Electroweak Meson Production
Reaction in the Nucleon resonance Region
T. Sato Osaka U
Collaborators : H. Kamano(RCNP),S.Nakamura(Osaka),
T. Murata(Osaka), T. –S. H. Lee(ANL), Jiajun Wu(ANL)
Contents
 Coupled channel approach of weak meson production reactions
in resonance region
 Pion production reaction on deuteron in the Delta resonance region
Aug. 2014 CETUP*
Coupled channel approach of weak meson
production reactions in resonance region
QE
DIS
Resonance region
W < 2GeV
RES
DIS
Atmospheric
W > 2GeV
Q^2 > 1 GeV^2
T2K
Collaboration at J-PARC Branch of KEK theory center
Y. Hayato(ICRR, U. of Tokyo), M. Hirai(Tokyo Science U.),H.
Kamano(RCNP,Osaka U.),S. Kumano(KEK),S.
Nakamura(YITP,Kyoto U.),T. Murata(Osaka U.),K. Saito(Tokyo
Science U.),T. Sato(Osaka U.),M. Sakuda(Okayama U.)
πN  X, πN
Δ (1232)
Delta(1232) resonance stands as clear peak
N*: 1440, 1520, 1535, 1650, 1675, 1680, ...
πN  X, πN
Δ : 1600, 1620, 1700, 1750, 1900, …
Delta(1232) resonance stands as clear peak
1.4 < W < 2GeV ~20 resonances
N*: 1440, 1520, 1535, 1650, 1675, 1680, ...
πN  X, πN
Δ : 1600, 1620, 1700, 1750, 1900, …
Feature of N*,Δ resonances
•
excite states of nucleons are unstable particles and appear as resonances
•
strong coupling of excited states with meson-baryon continuum
large width (~> 100MeV) and overlapping resonances
•
resonance informations are extracted from the partial wave analysis of the
meson production reaction amplitudes
amplitudes of MB channels are related through unitarity
Need for the coupled channel analysis of various Meson-Baryon channel
to disentangle nucleon resonances
Reaction Data
past two decades,
high precision data from
Jlab,Mainz, Bonn,
GRALL, Spring8
• Combined analysis of available single pion,eta, kaon production
incorporating two pion finat state with Coupled-Channels approach
• Extraction of resonance parameters(Mass, transition form factor) from the
partial wave amplitudes
Mass, Width,
Electromagnetic
N-N* form factors
Hadron Models
Lattice QCD
QCD
Dynamical Coupled channel approach:
ANL-Osaka, Julich
model of meson production reaction
in resonance region
D. Rein, L.M. Sehgal, Ann. Phys. 133, 79(1981)
O. Lalakulich, E. A. Paschos, G. Piranishvik,PRD74, 014009(2006)
T. Leitnerm, O. Buss,L. Alvarez-Ruso, U. Mosel, PRC79, 034601(2009)
dynamical coupled-channels (DCC) model
Building block of our model
s-channel
u-channel
t-channel
contact
p, r, s, w,..
N
N, D
Effective interaction generated by eliminating 1,3 particles channel
Bare N*
N*bare
Z-diagrams
Self energy
in piD green
function
each potential affects many partial waves
 partial waves, W-region, MB channels are related
 simultaneous analysis MB channels restricts model, but time consuming
to fit data
Scattering amplitude of pion and photon induced meson production amplitudes
are obtained by solving two body, coupled channel integral equation
(3-dim reduction) in momentum space (partial waves [I,J,P] )
Scattering amplitude can be rewritten as
Dynamical Coupled-Channels analysis
(JLMS)
(SL)
1996-2001
 pp  pN
W<1.3
•
2006-2009
2010-2013
(gN,pN,hN,pD,rN,sN)
(gN,pN,hN,pD,rN,sN,KL,KS)
W < 2 GeV
< 2.3 GeV
< 1.6 GeV
< 2 .1GeV
 p-p  hn
< 2 GeV
< 2.1 GeV
 gp  hp
―
< 2.1 GeV
 pp  KL, KS
―
< 2.1 GeV
 gp  KL, KS
―
< 2.1 GeV
 gp  pN
•
•
(ANL-Osaka)
< 1.3
Extended to include KY production reaction, higher W
Fully combined analysis of gN , pN  pN , hN , KL, KS reactions
SU(3) Meson (P,V octet), Baryon(octet,decuplet)
omega N, pipi N are not included in fit
SL
PRC 54, 2660(96), PRC63, 055201(01)
JLMS
PRC76, 065201(07)
ANL-Osaka PRC88, 035209(13)
•
•
Extensive data of differential cross section can be fitted very well for W<1.9GeV.
Not able to account forward peak W>1.933GeV
pi N  pi pi N reaction
Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79 025206 (2009)
Parameters used in the calculation are from pN  pN analysis.
Full result
Full result
C.C. effect off
Phase space
Data handled with the help of R. Arndt
resonance poles and residues
of scattering amplitudes
Spectrum of N* and Delta (ANL-Osaka)
Half width
Some freedom exists on the definition of partial width from the residue of
the amplitude. The numbers should be taken as a one estimation of the
MB-res coupling strength .
weak meson production reaction
DCC model for neutrino interaction
n
Vector current
Q2=0
gp  MB
gn  pN
Q2≠0

isospin separation necessary
(electromagnetic form factors for VNN* couplings) from (e,e’ p), (e,e’ X) data analysis
We’ve done first analysis of all these reactions  VNN*(Q2) fixed  neutrino reactions
Axial current
S
N*
i
Q2=0 non-resonant mechanisms
i
+
+
+ ...
A
N*
PCAC
p
N*
resonant mechanisms
Interference among resonances and background can be made under control within DCC model
Caveat for this presentation : phenomenological axial currents are added to maintain PCAC relation
ds / dW (g n  p-p) for W=1.1 – 2.0 GeV
Q2=0
Analysis of electron-proton scattering data
Purpose : Determine Q2 –dependence of vector coupling of p-N* : VpN*(Q2)
Data :
* 1p electroproduction
* Empirical inclusive inelastic structure functions sT , sL
 Christy et al, PRC 81 (2010)
Database
•
p(e,e’p0)p
•
p(e,e’p+)n
•
both
region where inclusive
sT & sL are fitted
N(e,e’pi)N cross section
Inclusive structure function
Result on single pion electroproduction
sT + e sL for W=1.1 – 1.68 GeV
p(e,e’p0)p
Q2=0.40 (GeV/c)2
p(e,e’p+)n
sT & sL (inclusive inelastic)
DCC
sT
sL
Christy et al PRC 81
region where inclusive
sT & sL are fitted
Q2=0.40 (GeV/c)2
Mechanisms for nm N  m p N
 D dominates for nm p  m- p+ p (I=3/2) for En ~ 2 GeV
 Non-resonant mechanisms contribute significantly
 Higher N*s becomes important En ~2 GeV for nm n  m- p N
Cross section for nm N  m- X
 pN & ppN are main channels in few-GeV region
 hN, KY cross sections are 10-1 – 10-2 smaller
single and two pion production cross section
Development of DCC model for nN interaction in resonance region
Start with DCC model for gN, pN  pN, ppN, hN, KL, KS
 extension of vector current to Q2≠0 region, isospin separation
through analysis of e—- p & e—-’n’ data for W ≤ 2 GeV , Q2≤ 3 (GeV/c)2
 Development of axial current for nN interaction; more study needed
Summary
 pN & ppN are main channels in few-GeV region
 DCC model prediction is consistent with ANL data
 D, N*s, non-resonant are all important in few-GeV region (for nm n  m- X )
 essential to understand interference pattern among them
 DCC model can do this; consistency between p interaction and axial current
Pion production reaction on deuteron
in the Delta(1232) Region
Pion production reaction on deuteron in the Delta(1232)
Region
J. Wu, T. –S. H. Lee, T. Sato
 Data of neutrino induced pion production on nucleus
nu-d data ANL(PRD19,2521, PRD26,1161), BNL(PRD34,2554,PRD42, 1331)
Fermi-motion L. Alvarez-Ruso et al. PRD59,3386
 How large nuclear effects?
Final State Interaction (nucleon-nucleon, pion-nucleon rescattering)
 Deuteron reaction:
microscopic theoretical estimation of FSI is possible
model can be tested by comparing data of pion photoproduction
predict nuclear effects on neutrino reaction
Impulse amplitude
Fermi motion is included
Final state interaction(one-loop)
~ DWIA
Nucleon-nucleon scattering
Pion-N rescattering
FSI in pion photoproduction
J.M. Laget Phys.Rep 69,1(1981),M.Schwamb Phys.Rep. 485,109(2010)
M.I.Levchuk et al., PRC74,014004(2006)
Model of pi-N, electroweak pion production T-matrix
for the delta(1232) resonance region (W<1.3GeV, SL model)
Start from Lagrangian based on chiral symmetry and
electroweak Standard Model
Sato,Uno,Lee
PRC67(2003)
Matsui,Sato,Lee
PRC72(2005)
CC
NC, PV(e,e’)
Effective Hamiltonian
resonance
Vector
Axial vector
Non-resonant int.
g N  D(1232) form factors
compared with Lattice QCD data (2006)
DCC
3/2+  1/ 2 +
Kitagaki et al. (90) BNL
Barish et al.(79) ANL
FSI : pion production reaction on deuteron
Pion photoproduction (Differential cross section)
With FSI, both pi- and pi0 production angular distribution is well reproduced.
Pion photoproduction(Total cross section) and role of FSI
Impulse
Impulse + NN
Impulse+NN+piN
Large FSI(NN) for pi0 production
Impulse
Impulse + NN
Impulse+NN+piN
~ Delta-QF kinematics
Summary
 Rescattering effects are examined for electroweak deuteron
reactions
 Using, pion production model of SL and Bonn-Pot, pion(pi^-,pi^0)
photoproduction on deuteron are reasonably well described.
 Neutrino induced pion production reaction(CC):
Within the kinematical region we have examined:
Large effects of nucleon rescattering even Delta-QE peak
especially FSI in 3S1 >1S0
Effects of piN rescattering were small