(1405)L の光発生反応

中村　聡　（阪大理）

共同研究者：　慈道　大介 ( 首都大）

Prog. Theor. Exp. Phys. (2014) 023D01

Introduction(1405) : L 1st excited state of L

EpS K N

_

1330 1430

(MeV)

(1405, -25)(1405) L

* Existence “predicted” by Dalitz and Tuan (1960)

in analysis of KN scattering length with - KN pS model

* First experimental evidence in K -p pppS (1961)

_ _

Alston et al., PRL 6 (1961)

K -p pppS

Controversial (1405) L structure

• 3-quark + mass splitting term Collins & Georgi, PRD 59 (1999) Schat et al., PRL 88 (2002)

• 5-quark Strottman, PRD 20 (1979) Zou, NPA 835 (2010) too many states

• Meson-baryon molecule Dalitz & Tuan, PRL 2 (1959) Oset & Ramos, NPA 635 (1998)

Too light to interpret as naïve 3-quark state

(i,j,k : meson-baryon channel)

(1405) L as pole of Scattering amplitude

Coupled-channel scattering equation for T-matrix (scattering amplitude)

Near pole position :

T-matrix for real energy W is used to calculate observables (cross sections, etc.)

Analytic continuation to complex energy W

Resonance is identified by : mass width

Resonance pole can be extracted from analyzing data

Why want to know (1405) L pole(s) ?

• Internal structure of (1405)L

constraint on hadron structure models

• Nuclear structure of deeply bound kaonic nuclei (e.g., K-pp )

K-p - pS amplitude is essential input

current status for K-pp : rather large model dependence

B.E. = 10 – 100 MeV, Width = 35 – 110 MeV

Pole structure of (1405)L

• Two-pole

cloudy bag model Veit et al. PRD 31, 1033 (1985)

chiral unitary model Jido et al. NPA 725, 181 (2002)

• Single-pole

potential models Fink et al., PRC 41, 2720 (1990)

Akaishi-Yamazaki model PRC 65, 044005 (2002)

Still, pole structure has not been established

Attempt to determine (1405) L pole from data

EpS K N

_

1330 1430(MeV)

(1405, -25)(1405) L

Ideal experiment p S p S Impossible !

N

K+

S

p

, g p

} Energy at (1405) L

Two-meson production experiment

difficulty in determining (1405) L pole structure

How to extract (1405)L pole from two-meson production data

• Construct a model that consists of production mechanism + final state interaction (FSI)

• FSI contains MB p S amplitude

• Fit data with adjustable parameters in production mechanism and MB p S amplitude

• Extract poles from MB p S amplitude

But, good data had not been available until recently

Photo-production of (1405)L

• LEPS/Spring-8 Ahn et al., NPA 721, 715 (2003)

• LEPS/Spring-8 Niiyama et al., PRC 78, 035202 (2008)

• CLAS/JLab Moriya et al., PRC 87, 035206 (2013) ( p S invariant mass distribution) PRC 88, 045201 (2013) (K+ angular distribution)

g p K+ L(1405) K+ p S

Experiments

p S line-shape data from CLAS/JLab g p K+ L(1405) K+ p S

Moriya et al., PRC 87, 035206 (2013)

Cleanest data for L(1405) progress toward pole extraction

What to do here ?

• Production mechanism + s-wave rescattering

• Gauge invariance at tree level

• Fit data

Develop cUM-based model for g p K+ p S

MODEL

• Chiral unitary model

• Photo-production mechanism

Chiral Unitary Model (cUM)

: Weinberg-Tomozawa interaction

Coupled-channel scattering equationOset & Ramos, NPA (1998)Oset et al., PLB (2002)

Chiral Unitary Model (cUM)

On-shell factorization

(m : renormalization scale )

(W : total energy)

Dimensional regularization

_

Subtraction constant, fitted to data

Chiral Unitary Model (cUM)

Good description of K-p K N, pS, pL data above and near K-p threshold_

Chiral Unitary Model (cUM)

pole position 1390 - 66i 1426 - 16i

pS 2.9 1.5

KN 2.1 2.7-Coupling strength

Jido et al. NPA 725, 181 (2002)Two-pole structure

Photo-production Model

Minimal substitution

Photo-production Model

Minimal substitution

Photo-production Model

Minimal substitution

Photo-production Model

Photo-production Model

Rescattering

cUM s-wave amplitude ( (1405) )L

Fit data• Subtraction constants (10 parameters)

• contact production mechanism (30 parameters) (total energy (W) dependent complex couplings, gauge invariant)

• Form factors (1 parameters)

* Good description of line-shape data

* Different peak position for different charge states

Two-pole structure plays a role ??

Results

Resonant and non-resonant contributions

Non-resonant Resonant

Resonant and non-resonant contributions

* Significant non-resonant contribution

Shifting peak positions

• Same resonance peak position

2nd pole (1426 – 16i) seems dominant

Single-pole model works as well ??

Isospin decomposition

• I=0 ( (1405)) L dominance

• Small but nonnegligible effect of I=2 contribution

Single Breit-Wigner model

Single Breit-Wigner model works !1 pole solution is still not excluded

K+ angular distribution

Moriya et al, PRC 88, 045201 (2013)

New data from CLAS/JLab

for g p K+ p S

Fitting only lineshape very different angular distributions is still possible

K+ angle data are important to constrain production mechanism

K+ angular distribution (not fitted)

Overall trend is captured in our model More fit will be done L(1405) pole structure will be extracted

Summary

• Pole structure of L(1405) has not been well confirmed by data

• New CLAS data for g p K+ p S ; cleanest data in L(1405)

region

hope to extract L(1405) pole structure

• g p K+ p S model is developed with cUM amplitude

-- meson-exchange + contact production mechanism

(gauge invariant @ tree level)

-- Line-shape data are well fitted

-- Single Breit-Wigner model also can fit line-shape data

Future work• Fit K+ angle data from CLAS

cUM amplitude (subtraction constant) is also varied

extraction of L(1405) pole structure

• Use different contact interactions, form factors

study model dependence of extracted poles

Future work

One- or two-pole structure ?

Very new data from CLAS (yesterday) for electroproduction of L(1405) PRC 88, 045202 (2013)

1.6 (GeV/c)2 < Q2 < 3.0 (GeV/c)2

Fairly clear two peaks ! two-pole solution ?

Higher statistics data hoped !

Possible ideas for (1405)L 　 photoproduction experiments at ELPH, LEPS, LEPS2

Data wanted for less model-dependent determination of (1405) L properties

• Double-differential cross sections

• Polarization observable

• Multi-channel data

• K*, S*(1385) unsubtracted data (cf. CLAS data)

gp K+ p S K+ K N K+ p L …

-

Backups

• p- p K0 (1405) L K0 p S Thomas et al., NPB 56, 15 (1973)

• K- p p0 (1405) L p0 p0 S0 Crystall Ball, PRC 70, 034605 (2004)

• K- d n (1405) L n p S J-PARC proposal

Attempt to determine pole structure of (1405)L

Hadron beam experiments

Confront theory with data below KN threshold

cUM-based calculation for p- p K0 p SHyodo et al., PRC 68, 065203 (2003)

…

p-

p

K0

Data: Thomas et al., NPB (1973)

cUM-based calculation for K- p p0 p0 S0 Magas et al., PRL 95, 052301 (2005)

+

Data: Crystall Ball, PRC (2004) the peak is due to second pole

d /sd

MI (

arbi

trar

y sc

ale)

K+ angular distribution

Moriya et al, arXiv:1305.6776

Very new data from CLAS/JLab

for g p K+ p S

LEPS/SPring8 dataForward K+ kinematics of g p K+ Y*

• LEPS and CLAS data are consistent at low energies• No LEPS data for normalized line shape for g p K+ p S

We analyze only CLAS data

Comparison with CLAS data for g p K+ Y*

Niiyama et al., PRC (2008)

• CLAS• LEPS

(Moriya et al, arXiv:1305.6776)

Lagrangians

Hidden local symmetry model

fixed by V gM decay width; relative phase by SU(3)

Tensor coupling

SU(3) relation for magnetic coupling

Nacher et al., PLB 455, 55 (1999)

Niiyama et al., PRC (2008)Nacher et al., PLB (1999)

Calculated line shape is :

• Wrong in ordering p-S+ and p+S-

• Too small cross section ?

P-wave scattering model (cUM)

+ (relativistic correction to WT term)

Jido et al., PRC 66, 055203 (2002)

Is (1405) L exotic ?

Naïve 3-quark picture is not likely

Nucleon (1/2+)

940 MeVN(1535) (1/2- )

1535 MeV

L (1/2+)

1116 MeVL(1405) (1/2- )1405 MeV

Radial excitation to L=1 costs ~ 600 MeV

~ 300 MeV

cUM-based calculation for g p K+ p S

Nacher et al., PLB 455, 55 (1999)

W=2.02 GeV

(1405) L in Lattice QCD

Quench 3-quark ~ 1.7 GeV Nemoto et al., PRD (2003)

Quench 5-quark ~ 1.89 GeV Ishii et al., PTP (2007)

Full 3-quark ~ 1.6 GeV Takahashi et al., PRD (2010)

Full 3-quark ~ 1.45 GeV Menadue et al., PRL (2012) (variational analysis)

operator M (1405)L

cUM-based calculation for g p K+ p S

Nacher et al., PLB 455, 55 (1999)

Contact photo-production (WT term) + s-wave cUM rescattering

Nacher et al., PLB (1999)W=2.02 GeV

Comparison with CLAS data

K. Moriya et al. PRC (2013)

Calculated line-shape is :• wrong in ordering

p-S+ and p+S-

• Overestimate in magnitude

Contributions from mechanisms

• Small contribution from WT

interference changed by subtraction const.• Large contribution from contact terms

short-range dynamics play important role