Neutrino-induced meson productions off

nucleon in the resonance region

Satoshi NakamuraOsaka University

Collaborators : H. Kamano (RCNP, Osaka Univ.), T. Sato (Osaka Univ.) T.-S.H. Lee (Argonne Nat’l Lab).

Contents

★ Introduction n interaction in resonance region

★ Dynamical coupled-channels (DCC) model for

, gN pN , , , , pN ppN hN KL

KS

extended to nN , , , , pN ppN hN KL KS

★ Future plan

matching with DIS cf. quark-hadron duality

Wide kinematical region with different characteristic

Combination of different expertise is necessary

Collaboration at J-PARC Branch of KEK Theory Center

http://j-parc-th.kek.jp/html/English/e-index.html

LBL

n-interaction (kinematics & characteristics)

Resonance region

D

2nd 3rd

Many nucleon resonances in 2nd and 3rd resonance region

(MeV)

Not only 1 p production but also …Multi-channel reaction

2p production is comparable to 1p

h, K productions (background of proton decay exp.)

Theoretical approach to n -interaction in resonance region

• PCAC (partially conserved axial current)　　 at Q2=0, axial coupling pion coupling Paschos et al. (2011); Kamano et al. (2012)

• Microscopic model resonant and non-resonant hadronic interactions Rein et al. (1981), (1987) ; Lalalulich et al. (2005), (2006) ;

Hernandez et al. (2007), (2010) ; Lalakulich et al. (2010);

Sato et al. (2003), (2005) ; …

Microscopic models for n-induced 1p production

Rein et al. (1981), (1987) ; Lalalulich et al. (2005), (2006)

Hernandez et al. (2007), (2010) ; Lalakulich et al. (2010)

Sato, Lee (2003), (2005)

resonant only

+ non-resonant (tree-level)

+ rescattering ( p N unitarity)

★ Dynamical coupled-channels (DCC) model for , gN pN , , , , pN ppN hN KL

KS

Hadron dynamics & vector current fixed

★ Extension to nN , , , , pN ppN hN KL KS

Axial form factors fixed

to overcome the problems…

Dealing with multi-channel reaction

We develop Unitary coupled-channel model

Unitarity is missing in previous models Important 2 p production model is missing Previous models for K and h production are not well tested by data

Problems

DCC model for

, gN pN , , , , pN ppN hN KL KS

Kamano, Nakamura, Lee, Sato, PRC 88, 035209 (2013)

Coupled-channel, 2&3-body unitarity is taken into acount

DCC analysis of meson production data

Fully combined analysis of , gN pN , , , pN hN KL KS

(W ≤ 2.1 GeV)

~380 parameters (N* mass, N* MB couplings, cutoffs)

to fit ~ 20,000 data points

Kamano, Nakamura, Lee, Sato, PRC 88 (2013)

Partial wave amplitudes of pi N scattering

Kamano, Nakamura, Lee, Sato, 2013

Previous model (fitted to pN pN data only)[PRC76 065201 (2007)]

Real part

Imaginary part

Kamano, Nakamura, Lee, Sato, 2012

Vector current (Q2=0) for 1 p

Production is well-tested by data

Eta production reactions

Kamano, Nakamura, Lee, Sato, 2012

Kamano, Nakamura, Lee, Sato, 2013

Vector current (Q2=0) for h

Production is well-tested by data

KY production reactions

1732 MeV

1845 MeV

1985 MeV

2031 MeV

1757 MeV

1879 MeV

1966 MeV

2059 MeV

1792 MeV

1879 MeV

1966 MeV

2059 MeV

Kamano, Nakamura, Lee, Sato, 2012

Kamano, Nakamura, Lee, Sato, 2013

Vector current (Q2=0) for K

Production is well-tested by data

Short Summary

• nN scattering in resonance region is multi-channel reaction

• Unitary coupled-channels model is ideal

• DCC model for , gN pN , , , , pN ppN hN KL KS is

developed

• Model is extensively tested by , gN pN , , , pN ppN hN

, KL KS data reliable vector current to be applied to n-

scattering

Extended DCC model for

nN , , , , pN ppN hN KL KS

1. PCAC-based calculation (Q2=0) Kamano, Nakamura, Lee, Sato, PRD 86, 097503 (2012)

2. Dynamical axial current (strategy)

3. Photon emission in NC process (some comments)

Objectives

Set a starting point for full dynamical model

Relative importance of different channels

Comparison with Rein-Sehgal model

PCAC-based calculation for forward scattering of

nN , , , , pN ppN hN KL KSKamano et al., PRD 86, 097503 (2012)

Cf. Paschos et al., arXiv:1212.4662

Formalism

Cross section for nN X ( X = , , , , pN ppN hN KL KS )

q 0

Q20

CVC & PCAC

LSZ & smoothness

Finally spNX is from our DCC model

Results

SLpN

ppN KShN

KL

Prediction based on model well tested by data

pN dominates for W ≤ 1.5 GeV

ppN becomes comparable to pN for W ≥ 1.5 GeV

Smaller contribution from hN and KY O(10-1) - O(10-2)

Agreement with SL (no PCAC) in D region

Comparison with Rein-Sehgal model

• Lower D peak of RS model

RS overestimate in higher energy regions (DCC model is tested by data) Similar findings by Leitner et al., PoS NUFACT08 (2008) 009

Graczyk et al., Phys.Rev. D77 (2008) 053001

Comparison in whole kinematical region will be done

after axial current model is developed

Short summary 2DCC model for forward nN , , , , pN ppN hN KL KS via PCAC

Prediction based on model well tested by data

ppN comparable to pN for W ≥ 1.5 GeV (first nN ppN)

First nN , hN KY based on data

Comparison with Rein-Sehgal model :

RS has Lower D peak

RS overestimates cross section at higher energies

Full DCC model for nN , , , , pN ppN hN KL KS

Kamano, Nakamura, Lee, Sato, in progress

Vector current

Q2=0

gp MB analysis has been done

gn , pN hn analysis is ongoing isospin separation

necessary for calculating n-interaction

Q2≠0 (electromagnetic form factors for VNN* couplings)

obtainable from (e,e’ p) data analysis ( will be done soon )

Previous analysis of 1p electroproduction dataJuliz-Diaz et al., PRC 80, 025207 (2009)

Fit to structure functions from CLAS for p (e,e’ p) p

W < 1.6 GeV

Q2 < 1.5 (GeV/c)2

Full DCC model for nN , , , , pN ppN hN KL KS

Kamano, Nakamura, Lee, Sato, in progress

Axial current

Q2=0

non-resonant mechanisms

resonant mechanisms

Q2≠0 (axial form factors of ANN*)

experimental information is necessary to fix this

A A

How to fix axial form factors of ANN*

Neutrino data on deuteron from ANL and BNL nm d m- NN p

p

Nd

N

W, Z

Elementaryamplitude

Fermi motion of deuteronHernandez et al., PRD 81 (2010)

d NN d p

p

Fermi motion of deuteron+ rescattering effectsJiajun and Lee in progress

Hernandez et al., PRD 76 (2006); 81 (2010)

How to fix axial form factors of ANN*

Discrepancy of ANL and BNL data new deuterium data are highly hoped

Neutrino data

= 1.00 ± 0.11

= 0.93 ± 0.07 (GeV)

How to fix axial form factors of ANN*

Neutrino data (BNL)

(Adler model)

D++ production

The discrepancy persists to higher energy

PRD 34, 2554 (1986)

How to fix axial form factors of ANN*

Neutrino data (BNL) Two-pion production

Even the discrepancy, still the most useful information

PRD 34, 2554 (1986)

Electron data : parity violation asymmetry

How to fix axial form factors of ANN*

G0@JLab, arXiv:1212.1637

−0.05 ± (0.35)stat

± (0.34)sys± (0.06)th

Comparison with theory

Theory

-0.196

Quark-hadron duality : coming back to this later

How to fix axial form factors of ANN*

Photon emission in NC

-D Region : Hill (2010), Zhang et al. (2012)+D 2nd resonance : Wang et al. (2013)

With our DCC model

Relevant to T2K and MiniBooNE

Photon emission in higher N* region relevant to future experiments ??

• Background for ne appearance in Cherenkov detector

• Low-energy ne excess in MiniBooNE PRL 98, 231801 (2007)

Motivation

Recent works

Matching with DIS

Purposes:

• Make sure smooth transition from RES to DIS (electron scattering)

• Fix axial form factors of ANN* (neutrino scattering)

Matching with DIS

Matching with DIS

In terms of matrix elements of hadronic currents

N(e, e’)

N(n, l’)

For CC n

In terms of parton distribution functions (PDF)

For N(e, e’)Matching FiDCC Fi

PDF at W ≈ 2 GeV, Q2 > 1 (GeV/c)2

(overlapping region)

Matching with DIS

• Make sure smooth transition for electron scattering

• Some axial form factors of ANN* can be fixed for neutrino scattering

• Unitarity, coupled-channels are essential for matching

only inclusive structure functions can be matched

2 p contribution is large

Matching with DISlow-Q2 region

low-Q2 region

Model for low-Q2 region

Kulagin and Petti, PRD 76, 094023 (2007) PCAC + extrapolation to finite Q2 from 0

Bodek and Yang, 　 arXiv:1011.6592 PDF extrapolated to lower Q2 from DIS region

Matching on the boundaryQuark-hadron duality

Quark-hadron dualityGlobal duality in electron-nucleon scattering

Ex. PDF from W≈3 GeV, Q2≈ 10 (GeV/c)2

Quark-hadron dualityLocal duality in Neutrino-nucleon scattering in D region

Nachtman variable :

Matsui, Sato, Lee, PRC 72 (2005)

Q2=0.4 (GeV/c)2

1

2 4

CTEQ06 vs. SL model

QH duality holds for isoscalar target

Quark-hadron dualityElectron-nucleus scattering

Broadening of resonance peaks Fermi motion, many-body correlation, FSI

Lalakulich et al, PRC 79 (2009)

Quark-hadron duality

HOPE : Utilize QH duality practically

PDF Structure functions in resonance region

Quantitative (theoretical) understanding of QH duality is prerequisite

Neutrino scattering PDF axial form factor of ANN*

1 &p 2 p model is necessary DCC model can do

Electron scattering Res SF PDF (in kinematics where data are scarce)

Sometimes, QH duality could do a very bad job

Q2=0.21 (GeV/c)2

0.35

0.62

0.92

1.37

Comparison of SL model and Wandzura-Wilczek formula for electron scattering

WW formula

Matsui, Sato, Lee, PRC 72 (2005)

Quark-hadron duality

HOPE : Utilize QH duality practically

PDF Structure functions in resonance region

Neutrino scattering PDF axial form factor of ANN*

Quantitative (theoretical) understanding of QH duality is prerequisite

1 &p 2 p model is necessary DCC model can do

Can be (has been ?) studied in electron scattering

critical comments are welcome

Electron scattering Res SF PDF (in kinematics where data are scarce)

Summary

★ Dynamical coupled-channels (DCC) model for

, gN pN , , , , pN ppN hN KL

KS

extended to nN , , , , pN ppN hN KL KS(ongoing)

★ Matching with DIS and low-Q2 regions cf. quark-hadron duality

Questions/comments

• DCC model for nN , , , , pN ppN hN KL KS being developed (done for Q2=0)

first serious 2 p production model (1 p and 2 p are comparable in resonance region)

• Rein-Sehgal model needs to be improved (replaced)

• New deuterium experiment is highly hoped

deuteron reaction model being developed

• NC photon emission in higher resonance region relevant ?

• Matching with DIS (low-Q2 ) needs all coupled-channels DCC model can do this

• Is making use of QH duality a promising direction to fix axial form factors ?

• Nuclear effects are another difficult problem

Neutrino-nucleus interaction

Neutrino-nucleus interaction

To be done with DCC model

Our previous experience with Sato-Lee model PRC 54 2660 (1996)

• pN channel only• D only

✔ Incoherent 1 p production✔ Coherent 1 p production

Difficult remaining issues

• Final state interactions• Medium effects (width broadening of resonances)

Sato-Lee (SL) model Sato and Lee, PRC 54 2660 (1996)

• pN channel only• D only

ANL data

Inclusive n-A scattering in D regionSzczerbinska et al., PLB 649 132 (2007)

• Quasi-elastic (QE)

• D-excitation (1p)

(To be done with DCC model)

Another big issue

• Final state interaction

transport model

optical potential

• Medium effects on resonance properties (shift of mass, width)

pion-nucleus scattering data

Coherent p production in n-A scattering in D region

Nakamura et al., PRC 81 035502 (2010)

Motivation

• NC p0 can fake (nm ne) event

• Puzzling experimental situation

No evidence for CC K2K (2005), SciBooNE (2008)

Signature for NC MiniBooNE

Naive expectation from isospin matrix element : σCC 2 ∼ σNC

Theoretical approaches to coherent π production

∗ PCAC (Partially Conserved Axial Current)-based model

• Rein, Sehgal, NPB 223 (1983)

• Kartavtsev et al., PRD 74 (2006)

• Berger, Sehgal, PRD 79, (2009)

• Paschos, Schalla, PRD 80 (2009)

∗ Dynamical microscopic model

• Kelkar et al., PRC 55 (1997) • Singh et al., PRL 96 (2006)

• Alvarez-Ruso et al., PRC 7576 (2007) • Amaro et al., PRD 79 (2009)

• Hernandez et al., PRD 82 (2010) • Leitner et al., PRC 79 (2009)

• Martini et al., PRC 80 (2009) • Nakamura et al, PRC 81 (2010)

Dynamical model for coherent production

∗ Elementary amplitudes ( νN → μ- π+ N , νN → νπ0N )

∗ Medium effect on Δ (mass, width, non-locality)

∗ Final state interaction

Ingredients

SL model

D-hole model}

Nakamura et al, PRC 81 (2010)

(SL model)

BACKUP

F2 from RS model

F2 from RS model

Spectrum of N* resonances

Real parts of N* pole values

L2I 2J

PDG Ours

N* with 3*, 4* 1816

N* with 1*, 2* 5

PDG 4*

PDG 3*

Ours

Kamano, Nakamura, Lee, Sato ,2012

SL model applied to -n nucleus scattering

1 p production

Szczerbinska et al. (2007)

SL model applied to -n nucleus scattering

coherent p production

g + 12C p0 + 12C nm + 12C m- + p0 + 12C

Nakamura et al. (2010)