Tina Leitner Oliver Buß, Ulrich Mosel und Luis Alvarez-Ruso

Neutrino nucleus scattering Tina Leitner Oliver Buß, Ulrich Mosel und Luis Alvarez-Ruso Institut für Theoretische Physik Universität Gießen, Germany XL. Arbeitstreffen Kernphysik, Schleching 26. Februar bis 5. März 29 European Graduate School Complex Systems of Hadrons and Nuclei Copenhagen - Gießen - Helsinki - Jyväskylä - Torino JUSTUS-LIEBIG- UNIVERSITÄT GIESSEN

Long baseline experiments M. Wascko

Motivation I: Link between nuclear effects & ν oscillations l - l - ν ν W W particle identification identify neutrino flavor, CCQE, background, reconstruction of neutrino quantities important for oscillations and cross section measurements: E &Q ν 2 influence of in-medium modifications and final state interactions

Motivation II: Weak probe for nuclear properties neutrinos probe nucleons / nuclei via V-A weak interaction structure: axial structure of the nucleon and baryonic resonances (in the medium!) nuclear effects (e.g. low-q² deficit in MiniBooNE) dedicated neutrino-nucleus experiment: Minerva Neutrino-nucleus nucleus reactions give information on properties of cold nuclei = necessary check for experiments such as CBM@FAIR which aims for clarifying the properties of dense hadronic matter

Outline l - l - ν ν W W GiBUU model initial iti state t interactions, ti final state t interactions ti general results inclusive and semi-inclusive MiniBooNE, K2K applications relation to oscillation measurements

Modelling in-medium reactions ν l - W

Modelling in-medium reactions ν l - W Initial state interaction (ISI) impulse approximation Fermi motion, Pauli blocking self energies medium-modified ν N cross sections

Modelling in-medium reactions ν l - W Initial state interaction (ISI) impulse approximation Fermi motion, Pauli blocking self energies medium-modified ν N cross sections Final state interactions (FSI) absorption particle production, rescattering,

GiBUU model outline what is GiBUU? semiclassical transport model in coupled channels more information & code download: http://theorie.physik.uni-giessen.de/gibuu/ GiBUU describes... heavy ion reactions pion and proton induced reactions low and high energy photon and electron induced reactions neutrino induced reactions... within the same unified framework using the same physics input! GiBUU allows to describe specific experiments (inclusion of detector acceptances) GiBUU has been checked extensively against experimental data for heavy-ion collisions, ea, γa, pa, A reactions

GiBUU model outline ν l - W dσ`a `X tot = g Z nucleus d 3 r Z d 3 p (2) 3 Θ(p F (r) p) 1 k p v rel k p dσmed tot P PB (r, p)m X

Neutrino nucleon cross section QE RES single BG R + N N' vector form factors determined from electron scattering data and via CVC axial form factors via PCAC and fixed by data where possible

Neutrino nucleon cross section QE single R + N N' P. Lipari, Nucl. Phys. Proc. Suppl. 112, 274 (22) note: 1-38 cm² = 1-11 mb

Neutrino nucleon cross section QE DIS single R + N N' note: 1-38 cm² = 1-11 mb P. Lipa ari, Nucl. Phys. Proc. Suppl. 112, 274 (2 2)

GiBUU model outline: ISI ISI ν l - W dσ`a `X tot = g Z nucleus d 3 r Z d 3 p (2) 3 Θ(p F (r) p) 1 k p v rel k p dσmed tot P PB (r, p)m X primary interaction of neutrino with one nucleon at a time QE, resonance excitation, non-resonant pion background medium modifications local Fermi gas, Pauli blocking full in-medium kinematics with nuclear potentials in-medium spectral functions

Medium modifications dσ`a `X tot = g Z nucleus d 3 r Z d 3 p (2) 3 Θ(p F (r) p) 1 k p v rel k dσmed tot P PB (r, p)m X p local Fermi gas local density approximation with realistic density profiles: Pauli blocking 3 p F (~r)= 2 2 ρ(~r) 1/3 in-medium ν N cross sections in-medium self energies density + momentum dependent mean-field potential collisional broadening collisional width in low-density approximation using GiBUU xsections full in-medium kinematics, Fermi motion

16 O(e,e') r)] dσ/(dω dω Ω k ) [nb/(mev sr 75 6.7 GeV, 32. Q 2 QE-peak =.134 GeV2 45 full in-med. SF 3 mom.-dep. pot. 15 3 22.5 15 7.5 12 9 6 3 9 6 3.88 GeV, 32. Q 2 2 QE-peak =.25 GeV 1.8 GeV, 32. Q 2 QE-peak =.32 GeV2 Q 2 QE-peak 1.2 GeV, 32. Q QE-peak =.366 GeV2 4 1.5 GeV, 32. 3 Q 2 QE-peak =.55 GeV2 2 1 T.L. et al., PRC in press, arxiv:812.587 [nucl-th].2.4.6.8 1 1.2 ω [GeV]

GiBUU model outline: FSI ν l - W dσ`a `X = g dσ tot Z nucleus Z d 3 r FSI d 3 p Θ(pF 1 k p med (2) 3 F (r) p) vrel k p dσ tot P PB (r, p)m X wishlist of experimentalists reliable FSI tracking of particles identification/multiplicities ways to model FSI Glauber/eikonal approximation optical model hadronic transport

GiBUU transport model BUU equation f i (~r, p, t) time evolution of phase space density (for i = N,,, ρ, ) under influence of Hamiltonian H given by BUU equation: df i dt = ³ t +( ~p H i ) ~r ( ~r H i ) ~p fi (~r, p, t) =I coll [f i,f N,f,f,...] fully-coupled channel problem Hamiltonian H i =H i (f i,f a,f b,...) connects particle species coupled through the collision integral: 61 baryons and 21 mesons collision integral accounts for changes in f i (gain and loss term): elastic and inelastic 2-body scattering decay of unstable particles 3-body reactions through detailed balance Pauli blocking for fermions

E µ [GeV V] E µ [GeV] CC nucleon knockout: ν µ 56 Fe µ - N X 1 1 p 5.8 4.8 3.6 2.6 1.4.4.2 E µ [GeV ev] w/o FSI.2 n 1 8 6 4 2 1 1.2.4.6.8 p 1 5.2.4.6.8 n 1 1.8 Q 2 [GeV 2 4.8 ] 3 Q 2 [GeV 2 8 ] 6.6 2.6 1.4 2 4.4.2.2.4.6.8 1 Q 2 [GeV 2 ] E µ [GeV] wfsi E ν = 1 GeV.2.2.4.6.8 1 Q 2 [GeV 2 ]

NC nucleon knockout: ν µ 56 Fe ν µ N X effects of FSI on nucleon kinetic energy spectrum at E ν = 1 GeV flux reduction at higher energies large number of rescattered nucleons at low kinetic energies dσ/dt cm 2 p [1-38 /GeV] 1 8 6 4 2 NC w/o FSI w FSI w FSI ( ) w FSI (QE) p dσ/dt cm 2 n [1-38 /GeV] 1 8 6 4 2 NC w/o FSI w FSI w FSI ( ) w FSI (QE) n.2.4.6.8 T p [GeV].2.4.6.8 T n [GeV] contribution to knock-out almost equals QE contribution (increases with E ν ν) ) coupled-channel effect T.L. et al., PRC 74, 6552 (26)

E µ [GeV V] E µ [GeV] CC pion production: ν µ 56 Fe µ - X 1.8.6.4.2 1 1 + 8.8 6 4.6 2.4 1 1.2.4.6.8 1 1.2.4.6.8 1.8 +.8 Q 2 [GeV 2 8 ] 6 Q 2 [GeV 2 ].6 4.6 2.4.4.2.2.4.6.8 1 Q 2 [GeV 2 ] E µ [GeV V] w/o FSI E µ [GeV] wfsi E ν = 1 GeV.2.2.2.4.6.8 1 Q 2 [GeV 2 ] 2 15 1 5 2 15 1 5

CC pion production: ν µ 56 Fe µ - X effects of FSI on pion kinetic energy spectrum at E ν = 1 GeV strong absorption in region side-feeding d from dominant + into channel secondary pions through FSI of initial QE protons dσ/dt 2 [1-38 cm /GeV] 4 12 w/o FSI 35 w FSI 1 3 w FSI (QE) 8 25 2 15 1 5 +.1.2.3.4.5.6.7.8 T [GeV] dσ/dt 2 [1-38 cm /GeV] 6 4 2 w/o FSI w FSI w FSI (QE).1.2.3.4.5.6.7.8 T [GeV] first calculation of realistic pion spectra T.L. et al., PRC 73, 6552 (26)

K2K and MiniBoonE CC1 + single- + /QE ratio 1. σ 1 + / σ + after FSI: 1.2 MiniBooNE definition for CCQE-like cross section.9 1.5 CC ν µ on 12 C (1) (2) 1.2 MiniBooNE data (3) (4) (5).6 2. σ 1 + / σ +1p after FSI: K2K definition for.3 CCQE-like cross section 3. σ 1 + / σ QE after FSI /σ QE σ 1 +/ 1.5 1.2.9 4. σ 1 + / σ QE before FSI including nuclear corrections.6 like mean fields and Fermi motion.3 CC ν µ on 12 C K2K data 5. σ 1 + / σ QE in the vacuum on an isoscalar target. T.L. et al., PRC in press, arxiv:812.1787 [nucl-th].6.8 1 1.2 1.4 1.6 1.8 2 E ν [GeV]

K2K and MiniBoonE NC1 2 1.5 no FSI, no SF full full, but only 1 NC ν on 12 C MiniBooNE PLB 664, 41 (28) dσ σ 1-38 cm 2 1 /dt [1 /G GeV].5 4 3 2 MiniBooNE flux NC ν on 16 O K2K flux K2K PLB 619, 255 (25) 1.1.2.3.4.5.6.7.8 T [GeV] T.L. et al., PRC in press, arxiv:812.1787 [nucl-th]

Connection to neutrino oscillation experiments CCQE dominant at low energies used to reconstruct the neutrino energy important for oscillations CC1 + second most important t cross section main background to CCQE (if pion is absorbed) NCQE interesting on its on: axial form factors NC1 + + may mimic the single mu signal if its charge isn t seen NC1 may mimic the signal of a single electron main background for v e appearance e

MiniBooNE oscillation result (ν e appearance) MiniBooNE PRL 98, 23181 (27) dominated d by background:

Different approaches to real CCQE MiniBooNE 7 7 6 + X 6 K2K σ [1-38 cm 2 ] 5 4 3 2 QE induced σ [1-38 cm 2 ] 5 4 3 2 + 1 p + X QE induced 1 induced (fakes) 1 induced (fakes).6.8 1 1.2 1.4 1.6 1.8 2 E ν [GeV].6.8 1 1.2 1.4 1.6 1.8 2 E ν [GeV] T.L. et al., NUFACT8 proceedings, arxiv:89.3986

Energy reconstruction via CCQE CCQE = no pion in FSI reconstruction via E B = 34 MeV 1 before FSI after FSI.8.6.4.2 E ν real =.5 GeV CC E ν real =.7 GeV CC a.u. 1.8.6.4.2 E ν real = 1 GeV CC E ν real = 1.5 GeV CC.5 1 1.5 FWHM ~.1 GeV.5 1 1.5 2 E ν rec [GeV]

Summary & Conclusions GiBUU is a multi-purpose theory to describe final state interactions including elastic and inelastic scattering side feeding g( (charge exchange) method allows to propagate particles out to detector cross section dominated by QE contribution & excitation for E ν < 1.5 GeV in-medium modifications: local Fermi gas, self energies, good description of electroproduction data LBL experiments need to identify initial process and produced hadrons reconstruct neutrino quantities from observables for both cross section & oscillation measurements simulate impact of in-medium modifications and FSI with GiBUU absorption, secondary particles, induced nucleon knockout,... work in progress: extension to neutrino energies of up to ~1 GeV straightforward cross section dominated by DIS good understanding of in-medium modifications and FSI necessary to distinguish profane from extraordinary effects