Transcript Neutrino Scattering Off Nucleons and Nuclei

Neutrino Interactions
with Nucleons and Nuclei
Tina Leitner, Oliver Buss,
Ulrich Mosel, Luis Alvarez-Ruso
Beijing 03/10
Soudan Mine,
Nova
770 km
Homestake Mine
Dusel
Beijing 03/10
Long baseline experiments
M. Wascko
Beijing 03/10
Neutrino oscillation search

neutrino oscillations: probability for 2 flavors:
Ã
P(º¹ !

º e; t ) = sin 2 2µ sin 2
¢ m2L
!
4E º
Crucial parameter: neutrino energy E
Flux: obtained from Event-Generators
for hadronic production and subsequent
weak decay
Energy must be reconstructed
from hadronic final state
Need to understand ‚classical‘ hadronic interactions
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Oscillation Minium at MiniBooNE
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Motivation

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, pionproduction or qe scattering difficult.
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Motivation


In-medium physics: vector and axial form factors in
medium have to be extracted from reactions on nuclei.
 NUTEV anomaly for Weinberg angle
 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
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The Rebirth of Low Energy Nuclear Physics
Low-Energy Nuclear Physics
determines response
of nuclei to neutrinos
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Outline

neutrino-nucleus reaction: l A  l hadrons
at ~ 0.5 – 1.5 GeV neutrino energy
 scattering off a single nucleon
l

○ free nucleon
○ nucleon bound in a nucleus
W, Z
 Total QE scattering off a nucleus
and  production
○ final state interactions (FSI)
 GiBUU transport model

Results: qe scattering,  production, nucleon knockout

Conclusions
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Model Ingredients: ISI

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)
Cross sections taken from


Electro- and Photoproduction for vector couplings
Axial couplings modeled with PCAC

Pauli-principle included

Shadowing by geometrical factor (Q2,) included
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Model Ingredients ISI
• Hole spectral function (local TF)
Potential
smoothes E-p
distributions
Local Thomas-Fermi Particles in mean-field potential!
• Particle spectral function: collisional broadening
• Inclusive cross section
Z
0
d¾tl Aot! l X
= g
Z
dE
d3 p
k ¢p l N
P
(~
p
;
E
)
d¾ PPB (~
p; E )
h
(2¼) 3
k 0 p0 t ot
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Neutrino nucleon cross section
single ¼
QE
‚ DIS
¼
N
N'
P. Lipari, Nucl. Phys. Proc. Suppl. 112, 274 (2002)
R+
note:
10-38 cm² = 10-11 mb
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Quasielastic scattering

CC: º l n ! l ¡ p
NC: º n ! º n; º p !
reactions:
with

hadronic
current:
º p
0
QE
QE
J®
= hN jJ ®
( 0) jN i = u
¹ ( p0) A ®u( p)
Ã
A® =
!
°® ¡
=
q q®
q2
F 1V +
i
2M
¾®¯ q¯ F 2V + ° ®° 5 F A +
q®° 5
M
FP
axial form factors
• related by PCAC
• dipole ansatz
extra term
• ensures
vector current conservation vector form factors
for nonequal masses
• related to EM form factors by CVC
• BBBA-2007 parametrization
in addition:
strange vector and axial form factors for NC
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Quasielastic scattering
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Quasielastic Scattering: Axial Mass

neutrinos probe nucleons / nuclei via V-A weak interaction

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
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Pion production through
resonance excitation
13 resonances with W < 2 GeV
 pion production dominated by P33(1232) resonance:
· V
¸
V
V
C
C
C
¹
3
J ¢®¹ =
(g®¹ =
q ¡ q®° ¹ ) + 42 (g®¹ q ¢p0 ¡ q®p0 ) + 52 (g®¹ q ¢p ¡ q®p¹ ) ° 5
MN
MN
MN

C3A ®¹
C4A ®¹
C6A ® ¹
® ¹
0
® 0¹
A ®¹
+
(g =
q¡ q ° )+
(g q ¢p ¡ q p ) + C5 g +
q q
2
2
MN
MN
MN


CV from electron data (MAID analysis with CVC)
CA from fit to neutrino data (experiments on hydrogen/deuterium)
BNL
ANL
10 % error in C5A(0)
discrepancy between ANL and BNL data
 uncertainty in axial form factor
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CC pion production on free nucleons

CC production of D+ and D++

subsequent decay into 3 channels:
including higher resonances (isospin ½):
P11 (1440); D 13 (1520); S11 (1535)
BNL data
ANL
data
How much is background??
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ºl p !
l ¡ p ¼+
ºl n !
l ¡ n ¼+
ºl n !
l ¡ p ¼0
Pion production through ¢
New V, old A
New V, new A
averaged over ANL flux, W < 1.4 GeV
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
Nuclear Targets (K2K, MiniBooNE, T2K,
MINOS, Minerva, ….
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Medium modifications of the
inclusive cross section


All cross sections Fermi smeared
D cross section is further modified in the nuclear medium:


 decay might be Pauli blocked: decrease of the free width
additional "decay" channels in the medium: collisional
width coll
"pion-less
decay"
overall effect:
increase of the width
 ! med = P + coll
collisional broadening
Beijing 03/10
Model validation: electron scattering
PRC 79, 034601 (2009)
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Transport vs. Quantummechanics

Fully inclusive reactions: no info on final states,
both



Both applicable, lead to same results.
Semi-Inclusive Reactions:



Quantum-mechanical reaction theory (Relativistic Impuls
Approximation RIA, Distorted Wave Impuls Approximation DWIA)
Transport theory
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
Exclusive Reactions (coherent production):

Phase coherence: Only QM applicable
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Model Ingredients: FSI

Simplicity

Theoretical Basis
Kadanoff-Baym equation
○ full equation can not be solved yet
– not (yet) feasible for real world problems

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, …)
○
no mean-fields, (no) Fermi motion
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GiBUU transport



what is GiBUU?
semiclassical coupled channels transport model
general information (and code available):
http://theorie.physik.uni-giessen.de/GiBUU/
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!
Beijing 03/10
Model Ingredients: FSI

time evolution of spectral phase space density
(for i = N, D, , r, …) given by BUU equation
one-particle spectral phase space density for particle species i
Hamiltonian

one equation for each particle species (61 baryons, 21 mesons)
coupled through the potential US and the collision integral Icoll

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)
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Pion production: model validation
with photon data

Ca
Ca
GiBUU describes photon-induced
pion production, in particular
momentum distribution
(Eur. Phys. J A22 (2004))
¾(A)=A 2=3
Rd =
¾( 2 H )=2
TAPS data
Beijing 03/10
Pb
Pb
CC nucleon knockout: m56Fe  m- N X
p
n
w/o FSI
p
n
w FSI
E = 1 GeV
Beijing 03/10
NC induced proton knockout: m56Fe  m pX

effects of FSI on nucleon kinetic energy spectrum at E = 1 GeV
 flux reduction at higher energies
 large number of rescattered nucleons at low kinetic energies
NC p
D contribution to knock-out almost equals QE contribution (increases with E)
 coupled-channel effect
Phys. Rev. C 74, 065502 (2006)
Beijing 03/10
Different approaches to identify CCQE
MiniBooNE
K2K
0¼+X
QE induced
0¼+1p+X
QE induced
¢ induced (fakes)
T.L. et al., NUFACT08 proceedings, arXiv:0809.3986
Beijing 03/10
¢ induced (fakes)
MiniBooNE CCQE
per nucleon
T. Katori, NUINT09
QE-like - QE-fake,
energy reconstruction
 data correction
model dependent




underestimate MiniBooNE by ~35%
agreement with other models
agreement with NOMAD
pion-electroproduction, former neutrino
experiments, NOMAD
consistent with MA = 1 GeV
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MiniBooNE

2
Q
distribution
CC º¹ on 12C averaged over MiniBooNE flux
 QE-fakes: background!
 reconstruction via

MiniBooNE “data” = Smith-Moniz Fermi gas
with “modified Pauli blocking” and MA = 1.35 GeV
 assume that non-QE background subtraction is perfect!

in addition: RPA correlations by Nieves et al. PRC 73 (2006)
Beijing 03/10
arXiv:0909.5123
Energy reconstruction via CCQE


all QE-like events enter energy reconstruction!
reconstruction under assumption that QE-like = QE and with free 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 CCQE


all QE-like events enter energy reconstruction!
reconstruction under assumption that QE-like = QE and with free kinematics:
EB = 34 MeV
QE fakes “fill in oscillation dip”
 error in extracted
oscillation parameters
Beijing 03/10
CC pion production: m56Fe  m-  X
¼0
¼+
w/o FSI
¼0
¼+
w FSI
E= 1 GeV
Beijing 03/10
CC pion production: m56Fe  m-  X

effects of FSI on pion kinetic energy spectrum at E = 1 GeV



strong absorption in D region
side-feeding from dominant + into 0 channel
secondary pions through FSI of initial QE protons
+
0
Spectra determined by ¼-N-¢ dynamics
Beijing 03/10
K2K and MiniBoonE

+
CC1¼
single-¼+/QE ratio
¾1+ / ¾0+1p after FSI:
K2K definition for
CCQE-like cross section
FSI corrected
¾1+ / ¾0+ after FSI:
MiniBooNE definition for
CCQE-like cross section
FSI corrected
¾1+ / ¾QE before FSI:
including nuclear corrections
like mean fields and Fermi motion
¾1+ / ¾QE in the vacuum
Beijing 03/10
MiniBooNE NC
0
1¼
data: C. Anderson, NUINT09
bands:
uncertainty of
axial form factor

NC1¼0 data consistent with calculation without FSI!

possible origins:
 elementary cross section too small
 neutrino-flux prediction (cf. discrepancy in QE channel)
 “data” contains “theory”: model dependence
arXiv:0910.2835
Beijing 03/10
Summary

Quasielastic scattering events contain admixtures of
Delta excitations



D excitations affect nucleon knockout, contaminate QE
experiments
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.
Beijing 03/10
Summary

Particle production at neutrino energies of ~1
GeV



Inclusive cross section dominated by D 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
Extension to higher energies (5 – 280 GeV)
successful for electroproduction, for neutrinos
(OPERA) to be done, straightforward
Beijing 03/10