Ulrich Mosel
General Motivation: Interactions n Pions (from resonances and DIS) are the most dominant background to QE
GiBUU : Theory and Event Simulation based on a BM solution of Kadanoff-Baym equations Physics content (and code available): Phys. Rept. 512 (2012) 1 http://gibuu.hepforge.org 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!
Practical Basis: GiBUU one transport equation for each particle species (61 baryons, 21 mesons) coupled through the potential in H and the collision integral C W < 2.5 GeV: Cross sections from resonance model (PDG and MAID couplings), consistent with electronuclear physics W > 2.5 GeV: particle production through string fragmentation (PYTHIA) n GiBUU: Only `Neutrino Event Generator that has widely been tested with various hadronic and em reactions, NO TUNING
GiBUU n GiBUU solves for phase-space distributions f(x,p) for all particles n GiBUU contains all known in-medium effects n GiBUU reduces to MC if no in-medium effects are present, no potentials
GiBUU n GiBUU produces multitudes of cross sections that are built in; code is transparent enough to code others n GiBUU produces in addition full event data files in 2 different formats: Les Houches and an own format
Check: pions in HARP HARP small angle analysis 12 GeV protons Curves: GiBUU K. Gallmeister et al, NP A826 (2009) CETUP* 2014
Neutrino-nucleon cross section CCQE 1π DIS π note: 10-38 cm² = 10-11 mb
Neutrino-Nucleon Cross Sections
SIS DIS by PYTHIA Shallow Inelastic Scattering, interplay of different reaction mechanisms à Ambiguity to switch from one mechanism to the other
Neutrino Beams n Neutrinos do not have fixed energy: Have to reconstruct energy from final state of reaction
Neutrino Oscillations appearance probability Vacuum oscillation Oscillation depends on difference of (squared) masses only Matter effects, n e = electron density Depends on sign of Δ 31
LBNE, δ CP Sensitivity From: Bishai et al., hep-ex 12034090 8 GeV 60 GeV proton energy From: Bishai et al arxiv:1203.409 δ CP = 0 δ CP = π/2 δ CP = - π/2 Need energy to distinguish between different δ CP
Axial Formfactor of the Nucleon n neutrino data agree with electro-pion production data M A 1.02 GeV world average M A 1.07 GeV world average Dipole ansatz is simplification, not good for vector FF
Quasielastic Scattering Vector form factors from e scattering axial form factors F A ó F P and F A (0) via PCAC dipole ansatz for F A with M A = 1 GeV:
Spectral Functions n Single particle spectral functions absorb effects of interactions in particle properties n Free Fermi gas (in generators): spiky E-dep. leads to artifacts in response n Now: dress particle with interactions, mean field and/or additional interactions à quasiparticles
Spectral Function in GiBUU Two essential features: 1. Local TF momentum distribution removes artifacts of sharp cut at p F 2. Particles bound in momentum- and coordinate-dependent potential, integration removes delta-function spikes in energy Spectral function in GiBUU contains interactions in mean field
Nuclear Groundstate From: Alvarez-Ruso, Hayato, Nieves GiBUU uses Local Fermi Gas + Nukleon mean field potential
Electrons as Benchmark for GiBUU 12 C No free parameters! no 2p-2h, contributes in dip region and under Δ usive electron-carbon cross section at beam energy E 730 MeV O. Benhar, spectral fctn
Pion Production n n n n 13 resonances with W < 2 GeV, non-resonant single-pion background, DIS pion production dominated by P 33 (1232) resonance: C V from electron data (MAID analysis with CVC) C A from fit to neutrino data (experiments on hydrogen/deuterium), so far only C A 5 determined, for other axial FFs only educated guesses
Pions n Pion production amplitude = resonance contrib + background (Born-terms) n Resonance contrib n V determined from e-scattering (MAID) n A from PCAC ansatz n Background: n Up to about Δ obtained from effective field theory n Beyond Δ unknown n 2 pi BG totally unknown
Pion Production 10 % error in C 5A (0) data: PRD 25, 1161 (1982), PRD 34, 2554 (1986) discrepancy between elementary data sets à impossible to determine 3 axial formfactors
events/0.02 GeV dσ/dw(nπ), events/0.03 GeV events/0.02 GeV 140 120 100 80 60 40 20 0 40 30 20 10 0 20 10 π-n inv. Mass Distributions ð Delta pole full model ANL ν p µ - p π + (a) ν n µ - p π 0 ν n µ - n π + (b) (c) dσ/dw(µ N), events/ 0.04 GeV Þ 80 60 40 20 30 20 10 30 20 10 ν p µ - p π + Delta pole full model ANL ν n µ - p π 0 ν n µ - n π + (a) (b) (c) dσ/dw(nπ), events/0.05 GeV 600 500 400 300 200 100 0 140 120 100 80 60 40 20 0 80 60 40 20 ð Þ Delta pole full model BNL ν p µ - p π + ν n µ - p π 0 ν n µ - n π + (a) (b) (c) Lalakulich et al., Phys. Rev. D 82, 093001 (2010) 0 1.1 1.2 1.3 1.4 1.5 1.6 W(Nπ), GeV 0 1.2 1.4 1.6 1.8 2 W(µN), GeV 0 1.1 1.2 1.3 1.4 1.5 1.6 W(Nπ), GeV ANL data BNL data
Check: Pions in Nuclei γ ->π 0 on Pb Photons illuminate the whole nucleus, test various pion mean free paths Data: TAPS, Krusche et al
Pions from HERMES at 27 GeV Data: Airapetian et al Curves: GiBUU Nucl.Phys. A801 (2008) 68-79
JLAB π + production Q 2 = 1:0 : : : 1:25 G ev 2 Q 2 = 1:85 : : : 2:4 G ev 2 º = 3:5 : : : 4 G ev R π 1.2 1 0.8 0.6 0.4 0.2 C Fe Pb data C Fe Pb data Data: W. Brooks et al., JLAB Same parameters as for HERMES 0 º = 2:2 : : : 3 G ev R π 1.2 1 0.8 0.6 0.4 0.2 C Fe Pb data 0 0 0.2 0.4 0.6 0.8 z h C Fe Pb data 0 0.2 0.4 0.6 0.8 z h 1
Pion Production in MB ANL-BNL Input Spectral shape determined by pi-n-delta dynamics in nuclei, spectral disagreement surprising!?
Pion Production in MB
Pion Production in MB Flux renormalization (data x 0.9 (cf. Nieves QE analysis))
Pion Production Discrepancy mainly in tail of flux distributions (large uncertainty) Upper line: BNL input Lower line: ANL input Tendency for theory too low, more so for π+, at E > 1 GeV DIS and higher resonances contribute for E > 1 GeV, not contained in Hernandez calcs.
Pions at NOvA Lalakulich et al, PR D86, 014607 (2012)
Pion FSI at MINERvA
MINERvA Pions CETUP* 2014
Pions at various experiments DIS DIS Multi π +, target: C for MB, T2K and MINERvA, Ar for LBNE NUINT 2014
Danger of cuts W distribution for Δ is significantly broadened due to Fermi-motion, Cut at 1.4 GeV cuts away 25% of total strength
NOMAD Flux
NOMAD W Distribution NOMAD results date back to yesterday: Preliminary!
NOMAD Pions
Kaons at MINOS and NOvA Lalakulich et al, PR D86, 014607 (2012) FSI increase the cross section! Semi-inclusive X-sections much larger than exclusive ones ( 1 order of magnitude, cf. Athar, Alvarez-Ruso)
MINERvA Fsi are most important, but different, for pions and kaons Elementary kaon vertices shielded by secondary production: π + N à K + Λ
Conclusion n It will be hard to understand the pion production data as long as the elementary X-section is not determined n Kaon production proceeds through DIS events and subsequent π + N -> K + Λ