N* and Y* physics within

a dynamical coupled-channels
approach
Hiroyuki Kamano(RCNP, Osaka U.)
Collaborators:
T.-S. H. Lee (Argonne )S. Nakamura (Osaka U.)
T. Sato (Osaka U.)
Workshop on “Progress on J-PARC hadron physics in 2014”
Tokai, Japan, Nov. 30-Dec. 2, 2014

Introductory remarks aboutlight-quark baryon spectroscopy
N*, Δ*, Λ*, Σ* “Light-quark baryon spectroscopy”= “Physics of very broad and highly overlapping resonances”
 Resonances are strongly correlated with each other in the reaction processes
over the wide energy region.
 Resonances appear in the cross sections as complicated interference.

 To disentangle the above complications and establish resonancemass spectrum, one must accomplish:
 Comprehensive partial-wave analysis (PWA) of various meson-production
reactions over the wide energy region using multichannel reaction framework.
 Multichannel reaction framework satisfying unitarity is indispensable forextracting the correct resonance information from data.

 This requires extensive and accurate data of various meson
production reactions that covers:
 Very wide energy and kinematical (angles, Q2,…) regions, both unpolarizaed and polarized observables.

Recent experimental and theoreticalefforts for N* and Δ* spectroscopyExperiments

Theoretical analyses
with multichannel framework

ANL-Osaka/EBAC-JLab
Bonn-Gatchina
Carnegie-Mellon-Berkeley
Dubna-Mainz-Taipei
Giessen
GWU/VPI
JuelichKarlsruhe-Helsinki…

JLab, ELSA, MAMI,GRAAL, SPring-8, ELPH,…

 Multichannel unitary condition:

ANL-Osaka DCC approach to N* and Δ*
Dynamical Coupled-Channels model [Matsuyama, Sato, Lee, Phys. Rep. 439(2007)193]

Coupled-channels effect Summing up all possible transitions between reaction channels !!
( satisfies two- and three-body unitarity)e.g.）πN scatteringπηπ＝NNVKπ

Λ

Δ＋＋N

 Momentum integral takes into account off-shell effects inthe intermediate processes.

＋ …

ANL-Osaka DCC approach to N* and Δ*
Dynamical Coupled-Channels model [Matsuyama, Sato, Lee, Phys. Rep. 439(2007)193]

Coupled-channels effectRegion our model can coverLatest published model for N* and Δ*:
HK, Nakamura, Lee, Sato, PRC88(2013)035209

Constructed by simultaneous analysis of- πN scattering (W < 2.3 GeV)
- πp  ηN, KΛ, KΣ (W < 2.1 GeV)
- γp  πN, ηN, KΛ, KΣ (W < 2.1 GeV)
γp reaction total cross sections in N* region~23,000 data points to analyzeANL-Osaka DCC approach to N* and Δ*
Dynamical Coupled-Channels model [Matsuyama, Sato, Lee, Phys. Rep. 439(2007)193]

Coupled-channels effectdσ/dΩ γ p  π0 p

1. Construct model(determine amplitudes)
by fitting data

3. Resonances are obtained as polesof amplitudes in complex energy
plane !!
mass & width = pole valuecoupling constants = (residue)1/2
at the pole

2. Analytic continuationof determined amplitudes
to complex energy plane !!
Suzuki et al (2009)

ANL-Osaka DCC approach to N* and Δ*
Dynamical Coupled-Channels model [Matsuyama, Sato, Lee, Phys. Rep. 439(2007)193]

Coupled-channels effect(Multichannel) unitarity isa key to making “correct”
analytic continuation !!
dσ/dΩ γ p  π0 p

1. Construct model(determine amplitudes)
by fitting data

3. Resonances are obtained as polesof amplitudes in complex energyplane !!
mass & width = pole value
coupling constants = (residue)1/2
at the pole

2. Analytic continuationof determined amplitudes
to complex energy plane !!
Suzuki et al (2009)Comparison of N* & Δ* spectrum
between multichannel analyses
HK, Nakamura, Lee, Sato, PRC88 (2013) 035209-2Im(MR)(“width”)

JP(L2I 2J)“N” resonance (I=1/2)

PDG: 4* & 3* states assigned by PDG2012
AO : ANL-Osaka (Ours, DCC)

JP(L2I 2J)

Re(MR)

MR : Resonancepole mass(complex)“Δ” resonance (I=3/2)

J : Juelich [DCC, πN reaction only, EPJA49(2013)44]
BG : Bonn-Gatchina [on-shell K-matrix, EPJA48(2012)5]

Comparison of N* & Δ* spectrum
between multichannel analyses
HK, Nakamura, Lee, Sato, PRC88 (2013) 035209
Spectrum for low-lying states with Re(MR) < 1.6 GeV
is now well established !!
(One exception is 2nd P33, Roper-like state of Δ)

JP(L2I 2J)“N” resonance (I=1/2)

PDG: 4* & 3* states assigned by PDG2012
AO : ANL-Osaka (Ours, DCC)

-2Im(MR)(“width”)

JP(L2I 2J)

Re(MR)

MR : Resonancepole mass(complex)“Δ” resonance (I=3/2)

J : Juelich [DCC, πN reaction only, EPJA49(2013)44]
BG : Bonn-Gatchina [on-shell K-matrix, EPJA48(2012)5]

What I expect of J-PARC for establishingN* spectrum
To tackle the spectrum of high-mass N* resonances(1.6 < MR < ~ 3 GeV), inelastic πN reaction data arehighly desirable:

πN  ππN, KΛ, KΣ, ηN, η’N, ωN, ΦN,…
Measurement ofπN  ππN, KY:
Hicks and Sako et al.,J-PARC E45 experiment
Expected to make asignificant impact onthe high-mass N*spectroscopy !!

Partial decay widths of N*HK, Nakamura,Lee, Sato, 2012

Current status of Y* spectroscopy(some points may be missed)

 Much less understood than N* and Δ* baryons.

 PDG(2012) lists only Y* mass spectrum defined by the“highly model-dependent” Breit-Wigner mass and width.

 Comprehensive & systematic PWA to extract
Y* resonances defined by poles of scattering amplitudes:
 KSU group (2013, on-shell K-matrix approach) Our group (2014, dynamical approach)Y* spectroscopy using anti-Kaon beam
 The simplest reactions for studying Y*.
K

Future goal:

KK, π, π, …
Λ*, Σ*

Λ*, Σ*
Ξ*B

 Deuteron reactions allow direct access to Λ(1405) region andstudy of YN and YY interactions.
Kπ, K(Noumi et al.,J-PARC E31) dY

KY+…
NdM

NN, Σ, Λ, …

NK+…

πYK

Y* spectroscopy using anti-Kaon beam
 The simplest reactions for studying Y*.
K

Future goal:KK, π, π, …
Λ*, Σ*K
Λ*, Σ*
Ξ*M

N
Diffractiveprocesses
with high-momentumpion beam:N, Σ, Λ,…

NB

high-p πK* (forward) Deuteron reactions allow direct access to Λ(1405) region andstudy of YN and YY interactions.
virtualK(Noumi et al.,J-PARC E31) dπ, KKpY+…
N

K, K*πYY*dπ(Noumi et al., J-PARC E50)

Σ, ΛY
K

can accessbelow KN
threshold+…

Y* spectroscopy using anti-Kaon beam
 The simplest reactions for studying Y*.
K

Future goal:KK, π, π, …
Λ*, Σ*K
Λ*, Σ*
Ξ*M

N
Diffractiveprocesseswith high-momentum
pion beam:N, Σ, Λ,…

N

B

high-p π

K* (forward) Deuteron reactions allow direct access to Λ(1405) region andstudy of YN and YY interactions.
virtualK(Noumi et al.,J-PARC E31) dπ, KKpY+…
NK, K*πYY*dπ(Noumi et al., J-PARC E50)

Σ, Λ

can accessbelow KN
threshold+…

YK

Most importantly, J-PARC can measure all of these reactions!!

What we have done so far
 Formulation of coupled-channels equations withKN, πΣ, πΛ, ηΛ, KΞ, πΣ*(ππΛ), K*N(πKN) channels
 Simultaneous analysis of all available polarized andunpolarized data of K-p  KN, πΣ, πΛ, ηΛ, KΞ fromthe threshold up to W = 2.1 GeV, by including
L = 0(S), 1(P), 2(D), 3(F) partial waves.
(HK, Nakamura, Lee, Sato, arXiv:1407.6839, to appear in PRC)

 Extraction of Λ* and Σ* mass spectrum defined bypoles of scattering amplitudes.
(HK, Nakamura, Lee, Sato, in preparation)

Database of our analysis (W < 2.1GeV)
Issues in the availability of data: Most data are from 60-70’s.
 Kinematical coverage is rathersparse for most reactions.

 No data for spin rotations (β, R, A).
 No data near the threshold forK- p  KN, πΣ, πΛ.

The K- p reaction data arefar from “complete”!!
 Need help of hadron
beam facilities such as
J-PARC !!

HK, Nakamura, Lee, Sato, arXiv:1407.6839 (with updates)
to appear in PRC
dσ/dΩ : 1465 MeV < W
P: 1730 MeV < W
β, R, A: No datadσ/dΩ : 1465 MeV < W
P: No dataβ, R, A: No datadσ/dΩ : 1535 MeV < WP: 1535 MeV < W < 1967 MeVβ, R, A: No datadσ/dΩ : 1535 MeV < W < 1763 MeV
P: 1535 MeV < W < 1696 MeVβ, R, A: No datadσ/dΩ : 1536 MeV < W
P: No dataβ, R, A: No datadσ/dΩ : 1535 MeV < W
P: 1535 MeV < W
β, R, A: No datadσ/dΩ : 1664 MeV < W < 1696 MeV
P: 1669 MeV < W < 1681 MeV
β, R, A: No datadσ/dΩ : 1970 MeV < W < 2070 MeV
P: No dataβ, R, A: No datadσ/dΩ : 1950 MeV < W < 2070 MeVP: No dataβ, R, A: No dataResults of the fits
K- p  MB total cross sections

HK, Nakamura, Lee, Sato, arXiv:1407.6839 (with updates)
to appear in PRC

Red: Model A
Blue: Model B“Incompleteness” ofthe current databaseallows us to have twoparameter sets thatgive similar qualityof the fit.

Results of the fits
K- p  K- p scatteringdσ/dΩ (1464 < W < 1831 MeV)

HK, Nakamura, Lee, Sato, arXiv:1407.6839 (with updates)
to appear in PRC

dσ/dΩ (1832 < W < 2100 MeV)P

Red: Model A Blue: Model B

What I expect of J-PARC for establishing
Y* spectrum
There is no doubt that K- p reactions are simplest
and most suitable for the Y* spectroscopy.
However, the kinematical coverage and accuracy of
K- p reaction data are still very much limited.
no data for spin-rotation observables (β, R, A),
no data near the KN threshold,…

J-PARC is a unique facility to overcome
this unsatisfactory situation !!

Back up

Extracted scattering lengths and effective
rangesHK, Nakamura, Lee, Sato, arXiv:1407.6839 (with updates)
to appear in PRC

 Visible model-dependency (sizable for some) is observed.
 This obviously reflects the lack of the data near the threshold !!

 Both models give almost the same value for a(K-p),a(K-p) = -0.65 + i0.74 fm for Model A & -0.65 + i0.76 fm for Model B,
which are consistent with recent extracted value in Ikeda et al
NPA881(2012)98, yet the isospin components give rather
different values between the two models.

P03 resonance just above the ηΛ threshold
HK, Nakamura, Lee, Sato, arXiv:1407.6839 (with updates)
to appear in PRC

 dσ/dΩ of K- p  ηΛ @W=1672 MeV (just 8 MeV above the threshold) Even in the region close to the threshold, dσ/dΩ shows a clear
angular dependence.
Model A

S-wave dominated Model Aseems not reproduce theangular distribution well.

Model B

Narrow P03 resonance (only seen in
Model B) seems important for angulardependence. (If it is turned off, dσ/dΩ
becomes dotted curve.)Predicted πΣ scattering total cross section at
low energies
HK, Nakamura, Lee, Sato, arXiv:1407.6839 (with updates)
to appear in PRC

 Predicted total cross sections of πΣ scatterings fromthe threshold up to W = 1.55 GeV
Model A Full
Model A S-wave only

KN threshold

Model B Full
Model B S-wave only

Contribution fromhigher partial waves
can be sizable alreadybelow the KN threshold !!
πΣthreshold

Comparison of extracted partial-wave
amplitudes
Extracted KN scattering amplitudes

Red : Model A
Blue: Model B
Circles: KSU single-energy solution[PRC88(2013)035204]

HK, Nakamura, Lee, Sato, arXiv:1407.6839 (with updates)
to appear in PRC

Why DCC approach ??
Suzuki, Julia-Diaz, HK, Lee, Matsuyama, Sato PRL104 065203 (2010)
Corresponds to N* instatic hadron models(quark models etc)

Two-pole structure of
the Roper resonance:
Roper et al. PRD32(1985)1085
Cutkosky et al. PRD42(1990)235
Arndt et al. PRC74(2006)045205
Doering et al. NPA829(2009)170

Dynamical origin ofP11(I=1/2, JP = 1/2+) N* resonances

Corresponds toN(1710) 1/2+

 Coupling to reaction channels can produce a sizable mass shift.

 Multichannel reaction dynamics can give rise to many physicalresonances from a single bare state.

Λ(1/2-) resonance near the ηΛ thresholdΛ(1/2-) pole at1669 – i9 MeV (Model A)(would correspond to Λ(1670)
in PDG) K- p  ηΛ data make the existence of
this Λ(1/2-) stable and model-independent.

ηΛIm(W)ηΛ
physicalsheet Next higher excited states of Λ(1405).

ηΛunphysicalsheet

Re(W) Dip at W ~ 1670 MeV seen in K- p  MB
total cross sections is produced by this Λ(1/2-).
[ηΛ cusp effect is hindered by the large
contribution from Λ(1/2-).]ηΛ cut (rotated from real W axis)

Sharp peak near thresholdrequires the existence ofΛ(1/2-) resonance.

Peak due to 1st Λ(3/2-)[known as Λ(1520)]

Dip due to Λ(1/2-)
near ηΛ threshold

Predicted spin-rotation angle βHK, Nakamura, Lee, Sato, arXiv:1407.6839 (with updates)
to appear in PRC
Model dependence is clearlyseen in observables not yetmeasured.
Measurement of suchobservables will give strong
constraints on the Y*
spectrum !!

Red: Model A
Blue: Model B
Black: KSU
The KSU results arecomputed by us using
their amplitudes in
PRC88(2013)035204.

## NOTE:β is modulo 2π

How do we access the region
below KN threshold with J-PARC?
 Deuteron-target reactions:πK

 Diffractive processes withhigh-momentum (pion) beam:
K* (forward)

high-p πΣ, ΛvirtualK, K*dN+…

See recent talk by Sang-Ho Kim@ Tohoku ELPH Workshop
http://www.lns.tohoku.ac.jp/workshop/c009/slides/
SanghoKim_ELPH-2014-11-04.pdf

πp

Y*
Σ, Λ

(Noumi et al., J-PARC E31)

(Noumi et al., J-PARC E50)

We DO have off-shell KN  MB and K*N  MB amplitudes
not only for S wave but also for P, D, and F waves !!

Polarization observables forspin-0 + spin-1/2  spin-0 + spin-1/2 reactions
e.g.) πN scattering (in c.m. frame)yxπz

Wolfenstein, Phys. Rev. 96(1954)1654
Kelly, Sandusky, Cutkosky, PRD10(1974)2309
Saxon, Whittaker, Z. Phys. C9(1981)35
Supek et al., PRD47(1993)1762

yxz

N

Suppose target nucleon polarization points z-axis( parallel to pion momentum):Polarization of the recoil nucleon is then expressed as

Note: Various conventions are taken for β, R, A in literatures.

Dynamical coupled-channels (DCC) model formeson production reactions
For details see Matsuyama, Sato, Lee, Phys. Rep. 439 (2007)193
HK, Nakamura, Lee, Sato, PRC88 (2013) 035209

 Partial wave (LSJ) amplitudes of a  b reaction:

coupled-channels effect Reaction channels:

 Transition Potentials:

Exchange potentials

Z-diagrams

bare N* states

Dynamical coupled-channels (DCC) model formeson production reactions
For details see Matsuyama, Sato, Lee, Phys. Rep. 439 (2007)193
HK, Nakamura, Lee, Sato, PRC88 (2013) 035209

 Partial wave (LSJ) amplitudes of a  b reaction:

coupled-channels effect Reaction channels:

 Meson-Baryon Green functions

Quasi 2-body channels

Stable channels
 Transition Potentials:

NDpDr, spp
Exchange potentials

ppZ-diagramsr, sN

Nbare N* states

Dynamical coupled-channels (DCC) model formeson production reactions
For details see Matsuyama, Sato, Lee, Phys. Rep. 439 (2007)193
HK, Nakamura, Lee, Sato, PRC88 (2013) 035209

 Partial wave (LSJ) amplitudes of a  b reaction:

coupled-channels effect Reaction channels:

Would be related with hadron states of thestatic hadron models (quark models, DSE,etc.) excluding meson-baryon continuums.
 Transition Potentials:

Exchange potentials

Z-diagrams

bare N* states

Dynamical coupled-channels (DCC) model formeson production reactions
For details see Matsuyama, Sato, Lee, Phys. Rep. 439 (2007)193
HK, Nakamura, Lee, Sato, PRC88 (2013) 035209

 Partial wave (LSJ) amplitudes of a  b reaction:

Physical N*s will be a “mixture” of the two pictures:
coupled-channels effectbaryonmeson cloud Reaction channels:
coremeson Transition Potentials:

Exchange potentials

Z-diagrams

bare N* states