Post on 07-Nov-2020
transcript
Spectral Function Implementation in Neutrino Event
Generator and Its Impact on Neutrino Oscillation Parameters
Chun-Min (Mindy) Jen, Center for Neutrino Physics, Virginia Tech
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Outline
Nuclear Models: Relativistic Fermi Gas vs. Spectral Function
The Role of Nuclear Models in Cross Section Calculation
Electron Validation
Neutrino Cross-section
Impact on Oscillation Parameters
Conclusions
�2Chun-Min (Mindy) Jen, Center for Neutrino Physics, Virginia Tech
Qualitative Comparison
white - RFGM
Green - Spectral Function
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• initial-state nucleon’s momentum distribution, kn, is uniform in between 0 and kF
• kn is non-uniform in the spectral function theory, and yields a much better prediction to the measured electron cross-section than RFGM
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N U C L E A R M O D E L R F G V S . S F
O N E - B O D Y C U R R E N T - M O D I F I E D S H E L L M O D E L
k [GeV/c]0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
]-3
n(k)
[GeV
210
310
410
510
610
momentum distribution
RFGM
k F~ 2 2 5 M e V / cE B~ 2 5 M e V
n(k)
[GeV
-3]
Chun-Min (Mindy) Jen, Center for Neutrino Physics, Virginia Tech
SF
• the spectrum of each shell is assumed to be delta-function like
• removal energy is averaged to be one constant parameter for each struck nucleon
• in reality, the spectrum instead is a gaussian distribution
• the overlapping of gaussian tails in between two adjacent shells leads to the (position) correlation
• removal energy is correlated to kn (momentum-dependent)
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N U C L E A R M O D E L R F G V S . S F
O N E - B O D Y C U R R E N T - M O D I F I E D S H E L L M O D E L
correlation
E [G
eV]
Chun-Min (Mindy) Jen, Center for Neutrino Physics, Virginia Tech
N U C L E A R M O D E L R F G V S . S F
O N E - B O D Y C U R R E N T - M O D I F I E D S H E L L M O D E L
• no nucleon-nucleon (short-range) correlation effects considered
• N-N (2N) correlation is not negligible
courtesy of S. Wood, JLab @ NUINT’07 talk
Chun-Min (Mindy) Jen, Center for Neutrino Physics, Virginia Tech�6
Quantitative Comparison
white - RFGM
Green - Spectral Function
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• RFG model
�8Chun-Min Jen, Center for Neutrino Physics, Virginia Tech
k [GeV/c]0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
]-3
n(k)
[GeV
210
310
410
510
610
momentum distribution
E B~ 2 5 M e Vk F~ 2 2 5 M e V / c
RFGM
n(k)
[GeV
-3]
neutrino
r (interaction length) ~ nucleon size ~ 1/|q|
nucleons (A-1) spectator system
muon
nucleon
energy-momentum conservationstep function
nucleons
SF
�9Chun-Min Jen, Center for Neutrino Physics, Virginia Tech
neutrino
r (interaction length) ~ nucleon size ~ 1/|q|
nucleons
(A-1) spectator system
muon
nucleon
nucleons
• SF model (1p-1h : the simplest situation)
energy-momentum conservationprobability amplitude of knocking out one nucleon
neutrinonucleons
the spectral function theory represents different joint probabilities to find different nucleons sitting on different shells (with different missing momentum (q) and missing energy (w))
!the delta function guarantees the
energy conservation.
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C R O S S - S E C T I O N O N E - B O D Y C U R R E N T
elementary process of each isolated nucleon
beam particles + outgoing leptons
Chun-Min (Mindy) Jen, Center for Neutrino Physics, Virginia Tech
the differential cross-section is composed of two separate parts: the lepton tensor and the target structure tensor (nucleon form factors) and is a function of (q, w)
!the total cross-section is the incoherent sum of differential cross-sections for different elementary scattering processes
struck nucleon + residual nuclear system
N U C L E A R M O D E L I N C R O S S - S E C T I O N O N E - B O D Y C U R R E N T
p2dp
�11Chun-Min (Mindy) Jen, Center for Neutrino Physics, Virginia Tech
in RFGM, nucleons sitting around Fermi sea are most likely to interact with beam particles
!according to the spectral function theory, the probability of interacting of each nucleon with beam particles, however, is different from the one of RFGM
!“the interaction probability” plays an important role in determining the contribution to every elementary cross-section for each struck nucleon
�12Chun-Min (Mindy) Jen, Center for Neutrino Physics, Virginia Tech
Electron Validation
�13Chun-Min (Mindy) Jen, Center for Neutrino Physics, Virginia Tech
Owing to the lack of electron scattering data, the energy and momentum dependence of the model, spectral functions of calcium and argon, is not strongly constrained
Electron Validation
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courtesy of O. Benhar, N. Farina, H. Nakamura, M. Sakuda, R. Seki PRD 72, 053005 (2005)
Chun-Min Jen, Center for Neutrino Physics, Virginia Tech
]2 [GeV2Q0 0.2 0.4 0.6 0.8 1 1.2 1.4
/sr G
eV]
2cm
-38
[10
2/d
Qmd
0
2
4
6
8
10
12
14 RFG - IA result, No FSIO. Benhar’s calc.
TiGENIE v.2.8.0+
]2 [GeV2Q0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
/sr G
eV]
2cm
-38
[10
2/d
Qmd
0
2
4
6
8
10
12 SF - IA result, PB, No FSIO. Benhar’s calc.
TiGENIE v.2.8.0+
Neutrino Cross-Section
!15Camillo Mariani, Center for Neutrino Physics, Virginia Tech
courtesy of A. M. Ankowski nucl-th/0608014v1 4 Aug 2006 courtesy of A. M. Ankowski, Jan T. Sobczyk PRC 77, 044311 (2008)
Neutrino Cross-Section
Experimental Setup
• Ideal&and&perfect&near&detector&(12C&or&16O),&1&km,&1kton&
• Far&detector&at&295&km,&22.5&kton&– Oxigen&– Carbon&(RFG&and&SF)&
• Use&T2K&flux,&peak&at&0.6&GeV,&750kW,&5&years&running&
• Use&SK&reconstrucNon&efficiency&as&funcNon&of&energy&
• Use&migraNon&matrices&produced&by&GiBUU(1.6),&GENIE(2.8.0)&and&GENIE&2.8.0+νT&
• Muon&neutrino&disappearance&only&V>&fit&to&atmospheric¶meters&
Workshop&on&neutrinoVnucleus&InteracNons& Okayama,&March&24,&2014& 18&
GENIE 2.8.0+νT Migration Matrix is reconstructed energies as a function of true energies
Chun-Min (Mindy) Jen, Center for Neutrino Physics, Virginia Tech
- Simulation
Oxygen
�17Chun-Min (Mindy) Jen, Center for Neutrino Physics, Virginia Tech
SF - reconstructed from the true QE dynamics
true
1, 2 and 3σ allowed regions
the event distribution is a convolution of cross-section, flux, detector efficiency, oscillation probability and migration matrix different nuclear models consider different nuclear effects in treating nucleon’s kinematics as a result, event distributions are different for different nuclear models
GLoBES Fit
hep-ph/1311.4506 Coloma, Huber, Jen, and Mariani (accepted by PRD)
hep-ph/1402.6651 Jen, Ankowski, Benhar, Furmanski, Kalousis and Mariani (submitted to PRD)
Conclusions
Argon spectral function already exists in GENIE (not yet released)
Comparison to another neutrino event generator is already done; GENIE outputs are consistent to NuWro’s
However, due to the lack of knowledge in Argon nuclear structure, more electron data are needed.
�18Chun-Min (Mindy) Jen, Center for Neutrino Physics, Virginia Tech
Q & A Acknowledgment: S. Dytman, H. Gallagher
Thanks for your attendance …
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