Two- and three-body resonances in the system N.V. Shevchenko Nuclear Physics Institute, Ř e ž,...
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Transcript of Two- and three-body resonances in the system N.V. Shevchenko Nuclear Physics Institute, Ř e ž,...
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
NKII
IiE
: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 )()(
1)(
:(1405) pole-1
222
2
222,
221,
221,
k
s
kkg
Kk
kg
Kk
kg
poleI
poleI
poleI
;1or 0 );channel (or )channel (
),'( )()',(
: potential total theof part Strong
INKK
kgkgkkV
VV
III
Cs
:(1405) generatedy dynamicall pole- twoand -one with
found werepotential theof parameters The
NK
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
NNNNK
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 , ,
00
0
0
,
0
00
0
,
00
00
00
: matrices,-body -Two
3
33
33
3
22
2
22
2
1
1
1
1
TNKT
NKTNKNKTT
TTTT
T
TT
TT
T
TT
T
TT
T
T
T
T
T
TT
K
KKKNK
NNNN
N
K
KKK
K
N
KKK
N
N
NN
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)
NNNK NK
Two-term NN (pp) potentialP. Doleschall, private communication, 2009
2
1,
2
1
jijijipp
iiiipp
ggT
ggV
2
122
2
22
3
122
1
11
2
122
)( ,)( :BVersion
2 ,1 ,)( :AVersion
mBm
BmB
mBm
BmB
mA
im
AimA
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
NI
NI
NI
NI
NI
NI
NI
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