Tina Leitner, Oliver Buss, Ulrich Mosel, Luis Alvarez-Ruso Neutrino Interactions with Nucleons and Nuclei TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAA Beijing 03/10

1300 km Soudan Mine, Nova 770 km Homestake Mine Dusel

Long baseline experiments M. Wascko Beijing 03/10

Neutrino oscillation search neutrino oscillations: probability for 2 flavors: neutrino oscillations: probability for 2 flavors: Crucial parameter: neutrino energy E Crucial parameter: neutrino energy E Need to understand ‚classical‘ hadronic interactions Flux: obtained from Event-Generators for hadronic production and subsequent weak decay Energy must be reconstructed from hadronic final state Beijing 03/10

Oscillation Minium at MiniBooNE Beijing 03/10

 Neutrino detectors nowadays all contain (heavy) nuclei, have to understand interactions of neutrinos with matter  Interactions of neutrinos with nuclei may make the identification of elementary processes, like knock-out, pion- production or qe scattering difficult. Beijing 03/10Motivation

Motivation In-medium physics: vector and axial form factors in medium have to be extracted from reactions on nuclei. In-medium physics: vector and axial form factors in medium have to be extracted from reactions on nuclei. NUTEV anomaly for Weinberg angle NUTEV anomaly for Weinberg angle Axial Mass: in MiniBooNE and K2K: 1.0 or 1.25 GeV? Axial Mass: in MiniBooNE and K2K: 1.0 or 1.25 GeV? Neutrino-energy must be reconstructed from detector response. Nuclear Physics Input is needed Neutrino-energy must be reconstructed from detector response. Nuclear Physics Input is needed Beijing 03/10

Low-Energy Nuclear Physics determines response of nuclei to neutrinos The Rebirth of Low Energy Nuclear Physics

 neutrino-nucleus reaction: l A  l hadrons at ~ 0.5 – 1.5 GeV neutrino energy scattering off a single nucleon scattering off a single nucleon ○ free nucleon ○ nucleon bound in a nucleus Total QE scattering off a nucleus and  production Total QE scattering off a nucleus and  production ○ final state interactions (FSI) GiBUU transport model GiBUU transport model  Results: qe scattering,  production, nucleon knockout  Conclusions Beijing 03/10 Outline

 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) 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 Electro- and Photoproduction for vector couplings Axial couplings modeled with PCAC Axial couplings modeled with PCAC  Pauli-principle included  Shadowing by geometrical factor (Q 2, ) included Beijing 03/10 Model Ingredients: ISI

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 section Potential smoothes E-p distributions

Neutrino nucleon cross section QEsingle ¼ P. Lipari, Nucl. Phys. Proc. Suppl. 112, 274 (2002) note: cm² = mb R+R+ ¼ N N' ‚ DIS Beijing 03/10

reactions: reactions: hadronic current: hadronic current: Beijing 03/10 Quasielastic scattering with axial form factors related by PCAC dipole ansatz vector form factors related to EM form factors by CVC BBBA-2007 parametrization extra term ensures vector current conservation for nonequal masses in addition: strange vector and axial form factors for NC

Beijing 03/10 Quasielastic scattering

Quasielastic Scattering: Axial Mass neutrinos probe nucleons / nuclei via V-A weak interaction neutrinos probe nucleons / nuclei via V-A weak interaction axial structure of the nucleon and baryonic resonances (in the medium!) axial structure of the nucleon and baryonic resonances (in the medium!) nuclear effects (e.g. low-Q² deficit in MiniBooNE) nuclear effects (e.g. low-Q² deficit in MiniBooNE) dedicated neutrino-nucleus experiment: Minerva dedicated neutrino-nucleus experiment: Minerva Beijing 03/10

Pion production through resonance excitation 13 resonances with W < 2 GeV 13 resonances with W < 2 GeV pion production dominated by P 33 (1232) resonance: pion production dominated by P 33 (1232) resonance: C V from electron data (MAID analysis with CVC) C V from electron data (MAID analysis with CVC) C A from fit to neutrino data (experiments on hydrogen/deuterium) C A from fit to neutrino data (experiments on hydrogen/deuterium) discrepancy between ANL and BNL data  uncertainty in axial form factor ANL BNL 10 % error in C 5 A (0) Beijing 03/10

CC production of  + and  ++ CC production of  + and  ++  subsequent decay into 3 channels : CC pion production on free nucleons including higher resonances (isospin ½): BNL data ANL data How much is background??

Pion production through ¢ averaged over ANL flux, W < 1.4 GeV New V, old A New V, new A Beijing 03/10

Nuclear Targets (K2K, MiniBooNE, T2K, MINOS, Minerva, …. Nuclear Targets (K2K, MiniBooNE, T2K, MINOS, Minerva, …. Beijing 03/10

  ll cross sections Fermi smeared    cross section is further modified in the nuclear medium:  decay might be Pauli blocked: decrease of the free width  decay might be Pauli blocked: decrease of the free width additional "decay" channels in the medium : collisional width  coll additional "decay" channels in the medium : collisional width  coll overall effect: overall effect: increase of the width   !  med =  P +  coll collisional broadening Beijing 03/10 Medium modifications of the inclusive cross section "pion-less decay"

Model validation: electron scattering PRC 79, (2009) Beijing 03/10

Fully inclusive reactions: no info on final states, both Fully inclusive reactions: no info on final states, both Quantum-mechanical reaction theory (Relativistic Impuls Approximation RIA, Distorted Wave Impuls Approximation DWIA) Quantum-mechanical reaction theory (Relativistic Impuls Approximation RIA, Distorted Wave Impuls Approximation DWIA) Transport theory Transport theory Both applicable, lead to same results. Both applicable, lead to same results. Semi-Inclusive Reactions: Semi-Inclusive Reactions: RIA and DWIA describes only loss of flux in one channel, does not tell where the flux goes and does not contain any secondary reactions or sidefeeding of channels RIA and DWIA describes only loss of flux in one channel, does not tell where the flux goes and does not contain any secondary reactions or sidefeeding of channels Transport describes elastic and inelastic scattering, coupled channel effects, full event history Transport describes elastic and inelastic scattering, coupled channel effects, full event history Exclusive Reactions (coherent production): Exclusive Reactions (coherent production): Phase coherence: Only QM applicable Phase coherence: Only QM applicable Beijing 03/10 Transport vs. Quantummechanics

 Kadanoff-Baym equation ○ full equation can not be solved yet – not (yet) feasible for real world problems – not (yet) feasible for real world problems Boltzmann-Uehling-Uhlenbeck (BUU) models Boltzmann-Uehling-Uhlenbeck (BUU) models ○ Boltzmann equation as gradient expansion of Kadanoff-Baym equations ○ include mean-fields ○ BUU with off-shell propagation (essential for propagating broad particles): GiBUU Cascade models (typical event generators, NUANCE, GENIE, …) Cascade models (typical event generators, NUANCE, GENIE, …) ○ no mean-fields, (no) Fermi motion Beijing 03/10 Model Ingredients: FSI Simplicity Theoretical Basis

 what is GiBUU? semiclassical coupled channels transport model  general information (and code available):  GiBUU describes (within the same unified theory and code) heavy ion reactions, particle production and flow heavy ion reactions, particle production and flow pion and proton induced reactions pion and proton induced reactions low and high energy photon and electron induced reactions low and high energy photon and electron induced reactions neutrino induced reactions neutrino induced reactions ……..using the same physics input! And the same code! Beijing 03/10 GiBUU transport

 time evolution of spectral phase space density (for i = N, , , , …) given by BUU equation  one equation for each particle species (61 baryons, 21 mesons)  coupled through the potential U S and the collision integral I coll  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) Beijing 03/10 Model Ingredients: FSI Model Ingredients: FSI one-particle spectral phase space density for particle species i Hamiltonian

GiBUU describes photon-induced pion production, in particular momentum distribution TAPS data (Eur. Phys. J A22 (2004)) GiBUU describes photon-induced pion production, in particular momentum distribution TAPS data (Eur. Phys. J A22 (2004)) Pion production: model validation with photon data Ca Pb Beijing 03/10 Ca Pb

Beijing 03/10 CC nucleon knockout:  56 Fe   - N X w FSI w/o FSI E = 1 GeV Dramatic FSI Effect

NC induced proton knockout:  56 Fe   pX effects of FSI on nucleon kinetic energy spectrum at E = 1 GeV effects of FSI on nucleon kinetic energy spectrum at E = 1 GeV flux reduction at higher energies flux reduction at higher energies large number of rescattered nucleons at low kinetic energies large number of rescattered nucleons at low kinetic energies NC p  contribution to knock-out almost equals QE contribution (increases with E )  coupled-channel effect Phys. Rev. C 74, (2006) Beijing 03/10

Different approaches to identify CCQE 0 ¼ + X 0 ¼ + 1 p + X QE induced ¢ induced (fakes) MiniBooNEK2K ¢ induced (fakes) T.L. et al., NUFACT08 proceedings, arXiv: Beijing 03/10

underestimate MiniBooNE by ~35% agreement with other models agreement with NOMAD pion-electroproduction, former neutrino experiments, NOMAD consistent with M A = 1 GeV T. Katori, NUINT09 per nucleon MiniBooNE CCQE QE-like - QE-fake, energy reconstruction  data correction model dependent Beijing 03/10

MiniBooNE Q 2 distribution CC º ¹ on 12 C averaged over MiniBooNE flux CC º ¹ on 12 C averaged over MiniBooNE flux QE-fakes: background! QE-fakes: background! reconstruction via reconstruction via MiniBooNE “data” = Smith-Moniz Fermi gas with “modified Pauli blocking” and M A = 1.35 GeV MiniBooNE “data” = Smith-Moniz Fermi gas with “modified Pauli blocking” and M A = 1.35 GeV assume that non-QE background subtraction is perfect! assume that non-QE background subtraction is perfect! in addition: RPA correlations by Nieves et al. PRC 73 (2006) in addition: RPA correlations by Nieves et al. PRC 73 (2006) arXiv: Beijing 03/10

Energy reconstruction via CCQE all QE-like events enter energy reconstruction! all QE-like events enter energy reconstruction! reconstruction under assumption that QE-like = QE and with free kinematics: reconstruction under assumption that QE-like = QE and with free kinematics: E B = 34 MeV error: “true” QE: ~ % QE-like (MB): ~ % QE-like (K2K): ~ % Beijing 03/10

Energy reconstruction via CCQE all QE-like events enter energy reconstruction! all QE-like events enter energy reconstruction! reconstruction under assumption that QE-like = QE and with free kinematics: reconstruction under assumption that QE-like = QE and with free kinematics: E B = 34 MeV QE fakes “fill in oscillation dip”  error in extracted oscillation parameters Beijing 03/10

CC pion production:  56 Fe   -  X w FSI E = 1 GeV w/o FSI

CC pion production:  56 Fe   -  X effects of FSI on pion kinetic energy spectrum at E = 1 GeV effects of FSI on pion kinetic energy spectrum at E = 1 GeV strong absorption in  region strong absorption in  region side-feeding from dominant   into   channel side-feeding from dominant   into   channel secondary pions through FSI of initial QE protons secondary pions through FSI of initial QE protons   Spectra determined by ¼-N-¢ dynamics Beijing 03/10

single-¼ + /QE ratio single-¼ + /QE ratio ¾ 1  + / ¾ 0  p  after FSI: K2K definition for CCQE-like cross section ¾ 1  + / ¾ 0  p  after FSI: K2K definition for CCQE-like cross section ¾ 1  + / ¾ 0  + after FSI: MiniBooNE definition for CCQE-like cross section ¾ 1  + / ¾ 0  + after FSI: MiniBooNE definition for CCQE-like cross section ¾ 1  + / ¾ QE before FSI: including nuclear corrections like mean fields and Fermi motion ¾ 1  + / ¾ QE before FSI: including nuclear corrections like mean fields and Fermi motion ¾ 1  + / ¾ QE in the vacuum ¾ 1  + / ¾ QE in the vacuum K2K and MiniBoonE CC1¼ + FSI corrected Beijing 03/10

Pion Production ‚Data‘ before FSI 1:  1  /  0  after FSI 2:  1  /  0  p after FSI 3:  1  /  QE after FSI 4:  1  /  QE before FSI (‚Data‘) 5:  1  /  QE in vacuum

NC1¼ 0 data consistent with calculation without FSI! NC1¼ 0 data consistent with calculation without FSI! possible origins: possible origins: elementary cross section too small elementary cross section too small neutrino-flux prediction (cf. discrepancy in QE channel) neutrino-flux prediction (cf. discrepancy in QE channel) “data” contains “theory”: model dependence “data” contains “theory”: model dependence MiniBooNE NC 1¼ 0 data: C. Anderson, NUINT09 bands: uncertainty of axial form factor arXiv: Beijing 03/10

Quasielastic scattering events contain admixtures of Delta excitations Quasielastic scattering events contain admixtures of Delta excitations  excitations affect nucleon knockout, contaminate QE experiments  excitations affect nucleon knockout, contaminate QE experiments Energy reconstruction good up to 10 – 20%. Experiments want 5%! 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. both absolute height and slope. Beijing 03/10 Summary

Summary Particle production at neutrino energies of ~1 GeV Particle production at neutrino energies of ~1 GeV Inclusive cross section dominated by  excitation, with QE contribution, good description of electroprod. Data 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 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 Extension to higher energies (5 – 280 GeV) successful for electroproduction, for neutrinos (OPERA) to be done, straightforward Beijing 03/10