscattering

- reactions:
- hadronic current:

with

- axial form factors
- related by PCAC
- dipole ansatz

- extra term
- ensures vector current conservationfor nonequal masses

- vector form factors
- related to EM form factors by CVC
- BBBA-2007 parametrization

in addition:

strange vector and axial form factors for NC

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Quasielasticscattering

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QuasielasticScattering: Axial Mass

- neutrinos probe nucleons / nuclei via V-A weak interaction
- axial structureof the nucleon and baryonic resonances (in the medium!)
- nuclear effects(e.g. low-Q² deficit in MiniBooNE)
- dedicated neutrino-nucleus experiment: Minerva

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Pion productionthroughresonanceexcitation

- 13 resonanceswith W < 2 GeV
- pionproductiondominatedbyP33(1232) resonance:
- CVfromelectrondata (MAID analysiswith CVC)
- CAfrom fit toneutrinodata(experiments on hydrogen/deuterium)

BNL

10 % error in C5A(0)

ANL

discrepancy between ANL and BNL data uncertainty in axial form factor

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CC pionproduction on freenucleons

- CC productionofD+andD++
- subsequent decayinto3channels:

BNL data

including higher resonances (isospin ½):

ANL data

How much is background??

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- Nuclear Targets (K2K, MiniBooNE, T2K, MINOS, Minerva, ….

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Medium modifications of the inclusive cross section

- All crosssections Fermi smeared
- D crosssectionisfurthermodified in thenuclear medium:
- p decaymightbe Pauli blocked: decreaseofthefreewidth
- additional "decay" channels in the medium: collisionalwidthcoll
overalleffect:

increaseofthewidth

!med = P + coll

collisional broadening

"pion-lessdecay"

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Transport vs. Quantummechanics

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- Fullyinclusivereactions: noinfo on final states, both
- Quantum-mechanicalreactiontheory (Relativistic Impuls Approximation RIA, Distorted Wave Impuls Approximation DWIA)
- Transport theory
Bothapplicable, leadto same results.

- Semi-InclusiveReactions:
- RIA and DWIA describesonlylossofflux in onechannel, does not tellwherethefluxgoesanddoes not containanysecondaryreactionsorsidefeedingofchannels
- Transport describeselasticandinelasticscattering, coupledchanneleffects, fulleventhistory

- ExclusiveReactions (coherentproduction):
- Phase coherence: Only QM applicable

Model Ingredients: FSI

- Kadanoff-Baymequation
- fullequationcan not besolvedyet
– not (yet) feasiblefor real worldproblems

- fullequationcan not besolvedyet
- Boltzmann-Uehling-Uhlenbeck (BUU) models
- Boltzmann equationasgradientexpansionofKadanoff-Baymequations
- includemean-fields
- BUU with off-shellpropagation (essential forpropagatingbroadparticles): GiBUU

- Cascademodels (typicaleventgenerators, NUANCE, GENIE, …)
- nomean-fields, (no) Fermi motion

- Theoretical Basis

Simplicity

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GiBUUtransport

- whatisGiBUU? semiclassical coupled channels transport model
- general information (and code available): http://theorie.physik.uni-giessen.de/GiBUU/
- GiBUU describes (within the same unified theory and code)
- heavy ion reactions, particle production and flow
- pion and proton induced reactions
- low and high energy photon and electron induced reactions
- neutrino induced reactions
……..using the same physics input! And the same code!

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Model Ingredients: FSI

- time evolution of spectral phase space density (for i = N, D,p,r, …) given by BUU equation
- one equation for each particle species (61 baryons, 21 mesons)
- coupled through the potential US and the collision integral Icoll
- Cross sections from resonance model (and data) for W < 2.5 GeV
- at higher energies (W > 2.5 GeV) particle production through string fragmentation (PYTHIA)

one-particle spectral phase space density for particle species i

Hamiltonian

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Pion production: model validationwithphotondata

- GiBUUdescribesphoton-inducedpionproduction, in particularmomentumdistributionTAPS data(Eur. Phys. J A22 (2004))

Ca

Pb

Ca

Pb

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NC inducedproton knockout: nm56Fe nmpX

- effectsof FSI on nucleonkineticenergyspectrumatEn = 1 GeV
- fluxreductionathigherenergies
- large numberofrescatterednucleonsatlowkineticenergies

NC p

Dcontribution to knock-out almost equals QE contribution (increases with E)

coupled-channel effect

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Phys. Rev. C 74, 065502 (2006)

Different approachestoidentify CCQE

MiniBooNE

K2K

0 ¼ + X

0 ¼ + 1 p + X

QE induced

QE induced

¢ induced (fakes)

¢ induced (fakes)

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T.L. et al., NUFACT08 proceedings, arXiv:0809.3986

MiniBooNE CCQE

per nucleon

T. Katori, NUINT09

QE-like - QE-fake,

energyreconstructiondatacorrection model dependent

- underestimate MiniBooNE by ~35%
- agreement with other models
- agreement with NOMAD
- pion-electroproduction, former neutrino experiments, NOMADconsistent with MA = 1 GeV

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MiniBooNE Q2 distribution

- CC º¹ on 12C averaged over MiniBooNE flux
- QE-fakes: background!
- reconstruction via
- MiniBooNE “data” = Smith-Moniz Fermi gas with “modified Pauli blocking” and MA = 1.35 GeV
- assume that non-QE background subtraction is perfect!

- in addition: RPA correlations by Nieves et al. PRC 73 (2006)

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arXiv:0909.5123

Energyreconstruction via CCQE

- all QE-like events enter energy reconstruction!
- reconstruction under assumption that QE-like = QE and with free kinematics:

EB = 34 MeV

error:

“true” QE: ~ 11-17 %

QE-like (MB): ~ 19-23 %

QE-like (K2K): ~ 13-18 %

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Energyreconstruction via CCQE

- all QE-like events enter energy reconstruction!
- reconstruction under assumption that QE-like = QE and with free kinematics:

EB = 34 MeV

QE fakes “fill in oscillation dip”

error in extracted oscillation parameters

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CC pionproduction: nm56Fe m-p X

- effectsof FSI on pionkineticenergyspectrumatEn = 1 GeV
- strong absorption in Dregion
- side-feedingfrom dominant p+ intop0 channel
- secondarypionsthrough FSI ofinitial QE protons

p+

p0

Spectradeterminedby¼-N-¢dynamics

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K2K and MiniBoonE CC1¼+

- single-¼+/QE ratio
¾1p+ / ¾0p+1pafter FSI: K2KdefinitionforCCQE-likecrosssection

¾1p+ / ¾0p+ after FSI: MiniBooNEdefinitionforCCQE-likecrosssection

¾1p+ / ¾QEbefore FSI: includingnuclearcorrectionslikemeanfieldsand Fermi motion

¾1p+ / ¾QE in thevacuum

FSI corrected

FSI corrected

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MiniBooNE NC 1¼0

- NC1¼0 data consistent with calculation without FSI!
- possible origins:
- elementary cross section too small
- neutrino-flux prediction (cf. discrepancy in QE channel)
- “data” contains “theory”: model dependence

data: C. Anderson, NUINT09

bands:uncertainty of axial form factor

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arXiv:0910.2835

Summary

- Quasielastic scattering events contain admixtures of Delta excitations
- excitations affect nucleon knockout, contaminate QE experiments

- Energy reconstruction good up to 10 – 20%. Experiments want 5%!
- Extraction of axial mass (1 GeV) strongly affected by nuclear structure (RPA correlations), difficult to get
both absolute height and slope.

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Summary

Particle production at neutrino energies of ~1 GeV

Inclusive cross section dominated by excitation, with QE contribution, good description of electroprod. Data

Semi-inclusive particle production incl. coupled channel FSI in GiBUU straightforward, tested against A and A

Extension to higher energies (5 – 280 GeV) successful for electroproduction, for neutrinos (OPERA) to be done, straightforward

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