Hiroyuki Kamano Research Center for Nuclear Physics (RCNP) Osaka University

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

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


γp πN reactions(2/2)γp π+nγp π0p


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

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)


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


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

Hiroyuki Kamano Research Center for Nuclear Physics (RCNP) Osaka University

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