Two- and three-body resonancesin the system

N.V. Shevchenko

Nuclear Physics Institute, Řež, Czech Republic

NNNK

K-pp bound state

Prediction of the existence of deep and narrow K- pp bound state: (T. Yamazaki and Y. Akaishi, Phys. Lett. B535 (2002) 70) EB = - 48 MeV, = 61 MeV

FINUDA collaboration: evidence for a deeply bound state: (M. Agnello et. al., Phys. Rev. Lett. 94 (2005) 212303) EB = -115 MeV, = 67 MeV

another interpretations of the experiment, different theoretical results…

Basic antikaon-nucleon interaction, existing models:• Potentials used in few-body (many-body) calculations:

too simple, poor reproducing of the experimental data,• “Alone” potentials: cannot be used in few- or many-body calculations

We need a potential: 1. reproducing all existing experimental data 2. suitable for using in few-body calculation.

1812003725

,2632001500

poles close twoofeffect an is (1405) : versioneAlternativ

channel 0in state bound-quasi a and 0in resonance a

:assuption Usual

0 MeV, 0.25 5.1406 :PDG

resonance (1405) through channel with coupledStrongly

) (. Phys. A . al, NuclD. Jido et

) ( B hys. Lett.eissner, Pr, U. G. MJ. A. Olle

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:ninteractio about n informatio Existing NK

611978139

,493197133

and , , ratios branching Threshold -

reactions, and of sections-Cross -

:data scattering Measured

) ( Bucl. Phys. et al., NR.J. Nowak

) ( Bucl. Phys. et al., ND.N. Tovee

RR

MBpKpKpK

nc

- obtained from Deser-Trueman formula. Experimentally measured are: strong interaction shift and width of the kaonic hydrogen atom 1s level state

eV 100208407 ,eV 1163323 1 1 KEKs

KEKsE

2366 (1998) 58 C Rev. Phys.

3067, (1997) 78 Lett. Rev. Phys.

fm )12.025.049.0( )03.015.078.0(

:(KEK)length scattering KEK

t al., T.M. Ito e

et al., M. Iwasaki

ia

pK

pK

Experimentally measured

eV 30111249 ,eV 637193 1 1 DEARs

DEARsE

212302 (2005) 94 Lett. Rev. Phys.

fm )036.0135.0302.0( )015.0090.0468.0(

:(DEAR)length scattering DEAR

al., G. Beer et

ia

pK

pK

Is it possible to construct a phenomenological potential with one- and two-pole structure of resonance,equally properly reproducing:

NK

Isospin-breaking effects:

1. Kaonic hydrogen: direct inclusion of Coulomb interaction2. Using of the physical masses during all calculation:

,)1(1

and ratios branching Threshold

reactions, and of sections-Cross

DEAR),or (KEK width andshift level pK 1 Measured

-

cn

c

RR

RR

MBpKpKpK

s

NKnpKKm ,m of instead m ,m ,m ,m 0-

and suitable for using in few-body calculations?J. Révai, N.V. Shevchenko, Phys. Rev. C 79 (2009) 035202

for ] )()( [

)(

)()(

1)(

for )()(

1)(

:(1405) pole-2

or for )()(

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:(1405) pole-1

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k

s

kkg

Kk

kg

Kk

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poleI

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;1or 0 );channel (or )channel (

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: potential total theof part Strong

INKK

kgkgkkV

VV

III

Cs

:(1405) generatedy dynamicall pole- twoand -one with

found werepotential theof parameters The

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Manifestation of (1405) resonance in cross-section:blue lines: 1-pole, red lines: 2-pole (1405) resonance

”1-pole” pole position: 1409 – i 32 MeV

“2-pole” poles positions: 1412 – i 32 MeV, 1380 – i 105 MeV

Comparison with experimental cross-sections

– DEAR data are inconsistent with the scattering data

Experimental and theoretical 1s K-p level shift and width:

The two-body result: both potentials describes the data equally well.

operators unknown define

:form Sandhas-rGrassberge-Alt in equations Faddeev

210211011

031

310311011

021

3103210211

ijU

UGTUGTGU

UGTUGTGU

UGTUGTU

(12)3(23)1 :

(31)2(23)1 :

(23)1(23)1 :

31

21

11

U

U

U

321321321 , , :

:)( channels Particle directly. included is channel

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Three-body coupled-channels calculation

N.V. Shevchenko, A. Gal, J. Mareš; Phys. Rev. Lett. 98 (2007) 082301 N.V. Shevchenko, A. Gal, J. Mareš, J. Révai; Phys. Rev. C 76 (2007) 044004

: , :

: , : : channel-2 of elements

matrices;- usual are and , ,

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: matrices,-body -Two

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i

ijUGG are operatorsn transitio, functionsGreen Free 00

, - usual Faddeev indexes

, - channel indexes

i j

Coulomb interaction is included in two-body , but not in three-body calculation. (for the three-body system Coulomb interaction plays a minor role and can be

omitted, only the strong part of isospin-mixing interaction is used)

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Two-term NN (pp) potentialP. Doleschall, private communication, 2009

2

1,

2

1

jijijipp

iiiipp

ggT

ggV

2

122

2

22

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)( ,)( :BVersion

2 ,1 ,)( :AVersion

mBm

BmB

mBm

BmB

mA

im

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i

kkg

kkg

ik

kg

fm 880.2)( fm, 558.16)(

fm 845.2)( fm, 553.16)(

pprppa

pprppaB

effB

Aeff

A

Reproduces: Argonne V18 NN phase shifts (with sign change!),

ninteractio )( New NN

22

1)(with

)'( )( )',(V

toscorrespond );',(T

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NI

NI

NI

NI

NI

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kkg

kgkgkk

zkk

All parameters were fitted to reproduce experimental cross-sections

I=3/2Real parameters, one-channel case

I=1/21. Two-channel potential, real parameters2. One-channel potential, complex strength parameter

NN N

Pure I=3/2 part

J. Révai, N.V. Shevchenko, 2009

Pure I=1/2 and I=1/2, I=3/2 mixtures

• Isospin-breaking interaction: one- and two-pole structure of resonance• Two-term NN (pp) potential• New interaction

New three-body calculations results (preliminary):

NK

NINNI 2/3 and )( 2/1

1-pole (1405) resonance2-pole (1405)

resonance

NN A-version – 29.63 – i 47.31 – 59.50 – i 41.13

NN B-version – 30.90 – i 47.38 – 59.66 – i 41.31