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Nucleon emision off nuclei induced by neutrinointeractions
M. Valverde
RCNP, Osaka University
NuFact09IIT, Chicago, Illinois, USA
July 22, 2009
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
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
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
∆
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
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’
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*
Main features of the model
We work in nuclear matter and get results via LDA
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
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
)
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
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
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
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
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
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
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
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
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
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
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
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)
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 :
Conclusions
General qualitative agreement on which nuclear effects arerelevant. . . and how they affect cross sections
Quantitative agreement not so good
Thanks!
Thanks to Profs. S. Boyd, S. Ditman and J. Sobczyk forpermission to use their plots
and to the audience!!
