Tina Leitner, Oliver Buss,Tina Leitner, Oliver Buss,

Ulrich Mosel, Luis Alvarez-RusoUlrich Mosel, Luis Alvarez-Ruso

Neutrino InteractionsNeutrino Interactions with Nucleons and Nuclei with Nucleons and Nuclei

Beijing 03/10

Beijing 03/10

1300 km

Soudan Mine,Nova

770 kmHomestake MineDusel

Long baseline experimentsLong baseline experimentsM

. Wasck

o

Beijing 03/10

Neutrino oscillation Neutrino oscillation searchsearch

P(º¹ ! ºe; t) = sin22µsin2Ã

¢ m2L4Eº

!

Flux: obtained from Event-Generatorsfor hadronic production and subsequentweak decay

Energy must be reconstructed from hadronic final state

Beijing 03/10

Oscillation Minium at Oscillation Minium at MiniBooNEMiniBooNE

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Neutrino detectors nowadays all Neutrino detectors nowadays all contain (heavy) nuclei, have to contain (heavy) nuclei, have to understand interactions of neutrinos understand interactions of neutrinos with matterwith matter

Interactions of neutrinos with nuclei Interactions of neutrinos with nuclei may make the identification of may make the identification of elementary processes, like knock-elementary processes, like knock-out, pion-production or qe scattering out, pion-production or qe scattering difficult.difficult.

Beijing 03/10

MotivationMotivation

MotivationMotivation In-medium physics: vector In-medium physics: vector andand axial form factors axial form factors

in medium have to be extracted from reactions in medium have to be extracted from reactions on nuclei.on nuclei. NUTEV anomaly for Weinberg angleNUTEV anomaly for Weinberg angle Axial Mass: in MiniBooNE and K2K: 1.0 or 1.25 Axial Mass: in MiniBooNE and K2K: 1.0 or 1.25

GeV?GeV?

Neutrino-energy must be reconstructed from Neutrino-energy must be reconstructed from detector response. detector response.

Nuclear Physics Input is neededNuclear Physics Input is needed

Beijing 03/10

Beijing 03/10

Low-Energy Nuclear Physics determines responseof nuclei to neutrinos

The Rebirth of Low Energy Nuclear Physics

neutrino-nucleus reaction: neutrino-nucleus reaction: ll AA l hadrons l hadrons at ~ 0.5 – 1.5 GeV neutrino energyat ~ 0.5 – 1.5 GeV neutrino energy scattering off a single nucleonscattering off a single nucleon

○ free nucleonfree nucleon○ nucleon bound in a nucleusnucleon bound in a nucleus

Total QE scattering off a nucleus Total QE scattering off a nucleus and and production production○ final state interactions (FSI)final state interactions (FSI)

GiBUU GiBUU transport modeltransport model

Results:Results: qe scattering,qe scattering, production, nucleon production, nucleon knockoutknockout

ConclusionsConclusions

Beijing 03/10

OutlineOutline

W, Z

l

Free primary interaction cross sections, cross Free primary interaction cross sections, cross sections boosted to restframe of moving sections boosted to restframe of moving nucleon in local Fermigasnucleon in local Fermigas no off-shell dependence, but include spectral functions no off-shell dependence, but include spectral functions

for baryons and mesons (binding + collision for baryons and mesons (binding + collision broadening)broadening)

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

Pauli-principle includedPauli-principle included

Shadowing by geometrical factor (QShadowing by geometrical factor (Q22,,) ) includedincluded

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Model Ingredients: Model Ingredients: ISIISI

Beijing 03/10

• Hole spectral function (local TF) Local Thomas-Fermi Particles in mean-field potential!

• Particle spectral function: collisional broadening

• Inclusive cross section

• Hole spectral function (local TF) Local Thomas-Fermi Particles in mean-field potential!

• Particle spectral function: collisional broadening

• Inclusive cross sectiond¾lA ! l0Xtot = g

ZdE

Zd3p

(2¼)3Ph(~p;E )k ¢pk0p0 d¾lN

tot PP B (~p;E )

Potential smoothes

E-p distribution

s

Neutrino nucleon cross Neutrino nucleon cross sectionsection

QE single ¼

P.

Lip

ari

, N

ucl.

Ph

ys.

Pro

c.

Su

pp

l. 1

12,

27

4 (

20

02

)

note:10-38 cm² = 10-11 mb

R+

¼N N'

‚ DIS

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reactions:reactions:

hadronic hadronic current: current:

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Quasielastic scatteringQuasielastic scattering

with

axial form factors • related by PCAC• dipole ansatz

CC: ºl n ! l¡ pNC: º n ! º n; º p! º p

J QE® = hN

0jJ QE

® (0)jNi = ¹u(p0)A®u(p)

A®=

Ã

°®¡q=q®

q2

!

F V1 +

i2M

¾®̄ q̄ F V2 +°®°5FA+

q®°5

MFP

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

extra term • ensures

vector current conservationfor nonequal masses

in addition: strange vector and axial form factors for NC

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Quasielastic scatteringQuasielastic scattering

Quasielastic Scattering: Axial MassQuasielastic Scattering: Axial Mass

neutrinos probe nucleons / nuclei via neutrinos probe nucleons / nuclei via V-A weak interactionV-A weak interaction axial structureaxial structure of the nucleon and baryonic resonances (in the medium!)of the nucleon and baryonic resonances (in the medium!)

nuclear effectsnuclear effects (e.g. low-Q² deficit in MiniBooNE)(e.g. low-Q² deficit in MiniBooNE) dedicated neutrino-nucleus experiment: Minervadedicated neutrino-nucleus experiment: Minerva

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Pion production through Pion production through resonance excitationresonance excitation

13 resonances with W < 2 GeV13 resonances with W < 2 GeV pion production dominated by pion production dominated by PP3333(1232) resonance:(1232) resonance:

CCVV from electron data (MAID analysis with CVC)from electron data (MAID analysis with CVC) CCAA from fit to neutrino data from fit to neutrino data (experiments on (experiments on hydrogen/deuteriumhydrogen/deuterium))

J ®¹¢ =

·CV

3

MN(g®¹ q=¡ q®°¹ ) +

CV4

M 2N

(g®¹ q¢p0¡ q®p0¹ ) +CV

5

M 2N

(g®¹ q¢p¡ q®p¹ )¸

°5

+CA

3

MN(g®¹ q=¡ q®°¹ ) +

CA4

M 2N

(g®¹ q¢p0¡ q®p0¹ ) + CA5 g®¹ +

CA6

M 2N

q®q¹

discrepancy between ANL and BNL data uncertainty in axial form factor

ANL

BNL

10 % error in C5

A(0)

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Beijing 03/10

CC production of CC production of ++ and and ++++ subsequent decay into subsequent decay into 33 channels channels::

CC pion production on free CC pion production on free nucleonsnucleons

ºl p ! l¡ p¼+

ºl n ! l¡ n ¼+

ºl n ! l¡ p¼0including higher resonances (isospin ½):

P11(1440);D13(1520);S11(1535)

BNL data

ANL data

How much is background??

Pion production through Pion production through ¢¢

avera

ged o

ver A

NL fl

ux, W

< 1

.4

GeV

New V, old A

New V, new A

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

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ll cross sections Fermi smearedll cross sections Fermi smeared cross section is further modified in the nuclear cross section is further modified in the nuclear

medium:medium:

decay might be Pauli blocked: decrease of the free decay might be Pauli blocked: decrease of the free widthwidth

additional "decay" channels in the mediumadditional "decay" channels in the medium: : collisional width collisional width collcoll

overall effect: overall effect: increase of the widthincrease of the width

!! medmed = = PP + + collcoll

collisional broadeningcollisional broadeningBeijing 03/10

Medium modifications of the Medium modifications of the inclusive cross sectioninclusive cross section

"pion-lessdecay"

Model validation: electron Model validation: electron scattering scattering

PRC 79, 034601 (2009)

Beijing 03/10

Fully inclusive reactions: no info on final Fully inclusive reactions: no info on final states, bothstates, both Quantum-mechanical reaction theory (Relativistic Impuls Quantum-mechanical reaction theory (Relativistic Impuls

Approximation RIA, Distorted Wave Impuls Approximation Approximation RIA, Distorted Wave Impuls Approximation DWIA) DWIA)

Transport theoryTransport theory

BothBoth applicable, lead to same resultsapplicable, lead to same results..

Semi-Inclusive Reactions: Semi-Inclusive Reactions: RIA and DWIA describes only loss of flux in one channel, does RIA and DWIA describes only loss of flux in one channel, does

not tell where the flux goes and does not contain any not tell where the flux goes and does not contain any secondary reactions or sidefeeding of channelssecondary reactions or sidefeeding of channels

Transport describes elastic and inelastic scattering, coupled Transport describes elastic and inelastic scattering, coupled channel effects, full event historychannel effects, full event history

Exclusive Reactions (coherent production):Exclusive Reactions (coherent production): Phase coherence: Only QM applicablePhase coherence: Only QM applicable

Beijing 03/10

Transport vs. Transport vs. QuantummechanicsQuantummechanics

Kadanoff-Baym equationKadanoff-Baym equation○ full equation can not be solved yet full equation can not be solved yet – – not (yet) feasible for real world problemsnot (yet) feasible for real world problems

Boltzmann-Uehling-Uhlenbeck (BUU) Boltzmann-Uehling-Uhlenbeck (BUU) modelsmodels○ Boltzmann equation as gradient expansion Boltzmann equation as gradient expansion

of Kadanoff-Baym equationsof Kadanoff-Baym equations○ include mean-fieldsinclude mean-fields○ BUU with off-shell propagation (essential for propagating BUU with off-shell propagation (essential for propagating

broad particles): broad particles): GiBUUGiBUU

Cascade models (typical event generators, Cascade models (typical event generators, NUANCE, GENIE, NUANCE, GENIE, …)…)○ no mean-fields, (no) Fermi motionno mean-fields, (no) Fermi motion

Beijing 03/10

Model Ingredients: Model Ingredients: FSIFSI Theoretical Basis

what is GiBUU? what is GiBUU? semiclassical coupled channels transport model semiclassical coupled channels transport model

general information (and code available): general information (and code available): http://theorie.physik.uni-giessen.de/GiBUU/

GiBUU describes (within the same unified theory and GiBUU describes (within the same unified theory and code)code) heavy ion reactions, particle production and flow heavy ion reactions, particle production and flow pion and proton induced reactionspion and proton induced reactions low and high energy photon and electron induced low and high energy photon and electron induced

reactionsreactions neutrino induced reactionsneutrino induced reactions…………..using the same physics input! And the same code!..using the same physics input! And the same code!

Beijing 03/10

GiBUU transportGiBUU transport

time evolution of spectral phase space density time evolution of spectral phase space density (for (for i = Ni = N, , ,, ,, ,, …) …) given by BUU equationgiven by BUU equation

one equation for each particle species (61 baryons, 21 one equation for each particle species (61 baryons, 21 mesons) mesons)

coupled through the potential coupled through the potential UUSS and the collision integral and the collision integral IIcollcoll Cross sections from resonance model (and data) for W < 2.5 GeVCross sections from resonance model (and data) for W < 2.5 GeV at higher energies (W > 2.5 GeV) particle production throughat higher energies (W > 2.5 GeV) particle production through

string fragmentation (PYTHIA) string fragmentation (PYTHIA)Beijing 03/10

Model Ingredients: Model Ingredients: FSIFSI

one-particle spectral phase space density for particle species i

Hamiltonian

GiBUU describes photon-induced GiBUU describes photon-induced pion production, in particular pion production, in particular momentum distribution momentum distribution

TAPS data TAPS data (Eur. Phys. J A22 (2004))(Eur. Phys. J A22 (2004))

Pion production: model Pion production: model validationvalidation

with photon data with photon dataCaPb

Rd

=¾

(A)=

A2=

3

¾(2

H)=

2

Beijing 03/10

Ca Pb

Beijing 03/10

CC nucleon knockout: CC nucleon knockout: 5656Fe Fe -- N X N X

w/o FSI

p

p n

n

E = 1 GeVD

ram

atic

FSI

Effe

ct

NC induced proton knockout: NC induced proton knockout: 5656Fe Fe

pX pX effects of FSI on nucleon kinetic energy spectrum at effects of FSI on nucleon kinetic energy spectrum at EE = 1 GeV = 1 GeV

flux reduction at higher energies flux reduction at higher energies large number of rescattered nucleons at low kinetic energieslarge number of rescattered nucleons at low kinetic energies

NC p

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

coupled-channel effectPhys. Rev. C 74, 065502 (2006)

Beijing 03/10

Different approaches to identify Different approaches to identify CCQECCQE

0 ¼ + X

0 ¼ + 1 p + XQE induced

QE induced

¢ induced (fakes)

MiniBooNE K2K

¢ induced (fakes)

T.L. et al., NUFACT08 proceedings, arXiv:0809.3986 Beijing 03/10

underestimate MiniBooNE by ~35% agreement with other models agreement with NOMAD pion-electroproduction, former neutrino

experiments, NOMADconsistent with MA = 1 GeV

T. Katori, NUINT09

per nucleon

MiniBooNE CCQEMiniBooNE CCQE

QE-like - QE-fake,energy reconstruction data correction model dependent

Beijing 03/10

MiniBooNE QMiniBooNE Q22 distribution distribution CC CC ºº¹¹ on on 1212C averaged over MiniBooNE fluxC averaged over MiniBooNE flux

QE-fakes: background!QE-fakes: background! reconstruction viareconstruction via

MiniBooNE “data” = Smith-Moniz Fermi gas MiniBooNE “data” = Smith-Moniz Fermi gas with “modified Pauli blocking” and with “modified Pauli blocking” and MMAA = 1.35 GeV = 1.35 GeV

assume that non-QE background subtraction is perfect!assume that non-QE background subtraction is perfect!

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

arXiv:0909.5123 Beijing 03/10

Energy reconstruction via Energy reconstruction via CCQECCQE

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

kinematics:kinematics:

EB = 34 MeV

error:“true” QE: ~ 11-17 %QE-like (MB): ~ 19-23 %QE-like (K2K): ~ 13-18 %

Beijing 03/10

Energy reconstruction via Energy reconstruction via CCQECCQE

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

kinematics:kinematics:

EB = 34 MeV

QE fakes “fill in oscillation dip”

error in extracted oscillation parameters

Beijing 03/10

Beijing 03/10

CC pion production: CC pion production: 5656Fe Fe -- X X

¼+ ¼0

¼+ ¼0

E= 1 GeV

w/o FSI

CC pion production: CC pion production: 5656Fe Fe --

XX effects of FSI on pion kinetic energy spectrum at effects of FSI on pion kinetic energy spectrum at EE = 1 GeV = 1 GeV

strong absorption in strong absorption in region region side-feeding from dominant side-feeding from dominant into into channelchannel secondary pions through FSI of initial QE protonssecondary pions through FSI of initial QE protons

Spectra determined by ¼-N-¢ dynamics

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single-single-¼¼++/QE ratio/QE ratio

¾¾11++ / / ¾¾00pp after FSI: after FSI: K2KK2K definition for definition for CCQE-like cross section CCQE-like cross section

¾¾11++ / / ¾¾00++ after FSI: after FSI: MiniBooNEMiniBooNE definition for definition for CCQE-like cross sectionCCQE-like cross section

¾¾11++ / / ¾¾QEQE before FSI: before FSI: including nuclear corrections including nuclear corrections like mean fields and Fermi motionlike mean fields and Fermi motion

¾¾11++ / / ¾¾QEQE in the vacuum in the vacuum

K2K and MiniBoonE CC1K2K and MiniBoonE CC1¼¼++

FSI corrected

FSI corrected

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NC1NC1¼¼0 0 data consistent with calculation without FSI! data consistent with calculation without FSI!

possible origins:possible origins: elementary cross section too smallelementary cross section too small neutrino-flux prediction (cf. discrepancy in QE channel)neutrino-flux prediction (cf. discrepancy in QE channel) ““data” contains “theory”: model dependencedata” contains “theory”: model dependence

MiniBooNE NC 1MiniBooNE NC 1¼¼00

data

: C. A

nderso

n, N

UIN

T0

9

bands:uncertainty of axial form factor

arXiv:0910.2835Beijing 03/10

Quasielastic scattering Quasielastic scattering events contain events contain admixtures of Delta excitationsadmixtures of Delta excitations excitations affect nucleon knockout, excitations affect nucleon knockout,

contaminate QE experimentscontaminate QE experiments

Energy reconstruction good up to 10 – 20%. Energy reconstruction good up to 10 – 20%. Experiments want 5%!Experiments want 5%!

Extraction of axial mass (1 GeV) strongly affected Extraction of axial mass (1 GeV) strongly affected by nuclear structure (RPA correlations), difficult to by nuclear structure (RPA correlations), difficult to getget

both absolute height and slope.both absolute height and slope.

Beijing 03/10

SummarySummary

SummarySummary Particle production Particle production at neutrino energies at neutrino energies

of ~1 GeV of ~1 GeV Inclusive cross section dominated by Inclusive cross section dominated by excitation, excitation,

with QE contribution, good description of with QE contribution, good description of electroprod. Dataelectroprod. Data

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

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

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