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&parameters&

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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