Nucleon emision off nuclei induced by neutrino...
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Nucleon emision off nuclei induced by neutrinointeractions
M. Valverde
RCNP, Osaka University
NuFact09IIT, Chicago, Illinois, USA
July 22, 2009
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Main Nuclear Effects
Pauli blocking: Fermi Gas
Fermi motion: Fermi Gas
Correlations in excited states: RPA
Nucleon binding: Nucleon spectral functions (hole states)
Final State Interactions: Nucleon spectral functions (particlestates)
Nucleon rescattering: Monte Carlo propagation
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Self-energy of the Gauge Boson
++
W W W
W W+ + +
+
p N N
π,ρ,...
∆,N*
∆ , N*
π,ρ... + ...
∆ , N*
+
W
W
+
q
pp+q
q
W
+
n
+
+
+
Many Body expansion of
Πνρ
W ,Z0,γ(q, ρ)
Absorption by one Nucleon , 2N,. . .
Real and virtual meson (π, ρ, · · · ) production
Excitation of ∆ or higher resonances
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N < F
++
W W W
W W+ + +
+
p N N
π,ρ,...
∆,N*
W n p W+ + N ∆, N*W+N N NNW+N N π , Νρ, ...
∆ , N*
π,ρ... + ...
∆ , N*
+
W
W
+
q
pp+q
q
W
+
n
+
+
+
W+
2
N
∆
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π,ρ,...
2
π,ρ,...
++
W W W
W W+ + +
+
p N N
∆,N*
W n p W+ + N ∆, N*W+N N NNW+N N π , Νρ, ...
∆ , N*
π,ρ... + ...
∆ , N*
+
W
W
+
q
pp+q
q
W
+
n
+
+
+
W+ N N’
N,N’ < F
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π,ρ,...
π,ρ,...
2
++
W W W
W W+ + +
+
p N N
∆,N*
W n p W+ + N ∆, N*W+N N NNW+N N π , Νρ, ...
∆ , N*
π,ρ... + ...
∆ , N*
+
W
W
+
q
pp+q
q
W
+
n
+
+
+
W+ N
N,N’ < FN’
N’
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N < F
++
W W W
W W+ + +
+
p N N
π,ρ,...
∆,N*
W n p W+ + N ∆, N*W+N N NNW+N N π , Νρ, ...
∆ , N*
π,ρ... + ...
∆ , N*
+
W
W
+
q
pp+q
q
W
+
n
+
+
+
W+ N
π,ρ,... 2
∆ , N*
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Main features of the model
We work in nuclear matter and get results via LDA
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Main features of the model
We work in nuclear matter and get results via LDAbut include whole range of nuclear corrections
Long (RPA) and short range correlations
∆(1232) degrees of freedom
Final State Interactions (FSI)
Nucleon Rescattering (Semi-inclusive Observables)
J. Nieves, J.E. Amaro, M. Valverde, Phys. Rev. C
J. Nieves, M. Valverde, M. J. Vicente Vacas Phys. Rev. C
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The Impulse Approximation
General expresion for the cross section
dσ ∼ LµνW µν
All nuclear physics is on the hadronic tensor
∫
d4pµ Sh(p0,p)Sp(p
0 + q0,p + q)︸ ︷︷ ︸
NuclearPhysics
Aµν(p, q)︸ ︷︷ ︸
Vertexinteraction
In Fermi Gas approximation:
∫d3p
2π3
M
Ep+q
M
Ep
Θ (kF (r) − |p|)Θ (|p| − kF (r)) δ(q0 + Ep − Ep+q
)
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The Impulse Approximation
General expresion for the cross section
dσ ∼ LµνW µν
All nuclear physics is on the hadronic tensor
∫
d4pµ Sh(p0,p)Sp(p
0 + q0,p + q)︸ ︷︷ ︸
NuclearPhysics
Aµν(p, q)︸ ︷︷ ︸
Vertexinteraction
In Fermi Gas approximation:
∫
d3r
∫d3p
2π3
M
Ep
Θ (kF (r) − |p|)M
Ep+q
Θ (|p| − kF (r))δ(q0 + Ep − Ep+q
)A
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RPA Response
ph excitation → series of ph and ∆h excitations.
+ +
q
V
V
V+
µ
ν
ν
ν
µ
µ
V
V
V
+ .....
ν
µ
Z
Z
Z
ZZZ
ZZ
Z
Neutrino Energy (GeV)0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
2 c
m−
38 1
0×
QE
C
Cσ
0
1
2
3
4
5
6
7
8
9
10 X on O16−µ → + n µνQE Cross−section with FSI for
Benhar
Nieves−SF.FSI.RPA
Nieves−SF.FSI
X on O16−µ → + n µνQE Cross−section with FSI for
Thanks to S. Dytman and S. Boyd for the plot
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12
A
10
12
2/GeV2] FG
+ mom.dep.pot.
+ SF
!" "#
6
8
[10-38 cm2/ + SF
+ correlations
MiniBooNE
"$ % "&'()*++, 2
4
d/dQ2 [10
-! " "!" ./"
0 0 0.2 0.4 0.6 0.8 1 1.2 1.4
d
Q2 [GeV
2]A Q [GeV ]
4
5
6
m2/GeV] total
MiniBooNE
7
8
9
10
cm2]
A
total
MiniBooNE
2
3
4
E [10-38 cm
3
4
5
6
7
dcos
[10-38 c
0
1
0 0.5 1 1.5 2
d/dE
0
1
2
3
-1 -0.5 0 0.5 1
d/dco
.0"1 "2" .3%4#%--"
0 0.5 1 1.5 2
E [GeV]-1 -0.5 0 0.5 1
cos
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Nucleon Spectral Functions
FSI dressing up the nucleon propagator in the ph excitation
q
p
p+q
Sp,h(ω,p ) = ∓1
π
ImΣ(ω,p)[
ω − p2
2M− ReΣ(ω,p )
]2
+ [ImΣ(ω,p)]2
Hole Interacting particles in a Fermi Sea FSParticle Interaction of the ejected nucleon with the finalnuclear state
In the limit Σ → 0 we recover Fermi Gas
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NuFact08
Qualitatively agreement with Benhar, Farina,
Nakamura, Sakuda and Seki [PRD 72 (2005)
053005]
– RPA corrections are not included, but probably
small for |~q| ≥ 500 MeV
– Pion production and 2N channels should be in-
cluded in the “dip” and ∆ regions.
J. Nieves, IFIC, CSIC & University of Valencia 28
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DWIA Vs. MC Vs. Transport model
DWIA → Complex optical potential distorts outgoing nucleonwave
Complex potential removes all events not in a given nuclearchannel
DWIA understimates cross sections in semi-inclusive reactions
Does NOT conserve probability (Violates Unitarity)
MC → Transport simulation through a cascade model keeps track:
Change in energy and angle of the emitted nucleon
Production of secondary nucleons
Transport model → Semiclassical transport equation explicitlysolved
Also allows for particle tracking
E.g. GiBUU
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The Cascade Model
For a given leptonic part kinematics qµ we randomly select apoint in the nucleus where the boson absorption takes placeaccording to the profile d5/dΩ′dE ′d3r
Pick a random nucleon from the local Fermi sea with givenmomentum p
Fix the kinematics imposing energy conservation
E = q0 +√
p2 + M2 − k2F (r)/2M
Pauli Blocking effects are explicitly included
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Nucleon propagation in nuclear medium
Move the nucleon through finite steps in a real potential
V (r) = −kF (r)/2M
Consider a NN collision at every step according to NN elastic crosssection and decide if a secondary nucleon is produced
σN1N2 =
∫
dΩCM
dσN1N2
dΩCM
CT (q, ρ)Θ
(
κ −|p · pCM |
|p||pCM |
)
Medium renormalization and Pauli blocking effects
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40Ar(ν, µ− + N), 40Ar(ν, µ+ + N)
no rescatt.rescat.
Eν = 500 MeV
ν+40Ar → ν + p + X
Tp [MeV]
1040dσ/d
Tp
[cm
2/M
eV]
40035030025020015010050
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
no rescatt.rescat.
Eν = 500 MeV
ν+40Ar → ν + n + X
Tn [MeV]
1040dσ/d
Tn
[cm
2/M
eV]
40035030025020015010050
2.5
2
1.5
1
0.5
0
no rescatt.rescat.
Eν = 150 MeVν+40Ar → ν + p + X
Tp [MeV]
1040dσ/d
Tp
[cm
2/M
eV]
140120100806040
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
no rescatt.rescat.
Eν = 150 MeV
ν+40Ar → ν + n + X
Tn [MeV]
1040dσ/d
Tn
[cm
2/M
eV]
140120100806040
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
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40Ar(ν, ν + N)
no rescatt.rescatt.
Eν = 500 MeVνµ+40Ar → µ− + p + X
Tp [MeV]
1040
dσ/d
Tp
[cm
2/M
eV]
400350300250200150100500
25
20
15
10
5
0
no rescatt.rescatt.
Eν = 500 MeV
νµ+40Ar → µ− + n + X
Tn [MeV]
1040
dσ/d
Tn
[cm
2/M
eV]
400350300250200150100500
20
18
16
14
12
10
8
6
4
2
0
no rescatt.rescatt.
Eν = 500 MeV
νµ+40Ar → µ+ + p + X
Tp [MeV]
1040
dσ/d
Tp
[cm
2/M
eV]
400350300250200150100500
4
3.5
3
2.5
2
1.5
1
0.5
0
no rescatt.rescatt.
Eν = 500 MeV
νµ+40Ar → µ+ + n + X
Tn [MeV]
1040
dσ/d
Tn
[cm
2/M
eV]
400350300250200150100500
7
6
5
4
3
2
1
0
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Effects on the extraction of g sA
no rescatt.rescatt.
gsA = 0.0
gsA = −0.19
Eν = 150 MeV
ν+16O → ν + N + X
TN [MeV]
(dσ/d
Tp)/
(dσ/d
Tn)
10090807060504030
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
no rescatt.rescatt.
gsA = 0.0
gsA = -0.19
Eν = 150 MeVν+40Ar → ν + N + X
TN [MeV]
(dσ/d
Tp)/
(dσ/d
Tn)
90807060504030
3
2.5
2
1.5
1
0.5
0
no rescatt.rescatt.
gsA = 0.0
gsA = -0.19
Eν = 500 MeVν+40Ar → ν + N + X
TN [MeV]
(dσ/d
Tp)/
(dσ/d
Tn)
30025020015010050
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
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Taken from J.Sobczyk@NuInt09
0.0 0.1 0.2 0.3 0.4 0.50
5
10
15
20
25
30
= 0.5 GeVν X for E_−µ → + C12 µνE_p for QE (FSI) :
GiBUUνMadrid
Ankowski
= 0.5 GeVν X for E_−µ → + C12 µνE_p for QE (FSI) :
0.0 0.2 0.4 0.6 0.8 1.00
5
10
15
20
25
30
= 1.0 GeVν X for E_−µ → + C12 µνE_p for QE (FSI) :
GiBUUνMadrid
Ankowski
= 1.0 GeVν X for E_−µ → + C12 µνE_p for QE (FSI) :
GiBUU: Transport Model
Madrid: Proton in a realistic potential
Ankowsky: Effective spectral functions
Nieves: FG + RPA + FSI + Rescattering (No π effects)
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Proton Kinetic Energy (GeV)0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
/GeV
2 c
m−
38 1
0×
p d
Tµθ
/d c
osQ
Eσ 2
d
0
10
20
30
40
50
60
70
80
Genie
Ankowski
Nuwro
Nieves
= 60 degreespΘ = 0.5 GeV and ν X for E_−µ → + C12 µνE_p for QE :
Proton Kinetic Energy (GeV)0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
/GeV
2 c
m−
38 1
0×
p d
Tµθ
/d c
osQ
Eσ 2
d
0
10
20
30
40
50
60
70
80
= 60 degreespΘ = 1.0 GeV and ν X for E_−µ → + C12 µνE_p for QE :
Genie
Ankowski
Nuwro
= 60 degreespΘ = 1.0 GeV and ν X for E_−µ → + C12 µνE_p for QE :
Proton Kinetic Energy (GeV)0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
/GeV
2 c
m−
38 1
0×
p d
Tµθ
/dco
sQ
Eσ 2
d
0
10
20
30
40
50
60
70
80
90
100
Ankowski
Genie
Neut
Nieves
= 60 degreespΘ = 0.5 GeV and ν X for E_− p→ + O16 pνE_p for QE :
Proton Kinetic Energy (GeV)0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
/GeV
2 c
m−
38 1
0×
p d
Tµθ
/dco
sQ
Eσ 2
d
0
10
20
30
40
50
60
70
80
90
100
= 60 degreespΘ = 1.0 GeV and ν X for E_− p→ + O16 pνE_p for QE :
Neut
Ankowski
Genie
= 60 degreespΘ = 1.0 GeV and ν X for E_− p→ + O16 pνE_p for QE :
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Conclusions
General qualitative agreement on which nuclear effects arerelevant. . . and how they affect cross sections
Quantitative agreement not so good
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Thanks!
Thanks to Profs. S. Boyd, S. Ditman and J. Sobczyk forpermission to use their plots
and to the audience!!