Dynamical Coupled-Channels Approach for Single- and Double-Pion Electroproductions:
Status and Plans
Hiroyuki Kamano
Research Center for Nuclear Physics (RCNP)Osaka University
EmNN*2012 Workshop @ USC, USA, August 13-15, 2012
Outline1. Background and motivation for N* spectroscopy
2. ANL-Osaka Dynamical Coupled-Channels (DCC) approach for N* spectroscopy
3. Status and plans for single- and double-pion electroproduction reactions
4. Related hadron physics program at J-PARC
Background and motivation for N* spectroscopy
(1 / 4)
N* spectroscopy : Physics of broad & overlapping resonances
Δ (1232)
Width: a few hundred MeV. Resonances are highly overlapping in energy except D(1232).
Width: ~10 keV to ~ 10 MeV Each resonance peak is clearly separated.
N* : 1440, 1520, 1535, 1650, 1675, 1680, ...D : 1600, 1620, 1700, 1750, 1900, …
Hadron spectrum and reaction dynamics Various static hadron models have been proposed to calculate hadron spectrum and form factors.
In reality, excited hadrons are “unstable” and can exist only as resonance states in hadron reactions.
Quark models, Bag models, Dyson-Schwinger approaches, Holographic QCD,… Excited hadrons are treated as stable particles. The resulting masses are real.
What is the role of reaction dynamics in interpretingthe hadron spectrum, structures, and dynamical origins ??
“Mass” becomes complex !! “pole mass” u
u d
Constituent quark modelN*
bare state
meson cloud
“molecule-like” states
core (bare state) + meson cloud
ANL-Osaka Dynamical Coupled-Channels (DCC) approach for N* spectroscopy
(2 / 4)
Objectives and goals:
Through the comprehensive analysis of world data of pN, gN, N(e,e’) reactions,
Determine N* spectrum (pole masses)
Extract N* form factors
(e.g., N-N* e.m. transition form factors)
Provide reaction mechanism information necessary for interpreting N* spectrum, structures and dynamical origins
ANL-Osaka Dynamical Coupled-Channels Approach for N* Spectroscopy
Spectrum, structure,…of N* states
QCD
Lattice QCDHadron Models
Analysis Based on Reaction Theory
Reaction Data
“Dynamical coupled-channels model of meson production reactions”
A. Matsuyama, T. Sato, T.-S.H. Lee Phys. Rep. 439 (2007) 193
Partial wave (LSJ) amplitudes of a b reaction:
Reaction channels:
Transition Potentials:
coupled-channels effect
Exchange potentials bare N* states
For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007)
Z-diagrams
Dynamical coupled-channels (DCC) model for meson production reactions
Meson-Baryon Green functions
Stable channels Quasi 2-body channels
N pD
p
D
ppp
r, s r, s
N N
p, r, s, w,..
N N, D
s-channel u-channel t-channel contact
Exchange potentials
Z-diagrams
Bare N* statesN*bare
Dp
N p
p
DDNp
r, s
Can be related to hadron states of the static hadron models (quark models, DSE, etc.)excluding meson-baryon continuum.
core
meson cloud
meson
baryon
Physical N*s will be a “mixture” of the two pictures:
DCC analysis (2006-2009)
p N p N : Analyzed to construct a hadronic part of the model up to W = 2 GeVJulia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007)
p N h N : Analyzed to construct a hadronic part of the model up to W = 2 GeVDurand, Julia-Diaz, Lee, Saghai, Sato, PRC78 025204 (2008)
p N p p N : Fully dynamical coupled-channels calculation up to W = 2 GeVKamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79 025206 (2009)
g(*) N p N : Analyzed to construct a E.M. part of the model up to W = 1.6 GeV and Q2 = 1.5 GeV2
(photoproduction) Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77 045205 (2008) (electroproduction) Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009)
g N p p N : Fully dynamical coupled-channels calculation up to W = 1.5 GeV Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC80 065203 (2009)
Extraction of N* pole positions & new interpretation on the dynamical origin of P11 resonancesSuzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 065203 (2010)
Stability and model dependence of P11 resonance poles extracted from pi N pi N dataKamano, Nakamura, Lee, Sato, PRC81 065207 (2010)
Extraction of gN N* electromagnetic transition form factorsSuzuki, Sato, Lee, PRC79 025205 (2009); PRC82 045206 (2010)
Hadronic part
Electromagnetic part
Extraction of N* parameters
gN, pN, hN, pD, rN, sN coupled-channelscalculations were performed.
Dynamical origin of nucleon resonances
Pole positions and dynamical origin of P11 resonances
Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 065203 (2010)
pole A: pD unphys. sheetpole B: pD phys. sheet Double-pole nature of the Roper is found
also from completely different approaches:
Eden, Taylor, Phys. Rev. 133 B1575 (1964)
Multi-channel reactions can generate many resonance poles from a single bare state !!
For evidences in hadron and nuclear physics, see e.g., in Morgan and Pennington, PRL59 2818 (1987)
Corresponds to hadron states from static hadron models
N-N* transition form factors at resonance poles
Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki PRC80 025207 (2009)Suzuki, Sato, Lee, PRC82 045206 (2010)
Real part Imaginary part
Nucleon - 1st D13 e.m. transition form factors
Coupling to meson-baryon continuum states makes N* form factors complex !!
Fundamental nature of resonant particles (decaying states)
Extracted from analyzing the p(e,e’p)N data from CLAS
Dynamical coupled-channels (DCC) analysis
pp pN
gp pN
pp hN
gp hp
pp KL, KS
gp K+L, KS
2006 - 2009
6 channels (gN,pN,hN,pD,rN,sN)
< 2 GeV
< 1.6 GeV
< 2 GeV
―
―
―
2010 - 2012
8 channels (gN,pN,hN,pD,rN,sN,KL,KS)
< 2.1 GeV
< 2 GeV
< 2 GeV
< 2 GeV
< 2.2 GeV
< 2.2 GeV
# of channels
Fully combined analysis of pN , gN pN , hN , KL, KS reactions !!
Kamano, Nakamura, Lee, Sato(2012)
(more than 20,000 data points to fit)
Partial wave amplitudes of pi N scattering
8ch DCC-analysis(Kamano, Nakamura, Lee, Sato2012)
6ch DCC-analysis(fitted to pN pN data only)[PRC76 065201 (2007)]
Real part
Imaginary part
Partial wave amplitudes of pi N scattering
8ch DCC-analysis(Kamano, Nakamura, Lee, Sato2012)
6ch DCC-analysis(fitted to pN pN data only)[PRC76 065201 (2007)]
Real part
Imaginary part
π- p ηn reactions
Analyzed data up to W = 2 GeV. p- p h n data are selected according to Durand et al. PRC78 025204.
Kamano, Nakamura, Lee, Sato, 2012
πN KY reactions (1/2) Kamano, Nakamura, Lee, Sato, 2012
π-p K0Σ0π- p K0Λ π+p K+Σ+
πN KY reactions (2/2) Kamano, Nakamura, Lee, Sato, 2012
π-p K0Σ0π- p K0Λ π+p K+Σ+
γp πN reactions(1/2)γp π+nγp π0p
Kamano, Nakamura, Lee, Sato, 2012
γp πN reactions(2/2)γp π+nγp π0p
Kamano, Nakamura, Lee, Sato, 2012
γp ηp reactionKamano, Nakamura, Lee, Sato, 2012
γp K+Σ0, K0Σ+ reactionsKamano, Nakamura, Lee, Sato, 2012
γp K+Σ0
γp K0Σ+
γp K+Λ reaction (1/4)Kamano, Nakamura, Lee, Sato, 2012
γp K+Λ reaction (2/4)Kamano, Nakamura, Lee, Sato, 2012
γp K+Λ reaction (3/4)Kamano, Nakamura, Lee, Sato, 2012
γp K+Λ reaction (4/4)Kamano, Nakamura, Lee, Sato, 2012
Status and plans for single- and double-pion electroproduction rections
(3 / 4)
Status and plans for analysis of electroproduction reactions
6-channel (2006-2009) 8-channel (2010-2012)
γp πN
γp ππN
ep e’πN
ep e’ππN
W < 1.6 GeV(the data analyzed)
W < 1.6 GeV(cross sections predicted)
W < 1.6 GeV, Q2 < 1.5 (GeV/c)2
(the data analyzed)
W < 2 GeV(the data analyzed)
Not yet done
Not yet done
Not yet done
[Plan 1]: After completing 8-ch analysis,immediately proceed to the analysisof CLAS p(e,eπ)N data and extractN-N* e.m. transition form factorsup to Q2 ~ 4 (GeV/c)2.
[Plan 2]: After Plan 1, we can giveprediction for p(e,eππ)N cross sections.
[Combined analysis of p(e,eπ)N and p(e,eππ)N will be a long term project.]
VERY preliminary results available
(Q2 = 0 point)
(nonzero Q2)
γp ππN calculation with 8-ch. DCC modelPrediction for γp ππ N total cross sections (not yet included in the fit)
8-ch. DCC Full(Kamano, Nakamura, Lee, Sato 2012)
6-ch. DCC Full [PRC80 065203 (2010)]
8-ch. DCC Nonresonant only
6-ch. DCC Nonresonant only
VERY PRELIMINARY !!
Related hadron physics program at J-PARC(4 / 4)
Hadron physics program at J-PARCWG on “Hadron physics with high-momentum beam line at J-PARC”
Currently J-PARC has high-momentum proton (< 30 GeV/c) and pion (~ 15 GeV/c) beams. Now considered as one of the highest priority projects at KEK/J-PARC from April 2013.
Hadron properties in nuclear medium pQCD, partonic structure of nucleon and nuclei Charmed-hadron physics Exotic hadrons and nuclei N* physics (N*, Δ*, ...) High-energy spin physics Short-range NN correlations Transition from hadron to quark degrees of freedom Exclusive processes (GPD, quark counting, ...) Quark/hadron interactions in nuclear medium (parton-energy loss, color
transparency) J/ψ production mechanisms and its interactions in nuclear medium Pion distribution amplitude, hadron-transition distribution amplitudes Intrinsic charm and strange … AND MORE TO COME!!
πN ππN: “Critical missing piece” in N* spectroscopy.
Measurement of πN ππN & KY in high-mass N* region (K. Hicks, K. Imai et al.)
The idea originates from “US-Japan Joint Workshop on Meson Production Reactions at Jefferson Lab and J-PARC” Hawaii, Oct. 2009.
There is NO practical data that can be used for partial wave analysis above W > 1.5 GeV.
Above W > 1.5 GeV, πN ππN becomes the dominant process of the πN reactions.
Most of the N*s decay dominantly to the ππN channel.
Hadron physics program at J-PARC
The current N* mass spectrum might receive significant modificationsand even new N* states might be discovered by the combined analysisincluding this new πN ππN data !!
Hadron physics program at J-PARC Measurement of forward p(π,ρ)X, p(π, K*)X reactions (T. Ishikawa, T. Nakano et al.)
p
virtual π
N*, Δ* (slow)
Q2
high-p π ρ (fast)
p
virtual K
Y* (slow)
high-p π K* (fast)
Can be used for extracting N-N* axial transition form factors
Can access to Λ(1405) region below KN threshold. Could be used for extracting strangeness changing axial form factors.
Crucial for constructing reliable neutrino-nucleon/nucleus reaction models in resonance and DIS region.
Collaboration@J-PARC Branch of KEK Theory Center [Y. Hayato, M. Hirai, H. Kamano, S. Kumano, S. Nakamura, K. Saito, M. Sakuda, T. Sato]
(http://j-parc-th.kek.jp/html/English/e-index.html)
Q2
Summary
;
pp pN
gp pN
pp hN
gp hp
pp KL, KS
gp K+L, KS
2006 - 2009
6 channels (gN,pN,hN,pD,rN,sN)
< 2 GeV
< 1.6 GeV
< 2 GeV
―
―
―
2010 - 2012
8 channels (gN,pN,hN,pD,rN,sN,KL,KS)
< 2.1 GeV
< 2 GeV
< 2 GeV
< 2 GeV
< 2.2 GeV
< 2.2 GeV
# of channels
Summary
After completing the combined analysis of πp, γp πN, ηN, KΛ, KΣ reactions, immediately proceed to the analysis of CLAS p(e,eπ)N data and extract N-N* e.m. transition form factors up to Q2 ~ 4 (GeV/c)2. Combined analysis of p(e,eπ)N and p(e,eππ)N is considered as a long term project in future. [Combined analysis of p(e,e’π)N, p(e,e’η)p, p(e,e’K)Y could be done quickly.]
With the new 8-channels model, nucleon resonance parameters(mass spectrum, decay widths, etc.) are being investigated.(As presented in T. Sato’s talk)
back up
Phenomenological prescriptions of constructing conserved-current matrix elements
As commonly done in practical calculations in nuclear and particle physics, currently we take a phenomenological prescription to construct conserved current matrix elements [T. Sato, T.-S. H. Lee, PRC60 055201 (2001)]:
: Full e.m. current matrix elements obtained by solving DCC equations
: photon momentum : an arbitrary four vector
A similar prescription is applied, e.g., in Kamalov and Yang, PRL83, 4494 (1999).
There are also other prescriptions that enable practical calculations satisfying current conservation or WT identity:
Gross and Riska, PRC36, 1928 (1987) Ohta, PRC40, 1335 (1989) Haberzettl, Nakayama, and Krewald, PRC74, 045202 (2006).
Since the late 90s, huge amount of high precision data of meson photo-production reactions on the nucleon target has been reported from electron/photon beam facilities.
JLab, MAMI, ELSA, GRAAL, LEPS/SPring-8, …
Experimental developments
E. Pasyuk’s talk at Hall-B/EBAC meeting
Opens a great opportunity to make quantitative study of the N* states !!
N* states and PDG *s
?
?
?
?
?
Arndt, Briscoe, Strakovsky, Workman PRC 74 045205 (2006)
Most of the N*s were extracted from
Need comprehensive analysis of
channels !!From PDG 2010
Note: Some freedom exists on the definition of partial width from the residue of the amplitudes.
Width of N* resonances(Current status)
Kamano, Nakamura, Lee, Sato, 2012
Spectrum of N* resonances(Current status)
Real parts of N* pole values
L2I 2J
PDG Ours
N* with 3*, 4* 1816
N* with 1*, 2* 5PDG 4*
PDG 3*
Ours
Kamano, Nakamura, Lee, Sato, 2012
γp πN reactions
6ch DCC-analysis [PRC77 045205 (2008)](fitted to gN pN data up to 1.6 GeV)
Angular distribution Photon asymmetry
1137 MeV 1232 MeV
1334 MeV
1462 MeV 1527 MeV 1617 MeV
1729 MeV 1834 MeV 1958 MeV
1137 MeV 1232 MeV 1334 MeV
1462 MeV 1527 MeV 1617 MeV
1729 MeV 1834 MeV 1958 MeV
8ch DCC-analysisKamano, Nakamura, Lee, Sato 2012
Single pion electroproduction (Q2 > 0)
Fit to the structure function data (~ 20000) from CLAS
Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009)
p (e,e’ p0) p
W < 1.6 GeVQ2 < 1.5 (GeV/c)2
is determinedat each Q2.
N*N
g (q2 = -Q2)q
N-N* e.m. transitionform factor
Single pion electroproduction (Q2 > 0)Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009)
p (e,e’ p0) p
p (e,e’ p+) n
Five-fold differential cross sections at Q2 = 0.4 (GeV/c)2
Data handled with the help of R. Arndt
pi N pi pi N reaction
Parameters used in the calculation are from pN pN analysis.
Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79 025206 (2009)
Full result
Phase spaceFull result
W (GeV)
s (m
b)
C. C. effect off