Nuclear aspects of neutrino energy reconstruction in current oscillation experiments

Nuclear aspects of neutrino energy reconstruction in current oscillation experiments Tina Leitner Oliver Buss, Luis Alvarez-Ruso, and Ulrich Mosel Institut für Theoretische Physik Universität Gießen, Germany DPG-Frühjahrstagung Freiburg, März 8 European Graduate School Complex Systems of Hadrons and Nuclei Copenhagen - Gießen - Helsinki - Jyväskylä - Torino JUSTUS-LIEBIG- UNIVERSITÄT GIESSEN

Sterile neutrinos at MiniBooNE?

MiniBooNE search for ν µ ν e neutrino oscillations: probability for flavors: Ã P(ν ν t) = sin θ sin m L ( µ e ; ) 4E ν LSND reported anti-ν µ anti-ν e oscillations with m = ev (PRL 75 (996)) which is in contrast to ν µ disappearance experiments (LBL and atmospheric): m ~ -3 ev ν e disappearance experiments (solar and reactor): m ~ -5 ev only way out: at least 4 mass eigenstates» sterile neutrino! aim of MiniBooNE: ib check LSND but: any oscillation measurement has uncertainties from: reconstruction of neutrino energy and lepton kinematics nuclear effects (detector response): neutrino-nucleus cross sections ability to identify neutrino flavor: π can fake ν e appearance signal Ã!

Link between nuclear effects and neutrino oscillations I cross section model (example for MiniBooNE, D. Casper, Nucl.Phys.Proc.Suppl. ()) CC QE scattering and resonance excitation (in particular ) are most important for MiniBooNE but: MiniBooNE uses C need nuclear cross sections

Link between nuclear effects and neutrino oscillations II reconstruction of neutrino energy important quantity for oscillations use simple -body kinematics of CC QE process: ν µ + n µ - + p definition of CCQE: charged muon, but NO pion decay products in detector E ν = M N E µ m µ (M N E µ + p µ cos θ µ ) nucleon at rest Ε ν cosθ E µ

Link between nuclear effects and neutrino oscillations II reconstruction of neutrino energy important quantity for oscillations use simple -body kinematics of CC QE process: ν µ + n µ - + p definition of CCQE: charged muon, but NO pion decay products in detector ν E ν = l - M N E µ m µ (M N E µ + p µ cos θ µ ) nucleon at rest W corrections in the nuclear medium: scattering of bound nucleons: Fermi motion, nuclear potentials, etc.

Link between nuclear effects and neutrino oscillations II reconstruction of neutrino energy important quantity for oscillations use simple -body kinematics of CC QE process: ν µ + n µ - + p definition of CCQE: charged muon, but NO pion decay products in detector E ν = l - M N E µ m µ (M N E µ + p µ cos θ µ ) nucleon at rest l - ν ν W W π corrections in the nuclear medium: scattering of bound nucleons: Fermi motion, nuclear potentials, etc. final state interactions CCQE fakes: influence on energy reconstruction?

Structure of our approach impulse approximation model: factorizes primary interaction and FSI primary interaction of neutrino with one bound nucleon at a time via: quasielastic scattering excitation of 3 resonances (MAID analysis) ν W, Z l nucleus is treated as local Fermi gas including Fermi motion, Pauli blocking, nuclear potentials, in-medium spectral functions FSI: coupled channel semiclassical transport model (GiBUU) more details: PRC 73 (6) / PRC 74 (6) / PRC 76 (7)

Structure of our approach impulse approximation model: factorizes primary interaction and FSI primary interaction of neutrino with one bound nucleon at a time via: quasielastic scattering excitation of 3 resonances (MAID analysis) ν W, Z l nucleus is treated as local Fermi gas including Fermi motion, Pauli blocking, nuclear potentials, in-medium spectral functions FSI: coupled channel semiclassical transport model (GiBUU) more details: PRC 73 (6) / PRC 74 (6) / PRC 76 (7)

Quasielastic scattering reactions: CC: ν l n l p NC: ν n ν n, ν p ν p hadronic current: J QE with A α = α Ã = hn J QE () Ni =ū(p )A α u(p) / γ α q/q α q α! F V + i M σ αβq β F V +γ αγ 5 F A + q αγ 5 M F P vector form factors related to EM form factors by CVC BBBA-7 parametrization ti ti axial form factors related by PCAC dipole ansatz σ [ -38 cm ].6.4..8.6.4. ν µ n µ - p 5% error in M A Barish, PRD 6 (977) Mann, PRL 3 (973) Baker, PRD 3 (98).5.5 E ν [GeV]

Resonance excitation possible reactions: fully relativistic formalism with phenomenological N-R transition form factors: vector form factors related to EM form factors by CVC MAID analysis for helicity amplitudes axial form factors axial coupling strength PCAC modified dipole

CC pion production on free nucleons CC production of resonances subsequent decay into 3 channels: ] σ [ -38 cm.8 π +.8.6.4 ] σ [ -38 cm.6.4 π x Kitagaki, PRD 8 (983) Radecky, PRD 5 (98) same with mass cut Barish, PRD 9 (979) same with mass cut Campell, PRL 3 (973)...5.5 E ν [GeV] pure dominance in grey ν.5.5 E ν [GeV] ν

Structure of our approach impulse approximation model: factorizes primary interaction and FSI primary interaction of neutrino with one bound nucleon at a time via: quasielastic scattering excitation of 3 resonances (MAID analysis) ν W, Z l nucleus is treated as local Fermi gas including Fermi motion, Pauli blocking, nuclear potentials, in-medium spectral functions FSI: coupled channel semiclassical transport model (GiBUU) more details: PRC 73 (6) / PRC 74 (6) / PRC 76 (7)

Medium modifications Fermi motion local density approximation: p F (~r)= 3 /3 π ρ(~r) density profiles from electron scattering & Hartree-Fock calculations Pauli blocking P Pauli = Θ(p F (~r) ~p ) mean-field potential density + momentum dependence from analysis of p+a data in-medium width collisional broadening dcosθ [ -38 cm /G GeV] d σ/de µ 6 4 8 6 4 E ν =.7 GeV on C, only QE peak local Fermi gas w/o potential w/ only density dep. potential w/ density & momentum dep. Potential ti 9 6 4.3.4.5.6.7 E µ [GeV]

Check for inclusive cross section: Electroproduction 6 O(e,e') at θ=3, data from Anghinolfi, NPA 6 (996)

Structure of our approach impulse approximation model: factorizes primary interaction and FSI primary interaction of neutrino with one bound nucleon at a time via: quasielastic scattering excitation of 3 resonances (MAID analysis) ν W, Z l nucleus is treated as local Fermi gas including Fermi motion, Pauli blocking, nuclear potentials, in-medium spectral functions FSI: coupled channel semiclassical transport model (GiBUU) more details: PRC 73 (6) / PRC 74 (6) / PRC 76 (7)

GiBUU transport model what is GiBUU? semiclassical transport model in coupled channels more information: http://theorie.physik.uniphysik uni-giessen.de/gibuu/ GiBUU describes... heavy ion reactions pion induced reactions low and high energy photon and electron induced reactions neutrino ti induced dreactions... within the same unified framework using the same physics input! GiBUU allows to describe specific experiments inclusion of detector acceptances, reliable FSI, tracking of particles GiBUU has been checked extensively against experimental data for heavy-ion collisions, ea, γa, πa reactions

GiBUU transport model BUU equation time evolution of phase space density (for i = N,, π, ρ, ) given by BUU eq.: one-particle phase space density for particle species i Hamiltonian one BUU equation for each particle species (6 baryons and mesons) coupled through the potential U S and the collision integral I coll collision integral accounts for changes in f i : elastic and inelastic scattering (coupled channels) Pauli blocking for fermions decay of unstable particles

E µ [GeV V] E µ [GeV] CC nucleon knockout: ν µ 56 Fe µ - N X p 5.8 4.8 3.6.6.4.4. E µ [GeV ev] w/o FSI. n 8 6 4..4.6.8 p 5..4.6.8 n.8 Q [GeV 4.8 ] 3 Q [GeV 8 ] 6.6.6.4 4.4...4.6.8 Q [GeV ] E µ [GeV] wfsi E ν = GeV...4.6.8 Q [GeV ]

E µ [GeV V] E µ [GeV] CC pion production: ν µ 56 Fe µ - π X.8.6.4. π + 8.8 π 6 4.6.4..4.6.8..4.6.8.8 π +.8 Q [GeV 8 π ] 6 Q [GeV ].6 4.6.4.4...4.6.8 Q [GeV ] E µ [GeV V] w/o FSI E µ [GeV] wfsi E ν = GeV....4.6.8 Q [GeV ] 5 5 5 5

Application: MiniBooNE CC ν µ absorption cross section on C averaged over MiniBooNE flux dσ/dcos sθ [ -38 cm ] 8 6 4 8 6 4 total QE Delta - -.5.5 cosθ dσ/de -38 cm µ [ /GeV] 9 8 7 6 5 4 3 total QE Delta.5.5 E µ [GeV]

Application: MiniBooNE CC ν µ cross section on C QE-like events: detector measures muon but no pion averaged over MiniBooNE flux dσ/dcosθ θ [ -38 cm ] 6 total 9 QE 8 5 Delta 7 4 6 5 3 4 3 - -.5.5 cosθ dσ/ /de -38 cm µ [ /GeV] total QE Delta.5.5 E µ [GeV]

Application: MiniBooNE CC ν µ absorption cross section on C reconstruction of Q E ν (M E B)E µ (E B ME B + m µ + M ) = [(M E ) E + p cosθ ] Q = mµ + E ν (Eµ pµ cosθµ B µ ) µ µ 6 4 Fermi gas model of MiniBooNE: E B = 34 MeV reconstruction works well for absorption cross section also for exclusive? -38 cm dσ/d dq [ /G GeV ] 8 6 4 total QE Delta QE reconstructed..4.6.8..4 Q [GeV ]

Application: MiniBooNE CC ν µ cross section on C QE-like events: detector measures muon but no pion averaged aged over MiniBooNE flux /GeV dσ σ/dq [ -38 cm ] 9 8 7 6 5 4 3 total QE Delta reconstructed..4.6.8..4 Q [GeV ] reconstruction works well also for exclusive cross section!

Summary & Conclusions cross section dominated by QE contribution and excitation for E ν <.5 GeV medium modifications required good description of electroproduction data GiBUU is a multi-purpose theory to describe final state interactions including elastic and inelastic scattering sidefeeding (charge exchange) method allows to propagate particles out to detector LBL experiments need to reconstruct neutrino energy from observables, in particular from QE-like events simulate impact of FSI on QE-like events: absorption, secondary particles, induced nucleon knockout exp. rely on simple -body kinematics for reconstruction of neutrino kinematics works well