neutrino-nucleus cross sections at miniboone and … · m. martini, frontiers in neutrino physics,...
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1 5/10/2011 M. Martini, Frontiers in Neutrino Physics, APC Paris
Neutrino-nucleus cross sections at MiniBooNE and T2K energies
Marco Martini CEA/DAM/DIF
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Outline
•Introduction - relevant channels for accelerator experiments - link with Ʋ oscillation physics - why nuclear physics is important? •Our model: nuclear response functions •Comparison with experimental results - quasielastic - pion production - coherent pion production - inclusive cross section In collaboration with:
M. Ericson, G. Chanfray, J. Marteau
Phys. Rev. C 80 065501 (2009) Phys. Rev. C 81 045502 (2010) arXiv:1110.0221
IPN Lyon
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Neutrino - nucleus cross sections
•Relatively precise measurements at high neutrino energies, where deep inelastic scattering is important
•Less precise measurements in few-GeV region, where many processes contribute
•Nuclear effects important at all energies, especially low energies
•Large uncertainties, some puzzles
p p n n n p p
n p
p n n Ʋ
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Neutrino - nucleus interaction @ EƲ ~ O (1 GeV)
p p
p
p p n n
n p p
n p
p n p p n
n n
p p n p
p n n
p p n n
n p p
n p
p n n
p p n n
n p p
n p
p n n
Two Nucleons knock-out (2p-2h)
Incoherent π production
Coherent π production
μ μ
μ
μ
π
n
π
Ʋ
Quasielastic (QE)
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νμ Disappearance – 2-3 sector – QE channel
MiniBooNE
The measurement of θ23 and Δm223 is based on comparing
the initial energy spectrum of Ʋμ measured at a near detector to the final spectrum measured at a far detector The ability to reconstruct neutrino energy, which is not known for broad fluxes, is crucial
EƲ from (Ʋμ n μ- p) CCQE
Eμ and θμ measured
EƲ reconstructed with two-body kinematics
but:
•This is exact only for free neutrons •Detector are composed of nuclei •EƲ is smeared due to momentum distribution of n •Events not CCQE but look identical to them: -Two nucleons knock-out -CC1π production if π is not detected
Cherenkov: μ,π detected n,p not detected
Ʋ beam θμ
μ
p p n n n p p
n p
p n n
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νe Appearance – 1-3 sector – NC π0 production
High sensitivity searches for Ʋμ Ʋe appearance associated with θ13 and CP violation
NC π0 most important background
NC π0 events can mimic CCQE νe signal events when 1 of the 2 γ associated with π0 γγ decay is not detected
24/02/2010 First T2K event seen is Super-Kamiokande
MiniBooNE
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νe and νe Appearance in MiniBooNE
PRL 102, 101802 (2009)
EƲ reconstructed through QE
NC π0 most important background
Events in the region 200<EνQE<475 MeV are
consistent with being either electron events produced by CC scattering or photon events produced by NC scattering.
!!
!!
!!
!
?
?
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Theoretical model: nuclear response functions
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Neutrino-nucleus cross-section
lepton
hadron
In terms of the nuclear response functions:
isovector nuclear response
]
isospin spin-longitudinal
isospin spin-transverse
interference V-A
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Nuclear response functions
Nuclear matter
QE Δ(πN)
p p n n
n p p
n p
p n n
(q,ω)
NN interaction switched off
Nucleons respond individually
Nucleus excitations Nucleon excitations (e.g. Δ resonance)
Nucleon at rest: R δ(ω-q2/2MN)
Fermi momentum spreads δ distribution (Fermi Gas)
NN interaction switched on (RPA)
Force acting on 1N is transmitted
The response R becomes collective
Decrease, increase, divergences,…
Ext. perturbation
γ,W,Z0,π,…
NN off
FG
NN on
The nucleus is one of the multi-faceted many-body systems in the universe. It exhibits a multitude of responses depending on the way one probes it.
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Response functions
Response picture
p h π
∆
p p p n
n n
p p n p
p n
easy to separate the several channels
p
p p n n
n p p
n p
p n n π
n
h
p
p
p p n n
n p p
n p
p n n
∆
p p p
p
1p-1h QE
1p-1h 1π production
h h h h
2p-2h: two examples
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NN QE NN 2p-2h NΔ 2p-2h
ΔΔ πN ΔΔ 2p-2h ΔΔ 3p-3h
q=300 MeV/c
•QE (1 nucleon knock-out) •Pion production •Multinucleon emission
Several partial components (final state channels)
Bare nuclear responses
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Nucleon-hole
Bare polarization propagators
Quasielastic
Delta-hole
Pion production
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Three equivalent representations of the same process
Final state: two particles-two holes
2 body current 2p-2h matrix element 2p-2h response
Cut (optical theorem)
p p h h
Two particle-two hole sector (2p-2h)
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Some diagrams for 2 body currents
Nucleon-Nucleon correlations
Meson Exchange Currents (MEC)
Pion in flight Contact Delta
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Some diagrams for 2p-2h responses
NN correlation-MEC interference
MEC NN correlations
16 diagrams 49 diagrams 56 diagrams
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Where 2p-2h enter in Ʋ-A cross-section?
isovector nuclear response
]
isospin spin-longitudinal
isospin spin-transverse
interference V-A
(spin-isospin, στ excitation operator)
The 2p-2h term affects the magnetic and axial responses (terms in GM , GA )
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Other processes, with the same excitation operator (στ), where 2p-2h are relevant
•Pion absorption
•Transverse response in electron scattering
Absorptive part of the p-wave pion-nucleus optical potential at threshold:
UπNopt =
•Photon absorption
Two-nucleon mechanism: πNN --> NN (πN --> N strongly suppressed)
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RPA
coherent π production
π,ρ,g’
Switching on the interaction: random phase approximation
π
exclusive channels: QE, 2p-2h, ΔπN …
Several partial components treated in self-consistent, coupled and coherent way
q=300 MeV/c
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Effects of the RPA in the quasielastic channel
QE totally dominated by isospin spin-transverse response Rστ(T)
RPA reduction •expected from the repulsive character of p-h interaction in T channel •mostly due to interference term RNΔ < 0 (Lorentz-Lorenz or Ericson-Ericson effect)
Lowest order contribution to QE
RNN RN∆ RΔ∆ QE QE QE
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Testing our responses: QE and np-nh
Electron scattering
QE pic
DIP
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Pion-nucleus cross-section
π+ - 12C
Overestimation of inelastic ch. in the
peak region
Underestimation of absorption
Absence of π FSI
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Coherent channel
π on-shell
Reshaped by collective effects per nucleon
Softening of the responses
Test: π - 12C elastic cross-section
q=300 MeV/c
Dominated by Rστ longitudinal
π
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Comparison with data I) Quasielastic
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MiniBooNE Quasielastic cross section
Comparison with a prediction based on RFG with MA=1.03 GeV (standard value) reveals a discrepancy
In RFG an axial mass of 1.35 GeV is needed to account for data
AIP Conf. Proc. 1189: 139-144 (2009); Phys. Rev. D 81, 092005 (2010)
The introduction of a realistic spectral function does not alter this conclusion (Benhar et al, PRD 80: 073003, 2009; PRL 105:132301, 2010 )
puzzle??
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A possible explanation of this puzzle
M. Martini, M. Ericson, G. Chanfray, J. Marteau Phys. Rev. C 80 065501 (2009)
Agreement with MiniBooNE without increasing MA
N
N’ μ
Ʋ W+
μ
Ʋ
W+
N N
N’ N’
p
p p n n n p p
n p
p n
p
p
p p n n n p p
n p
p n n
Genuine CCQE
Two particles-two holes (2p-2h)
W+ absorbed by a pair of nucleons
Inclusion of the multinucleon emission channel (np-nh)
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Ʋ p
p p n n
n p p
n p
p n μ
CCQE e.g. NOMAD
p p
p p n n
n p p
n p
p n n
μ
p
p p n n
n p p
n p
p n μ + +...
CCQE-like e.g. MiniBooNE
CCQE and CCQE-like
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Theoretical studies on 2p-2h excitations in CCQE-like
M. Martini, M. Ericson, G. Chanfray, J. Marteau Phys. Rev. C 80 065501 (2009)
Phys. Rev. C 81 045502 (2010)
J.E. Amaro, M.B. Barbaro, J.A. Caballero, T.W. Donnelly
Phys. Lett. B 696 151-155 (2011)
Phys. Rev. D 84 033004 (2011)
+ C. F. Williamson
+ J.M. Udias
J. Nieves, I. Ruiz Simo, M.J. Vicente Vacas Phys. Rev. C 83 045501 (2011)
arXiv: 1106.5374
A. Bodek, H.S. Budd, M.E. Christy EPJ C 71 1726 (2011)
arXiv: 1110.0221
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Total CCQE and comparison with flux unfolded MB
Bodek et al.
Martini et al. Nieves et al.
Amaro et al.
{ QE
-only vector -only MEC 2p2h
N.B. The experimental unfolding is model dependent
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MiniBooNE CCQE-like flux-integrated double diff. X section
MiniBooNE, Phys. Rev. D 81, 092005 (2010)
p p n n n
p p n p
p n n Ʋ
Tμ
μ ) θμ
MiniBooNE flux
Model independent measurement
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Flux-integrated double differential X section vs cos θμ
Agreement with MiniBooNE without increasing MA Martini, Ericson, Chanfray, arXiv: 1110.0221
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Flux-integrated double differential X section versus Tμ
Important multinucleon contribution at low muon energy
The algorithm commonly used to reconstruct the neutrino energy is badly suited for this region
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Charged current Q2 distribution
low Q2: opposite actions of RPA quenching and np-nh enhancement
Historically of interest for the determination of the axial form factor
Q2 > 0.2 GeV2: np-nh contribution singled out
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Neutral current Q2 distribution
Exp. Data: MiniBooNE, Phys. Rev. D 82, 092005 (2010)
obtained indirectly from the energy of ejected nucleons
is not clear how multinucleon component shows up in the data
low Q2: opposite actions of RPA quenching and np-nh enhancement
Q2 > 0.3 GeV2: np-nh contribution singled out
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Antineutrino vs Neutrino-nucleus cross-section
The 2p-2h term affects the magnetic and axial responses (terms in GA ,GM)
The isovector response Rτ (term in GE ) is not affected
isovector nuclear response
]
isospin spin-longitudinal
isospin spin-transverse
interference V-A
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Various response contributions to the ν and ν CCQE
The role of interference term (in GAGM) is crucial: it enhances the contribution of Rστ(T) for neutrinos. For antineutrinos instead the destructive interference partially suppresses this contribution leaving a larger role for isovector Rτ which is insensitive to 2p-2h
Rστ ν
Rστ ν
Rτ ν or ν
Hence the relative role of 2p-2h should be smaller for antineutrinos
Martini et al. Phys. Rev. C 81 045502 (2010)
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Martini et al. Phys. Rev. C 81 045502 (2010)
Nieves et al. Phys. Rev. C 83 045501 (2011)
A.Bodek et al. EPJC 71, 1726 (2011)
Total cross sections for antineutrinos
Antineutrino X section very sensitive to RPA
Attention: not Martini QE
cfr to corresponding neutrino case: different behavior
!!
relative role of 2p-2h smaller for antineutrinos
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Inclusive CC cross section on Carbon
SciBooNE, Phys. Rev. D. 83, 012005 (2011)
QE + np-nh + π
QE + np-nh
QE
Less affected by background subtraction with respect to exclusive channels
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Comparison with data II) pion production
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Charged current total 1π+ production over QE ratio
MiniBooNE, Phys. Rev. Lett. 103, 081801 (2009)
In our model π FSI are not included; a reduction of ~ 15 % is expected
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Total cross section MiniBooNE PRD 81, 013005 2010
σ [10^-40 cm^2/nucleon]
Our model
σ [10^-40 cm^2/nucleon]
ν @ 808 MeV 4.76 ± 0.05 st ± 0.76 sy 5.42
ν @ 664 MeV 1.48 ± 0.05 st ± 0.23 sy 1.37
Incoherent exclusive NC 1π0
corrected for FSI effects Our model
ν @ 808 MeV 5.71 ± 0.08 st ± 1.45 sy 5.14
ν @ 664 MeV 1.28 ± 0.07 st ± 0.35 sy 1.17
NC π0 production cross sections
π0 total NC/
σ total CC SciBooNE PRD 81 033004 ‘10 Our model
ν @ 1.1 GeV (7.7 ± 0.5 st ± 0.5 sy) 10-2 7.9 10-2
(without np-nh: 9.8)
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Ratio of σ Experiment Our model
π+ coherent CC/
σ total CC
SciBooNE
u.l.@ EƲ 1.1 GeV
0.67 10-2
PRD 78 112004 ’08
0.71 10-2
(without np-nh: 0.89)
π0 coherent NC/
π0 total NC
MiniBooNE
(19.5±1.1±2.5) 10-2
Phys. Lett. B 664,41 ’08
6 10-2
π0 coherent NC/
σ total CC
SciBooNE
(0.7±0.4) 10-2
PRD 81 033004 ’10
0.4 10-2
(without np-nh: 0.5)
π+ coherent CC/
π0 coherent NC
SciBooNE
0.14 +0.30-0.28
PRD 81 111102 ‘10
1.5
Coherent pion production
coherent puzzle
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Coherent puzzle
π+ coh. CC
π0 coh. NC 30.0
28.014.0
π+ coh. CC
π0 coh. NC =1.5 ~2 !!
SciBooNE:
Theoretical models:
Boyd S. et al. AIP Conf. Proc. 1189 60 (2009)
CC/NC
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Summary
Theory of neutrino interactions with nuclei
Nuclear responses treated in RPA
Unified description of several channels:
Comparison with experiments
•Quasielastic σ , d2σ/dTμ/dcosθ , dσ/dQ2
measured by MiniBooNE can be explained without any modification of MA
•Quasielastic ⇔ Eν reconstruction •Pion production ⇔ CC1π background of CCQE;
NC π0 background of νe appearance •Multinucleon emission ⇔ QE like scattering ⇔ Eν reconstruction
including the multinucleon emission channel
•coherent pion production puzzle
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T2K ``
’’
[28] SciBooNE Inclusive [29] MiniBooNE « Quasielastic » [30] SciBooNE
NC π0 •total •coherent
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N U I N T 0 9
QE tot
QE diff
Monte Carlo
microscopic
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NUINT09
π+ cohérent π0 cohérent
π0 cohérent
π+ incoh.
Tπ (GeV)
Monte Carlo
•Neut: SuperKamiokande, K2K, T2K, SciBooNE
•Nuance: SuperKamiokande, MINOS, MiniBooNE
•Genie: T2K, MINOS, Minerva, NOvA,ArgoNEUT
•NuWro:Wroclaw theo. group
QE: Fermi Gas
π prod:Rein-Sehgal
MC larger than microscopic models
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Quasielastic total cross section
L. Alvarez-Ruso, arXiv:1012.3871; (Neutrino 2010)
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Two different parameterizations of the multinucleon channel
a) from pion absorption b) from electron scattering
(a)
(b)
A few more words about our model
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Delta in the medium
Mass
Width
Self energy
Δπ N Pauli correction (FP)
Pion distortion (CQ)
2p-2h 3p-3h
E. Oset and L. L. Salcedo, Nucl. Phys. A 468, 631 (1987)
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a) np-nh contributions from pion absorption
•Reducible to a modification of the Delta width in the medium
•Not reducible to a modification of the Delta width
E. Oset and L. L. Salcedo, Nucl. Phys. A 468, 631 (1987):
Microscopic calculation of π absorption at threshold: ω=mπ Shimizu, Faessler, Nucl. Phys. A 333,495 (1980)
Extrapolation to other energies
But no q dependence for NN corr. and NΔ interf. contributions !!
e.g.
2p-2h 3p-3h
NΔ interference
Nieves et al. in PRC 83 (2011) and in 1106.5374 use the same model for these contributions
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Transverse magnetic response of (e,e’)
for some values of q and ω,but:
56Fe, few q and ω, too large Im C0
•Parameterization of the responses in terms of Extrapolation to
cover Ʋ region
•Global reduction 0.5 to reproduce the absorptive p-wave π-A optical potential
b) 2p-2h contributions from RT in electron scattering
Alternative treatment of NN correlations and NΔ interference in order to have a q dependence in these 2p-2h contributions
Microscopic evaluation: Alberico, Ericson, Molinari, Ann. Phys. 154, 356 (1984)
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Main difficulties in the 2p-2h sector
•Huge number of diagrams -non relativistic calculation
Alberico, Ericson, Molinari, Ann. Phys. 154, 356 (1984) 49 from MEC 16 from NN correlations 56 from interference
- fully relativistic calculation (just of MEC !) 3000 direct terms More than 100 000 exchange terms
•Divergences in NN correlations
-nucleon propagator only off the mass shell (Alberico et al. Ann. Phys. 1984 )
-kinematical constraints + nucleon self energy in the medium (Nieves et al PRC 83 )
- regularization parameter taking into account the finite size of the nucleus to be fitted to data (Amaro et al. PRC 82 044601 2010 )
prescriptions:
De Pace, Nardi, Alberico, Donnelly, Molinari, Nucl. Phys. A741, 249 (2004)
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MEC
NN corr.
MEC
Δ-MEC
Analogies and differences of 2p-2h
M. Martini, M. Ericson, G. Chanfray, J. Marteau
J. Nieves, I. Ruiz Simo, M.J. Vicente Vacas
Non Relativistic
Non Relativistic
Relativistic
Axial and Vector
Axial and Vector
Only Vector
N∆ interf.
N-MEC interf. NN corr.
[ Genuine CCQE (1p-1h): LFG+RPA ]
[ Genuine CCQE (1p-1h): LRFG+SF+RPA ]
[ Genuine CCQE (1p-1h): Superscaling ]
J.E. Amaro, M.B. Barbaro, J.A. Caballero, T.W. Donnelly et al.
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Flux-integrated double differential X section versus Tμ
Amaro et al, PRD 84, 033004 (2011) Nieves et al, arXiv: 1106.5374
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Ʋμ-12C Cross sections
as a function of Ʋ energy
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Inclusive CC cross section on Carbon
Experimental data: SciBooNE, Phys. Rev. D. 83, 012005 (2011)
Nieves et al. Phys. Rev. C 83 045501 (2011) Our calculation
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Charged current coherent π+ production
σ CC π+coherent
σ CC total
K2K: 0.60 10-2 averaged over Ʋ flux <EƲ> 1.3 GeV PRL 95 252301
SciBooNE: 0.67 10-2 @ EƲ =1.1 GeV 1.36 10-2 @ EƲ =2.2 GeV
(2005)
PRD 78 112004 (2008)
Our model @
EƲ=1.1 GeV
Upper limits
0.71 10-2
Just compatible
Without np-nh in σ CC total
0.89 10-2
Appreciably above u.l.
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Ʋμ induced coherent pion production off 12C
pion kinetic energy
neutrino energy
Total cross section
Differential cross section