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

Meson Produc1ons in Neutrino-Nucleon Delta Resonance Reac1ons in Resonance Region 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 )

Introduc1on

Neutrino-nucleus sca7ering for ν -oscilla1on experiments All ν -oscilla1on experiments measure ν -flux through ν -nucleus interac1on Next-genera1on exp. è leptonic CP, mass hierarchy, sterile neutrinos ν - nucleus sca@ering needs to be understood more precisely ( ∼ 5%) ν Q 2 = - q 2 ν = q 0

Neutrino-nucleus sca7ering for ν -oscilla1on experiments QE region DIS region ν RES region Q 2 = - q 2 ν ν = q 0 Atmospheric ν Q 2 = - q 2 T2K ν = q 0 Collabora1on at J-PARC Branch of KEK Theory Center Wide kinema1cal region with different characteris1c è Combina1on of different exper1se is necessary h7p://j-parc-th.kek.jp/html/English/e-index.html A review ar1cle to be published in Reports on Progress in Physics ( arXiv:1610.01464 )

Resonance region Main reac1on mechanism : resonance excita1ons γ , W ± , Z 0 π N * i Σ i N N • N * are unstable and strongly couple to meson-baryon con1nuum states • Width ∼ 100 MeV, several N *’ s are overlapping (Sub-leading) non-resonant mechanisms Σ + + + ...

Resonance region (single nucleon) γΝ è X 2nd 3rd Δ (MeV) Ÿ Several resonances form characteris1c peaks Ÿ 2 π produc1on is comparable to 1 π Ÿ η , Κ produc1ons (mul1-channel reac1on)

Neutrino interac1on data in Δ (1232) region ν µ p è µ - π + p Wilkinson et al. PRD 90 (2014) 1 0.8 σ (x 10 -38 cm 2 ) 0.6 0.4 0.2 ANL (1979) BNL (1986) 0 0 0.5 1 1.5 2 E ν (GeV) Recent reanalysis of original data • Data to fix nucleon axial current ( g ΑΝΔ ) à discrepancy resolved (probably) • Discrepancy between BNL & ANL data à theore1cal uncertainty in neutrino-nucleus σ (CC1 π ;data) σ (CC0 π ;data) × σ (CCQE;model) cross sec1ons Flux uncertainty is cancelled out FSI ma@ers ? à to be discussed later

Neutrino interac1on data in Δ (1232) region MiniBooNE PRD 83 (2011) MINERvA PRD 92 (2015) ν µ CH è µ - π ± X ν µ CH 2 è µ - π 0 X 〈 E ν 〉 = 0.8 GeV 〈 E ν 〉 = 4.0 GeV , W < 1.4 GeV } 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 • MINER ν A data favor FSI Current FSI models are not sa1sfactory

Neutrino interac1on beyond Δ (1232) region MINERvA PRD 92 (2015) ν µ CH è µ - N π ± X ( N =1,2,3, …) 〈 E ν 〉 = 4.0 GeV , W < 1.8 GeV 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 on single nucleon is s1ll an issue T : # of nucleons in fiducial volume Φ : integrated flux

Previous models for ν - induced 1 π produc1on in resonance region resonant only Rein et al. (1981), (1987) ; Lalalulich et al. (2005), (2006) VNN* : helicity amplitudes listed in PDG N * i Σ ANN* : quark model, PCAC rela1on to | π NN* | (PDG) i rela1ve phases among N* ’s are out of control + non-resonant (tree-level non-res) Hernandez et al. (2007), (2010) ; Lalakulich et al. (2010) N * i Σ + + + ... i + resca@ering ( π N unitarity, Δ (1232) region) Sato, Lee (2003), (2005) ∆ + + ... + + ...

GOAL : Develop νΝ -interac1on model in resonance region Problems in previous models 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 Our strategy to overcome the problems… We develop a dynamical coupled-channels model ★ 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 )

Dynamical Coupled-Channels model for meson produc1ons

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 ,

Kamano et al., PRC 88, 035209 (2013) Coupled-channel Lippmann-Schwinger equa1on for meson-baryon sca@ering , T V V V By solving the LS equa1on, coupled-channel unitarity is fully taken into account In addi1on, γΝ , W ± N, ZN channels are included perturba1vely T

Rela1on between neutrino and electron (photon) interac1ons Charged-current (CC) interac1on (e.g. ν µ + n à µ - + p ) λ + h . c . ] L cc = G F V ud cc = V λ − A λ λ = ψ µ γ λ (1 − γ 5 ) ψ ν cc  cc [ J λ  cc J λ 2 Electromagne1c interac1on (e.g. γ ( * ) + p à p ) L em = e J λ em = V λ + V IS λ em A em J λ λ V and V IS in J em can be separately determined by analyzing photon ( Q 2 =0) and electron reac1on ( Q 2 ≠0) data on both proton and neutron targets, because: < p | V IS λ | p > = < n | V IS < p | V λ | p > = − < n | V λ | n > λ | n > Matrix element for the weak vector current is obtained from analyzing electromagne1c processes < p | V λ | n > = 2 < p | V λ | p >

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 PCAC rela1on X | q ⋅ A | X > ~ i f π < ! X | T | π X > ! < Q 2 =0 non-resonant mechanisms Σ + + ... ∂ µ π → f π A external µ A π resonant mechanisms PCAC N * N * Interference among resonances and background can be uniquely fixed within DCC model

DCC model for axial current Q 2 ≠0 : axial form factors F A ( Q 2 ) 2 ! $ 1 non-resonant mechanisms F A ( Q 2 ) = # & M A = 1.02 GeV 1 + Q 2 / M A 2 " % 2 ! $ 1 resonant mechanisms F A ( Q 2 ) = # & 1 + Q 2 / M A 2 " % More neutrino data are necessary to fix axial form factors for ANN * Neutrino cross secBons will be predicted with this axial current

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

DCC analysis of meson produc1on data Kamano, Nakamura, Lee, Sato, PRC 88 (2013) Fully combined analysis of γΝ , πΝ è πΝ , ηΝ , ΚΛ , ΚΣ data and polariza1on observables (W ≤ 2.1 GeV) d σ / d Ω ~ 23,000 data points are fi@ed by adjus1ng parameters ( N* mass, N* è MB couplings, cutoffs) Data for electron sca@ering on proton and neutron are analyzed by adjus1ng γ * Ν è Ν * coupling strength at different Q 2 values ( Q 2 ≤ 3 (GeV /c ) 2 )

Par1al wave amplitudes of π N sca7ering Real part Kamano, Nakamura, Lee, Sato, PRC 88 (2013) Previous model (fitted to π N à π N data only) [PRC76 065201 (2007)] Imaginary part Data: SAID πΝ amplitude

Par1al wave amplitudes of π N sca7ering Real part Constraint on axial current through PCAC Kamano, Nakamura, Lee, Sato, PRC 88 (2013) Previous model (fitted to π N à π N data only) [PRC76 065201 (2007)] Imaginary part Data: SAID πΝ amplitude

γp à π 0 p dσ/dΩ for W < 2.1 GeV Kamano, Nakamura, Lee, Sato, PRC 88 (2013) Kamano, Nakamura, Lee, Sato, 2012 Vector current (Q 2 =0) for 1 π Produc1on is well-tested by data

Predicted π N à ππ N total cross sections with our DCC model π + p à π + π + n π - p à π + π - n π - p à π - π 0 p π + p à π + π 0 p π - p à π 0 π 0 n Kamano, PRC88(2013)045208 Kamano, Julia-Diaz, Lee, Matsuyama, Sato PRC79(2008)025206

Single π produc1on in electron-proton sca7ering Purpose : Determine Q 2 –dependence of vector coupling of p-N* : VpN* ( Q 2 ) σ Τ + ε σ L for Q 2 =0.40 (GeV/ c ) 2 and W= 1.1 – 1.68 GeV p ( e,e’ π 0 ) p p ( e,e’ π + ) n 30 20 1100 1120 1140 1160 1180 1110 1130 1150 1170 1190 20 10 10 1200 1210 0 0 1260 1280 1300 1320 1230 1250 1270 1290 1310 1330 20 10 10 1220 1240 0 0 4 1420 1440 1350 1370 1390 1410 1430 1450 10 5 1340 1360 1380 1400 0 0 1460 1540 1560 4 0 1 1470 1490 1510 1530 1550 10 cos θ π * 5 1480 1500 1520 0 0 1580 1600 1620 1640 1660 1680 4 -1 0 1 0 1 0 1 0 1 0 1 cos θ π * cos θ π * cos θ π * cos θ π * cos θ π * 0 -1 0 1 0 1 0 1 0 1 0 1 0 1 cos θ π * cos θ π * cos θ π * cos θ π * cos θ π * cos θ π *

Inclusive electron-proton sca7ering 3000 E e =5.498 GeV θ =30.45 o Q 2 =0.21-0.40 (GeV/c) 2 200 d σ /d Ω d E’ (nb/Sr GeV) d σ /d Ω d E’ (nb/Sr GeV) 2000 1 π 100 1000 E e =5.498 GeV 1 π θ =12.97 o Q 2 =0.96-1.3 (GeV/c) 2 0 0 1.2 1.4 1.6 1.8 2 1.2 1.4 1.6 1.8 2 W (GeV) W (GeV) Data: JLab E00-002 (preliminary) • Reasonable fit to data for applica1on to neutrino interac1ons • Important 2 π contribu1ons for high W region Similar analysis of electron-neutron sca@ering data has also been done DCC vector currents has been tested by data for whole kinemaBcal region relevant to neutrino interacBons of E ν ≤ 2 GeV

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