DN and N interactions with the Jülich meson-exchange...

DN and K N interactions with the Jülichmeson-exchange model

Johann Haidenbauer

IAS & JCHP, Forschungszentrum Jülich, Germany

ELPH Workshop C013, Sendai, September 12-14, 2015

Johann Haidenbauer DN and K N interactions

Outline

1 Introduction

2 The Jülich model

3 K N Results

4 DN Results

5 Summary


Introduction

Λ(1405) S01 resonance⇔ K N threshold ≈ 1435 MeV

χPT + unitarization:

dynamically generated Λ(1405)

two-pole structure of the Λ(1405)

N. Kaiser, P.B. Siegel, W. Weise, Nucl. Phys. A 594 (1995) 325E. Oset and A. Ramos, Nucl. Phys. A 635 (1998) 99J. A. Oller and U.-G. Meißner, Phys. Lett. B 500 (2001) 263M.F.M. Lutz and E.E. Kolomeitsev, Nucl. Phys. A 700 (2002) 193C. Garcia-Recio, J. Nieves, E. Ruiz Arriola, and M. J. Vicente Vacas, Phys. Rev. D 67 (2003) 076009D. Jido, J. A. Oller, E. Oset, A. Ramos, and U.-G. Meißner, Nucl. Phys. A 725 (2003) 181J.A. Oller, J. Prades, and M. Verbeni, Phys. Rev. Lett. 95 (2005) 172502B. Borasoy, U.-G. Meißner, and R. Nißler, Phys. Rev. C 74 (2006) 055201

...

What about other approaches?meson exchange→ Jülich K N modelA. Müller-Groehling, K. Holinde, J. Speth, Nucl. Phys. A 513 (1990) 557


The Jülich K N model

K N - πΛ - πΣ coupled channel model

T = V + TG0V

V =

VK N VK N←πΛ VK N←πΣ

VπΛ←K N VπΛ VπΛ←πΣ

VπΣ←K N VπΣ←πΛ VπΣ

; G0 =

G0,K N 0 00 G0,πΛ 00 0 G0,πΣ

σ,ρ

K N

K N

y y N

K N

Λ π

y y ←W K ΛN = ΓK ΛN gK ΛN F K ΛN(~q2K )

F K ΛN(~q2K ) =

Λ2K ΛN −m2

K

Λ2K ΛN + ~q2

K

gK ΛN , ΛK ΛN ... fixed from SU(3) and YN; gρNN , ΛρNN , ... fixed from NN

gρK K , ... fixed from decay width ρ→ ππ + SU(3)

gσK K , ΛσK K , ... free parameters – and there is a σrep !


K N and K N

K N and K N are connected via G-parity(G-parity: Charge conjugation plus 180o rotation around the y axis in isospin space)

⇒

VK N( ω) = −VK N( ω) − odd G− parity

VK N(σ, ρ) = +VK N(σ, ρ) − even G− parity

R. Büttgen et al., ZPC 46 (1990) S167:

K N data (S-waves) require a stronger repulsion than generated by ωexchange with a SU(3) ωNN (ωK K ) coupling constant

K N data (S-waves) require a shorter ranged repulsion than generatedby ω exchange

K N and K N data cannot be described simultaneously with the same ωexchange (fixed by G-parity)

⇒ A phenomenological short-ranged repulsion was introduced (mσrep ≈ 1.2GeV) with different coupling constants for K N and K N


Number of channels

How many channels (and which ones) should be taken into account?

chiral unitary approaches:all channels involving members of the SU(3) pseudo-scalar octet andthe SU(3) JP = (1/2)+ baryon octet:(πΛ, πΣ, K N, ηΛ, ηΣ, K Ξ)

Jülich meson-exchange model:all channels that are already open at the K N threshold:→ πΛ, πΣchannels that contribute significantly to the K N inelasticities:→ K ∆, K ∗N, K ∗∆

Missing in both approaches:ππΛ ≈ σΛ, ρΛ


Kinematics

1200 1300 1400 1500 1600 1700 1800

s(1/2)

[MeV]

ππΛ ηΛΚΝπΣπΛ ΚΞK

*N

ηΣΚ∆

ΚΝπ


Contributions to K N in the Jülich model

ρ, ω

K N

K N

u u σ, σrep

K N

K N

u u Λ, Σ

K N

K N

uu

K N

K N

K∗ N

π, ρ

π, ρ

u uu u

K N

K N

K∗ ∆

π, ρ

π, ρ

u uu u

K N

K N

K ∆

ρ

ρ

u uu u

K∗

π Λ,Σ

K N

u uπ Λ,Σ

N

K N

uu

Σ [Λ]

K N

π Λ,Σ

uu

ρ

π Σ

π Λ

u u ρ

π

Σπ

Σ

u u


Jülich K N model

later developements:

• 1995: σ is replaced by correlated ππ − K K exchangeA new K N model is presented(M. Hoffmann et al., NPA 593 (1995) 341)

• 2002: a modified Jülich K N model is published(D. Hadjimichef, J.H., G. Krein, PRC 66 (2002) 055214)

The “σrep” of the original Jülich modelcan be explained (replaced) by genuine quark-gluon exchangeprocesses ( + a0(980) exchange)A comparable if not better description of the K N phase shifts anddata can be achieved.

• 2007-11: Extension of the Jülich K N model to DN and DN underthe assumption of SU(4) symmetry

However, no activity with regard to the K N interaction since 1990!


Jülich meson-exchange K N model580 A. Miiller-Groeling et al. / K-N interaction

60

50

40

30

-ioo ’ 140 * rtio , 2io * 260 ' 300 Plab (t&V/c)

. 1975

180 220 260 300 Plab (MeV/c)

20

10

0 60 80 120 160 200 240 280

Plab (MeV/c)

lo-

::o Plab (MeV/c)

230

E -25

&O .$

15

IO

5

o! I I , , , , ( , , J 100 140 180 220 260 300

Plab (MeV/c)

,120

9,oo

i a0

?z 60

0

60 80 120 160 200 240 280 Plab (MN/c)

Fig. 5. Total cross sections in six different particle channefs as predicted by model II which, in addition

to model I, contains a pole graph motivated by A(1670).

g,_ = -12.5 suggested from interpreting the short-ranged repulsion in the KN system as consisting entirely of contributions with negative G-parity.

Finally, fig. 6 demonstrates that model II predicts essentially the same mass spectrum for A (1405).

Thus the conclusion obtained before about the nature of the A(1405), as well as our arguments concerning the short-ranged part of the interaction, remain unchanged.

A. Müller-Groeling al.,NPA 513 (1990) 557K−p → K−p

K−p → K 0n

K−p → π0Λ

K−p → π0Σ0

K−p → π−Σ+

K−p → π+Σ−


Jülich meson-exchange K N model

358 M.Hoffmann et al./Nuclear Physics A 593 (1995) 341-361

2.5

2.0-

.Q

E 1.5- I - , - ]

C 1.o. I0

b 0.5- "o

0.0

p,o, : 6~8 ,ievl~ K+p

'11 - I

-(;.5 ; 0:5 cos'@

2.5

2.0 •

aQ

1.5.

~.~ 1.0.

b 0.5

0.0 -I -).5

p,,~: 7:48 ,~vl~ K+p

I I ../'':

6 0:5 COS~

2.5 2.5

p,= = 9~2 M~v/i K+p ~ 2.o. ~ 2.0.

E 1.5. E 1.5

C 1.o. ~ 1.o.

b 0.5. b 0.5. "o "o

0.0 0.0 - -6.5 6 0:5 - -6.5 6 0:5

COS't~ COS ~,~

Fig. 9. The same as in Fig. 7 for K+p differential cross sections. Experimental data are taken from Ref. [ 18],

2.0 - 2.0

p,., : 6~o Ni.vl£ K+n r-c p,,,,, = 7)0 MeV/c K+n .~.,.5- <1.5- ..Cl c~ E E

IJ-I C C ! ~

I I "~-o.5 r~.;~.!.~!ri..h.:_,3'.iT.l.£...~ ~.o.~.L I _ . L ...... . .............. ~ :'i'""'"Ti-ll'" "

o.o o,oi - -6:5 6 0:5 - -E5 ~ 0:5

COS'~l COS~

p,.~ : 969 "evl; K+p

I

2.0 p,°~ = 7i3o ,,ieV/,~ K + n

1.0. !

"~0.5. "O

0.0 - - ; .5 ; 0:5

COS~ll

.o E

L J 1 . O. C

"~0 .5 . "o

0.0

Fig. 10. The same as in Fig. 7 for K+n differential cross sections.

p,.,. = a~o M~vl; K+n

t : : 1 ..... .....

-~.5 b o'.5 COS't9

Experimental data are taken from Ref. [ 19].

M. Hoffmann et al., NPA 593 (1995) 341


Jülich meson-exchange K N model

M.Hoffmann et al./Nuclear Physics A 593 (1995) 341-361 359

1.0

0.8 E

o_O '6 o.6. N

"E o 0.4. -5

0.2.

0.0.

P,o, = 6~so M~V/c K+p

-;.s 6 o:s COS't9

1.0

0 . 8 - E O

"~ 0.6- N

0 0 . 4 -8 13_

0.2

0.0,

p,.~ = 81~s M.Vlc K+p

-Es ~ 0:5 COS,dl

0.5

E 0.0- ,0

.~-0,5- o

i t _ 1.0-

- 1 . 5

-1 -0 .5

p,.= 8~I M~VI~ K+n

o:s COS'~

0.5

E 0.0. 0

.~-0.5. 0 -5 a---1. O.

--1.5 - -().5

P,*b = 9;55 M e V / c K+n

6 o'.s CO$-,dl

Fig. 11. The same as in Fig. 7 for K+p and K+n polarizations. Experimental data are taken from Ref. [20]

(K~p) and Ref. 1211 (K+n).

5. Summary

In this paper we have presented a microscopic model for correlated 27r (and KK) exchange between kaon and nucleon, in the scalar-isoscalar (tr) and vector-isovector (p) channels. We first constructed a model for the reaction NI~I --+ K [ ( with intermediate 2~r and KK states, based on a transition in terms of baryon (N, A, A, ~:) exchange and a realistic coupled channel 7rTr ~ 7rTr, 7rTr --+ KK and KK --+ KK amplitude. The contribution in the s-channel is then obtained by performing a dispersion relation over the unitarity cut.

In the o--channel, the result can be suitably represented by an exchange of a scalar

Table 3 Low energy parameters

a° s [fm] a lls [fm] r~s [fm]

Experiment a 0.03 4- 0.15 -0 .30 -4- 0.03 0.43:1:0.22 Model I 0.057 -0.316 0.373 Model I1 A 0.038 -0.304 0.261 Model 1I B -0.080 -0.333 0.130

a Empirical data are taken from Refs. [22,23].

M. Hoffmann et al., NPA 593 (1995) 341


K N Observables

Threshold ratios of the K−p systemR.J. Nowak et al., NPB 139 (1978) 61

γ =Γ(K−p → π+Σ−)

Γ(K−p → π−Σ+)

Rc =Γ(K−p → charged particles)

Γ(K−p → all)

Rn =Γ(K−p → π0Λ)

Γ(K−p → all neutral states)

Strong-interaction energy shift ∆E and the width Γ of the 1s level ofkaonic hydrogen - using the modified Deser-Trueman formula:

∆E − i2

Γ = −2α3µ2K NaK−p[1− 2αµK N(lnα− 1)aK−p]

→ JH, Krein, Meißner, Tolos, EPJA 47 (2011) 18


K N results for the Jülich model

Jülich model experimentscattering lengths [fm]

aI=0 −1.21 + i 1.18aI=1 1.01 + i 0.73aK−p (I) −0.10 + i 0.96aK−p −0.36 + i 1.15 -0.65±0.10 + i 0.81±0.15

kaonic hydrogen∆E 217 eV 323±63±11 eV [KEK]

283±36±6 eV [SIDDHARTA]Γ 849 eV 407±208±100 eV [KEK]

541±89±22 eV [SIDDHARTA]threshold ratios

γ 2.30 2.36±0.04 [Nowak]Rc 0.65 0.664±0.011 [Nowak]Rn 0.22 0.189±0.015 [Nowak]

pole positions [MeV]S01 1435.8 - i 25.6 1405.1±1.3 - i 25±1 [PDG]S01 1334.3 - i 62.3


Pole positions

poles interaction1334 - i 62 1436 - i 26 Jülich1381 - i 81 1424 - i 26 IHW1355 - i 86 1418 - i 44 CS NLO301467 - i 75 1428 - i 8 MM1436 - i 126 1417 - i 24 GO Fit I1388 - i 114 1421 - i 19 GO Fit II1352 - i 48 1419 - i 29 RO γp → K +πΣ

1330 - i 56 1434 - i 10 MM [2015] γp → K +πΣ (#2)

1390 - i 66 1426 - i 16 1680 - i 20 OR LO1379 - i 27 1434 - i 11 1692 - i 14 OM LO+B1321 - i 44 1402 - i 40 OPV A+

4 (full)1361 - i 30 1433 - i 32 OPV B+

4 (full)

IHW: Ikeda, Hyodo, Weise - 2011; CS: Cieply, Smekal - 2012

MM: Mai, Meißner - 2013,15; GO: Guo, Oller - 2013; RO: Roca, Oset - 2015

OR: Oset, Ramos - 1998; OM: Oller, Meißner - 2001

OPV: Oller, Prades, Verbeni - 2005


πΣ invariant mass distribution

is usually calculated from

dσdmπΣ

= N · |TπΣ→πΣ|2 qπΣ

utilizing just the isospin I = 0 amplitude.but for a realistic comparison

dσdmπΣ

= |∑

X=K N,πΛ,πΣ

NX · TX→πΣ|2 qπΣ

and πΣ = π+Σ−, π0Σ0, or π−Σ+

→ I = 1 amplitude contributes with different weight, e.g.

TpK−→Σ+π− =12

T 1NK→Σπ +

1√6

T 0NK→Σπ

TpK−→Σ0π0 = − 1√6

T 0NK→Σπ

TpK−→Σ−π+ = −12

T 1NK→Σπ +

1√6

T 0NK→Σπ


πΣ versus ππ phase shift

1320 1360 1400 1440s

1/2 (MeV)

0

50

100

150

200

250

300δ

(de

gree

s)

JülichOset-Ramos

πΣ (S01)

TπΣ(q) = − exp(iδ(q)) sin(δ(q))/q

|TπΣ|2 · q = sin2(δ(q))/q

300 600 900 1200s

1/2 (MeV)

0

50

100

150

200

250

300

δ (d

egre

es)

Jülich model

ππ (S00)

<-- f0(980)

<-- "σ(500)"


Invariant mass distributions

1320 1360 1400 1440s

1/2 (MeV)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

|T|2 q

(a.u

.)

π−Σ+

π0Σ0

π+Σ−

πΣ −> πΣ

1320 1360 1400 1440s

1/2 (MeV)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

|T|2 q

(a.u

.)

K-p -> π−Σ+

K-p -> π0Σ0

K-p -> π+Σ−

KN -> πΣ

R.J. Hemingway (1985): M(Σ−π+), M(Σ+π−)


πΣ scattering length

T. Hyodo at Strangeness in Nuclei, Trento, October 2010:(Y. Ikeda et al., Prog. Theor. Phys. 125 (2011) 1205)

Information on the strength of the πΣ interaction (scattering length) would providefurther constraints for

• existence of deeply bound K states• sub-threshold K N amplitude→ possible determination of aπΣ from precise data of the πΣ spectrum(CLAS, ELSA, HADES, COSY, ...)

Oset- Y. Ikeda et al. Jülich

Ramos A2 B E-dep B E-indep

pole 1 1426 - i 16 1425 - i 11 1422 - i 22 1423 - i 29 1435 - i 26

pole 2 1390 - i 66 1321 1349 - i 54 1325 1334 - i 62

aπΣ [fm] 0.789 -2.30 1.44 5.50 1.69

aK N [fm] -1.65+i 0.89 -1.70+i 0.68 -1.70+i 0.68 -1.70+i 0.68 -1.21+i 1.18


The DN and DN interactions

theoretical studies of the DN and DN interaction

effective SU(4) hadronic Lagrangian; based on ρ exchange;Born approximationZ.-W. Lin et al., PRC 61 (2000) 024904

phenomenological (separable) coupled-channels model (for DNsystem)L. Tolós et al., PRC 70 (2004) 025203

chiral Lagrangians; unitarizationM.F.M. Lutz & E.E. Kolomeitsev, NPA 730 (2004) 110

J. Hofmann & M.F.M. Lutz, NPA 763 (2005) 90

T. Mizutani & A. Ramos, PRC 74 (2006) 065201

L. Tolós et al., PRC 77 (2008) 015207

C. Garcia-Recio et al., PRD 79 (2009) 054004

W.H. Liang et al., EPJA 51 (2015) 16


Kinematics

1200 1300 1400 1500 1600 1700 1800

s(1/2)

[MeV]

ππΛ ηΛΚΝπΣπΛ ΚΞK

*N

ηΣΚ∆

ΚΝπ

2400 2500 2600 2700 2800 2900 3000

s(1/2)

[MeV]

ππΛc ηΛcDNπΣcπΛc ΚΞcD*N

ηΣc


K N → DN (K N → DN)

Mesonic sector: working hypothesis SU(4) symmetry

gDDρ = gDDρ = gK KρgDDω = −gDDω = gK Kω

scalar mesons (S=σ, ao): member of a SU(3) multiplet ?what is the σrep?in the Jülich model: gDDS (gK K S) ∼= correlated ππ/K K /DD exchange

K N

K N

K∗π π

π π

T

K N

K N

ρ

K π

K π

T

D N

D N

D∗π π

π π

T

(a) (b) (c)

in practice: fix coupling constants of scalar mesons by a fit to data⇒ fine-tune coupling constants of scalar mesons to the mass of Λc (2595)


K N → DN (K N → DN)

form factors at the meson-meson-meson vertices are taken over fromK N (K N)

most baryon-baryon-meson vertices are the same as in K N (K N)!⇒ take over coupling constants and form factors

for vertices involving Λc and/or Σc SU(4) is invoked

• K N and K N (DN and DN) connected by G-parity


Dynamics

ρ, ω

D N

D N

σ, ao

D N

D N

Λc, Σc

D N

D N

D N

D N

D∗ N

π, ρ

π, ρ

D N

D N

D∗ ∆

π, ρ

π, ρ

D N

D N

D ∆

ρ

ρ

D∗

π Λc,Σc

D N

π Λc,Σc

N

D N

Σc [Λc]

D N

π Λc,Σc

ρ

π Σc

π Λc

ρ

π

Σcπ

Σc

Σc [Λc]

π Λc,Σc

π Λc,Σc


The DN channel

Jülich K N model: those channels that are open at the K N thresholdare taken into account

• model predicts the Λ(1405) to be a quasibound K N state!

DN:include likewise the coupling to those channels that are open atthreshold→ πΛc(2285) and πΣc (2455)

• model generates quasibound DN states in S01, S11 and P01 partialwaves (LI 2J )

⇒ identify S01 state with Λc(2595), and S11 state with Σc(2800)(fine tuning is needed to reproduce masses quantitatively!)

P01 state→ Λc(2765) ?


Scattering lengths

meson-exchange model SU(4) WT DN model(∗)

scattering lengths [fm]

aI=0 −0.41 + i 0.04 −0.57 + i 0.001

aI=1 −2.07 + i 0.57 −1.47 + i 0.65

pole positions [MeV]

S01 2593.9 - i 2.88 2595.4 - i 1.0

S01 2603.2 - i 63.1 2625.4 - i 51.5

S01 2799.5 - i 0.0

S11 2797.3 - i 5.86 2661.2 - i 18.2

S11 2694.7 - i 76.5

P01 2804.4 - i 2.04

(∗) T. Mizutani, A. Ramos, PRC 74 (2006) 065201

PDG: 2592.25± 0.28 MeV, Γ/2 = 1.3± 0.3 MeV; (Σ++c ) 2801± 4 MeV, Γ/2 ≈ 37.5± 10 MeV


Cross sections

0 25 50 75 100 125 150

s1/2

-mN-mD (MeV)

0

100

200

300

400

500

σ tot (

mb)

I=0

0 25 50 75 100 125 150

s1/2

-mN-mD (MeV)

0

100

200

300

400

500

σ tot (

mb)

I=1

—– Jülich DN model- - - WT SU(4) - Mizutani, Ramos· · · Jülich K N model


Results for DN

a) D0n→ D0n (– –)b) D0p → D0p (—)c) D0p → D+n (·−)


Invariant mass distributions

2580 2590 2600 2610s

1/2 (MeV)

0

1

2

3

4|T

|2 q (

a.u.

)

π−Σ++

π0Σ+

π+Σ0

πΣc -> πΣc

2580 2590 2600 2610s

1/2 (MeV)

0

1

2

3

4

|T|2 q

(a.

u.)

D0p -> π−Σc

++

D0p -> π0Σc

+

D0p -> π+Σc

0

DN -> πΣc

H. Albrecht et al., PLB 402 (1996) 207 (open squares); J. Zheng, PhD thesis (1999) (filled circles)


S01 Phase shifts

1320 1360 1400 1440s

1/2 (MeV)

0

20

40

60

80

100

120

140

160

180

200

220

240

δ (

degr

ees)

πΣ

2600 2620 2640 2660s

1/2 (MeV)

0

20

40

60

80

100

120

140

160

180

200

220

240

δ (

degr

ees)

πΣc

—– Jülich DN model; - - - WT SU(4) - Mizutani, Ramos


Summary

Jülich meson-exchange potential for K N (Müller-Groehling, 1990)

near-threshold elastic and inelastic K N scattering data are wellreproduced

deficiencies in the energy shift ∆E and the width Γ of the 1s level ofkaonic hydrogen

the Λ(1405) resonance is generated dynamically

predicts two poles in the S-wave with isospin I = 0

Predictions for DN and DN within the meson-exchange picture

model is constructed in close analogy to the Jülich K N and K Npotentials utilizing SU(4) symmetry

cross sections are comparable (somewhat larger) than those for K N

cross sections are of the same order as predicted by other approachesto DN (DN)

three states (Λc(2595), Σc(2800), Λc(2765)) are generated dynamically


Outlook

Proposal for the J-PARC 50-GeV Proton Synchrotron(Proposal E31, S. Ajimura et al., July 2012)

Spectroscopic study of hyperon resonances below K N threshold via the(K−, n) reaction on the deuteronperform measurement at pK

− ≈ 800 MeV/c and θn = 0− 5o

primary goal: study the position and width of the Λ(1405) resonanceproduced in the K N → πΣ channel

⇒ calculate K−d → πΣn within a Faddeev-type approach utilizing

Jülich K N potential

Oset-Ramos chiral potential

other more recent K N interactions

K. Miyagawa and JH, PRC 85 (2012) 065201 [one- and two-step processes only]


initial calculationThree processes included

Main contribution comes from (B2)

(B1)(A) (B2)

Ft

It

PWIAt

p

K

n

0K

K

d

n n

n

Ft

It

Contribution from process (A) is small for 600 MeV/c, 0nKP

0 pKK N

nK

p

p

n

n

d dK K

( ) -1threshold3.9 fm atnP K p

main contribution comes from (B2)

⇒ signal from Λ(1405) in K−d → πΣn is weak - but disputed by Jido et al.


Faddeev calculation

Faddeev calculation

0K p n K n n

K p n

0K n n

Coupled with 2-body interaction

Isospin interaction

K pn 0

K nn

5 MeV

14371432

K

d

K

n

N

processes

1T

0 1,T

KNt

treat K NN in three-body framework


preliminary results

K−d → πΣn invariant mass spectrum

Faddeev calculation of K−d → πΣn reactionin the Λ(1405) resonance region

K.Miyagawa1, J.Haidenbauer2

1 Faculty of Applied Physics, Okayama University of Science, 1-1 Ridai-cho, Okayama, Japan2Institute for Advanced Simulation, Forschungszentrum Julich, D-52425 Julich, Germany

This study is motivated by the J-PARC experiment E31 [1], which aims at a spectroscopicstudy of the Λ(1405) resonance via the (K−, n) reaction on the deuteron. Among previous the-oretical predictions which took into account single and double scattering processes, our analysis[2] showed that no clear peak is seen around relevant energy regions below KN threshold forthe beam momentum PK−=600 MeV/c. It thereby emphasised the necessity for Faddeev-typeapproaches where all rescattering processes can be summed up to infinite order.

dσ/

dM

πΣd

Ωn[µ

b/M

eV

sr]

thresholdK N

0

5

10

15

1400 1420 1440

pi+_18step

pi0_18step

pi-18step

800 MeV/cK

P − =

0

5

10

1400 1420 1440

pi+_18stepP

pi0_18stepP

pi-18stepP

π + −Σ

π − +Σ

0n

θ = °

0 0π Σ

[MeV]

Mπ Σ

π + −Σ

π − +Σ

0 0π Σ

1000 MeV/cK

P − =0

nθ = °

Figure 1: πΣ invariant mass spectra for the reaction K−d → πΣn. Colored lines indicate threecharge states.

In this work we solve the Faddeev equation for the coupled KNN − πΣN systems. Atpresent, KNN three-body scattering processes are fully incorporated, but transitions to theπΣN system is treated perturbatively with the t-matrix tπΣ,KN . For the KN -πΣ system, s-wave and isospin-basis interaction of a chiral unitary model [3] is used. The results are shownin Fig.1. In both cases of PK−=800 and 1000 MeV/c, the invariant mass spectra for the π0Σ0

final state show peaks around 1425 MeV.

In this analysis, we find that KN interaction in high-enegy region gives influence on thespectra. Now more elaborated calculations are prepared in which interactions in higher partialwaves are incorporated, and updated KN interaction models by recent low-energy data areused.

[1] S. Ajimura et al., http://j-parc.jp/researcher/Hadron/en/pac 0907/pdf/Noumi.pdf

[2] K.Miyagawa and H.Haidenbauer, Phys. Rev. C 85, 065201 (2012).

[3] E. Oset and A. Ramos, Nucl. Phys. A 635, 99 (1998).

K. Miyagawa, J.H., in preparation


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