Meson Produc1ons in Neutrino-Nucleon Delta Resonance Reac1ons in - - PowerPoint PPT Presentation

Delta Resonance

中村 聡

大阪大学理学研究科

共同研究者 : 鎌野寛之 (KEK), 佐藤透 (阪大理)

Meson Produc1ons in Neutrino-Nucleon Reac1ons in Resonance Region

Introduc1on

ν

Next-genera1on exp. è leptonic CP, mass hierarchy, sterile neutrinos

Neutrino-nucleus sca7ering for ν-oscilla1on experiments

Q2 = - q2 ν = q0 ν-nucleus sca@ering needs to be understood more precisely (∼ 5%) All ν-oscilla1on experiments measure ν-flux through ν-nucleus interac1on

Q2 = - q2 ν = q0

ν

DIS region QE region RES region

Wide kinema1cal region with different characteris1c è Combina1on of different exper1se is necessary

Collabora1on at J-PARC Branch of KEK Theory Center

h7p://j-parc-th.kek.jp/html/English/e-index.html

T2K

Neutrino-nucleus sca7ering for ν-oscilla1on experiments

Atmospheric ν

A review ar1cle to be published in Reports on Progress in Physics (arXiv:1610.01464) ν

Q2 = - q2 ν = q0

Resonance region

N*

i

Σ

i

π N N γ, W±, Z0

• N* are unstable and strongly couple to meson-baryon con1nuum states
• Width ∼ 100 MeV, several N*’s are overlapping

Main reac1on mechanism : resonance excita1ons (Sub-leading) non-resonant mechanisms

Σ

+ + + ...

Resonance region (single nucleon)

Δ 2nd 3rd

Ÿ Several resonances form characteris1c peaks Ÿ 2π produc1on is comparable to 1π Ÿ η, Κ produc1ons (mul1-channel reac1on)

(MeV)

γΝ è X

0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 σ (x 10-38 cm2) Eν (GeV) ANL (1979) BNL (1986)

Neutrino interac1on data in Δ(1232) region

νµ p è µ-π+ p

• Data to fix nucleon axial current (gΑΝΔ)
• Discrepancy between BNL & ANL data

à theore1cal uncertainty in neutrino-nucleus cross sec1ons Wilkinson et al. PRD 90 (2014)

Recent reanalysis of original data à discrepancy resolved (probably)

σ (CC1π;data) σ (CC0π;data) ×σ (CCQE;model)

Flux uncertainty is cancelled out FSI ma@ers ? à to be discussed later

Neutrino interac1on data in Δ(1232) region

νµ CH2 è µ-π 0 X

} PRC 87 (2013)

• Final state interac1on (FSI) changes charge, momentum, number of π
• Current FSI models are classical (cascade) models
• MiniBooNE cross sec1on shape is worse described with FSI
• MINERνA data favor FSI

〈Eν 〉 = 0.8 GeV 〈Eν 〉 = 4.0 GeV ,W < 1.4 GeV

MiniBooNE PRD 83 (2011) MINERvA PRD 92 (2015)

νµ CH è µ-π ± X

Current FSI models are not sa1sfactory

Neutrino interac1on beyond Δ(1232) region

〈Eν 〉 = 4.0 GeV ,

MINERvA PRD 92 (2015)

νµ CH è µ- N π ± X

W < 1.8 GeV

T : # of nucleons in fiducial volume Φ : integrated flux

Main decay mode of higher resonances à Two pions à Described with DIS model in common neutrino interac1on generators (GENIE, etc.) not correct Development of a reac1on model

• n single nucleon is s1ll an issue

(N=1,2,3, …)

Previous models for ν-induced 1π produc1on in resonance region

N*

i

Σ

i

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

N*

i

Σ

i

+ + + ...

Hernandez et al. (2007), (2010) ; Lalakulich et al. (2010) Sato, Lee (2003), (2005)

+ + + ... + ... ∆

resonant only + non-resonant (tree-level non-res) + resca@ering (π N unitarity, Δ(1232) region)

VNN* : helicity amplitudes listed in PDG ANN* : quark model, PCAC rela1on to |πNN*| (PDG) rela1ve phases among N*’s are out of control

GOAL : Develop νΝ-interac1on model in resonance region

We develop a dynamical coupled-channels model Ÿ Channel-couplings required by unitarity is missing Ÿ Important 2 π produc1on model is missing Ÿ Rela1ve phases among different ANN* are out of control Problems in previous models ★ Dynamical coupled-channels (DCC) model for γ(*)Ν, πΝ è πΝ, ππΝ, ηΝ, ΚΛ, ΚΣ ★ Extension to νΝ è l-X ( X= πΝ, ππΝ, ηΝ, ΚΛ, ΚΣ )

Our strategy to overcome the problems…

Dynamical Coupled-Channels model for meson produc1ons

By solving the LS equa1on, coupled-channel unitarity is fully taken into account

,

Kamano et al., PRC 88, 035209 (2013)

Coupled-channel Lippmann-Schwinger equa1on for meson-baryon sca@ering

,

Kamano et al., PRC 88, 035209 (2013)

Coupled-channel Lippmann-Schwinger equa1on for meson-baryon sca@ering

By solving the LS equa1on, coupled-channel unitarity is fully taken into account

,

Kamano et al., PRC 88, 035209 (2013)

Coupled-channel Lippmann-Schwinger equa1on for meson-baryon sca@ering T V V V In addi1on, γΝ, W±N, ZN channels are included perturba1vely

T

Rela1on between neutrino and electron (photon) interac1ons

Lcc = GFVud 2 [Jλ

cccc

λ + h.c. ]

Charged-current (CC) interac1on (e.g. νµ + n à µ- + p )

Jλ

cc =Vλ − Aλ

cc

λ =ψµγ λ(1−γ5)ψν

Electromagne1c interac1on (e.g. γ (*) + p à p )

Lem = e Jλ

emAem

λ

Jλ

em =Vλ +V IS λ

< p |Vλ | p > = − < n |Vλ | n > < p |V IS

λ | p > = < n |V IS λ | n >

V and VIS in Jem

can be separately determined by analyzing photon (Q2=0)

and electron reac1on (Q2≠0) data on both proton and neutron targets, because: Matrix element for the weak vector current is obtained from analyzing electromagne1c processes

< p |Vλ | n > = 2 < p |Vλ | p >

Q2=0 non-resonant mechanisms resonant mechanisms Interference among resonances and background can be uniquely fixed within DCC model

Σ

+ + ...

N* N* π A PCAC

∂µπ → fπ Aexternal

µ

DCC model for axial current

Because neutrino reac1on data are scarce, axial current cannot be determined phenomenologically à Chiral symmetry and PCAC (par1ally conserved axial current) are guiding principle < ! X | q⋅ A | X > ~ i fπ < ! X |T | π X >

PCAC rela1on

Q2≠0 non-resonant mechanisms resonant mechanisms

DCC model for axial current

FA(Q2) = 1 1+Q2 / M A

2

! " # $ % &

2

MA=1.02 GeV

: axial form factors More neutrino data are necessary to fix axial form factors for ANN* Neutrino cross secBons will be predicted with this axial current

FA(Q2) FA(Q2) = 1 1+Q2 / M A

2

! " # $ % &

2

DCC analysis of γΝ γΝ, , πΝ πΝ è πΝ πΝ, , ηΝ ηΝ, , ΚΛ, , ΚΣ and electron sca7ering data

DCC analysis of meson produc1on data

Fully combined analysis of γΝ, πΝ è πΝ, ηΝ, ΚΛ, ΚΣ data and polariza1on observables

(W ≤ 2.1 GeV)

~ 23,000 data points are fi@ed by adjus1ng parameters (N* mass, N* è MB couplings, cutoffs)

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

dσ / dΩ

Data for electron sca@ering on proton and neutron are analyzed by adjus1ng γ* Ν è Ν* coupling strength at different Q2 values ( Q2 ≤ 3 (GeV/c)2 )

Par1al wave amplitudes of π N sca7ering

Kamano, Nakamura, Lee, Sato,

PRC 88 (2013)

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

Real part Imaginary part

Data: SAID πΝ amplitude

Par1al wave amplitudes of π N sca7ering

Kamano, Nakamura, Lee, Sato,

PRC 88 (2013)

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

Real part Imaginary part

Data: SAID πΝ amplitude

Constraint on axial current through PCAC

Kamano, Nakamura, Lee, Sato, 2012

Vector current (Q2=0) for 1π Produc1on is well-tested by data

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

γp à π0p

dσ/dΩ for W < 2.1 GeV

Predicted πN à ππN total cross sections with our DCC model

Kamano, PRC88(2013)045208 Kamano, Julia-Diaz, Lee, Matsuyama, Sato PRC79(2008)025206

π+p à π+π+n π-p à π+π-n π-p à π-π0p π+p à π+π0p π-p à π0π0n

Single π produc1on in electron-proton sca7ering

σΤ + ε σL for Q2=0.40 (GeV/c)2 and W=1.1 – 1.68 GeV p(e,e’π0)p p(e,e’π+)n

10 20 30 1100 1120 1140 1160 1180 1200 10 20 1220 1240 1260 1280 1300 1320 4 1340 1360 1380 1400 1420 1440 4 1460 1480 1500 1520 1540 1560 4

• 1

1 cos θπ* 1580 1 cos θπ* 1600 1 cos θπ* 1620 1 cos θπ* 1640 1 cos θπ* 1660 1 cos θπ* 1680 10 20 1110 1130 1150 1170 1190 1210 10 1230 1250 1270 1290 1310 1330 5 10 1350 1370 1390 1410 1430 1 cos θπ* 1450 5 10

• 1

1 cos θπ* 1470 1 cos θπ* 1490 1 cos θπ* 1510 1 cos θπ* 1530 1 cos θπ* 1550

Purpose : Determine Q2 –dependence of vector coupling of p-N* : VpN*(Q2)

1000 2000 3000 1.2 1.4 1.6 1.8 2 d σ/d Ω d E’ (nb/Sr GeV) W (GeV) Ee=5.498 GeV θ=30.45o Q2=0.21-0.40 (GeV/c)2 100 200 1.2 1.4 1.6 1.8 2 d σ/d Ω d E’ (nb/Sr GeV) W (GeV) Ee=5.498 GeV θ=12.97o Q2=0.96-1.3 (GeV/c)2

1π 1π Data: JLab E00-002 (preliminary)

• Reasonable fit to data for applica1on to neutrino interac1ons
• Important 2π contribu1ons for high W region

Inclusive electron-proton sca7ering

DCC vector currents has been tested by data for whole kinemaBcal region relevant to neutrino interacBons of Eν ≤ 2 GeV Similar analysis of electron-neutron sca@ering data has also been done

Neutrino Results

SXN et al., Phys. Rev. D 92, 074024 (2015)

0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 σ (x 10-38 cm2) Eν (GeV) πN ππN KΣ

Cross sec1on for νµ N è µ- X

• πΝ & ππΝ are main channels in few-GeV region
• DCC model gives predic1ons for all final states
• ηΝ, ΚY cross sec1ons are 10-1 – 10-2 smaller

0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 σ Eν (GeV) πN ππN ηN KΛ KΣ

νµ n è µ- X νµ p è µ- X

0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 σ (x 10-38 cm2) Eν (GeV) πN ππN KΣ

Cross sec1on for νµ N è µ- X

• πΝ & ππΝ are main channels in few-GeV region
• DCC model gives predic1ons for all final states
• ηΝ, ΚY cross sec1ons are 10-1 – 10-2 smaller

0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 σ Eν (GeV) πN ππN ηN KΛ KΣ 0.0001 0.001 0.01 0.1 1 0.5 1 1.5 2 σ (x 10-38 cm2) Eν (GeV) πN ππN ηN KΛ KΣ

νµ n è µ- X

0.0001 0.001 0.01 0.1 1 0.5 1 1.5 2 σ (x 10-38 cm2) Eν (GeV) πN ππN KΣ

νµ p è µ- X

Comparison with single pion data

ANL Data : PRD 19, 2521 (1979) BNL Data : PRD 34, 2554 (1986)

DCC model predic1on is consistent with data

• DCC model has flexibility to fit data (ANN*(Q2))
• Data should be analyzed with nuclear effects

νµ n è µ- π0 p νµ p è µ-π+ p νµ n è µ- π + n

0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 σ (x 10-38 cm2) Eν (GeV) DCC ANL BNL 0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 σ Eν (GeV) DCC ANL BNL 0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 σ Eν (GeV) DCC ANL BNL

(Wu et al. , PRC91, 035203 (2015); to be discussed later)

σ

ν

Comparison with double pion data

ANL Data : PRD 28, 2714 (1983) BNL Data : PRD 34, 2554 (1986)

Fairly good DCC predica1on First dynamical model for 2 π produc1on in resonance region

νµ p è µ- π +π + n νµ p è µ-π+πo p

0.05 0.1 0.15 0.2 0.5 1 1.5 2 σ (x 10-38 cm2) Eν (GeV) DCC ANL 0.05 0.1 0.15 0.2 0.5 1 1.5 2 σ Eν (GeV) DCC ANL

νµ n è µ- π +π - p

0.05 0.1 0.15 0.2 0.5 1 1.5 2 σ Eν (GeV) DCC ANL BNL

0.5 0.5

0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 σ Eν (GeV) Full ∆ higher N*s non-resonant 0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 σ (x 10-38 cm2) Eν (GeV) Full ∆ higher N*s non-resonant

Mechanisms for νµ N è µ- π Ν

• Δ(1232) dominates for νµ p è µ- π+ p (I=3/2) for Eν ≤ 2 GeV
• Non-resonant mechanisms contribute significantly
• Higher N*s becomes important towards Eν ≈ 2 GeV for νµ n è µ- π Ν

νµ n è µ- π N νµ p è µ-π+ p

Δ(1232) Δ(1232)

1 1.5 2 W (GeV) 1 2 3 Q2 (GeV/c)2 0.2 0.4 0.6 1 1.5 2 W (GeV) 1 2 3 Q2 (GeV/c)2 0.5 1 1.5 2

νµ n è µ- π N νµ p è µ-π+ p

Eν = 2 GeV

dσ / dW dQ2 ( ×10-38 cm2 / GeV2)

1 1.5 2 W (GeV) 1 2 3 Q2 (GeV/c)2 0.2 0.4 0.6 1 1.5 2 W (GeV) 1 2 3 Q2 (GeV/c)2 0.5 1 1.5 2

νµ n è µ- π N νµ n è µ- π+ π - p νµ p è µ-π+ p νµ p è µ-π+ π0 p

Eν = 2 GeV

dσ / dW dQ2 ( ×10-38 cm2 / GeV2)

1 1.5 2 W (GeV) 1 2 3 Q2 (GeV/c)2 0.01 0.02 0.03 0.04 0.05 1 1.5 2 W (GeV) 1 2 3 Q2 (GeV/c)2 0.01 0.02 0.03

Further development of DCC model for neutrino reac1ons

Neutrino reac1ons on the deuteron

• ANL and BNL data on νµ N è µ- π Ν are actually from νµ d è µ- π ΝΝ data
• Quasi-free kinema1cs is chosen but possible FSI effects are concern
• First step has been taken by Wu et al. PRC91, 035203 (2015)

d d d TNN

γ ,W± π N N

Impulse ΝΝ resca@ering πΝ resca@ering

π γ N, W±N à π N amplitude ç SL model ( PRC 54 (1996), PRC 67 (2003) ) π N à π N amplitude ç SL model ΤΝΝ , deuteron w.f. ç CD-Bonn poten1al (PRC 63 (2001) )

Model for γ d, W± d à π N N

SL model is for Δ region and includes π N channel only

5 10 15 20 25 30 60 90 120 150 180 dσ/dΩ (µb/sr) θπ

Lab (deg)

γ d --> π- pp (Eγ

Lab = 290 MeV)

IA IA+NN IA+NN+πN

• Model predic1on is reasonably consistent with data
• Large ΝΝ (small πΝ) resca@ering effect for π0 produc1on
• rthogonality between deuteron and pn sca@ering wave func1ons
• Small resca@ering effect for π- produc1on

Data: EPJA 6, 309 (1999) Data: NPB 65, 158 (1973)

10 20 30 40 30 60 90 120 150 180 dσ/dΩ (µb/sr) θπN

* (deg)

γ d --> π0 pn (Eγ

Lab = 285 MeV)

IA IA+NN IA+NN+πN

γ d à π N N

Purpose : test the soundness of the model

Wu, Sato, and Lee , PRC 91, 035203 (2015)

νµ

d à µ- π+ n p cross sec1ons

Wu, Sato, and Lee , PRC 91, 035203 (2015)

Εν = 1 GeV, θµ

Lab = 25ο

φπ = 0ο IA IA + NN IA + NN + πN

• Large ΝΝ (small πΝ) resca@ering effect
• rthogonality between deuteron and pn sca@ering wave func1ons
• ANL and BNL data did not consider FSI

à calling for reanalysis with FSI taken into account à ongoing with DCC model Δ QF kinema1cs is chosen

Conclusions

Matching with DIS

DIS region RES region

0.1 0.2 0.3 0.4 0.5 0.2 0.4 0.6 0.8 1 F2

ep

x DCC PDF CLAS

Q2=2.425 (GeV/c)2 W=2 GeV

Vector current We are currently working on the axial current

arXiv:1610.01464

Conclusion

Development of DCC model for νΝ νΝ interac1on in resonance region

• πΝ & ππΝ are main channels in few-GeV region
• DCC model predic1on is consistent with BNL data
• Δ, N*s, non-resonant are all important in few-GeV region (for νµ n è µ- X )

è essen1al to understand interference pa@ern among them è DCC model can do this; consistency between π interac1on and axial current Start with DCC model for γΝ, πΝ è πΝ, ππΝ, ηΝ, ΚΛ, ΚΣ è extension of vector current to Q2≠0 region, isospin separa1on through analysis of e—- p & e—-’n’ data for W ≤ 2 GeV , Q2≤ 3 (GeV/c)2 è Development of axial current for νΝ interac1on; PCAC is maintained Conclusion

Further development

• Neutrino reac1ons on the deuteron à reanalysis of ANL and BNL data with FSI effects
• Matching with DIS region

BACKUP

,

Coupled-channel unitarity is fully taken into account

Kamano et al., PRC 88, 035209 (2013)

In addi1on, γΝ, W±N, ZN channels are included perturba1vely

,

Coupled-channel unitarity is fully taken into account

Kamano et al., PRC 88, 035209 (2013)

In addi1on, γΝ, W±N, ZN channels are included perturba1vely

Contents

★ Introduc1on ★ Dynamical coupled-channels (DCC) model Analysis of γ Ν, πΝ è πΝ, ηΝ, ΚΛ, ΚΣ data and electron sca@ering data Extension to νΝ è l-X ( X= πΝ, ππΝ, ηΝ, ΚΛ, ΚΣ ) ★ Results for νΝ è l-X

νΝ sca@ering in resonance region and relevance to baryon spectroscopy

Relevance to baryon spectroscopy

Vector (magne1c) form factor from electron reac1ons Axial form factor from neutrino reac1ons e.g. N-Δ(1232) transi1on form factors

Sato et al., PRC 63 (2001); PRC 67 (2003)

Relevance to baryon spectroscopy

Vector (magne1c) form factor from electron reac1ons Axial form factor from neutrino reac1ons e.g. N-Δ(1232) transi1on form factors

Sato et al., PRC 63 (2001); PRC 67 (2003)

• Axial structure of bayrons can be learned from neutrino reac1on data
• Different pion cloud contribu1ons to magne1c and axial form factors (slope)

Q2 – dependence

νµ p è µ-π+ p

0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 σ (x 10-38 cm2) Eν (GeV) ANL (1979) BNL (1986)

Neutrino interac1on data in resonance region

νµ p è µ-π+ p νµ CH2 è µ-π 0 X

, PRD 83 (2011)

} PRC 87 (2013)

• Data to fix nucleon axial current (gΑΝΔ)
• Discrepancy between BNL & ANL data
• Recent reanalysis of original data

à discrepancy resolved (!?) PRD 90, 112017 (2014)

• Final state interac1on (FSI) changes

charge, momentum, number of π

• Cross sec1on shape is worse described with FSI
• MINERνA data (arXiv:1406.6415) favor FSI

〈Eν 〉 = 0.8 GeV 〈Eν 〉 = 4.0 GeV

More data are coming à beLer understanding of neutrino-nucleus interacBon

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

“N” resonances (I=1/2)

JP(L2I 2J)

Re(MR)

“Δ” resonances (I=3/2)

PDG: 4* & 3* states assigned by PDG2012 AO : ANL-Osaka J : Juelich (DCC) [EPJA49(2013)44, Model A] BG : Bonn-Gatchina (K-matrix) [EPJA48(2012)5]

• 2Im(MR)

(“width”)

• p(e,e’π0)p
• p(e,e’π+)n
• both

Analysis of electron-proton sca@ering data

Purpose : Determine Q2 –dependence of vector coupling of p-N* : VpN*(Q2) Data : * 1π electroproduc1on

1 2 3 1.2 1.4 1.6 1.8 2 Q2 (GeV/c)2 W (GeV)

Database * Empirical inclusive inelas1c structure func1ons σΤ , σL ç Christy et al, PRC 81 (2010)

region where inclusive σΤ & σL are fi@ed

1 2 3 1.2 1.4 1.6 1.8 2 Q2 (GeV/c)2 W (GeV)

Purpose : Vector coupling of neutron-N* and its Q2 –dependence : VnN*(Q2) (I=1/2) I=3/2 part has been fixed by proton target data

Analysis of electron-’neutron’ sca@ering data

Data : * 1π photoproduc1on (Q2=0) * Empirical inclusive inelas1c structure func1ons σΤ , σL (Q2≠0)

ç Christy and Bosted, PRC 77 (2010), 81 (2010)

DCC vector currents has been tested by data for whole kinemaBcal region relevant to neutrino interacBons of Eν ≤ 2 GeV Done

Formalism

Cross sec1on for νΝ è l X ( X = πΝ, ππΝ, ηΝ, ΚΛ, ΚΣ )

θ è0 Q2è0

CVC & PCAC LSZ & smoothness Finally

σπΝèX is from our DCC model

Results

1.2 1.4 1.6 1.8 2 W (GeV) 0.001 0.01 0.1 1 10 F2 CC ν-proton / CC ν-neutron 1.2 1.4 1.6 1.8 2 W (GeV) 0.001 0.01 0.1 1 10 F2 CC ν-neutron / CC ν-proton

SL πN ππN ΚΣ ηN ΚΛ

Ÿ Predic1on based on model well tested by data (first νΝ è ππΝ) Ÿ πΝ dominates for W ≤ 1.5 GeV Ÿ ππΝ becomes comparable to πΝ for W ≥ 1.5 GeV Ÿ Smaller contribu1on from ηΝ and ΚY O(10-1) - O(10-2) Ÿ Agreement with SL (no PCAC) in Δ region

Comparison with Rein-Sehgal model

• Lower Δ peak of RS model

Ÿ RS overes1mate in higher energy regions (DCC model is tested by data)

1 2 3 1.2 1.4 1.6 1.8 2 F2 W (GeV) νe + p -> e- + p + π+ DCC RS

Similar findings by Leitner et al., PoS NUFACT08 (2008) 009 Graczyk et al., Phys.Rev. D77 (2008) 053001

0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8 2 F2 W (GeV) νe + n -> e- + p + π0 DCC RS 0.2 0.4 1.2 1.4 1.6 1.8 2 W (GeV) νe + n -> e- + n + π+ DCC RS

Comparison in whole kinema1cal region will be done a}er axial current model is developed

F2 from RS model

0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8 2 F2 W (GeV) e + n -> e- + p + 0 w/o non-res w non-res

SL model applied to ν-nucleus sca@ering

1 π produc1on

Szczerbinska et al. (2007)

SL model applied to ν-nucleus sca@ering

coherent π produc1on

γ + 12C è π0 + 12C νµ + 12C è µ- + π0 + 12C

Nakamura et al. (2010)

0.2 0.4 0.6 30 60 90 d2σ/dΩπ

CM (mb/sr)

θπ

CM (degree)

Full w/o medium effects 0.5 1 0.2 0.4 0.6 0.8 dσ/dpπ (10-38 cm2/GeV) pπ (GeV) Full w/o medium effects

Eta production reactions

Kamano, Nakamura, Lee, Sato, 2012

KY KY pr product

• duction

ion react eactions ions

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, arXiv:1305.4351

Vector current (Q2=0) for η Produc1on is well-tested by data

Vector current (Q2=0) for Κ Produc1on is well-tested by data

Kamano, Nakamura, Lee, Sato, arXiv:1305.4351

Analysis result

Q2=0.16 (GeV/c)2 σΤ & σL (inclusive inelas1c)

200 400 600 1200 1400 1600 1800 2000 σT,L (µb) W (MeV)

DCC Christy et al PRC 81

σΤ σL

region where inclusive σΤ & σL are fi@ed

200 400 1200 1400 1600 1800 2000 σT,L (µb) W (MeV)

Analysis result

Q2=0.40 (GeV/c)2 σΤ & σL (inclusive inelas1c) DCC Christy et al PRC 81

σΤ σL

region where inclusive σΤ & σL are fi@ed

10 20 1200 1400 1600 1800 2000 σT,L (µb) W (MeV)

Analysis result

Q2=2.95 (GeV/c)2 σΤ & σL (inclusive inelas1c) DCC Christy et al PRC 81

σΤ σL

region where inclusive σΤ & σL are fi@ed

DCC model for neutrino interac1on

ν

σπΝèX is from our DCC model via PCAC νΝ è l X ( X = πΝ, ππΝ, ηΝ, ΚΛ, ΚΣ ) at forward limit Q2=0

Kamano, Nakamura, Lee, Sato, PRD 86 (2012)

πN ππN ΚΣ

F2(Q2=0) from DCC model and PCAC

1 2 3 1.2 1.4 1.6 1.8 2 F2

CCp(Q2=0)

W (GeV) 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 F2

CCn(Q2=0)

W (GeV)

1π inclusive inclusive 1π

• ---- : q Ÿ A

☐ : fπ TπΝ àπΝ DCC model keeps good consistency with PCAC

Comparison with LPP model

1 2 3 1 1.25 1.5 1.75 2 F2 (Q2=0) W (GeV) DCC(inclusive) DCC(1π) LPP (inclusive=1π) 0.5 1 1 1.25 1.5 1.75 2 F2 (Q2=0) W (GeV) DCC(inclusive) DCC(1π) LPP (inclusive) LPP (1π)

LPP model : Lalakulich et al, PRD 74 (2006)

CCνp CCνn

• Large difference beyond Δ(1232) region
• Importance of consistency between axial-current and πΝ interac1on

Analysis result (single π)

Q2=0 dσ / dΩ (γ n è π-p) for W=1.1 – 2.0 GeV

20 40 1130 1143 1148 1155 1163 1171 1179 1187 1195 1200 1206 1212 20 1218 1224 1230 1237 1245 1252 1257 1263 1271 1276 1282 1288 10 1300 1308 1315 1320 1329 1336 1343 1349 1357 1363 1371 1378 10 1391 1398 1405 1411 1418 1425 1431 1438 1444 1449 1457 1463 10 1469 1476 1483 1490 1495 1508 1514 1520 1526 1533 1539 1545 5 1551 1557 1569 1575 1587 1604 1616 1625 1633 1648 1662 1673 5 1690 1704 1718 1728 1734 1739 1745 1758 1771 1785 1798 1 cos θπ* 1819 2 4

• 1

1 cos θπ* 1824 1 cos θπ* 1844 1 cos θπ* 1849 1 cos θπ* 1869 1 cos θπ* 1875 1 cos θπ* 1894 1 cos θπ* 1899 1 cos θπ* 1924 1 cos θπ* 1948 1 cos θπ* 1972 1 cos θπ* 1996

Analysis result (inclusive e--d)

Data: NP Proc. Suppl. 159, 163 (2006)

• Our calcula1on : [ σ(e--p) + σ(e--n) ] / 2
• Too sharp resonant peaks à fermi mo1on smearing, other nuclear effects needed
• Reasonable star1ng point for applica1on to neutrino interac1ons

500 1000 1500 1.2 1.4 1.6 1.8 2 d σ/d Ω d E’ (nb/Sr GeV/A) W (GeV) Ee=4.628 GeV θ=10.65o Q2=0.44-0.66 (GeV/c)2 50 100 1.2 1.4 1.6 1.8 2 d σ/d Ω d E’ (nb/Sr GeV/A) W (GeV) Ee=4.628 GeV θ=16.00o Q2=0.90-1.34 (GeV/c)2

1π 1π

For applica1on to neutrino interac1ons

Analysis of electron sca@ering data è VpN*(Q2) & VnN*(Q2) fixed for several Q2 values è Parameterize VpN*(Q2) & VnN*(Q2) with simple analy1c func1on of Q2 I=3/2 : VpN*(Q2) = VnN*(Q2) è CC, NC I=1/2 isovector part : ( VpN*(Q2) - VnN*(Q2) ) / 2 è CC, NC I=1/2 isoscalar part : ( VpN*(Q2) + VnN*(Q2) ) / 2 è NC DCC vector currents has been tested by data for whole kinemaBcal region relevant to neutrino interacBons of Eν ≤ 2 GeV

1 2 3 1150 1170 1190 1210 1230 1250 1 2 1270 1290 1310 1330 1350 1370 1 2 1390 1410 1430 1450 1470 1490 1 2 1510 1530 1550 1570 1590 1610 1 2 1620 1630 1650 1660 1670 1700 1 2

• 1

1 cos θπ* 1740 1 cos θπ* 1780 1 cos θπ* 1830 1 cos θπ* 1890 1 cos θπ* 1950 1 cos θπ* 2010

Analysis result (single π)

Q2=1.76 (GeV/c)2 σΤ + ε σL for W=1.10 – 2.01 GeV p(e,e’π0)p p(e,e’π+)n

1 2 3 1100 1120 1140 1160 1180 1200 1 2 1220 1240 1260 1280 1300 1320 1 2 1340 1 cos θπ* 1360 1 cos θπ* 1380 1 cos θπ* 1400 1 cos θπ* 1420 1 cos θπ* 1440 1 2

• 1

1 cos θπ* 1460

Analysis result (single π)

Q2=2.91-3.00 (GeV/c)2 σΤ + ε σL for W=1.10 – 1.67 GeV p(e,e’π0)p p(e,e’π+)n

0.5 1 1100 1130 1150 1170 1190 1210 0.5 1230 1250 1270 1 cos θπ* 1290 1 cos θπ* 1310 1 cos θπ* 1330 0.5

• 1

1 cos θπ* 1350 1 cos θπ* 1370 1 cos θπ* 1390 0.5 1 1150 1170 1190 1210 1230 1250 0.5 1270 1290 1310 1330 1350 1370 0.5 1 1390 1410 1430 1450 1470 1490 0.5 1 1510 1530 1550 1 cos θπ* 1570 1 cos θπ* 1590 1 cos θπ* 1610 0.5

• 1

1 cos θπ* 1630 1 cos θπ* 1650 1 cos θπ* 1670