WG2 goals (Theory and Calculations)

25 June 2005 Zeller/Sakuda@NuFact05

WG2 goals (Theory and Calculations)

How accurately can we calculate the neutrino-nucleus interactions?? How do we vadidate the calculation? Note: Neutrino data are not simple: neutrino spectrum is wide and ac

curate to 10-20%; measured events are the mixture of various neutrino interactions (quasi-elastic, , DIS).

We are using not only new neutrino scattering data (MiniBOONE, K2K, NOMAD, and MINOS), but also electron scattering data which

are new (Jupiter/JLAB) or which already exist, to test/evaluate the accuracy of the calculations.


We need accurate Electron-nucleon scattering data to test and improve Neutrino-nucleon scattering data　　

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Developments in Theoretical Calculations

1. O. Benhar, Comparison of Electron and Neutrino Nucleus Scattering Data with LDA Calculations, hep-ph/0506116 (PRD)

2. M. Barbaro, Using Electron Scattering Superscaling to Predict Neutrino-Nucleus Scattering, PRC71,015501,2005

3. N. Jachowicz, Relativistic Models for Quasi-Elastic Neutrino-Nucleus Scattering, Nucl-th/0505008

4. M. Valverde, Inclusive Nucleon Emission Induced by Quasi-Elastic Neutrino-Nucleus Interactions, PRC70, 05503,2004

5. A. Botrugno, Neutrino Nucleus Scattering in Giant Resonance Region and in Quasi-Elastic Peak

6. Y. Sakemi, Study for the Neutrino Coherent Pion Production Experiment ---experimental proposal

7. A. Kataev, The Relations Between Bjorken Polarized, Bjorken Unpolarized, and Gross-Llewellyn Smith Sum Rules


Energy region

Physics interest1. 1-100 MeV Reactor, Supernova Nuclear shell structure is important.2. 100-500 MeV Supernova, ATM, LSND3. 500-2000 MeV MiniBOONE, K2K, ATM, T2K Quasi-elastic and production are important.4. E>5 GeV MINOS, CNGS, ATM Nulcear effects in DIS


Achievements


1. Energy region: 500-2000 MeV Considering correct Fermi momentum distribution is import

ant. P(p,E):

10-20% effect in cross section and spectrum wrt a simple relativistic Fermi-gas model.

See NuInt04 Proceedings NPB(Proc)139.

We now consider the final state interaction (FSI). Benhar/Jachowicz/Valvelde try to evalate this effect using nulcear transparency data.


d/de,e’EeEe’Enegy transfer (GeV)Ee=700-1200 MeV

Blue: Fermi-gasGreen: SPRed: SP+FSI

QE


Prediction for d/dQ2 of FG, SP, SP+FSI validated by electron scattering data, Benhar et al., hep-ph/0506116, PRD

FGSP

SP+FSI


Validation of FSI effect: Calculated transparency compared to data

Benhar et al., hep-ph/0506116Jachowicz et al., nucl-th/0505008

Transparency= Probability that a nucleon can escape from the nucleus without being subject to any interaction.i.e. T=1.0 = Completely transparent=No interaction


The effect of FSI (rescattering)-Valverde


Use scaling to understand/parametrize data better and quantify -Barbaro et al



production –Some differences

QE

Benhar(Bodek-Ritchie)

Nakamura (Paschos)

Valverde


500-2000 MeV Quasi-elastic interaction

Calculation of neutrino-nucleus quasi-elastic interaction (500-2000MeV) is in good shape. Going from a simple FG to spectral function S(p,E) improves the cross section calculation by 10-20%.

FSI (nuclear rescattering) makes the cross section changes by another 5-10%.

Overall, the calculation is good to 10% level, considering those effect.

production There are some differences between the calculations at Delta pea

k. Dip region between quasi-elastic and Delta need to be studied. Valverde’s calculation looks good. 30-40% differences exist betwe

en the calculations. We need further checks.


2. Energy region: 10-500 MeV

Butrogno (CRPA, Lecce) and Valverde (RPA, Granada) seems to reproduce LSND cross sections.

Butrogno (CRPA) can reproduce C(e,e’)C* E=10-50 MeV and O(e,e’) E=300-800 MeV r

easonably.


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xTransferred Energy

Continuum Random Phase Approximation+FSI --By Botrugno

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Valverde (RPA)


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Energy Region: I) Quasielastic Peak


3. Coherent pion production

Rein-Seghal calculation is 20 years old. New calculations (Mateau, Paschos) seem to predict less. K2K showed a suppressed cross section. Sakemi (RCNP) performs a new relevant measurement usi

ng proton beam and will compare it with the calculation. p + A → n + π+ + A (g.s.)

We need to update the calculations.


Coherent Pion Production at RCNP, Osaka

g’ΔΔ ~ extract from Coherent Pion Productionp + A → n + π+ + A (g.s.)

Peak shift from Delta residual interaction ΔE ≈ g’ΔΔ(ћcfpND/mp

2)ρ0

Longitudinal response function :RL~ dominant at 0 degree scpp(0°) → RL → g’ (g’NN, g’ND, g’DD)

Light ion induced CPP experiment status : RCNP 12C(p,nπ+)12C(G.S.)~ in progress

Experiment Beam ~ proton 400MeV un-polarized ⊿E~100keV Target ~ 12C (100mg/cm2) Detector

Netron detector ~ ⊿E~300 keV π detector ~ ⊿E~1 MeV

Identification of CPP select the ground state of residual nucleus

RCNP

correlation of cross section and g’ΔΔ[3].

coherent pion cross section[2].

[2] E. Oset, Nucl. Phys. A 592 (1995) 472.[3] T. Udagawa et al., Phys. Rev. C 49 (1994) 6.


4. Plans for the next NuFact06 500-2000MeV: cross section and Dip region sh

ould be checked. 10-500 MeV: Validate CRPA, RPA calculations mo

re. Calculation of coherent pion production will be ex

amined and more comparison with other data (K2K NC, MiniBOONE) will be done.

Non-resonant and DIS will be examined.

First of all, we ask the theorists to make a calculation usable and open for us experimenters, so that we can use/test it in the experiments.


The 4th Workshop on Neutrino-Nucleus Interactions In the Few-GeV Region (NuInt

05) Okayama University, 26-29 September, 2005

Supported by JSPS (Japan) and CNR (Italy)

NuInt04 (Gran Sasso)Nucl.Phys.B(Proc.Suppl.)139.


Spectral Function for Various Nuclei

Spectral Functions P(p,E) for various nuclei, eg.16O, are estimated by Benhar et al. using e-N data.

P(p,E) : Probability of removing a nucleon of momentum p from ground state leaving the residual nucleus with excitation energy E.

Fermi momemtum

Fermi Gas model

p

Documents

WG2 goals (Theory and Calculations)