Signature of L (1405) in - PowerPoint Presentation

Slide1

Signature of L(1405) in K-dpSn reaction

2015/9/8

1

Shota Ohnishi(Hokkaido Univ.)

in collaboration

with

Yoichi Ikeda (RIKEN)

Tetsuo

Hyodo

(YITP, Kyoto Univ.

)

Emiko

Hiyama

(RIKEN)

Wolfram Weise (ECT*/TUM)

Slide2

2015/9/8

2

K

bar

N

interaction

In order to understand the structure of

L

(1405),

precise determination of

K

bar

N-

pS

(

I

=0) interaction is necessary.

above

K

bar

N

threshold energy

:

-

K

-

p

cross section

at/just-below

KN

threshold energy:

- Branching ratio - kaonic atom(new data by SIDDHARTA)below the KbarN threshold energy: - So far, cannot perform pS elastic scattering experimentally - pS mass spectra from L(1405) production reactions (CLAS, LEPS, HADES, J-PARC)

experimental constraint

Planed

K

-

d

reaction at J-PARC (E31) is our target

Slide3

2015/9/83

J-PARC E31 experiment

http://j-parc.jp/researcher/Hadron/en/pac_0907/pdf/Noumi.pdf

pKlab.= 1GeVdetect forward neutronMissing mass distribution for p+S-/p0S0/p-S+L(1405) production via

the (

K

-

,n

) reaction on

deuteron target.

We can access below the

K

bar

N

threshold.

L

(1405) in K

barN channel

Jido

,

Oset

,

Sekihara

, EPJA42, 257(2009).

Slide4

Strategy of this work2015/9/84Study the cross section for J-PARC

E31 with KbarNN-

pYN

Faddeev (AGS) approach based on chiral SU(3) dynamicsFull three-body calculation for KbarNN-pYN systems with relativistic kinematics and higher partial waves for 1GeV incident momentuminvestigate how the signal of L(1405) resonance appears on pS mass spectrumTwo-step: Jido, Oset, Sekihara, EPJA42, 257(2009). Miyagawa, Haidenbauer, PRC85,065201(2012). Yamagata-Sekihara,

Sekihara

,

Jido

, PTEP043D02(2013).

Faddeev

:

Miyagawa

(Next talk)

Slide5

Meson-baryon potential based on chiral SU(3)Leading order of chiral perturbation theory: Weinberg-Tomozawa (WT) term

“energy-dependent” potentials

E; two body scattering energy

; determined by flavor SU(3) structure2015/9/85; baryon mass; meson mass

“energy-independent” potentials

Derive the potentials by matching with WT amplitude

f

: PS meson fields,

B

: baryon fields

Energy is fixed at threshold

We introduce phenomenological dipole form factor to regularize loop integrals

Cutoff parameters

L

are determined to reproduce the

K

-

p

cross section

Weinberg, PRL 17, 616 (1966).

Tomozawa

,

Nuov

.

Cim

. 46A, 707 (1966).

NG boson associated with spontaneous breaking of chiral SU(3)

symmetry

Slide6

cutoff (model parameters)We determine the cutoff parameters to reproduce K-p cross sections. 2015/9/8

6

Slide7

KbarN amplitude and scattering length (output)2015/9/87

SIDDHARTA

xSU

(3) NLOE-dep.E-indep.

Ikeda,

Hyodo

, Weise

NPA

881 (2012) 98.

Slide8

L

Alt-Grassberger-Sandhas(AGS) eq.

:

X

ij

；

quasi two-body amplitude

K

-

d ->

pS

n

reaction

2015/9/8

8

=

+

X

t

g

L

L

+

X

t

g

L

L

+

X

t

g

L

L

X

t

g

L

L

Slide9

2015/9/8

9

pS

invariant mass spectrumFor E-dep. model, signature of L(1405) appears on pS invariant mass spectrum around the binding energy of L(1405)For E-indep. model, signature of L(1405) is weak, and cusp appears at pS threshold

L

Slide10

2015/9/810pS invariant mass spectrum

For E-dep. model, signature of

L

(1405) appears on pS invariant mass spectrum around the binding energy of L(1405)For E-indep. model, signature of L(1405) is weak, and cusp appears at pS thresholdBump appears above the KbarN threshold

L

Slide11

Angular dependence2015/9/811KN threshold cusp is enhanced in forward angle

Channel dependence is also large in forward angle

L

q

;

n

angle in C.M.

Slide12

Angular dependence2015/9/812KN threshold cusp is enhanced in forward angle

Channel dependence is also large in forward angle

bump above K

barN threshold energy is enhanced in q=0

L

q

;

n

angle in C.M.

Slide13

SummaryWe investigate how the signature of the L(1405) appears in K-d scattering reaction.How the signatures appear depends on the two-body interaction models.

The production reaction would be used to distinguish dynamical model of

L(1405).Channel dependence of the cross section is large

We would also obtain the information on I=1 KbarN-pS interactions from K-d scattering.Bump appears above the KN threshold, and it is enhanced in q=02015/9/813

Slide14

Future workImprove the two-body interaction modelHigher order of chiral perturbationHigher partial waveCutoff parameters dependenceCompare with forthcoming J-PARC E312015/9/8

14

Slide15

Backup slides2015/9/815

Slide16

L

Alt-Grassberger-Sandhas(AGS) eq.

:

X

ij

；

quasi two-body amplitude

K

-

d ->

pS

n

reaction

2015/9/8

16

=

+

X

t

g

L

L

+

X

t

g

L

L

+

X

t

g

L

L

X

t

g

L

L

Slide17

Contribution of each amplitude2015/9/817

X

YK,d

component is dominant

X

t

g

L

L

Slide18

Bump structure above KN threshold2015/9/818

One- and two-step

One-step

Slide19

Bump structure above KN threshold

2015/9/8

19

One- and two-stepOne-step

Two-step

Slide20

cutoff dependenceWe determine the cutoff parameters to reproduce K-p cross sections.

2015/9/8

20

SIDDHARTA

Slide21

cutoff dependence2015/9/821

Preliminary

Slide22

Partial wave decomposition2015/9/822S- and d-wave components are dominant in low-energy region

p-wave component is also large around

KN threshold energy

Slide23

Angular dependence2015/9/823KN threshold cusp is enhanced in forward angle

Channel dependence is also large in forward angle

bump above K

barN threshold energy is enhanced in q=0

L

q

;

n

angle in C.M.

Slide24

Contribution of each amplitude2015/9/824

X

YK,d

component is dominant

X

t

g

L

L

Slide25

Model of b

aryon-baryon interaction

Nijimegen93

NN potential

Y

N potential

Torres,

Dalitz

,

Deloff

, PLB 174, 213 (1986)

2015/9/8

25

CD-Bonn

q (MeV)

q

2

f

2

(1/MeV)

Julich’04

Slide26

Coupled channel equation for Faddeev eq.

separable 2-body Interaction；

Alt-Grassberger-Sandhas(AGS) eq.

: Xij；quasi two-body amplitude

X

ij

X

nj

Z

ij

Z

in

t

n

=

+

i

j

i

j

i

j

n

2015/9/8

26

Slide27

Singularity of particle exchange interactionmethods to handle moon shape singularity numerically

point method

moon shape singularity

Z-diagram

2015/9/8

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L.

Schlessinger

, PR 167, 1411(1968)

Kamada, Koike,

Glökle

, PTP 109, 869(2003)

Slide28

Point methodL. Schlessinger, PR 167, 1411(1968)

evaluate X at finite

e

i

X at

e

=0

continued

fraction

Kamada, Koike,

Glökle

, PTP 109, 869(2003)

2015/9/8

28