antikaon nuclear few body systems - theory … · antikaon-nuclear few-body systems - theory status...

Strangeness in Nuclei ECT* Trento 4 October 2010

ANTIKAON-NUCLEAR FEW-BODY SYSTEMS- Theory Status -

Wolfram Weise

Low-energy QCD with strange quarks

Theory status report

Important observables and constraints:

KN threshold physics mass spectra!!

Nature and properties of !(1405):

quasibound systems ?KNN

the two-poles scenario

LOW-ENERGY QCD

with STRANGE QUARKS

and SPONTANEOUSLY BROKEN

CHIRAL SYMMETRY

1.

. . . realized as an EFFECTIVE FIELD THEORY with SU(3) octet of pseudoscalar Nambu-Goldstone bosons coupled to the baryon octet

Non-zero quark masses: PCAC m2!f2!

= !mq "!!# + O(m2

q)

NAMBU - GOLDSTONE BOSONS:

Spontaneously Broken CHIRAL SYMMETRY

Low-Energy QCD with N = 3 MASSLESS QUARKSf

SU(3)L ! SU(3)R

Aµ

a(x) = !(x) "µ"5

#a

2!(x)

! = (u, d, s)T

Axial Vector Current:

Pseudoscalar SU(3) meson octet {!a} = {!, K, K, "8}

DECAY CONSTANTSORDER PARAMETERS:

µ

!

axial current

!

K

f! = 92.4 ± 0.3 MeV

fK = 113.0 ± 1.3 MeV

chiral limitf = 86.2 MeV( )

!0|Aµa(0)|!b(p)" = i"ab pµ

fb

CHIRAL SU(3) EFFECTIVE FIELD THEORY

Interacting systems of NAMBU-GOLDSTONE BOSONS (pions, kaons) coupled to BARYONS

+ + ...

Low-Energy Expansion: CHIRAL PERTURBATION THEORY

“small parameter”: energy / momentum

+

p

4! f!

Leff = Lmesons(!) + LB(!, "B)

Leading DERIVATIVE couplings (involving )!µ!

determined by spontaneously broken CHIRAL SYMMETRY

!! ! !B B

works well for low-energy pion-pion and pion-nucleon interactions

... but NOT for systems with strangeness S = !1 (KN, !!, ...)

1 GeV

higher orders with additional

low-energy constants

!

2 M.F.M. Lutz et al.

Thus, it is useful to review also in detail e!ective coupled-channel field theoriesbased on the chiral Lagrangian.

The task to construct a systematic e!ective field theory for the meson-baryonscattering processes in the resonance region is closely linked to the fundamental ques-tion as to what is the ’nature’ of baryon resonances. The radical conjecture10), 5), 11), 12)

that meson and baryon resonances not belonging to the large-Nc ground states aregenerated by coupled-channel dynamics lead to a series of works13), 14), 15), 17), 16), 18)

demonstrating the crucial importance of coupled-channel dynamics for resonancephysics in QCD. This conjecture was challenged by a phenomenological model,11)

which generated successfully non-strange s- and d-wave resonances by coupled-channeldynamics describing a large body of pion and photon scattering data. Of course,the idea to explain resonances in terms of coupled-channel dynamics is an old onegoing back to the 60’s.19), 20), 21), 22), 23), 24) For a comprehensive discussion of thisissue we refer to.12) In recent works,13), 14) which will be reviewed here, it was shownthat chiral dynamics as implemented by the !!BS(3) approach25), 10), 5), 12) providesa parameter-free leading-order prediction for the existence of a wealth of strange andnon-strange s- and d-wave wave baryon resonances. A quantitative description ofthe low-energy pion-, kaon and antikaon scattering data was achieved earlier withinthe !-BS(3) scheme upon incorporating chiral correction terms.5)

§2. E!ective field theory of chiral coupled-channel dynamics

Consider for instance the rich world of antikaon-nucleon scattering illustrated inFig. 1. The figure clearly illustrates the complexity of the problem. The KN statecouples to various inelastic channel like "# and "$, but also to baryon resonancesbelow and above its threshold. The goal is to bring order into this world seeking adescription of it based on the symmetries of QCD. For instance, as will be detailedbelow, the $(1405) and $(1520) resonances will be generated by coupled-channeldynamics, whereas the #(1385) should be considered as a ’fundamental’ degree offreedom. Like the nucleon and hyperon ground states the #(1385) enters as anexplicit field in the e!ective Lagrangian set up to describe the KN system.

The starting point to describe the meson-baryon scattering process is the chiralSU(3) Lagrangian (see e.g.26), 5)). A systematic approximation scheme arises due to asuccessful scale separation justifying the chiral power counting rules.27) The e!ectivefield theory of the meson-baryon scattering processes is based on the assumption

s1/2KN

[MeV]

poles

thresholdsΣηΛη

Λ**(1520)

Λ*(1405)Σ

*(1385)

Σ(1195)Λ(1116)

KNΣπΛπ

15001000

Fig. 1. The world of antikaon-nucleon scattering

KN_

!

s [MeV]

Author's personal copy

W. Weise, R. Härtle / Nuclear Physics A 804 (2008) 173–185 177

Fig. 1. Real and imaginary parts of the K!p forward scattering amplitude calculated in the chiral SU(3) cou-pled-channels approach [23], as functions of the invariant KN center-of-mass energy

"s. Real and imaginary parts of the

scattering length deduced from the DEAR kaonic hydrogen measurements [27] are also shown. The dotted line indicatesthe leading order (Tomozawa–Weinberg) K!p # K!p amplitude for comparison.

The off-shell s-wave K!p amplitude resulting from the coupled-channel calculation [23] canbe given a convenient approximate parametrisation as follows:

F s-waveK!p = MN

4!f 2K

"s

!" + apm2

K + bp"2"#

1 +"

s#0

M20 ! s ! i

"s$0(s)

$, (3)

with the kaon decay constant fK $ 0.11 GeV, ab $ !bp $ 1 GeV!1, #0 $ 0.25 GeV and the%(1405) mass and energy-dependent width (M0,$0(s)), notably with M0 shifted upward byabout 10 MeV from its nominal value. This form is useful for practical purposes and reflectsthe behavior of the leading and next-to-leading order terms as well as the non-perturbative partinvolving the dynamically produced resonance.

2.3. An equivalent pseudopotential

In applications to nuclear few-body systems it is convenient to translate the leading KN

s-wave interaction into an equivalent potential in the laboratory frame (where the nucleon is ap-proximately at rest). The leading order piece (the Tomozawa–Weinberg term) can be viewed asresulting from vector meson exchange [28]. Starting from the non-linear sigma model in SU(3),introduce gauge couplings of the vector meson octet to the pseudoscalar octet and fix a universalvector coupling constant g $ 6 such the & # !+!! width is reproduced. Then construct vectormeson couplings to the SU(3) octet baryons through their conserved vector currents. The corre-sponding piece of the reduced KN interaction Lagrangian which generates the t-channel vectormeson exchange KN amplitude at tree level, with vector meson mass mV , is

'L(KN) = ig2

4

!K!(µK+ ! K+(µK!"%

(2 + m2V

&!1)N# µ(*3 + 3))N, (4)

where K± are the charged kaon fields and )N = (p,n)T is the isodoublet nucleon field. Theisovector (*3) piece comes from & exchange and the isoscalar part (with its typical factor of 3)comes from " exchange, while + exchange does not contribute as long as there are no strange

Low-Energy K N Interactions_

Chiral Perturbation Theory NOT applicable: !(1405) just below K p threshold-

Non-perturbative Coupled Channels

approach based on Chiral SU(3) Dynamics

N. Kaiser, P. Siegel, W. W. (1995)E. Oset, A. Ramos (1998)

!!

!+ mass spectrumK!p scattering amplitude

Ima(K!p)

Rea(K!p)

0 !

1 GeVu,d s c

“light” quarks “heavy” quarks

0 !

1 GeVu,d s c


K N

!

!

0 !

1 GeVu,d s c


K N

! !

K N !

!

CHIRAL SU(3) COUPLED CHANNELS DYNAMICS

Tij = Kij +

!

n

Kin Gn Tnj

12 ! 21 :

|1! = |KN, I = 0! |2! = |!!, I = 0!

!!bound stateKN resonance

driving interactions individually strong enough to produce

strong channel coupling

K11 =3

2 f2K

(!

s " MN) K22 =2

f2!

(!

s " M!)

K12 =!1

2 f! fK

!

3

2

"

"

s !M! + MN

2

#

Note: ENERGY DEPENDENCE characteristic of Nambu-Goldstone BosonsLeading s-wave I = 0 meson-baryon interactions (Tomozawa-Weinberg)

CHIRAL SU(3) COUPLED CHANNELS DYNAMICS

Tij = Kij +

!

n

Kin Gn Tnj

(contd.)

Loop integrals (with meson-baryon Green functions) using dimensional regularization:

finite parts including subtraction constants a(µ) :

The TWO POLES scenario

D. Jido et al.Nucl. Phys. A725 (2003) 181

KN!!

-100

-80

-60

-40

-20

0

Im z

[M

eV

]

14401420140013801360Re z [MeV]

z2(BMN)z2(HNJH)

z2(ORB)

z1(HNJH)z1(ORB)

z1(BMN)z2(BNW)

z1(BNW)

!

!

2

thr

-120

-100

-80

-60

-40

-20

0

20

Im z

[MeV

]

14401420140013801360Re z [MeV]

z2 ( only)

z2(2)

z2(4)

z1(2)z1

(4)

z1 (KN only)

The TWO POLES scenario

starting point: no channel coupling KN

!!

bound state

resonanceKN )

Pole 1

(dominantly

channel coupling at work

Pole 1I (dominantly )!!

Singularities of KN amplitudein the complex energy plane

T. Hyodo, W. W. , Phys. Rev. C77 (2008) 03524

4

4

2

0

-2

FK

N [

fm]

1440140013601320

s1/2

[MeV]

Re F

KN(I=0)

1.5

1.0

0.5

0.0

-0.5

-1.0

F!" [

fm]

1440140013601320

s1/2

[MeV]

!"(I=0)

Im F

Fig. 2 Forward scattering amplitudes FKN (left) and F!" (right). Real parts are shown assolid lines and imaginary parts as dashed lines. The amplitudes shown are related to the Tij

in Eq. (2) by Fi = !MiTii/(4!"

s).

valance of the two attractive forces. As we emphasized in the previous section, themeson-baryon interaction is governed by the chiral low energy theorem. Hence, weconsider that the two-pole structure of the !(1405) is a natural consequence of chiralsymmetry.

4 E!ective single-channel interaction

Keeping the structure of the !(1405) in mind, we construct an e!ective single-channelKN interaction which incorporates the dynamics of the other channels 2-4 ("#, $N ,and K%). We would like to obtain the solution T11 of Eq. (2) by solving a single-channelequation with kernel interaction V e!, namely,

T e! = V e! + V e! G1 T e! = T11.

Consistency with Eq. (2) requires that V e! be the sum of the bare interaction inchannel 1 and the contribution V11 from other channels:

V e! = V11 + V11, V11 =4X

m=2

V1m Gm Vm1 +4X

m,l=2

V1m Gm T(3)ml Gl Vl1, (3)

T(3)ml = Vml +

4X

k=2

Vmk Gk T(3)kl , m, l = 2, 3, 4.

where T(3)ml is the 3 ! 3 matrix with indices 2-4, and expresses the resummation of

interactions other than channel 1. Note that V11 includes iterations of one-loop termsin channels 2-4 to all orders, stemming from the coupled-channel dynamics. This is anexact transformation, as far as the KN scattering amplitude is concerned.

The e!ective KN interaction V e! is calculated within a chiral coupled-channelmodel [14]. It turns out that the "# and other coupled channels enhance the strengthof the interaction at low energy, although not by a large amount. The primary e!ectof the coupled channels is found in the energy dependence of the interaction kernel. Inthe left panel of Fig. 2, we show the result of KN scattering amplitude T e!, which isobtained by solving the single-channel scattering equation with V e!. The full amplitudein the "# channel is plotted in the right panel for comparison. It is remarkable that theresonance structure in the KN channel is observed at around 1420 MeV, higher thanthe nominal position of the !(1405). What is experimentally observed is the spectrum

14051420

T. Hyodo, W. W. : Phys. Rev. C77 (2008) 03524

The TWO POLES scenario (contd.)

Note difference in pole positions and spectra of and !!

Equivalent KN effective interaction should produce

KN

D. Jido et al. , NP A725 (2003) 263

KN !! amplitudesand

quasibound state at 1420 MeV (not 1405 MeV)

The TWO POLES scenario (contd.)

Y. Ikeda, H. Kamano, T. SatoarXiv:1004.4877 [nucl-th]

Two-pole scenario confirmed

Role of energy dependenceof (chiral) driving interactions

energy dependent

energy independent

Pole 1

Pole 1I

Re tIm t

Note: NO differences at and above threshold

But: STRONG differences for subthreshold extrapolations

KN

KN

!"

#

$

%

&

"

'&

'%

()*+,-./

!%%"!%""!0$"!0&"!1+,234/

+53+67839:+53+6;8<=>?: @A"

!B"

"B#

"B$

"B%

"B&

"B"

()*+,-./

!%%"!%""!0$"!0&"!1+,234/

+@.+67839:+@.+6;8<=>?: @A!

!"

#

$

%

&

"

'&

'%

()*+,-./

!%%"!%""!0$"!0&"!1+,234/

+53+67839:+53+6;8<=>?: @A"

!B"

"B#

"B$

"B%

"B&

"B"

()*+,-./

!%%"!%""!0$"!0&"!1+,234/

+@.+67839:+@.+6;8<=>?: @A!

FK

N[fm

]

I = 0 Effective Interaction

I = 0

is:complex energy dependent non-local

Figure 1: Diagrammatic representation of Eqs. (3), (4) and (6). Black blob stands for T e!. = T11,shaded blobs stand for V e!., and white blobs denote T single

22

1.2 Two-channel problem

Let us start with the simplest case of two-channel scattering. We want to include the dynamicsof channel 2 into an e!ective interaction of channel 1 (V e!.). We would like to obtain the solutionT11 of Eq. (1) by solving a single channel problem with the kernel interaction V e!.. Namely,

T e!. =V e!. + V e!.G1Te!. (3)

=[(V e!.)!1 ! G1]!1

=T11

To be consistent with Eq. (1), V e!. should be constructed by the sum of the bare interaction inthis channel V11 and the contribution from channel 2 V11 as

V e!. =V11 + V11 (4)

V11 =V12G2V21 + V12G2Tsingle22 G2V21 (5)

where T single22 is the single-channel resummation of channel 2:

T single22 =V22 + V22G2T

single22 (6)

=[V !122 ! G2]

!1

Eqs. (3), (4) and (6) are diagrammatically illustrated in Fig. 1. Note that V11 consists of thecontribution from one loop to the channel 2 and that from the coupled channel resummation inchannel 2:

V12G2V21 : one loop, V12G2Tsingle22 G2V21 : resummation (7)

1.3 N-channel problem

It is straightforward to extend the above framework to the case with N channels. We can generalizethe formula (5) and (6) to include the e!ect of N ! 1 channels (2, 3, . . . , N) into channel 1:

(5) " V11 =N!

m=2

V1mGmVm1 +N!

m,l=2

V1mGmT (N!1)ml GlVl1 (8)

2

Ve! (KN ! KN)

KN

!!!!

KN

T. Hyodo, W. W. : Phys. Rev. C 77 (2008) 03524

KN

Ve! (KN ! KN)

chiral SU(3)

dynamics

Akaishi-Yamazaki phenom.potential

large differences in

subthreshold extrapolations

Chiral dynamics predicts significantly weaker attraction than Akaishi - Yamazaki (local, energy independent) potential

THRESHOLD

OBSERVABLES

2.KN

Kaonic hydrogen

Threshold branching ratios

“WT” approach

100 150 200 250 300 350 400 450 500

200

400

600

800

DEAR KEK

!E (eV)

"(e

V)

!2/d.o.f. < 1.4

1.4 < !2/d.o.f. < 1.6

1.6 < !2/d.o.f. < 2.33

2.33 < !2/d.o.f. < 4.0

4.0 < !2/d.o.f. < 6.0

6.0 < !2/d.o.f. < 9.0

“WTB” approach

100 150 200 250 300 350 400 450 500

200

400

600

800

DEAR KEK

!E (eV)

"(e

V)

!2/d.o.f. < 0.95

0.95 < !2/d.o.f. < 1.15

1.15 < !2/d.o.f. < 1.93

1.93 < !2/d.o.f. < 3.0

3.0 < !2/d.o.f. < 5.0

5.0 < !2/d.o.f. < 8.0

“full” approach

100 150 200 250 300 350 400 450 500

200

400

600

800

DEAR KEK

!E (eV)

"(e

V)

!2/d.o.f. < 0.8

0.8 < !2/d.o.f. < 1.0

1.0 < !2/d.o.f. < 1.76

1.76 < !2/d.o.f. < 3.0

3.0 < !2/d.o.f. < 5.0

5.0 < !2/d.o.f. < 8.0

Figure 4: Strong energy shift !E and width " of kaonic hydrogen for the three approaches.The shaded areas represent di#erent upper limits of the overall !2/d.o.f. The 1" confidenceregion is bordered by the dashed line. See text for further details.

10

NEWS from SIDDHARTA

New kaonic hydrogen precision data (2010)

E [eV]

counts

/lu

min

osi

ty[p

b!

1]

K!

Kcomplex

SIDDHARTA

PRELIMINARY

WT

SIDDHARTA

strong interaction shift and width:

note: remarkable agreement with Tomozawa-Weinberg (leading order) prediction from chiral SU(3) dynamics

update in progress

B. Borasoy, R. Nissler, W. W. Eur. Phys. J. A25 (2005) 79

R. Nissler PhD thesis (2008)

T. Hyodo, Y. Ikeda, W. W. (2010)

!E = 305 ± 31 eV

! = 512 ± 77 eV

PRELIMINARY ( talk by S. Okada )

( next slide )

280 ± 35

520 ± 80

physical values of decay constants

UPDATED ANALYSIS of K!p THRESHOLD PHYSICS

T. Hyodo, Y. Ikeda, W.W. (2010)

Chiral SU(3) coupled-channels dynamics with Weinberg-Tomozawa driving interactions

!(K!p ! !+"!)

!(K!p ! !!"+)

!(K!p ! !+"!

, !!"+)

!(K!p ! all inelastic channels)

!(K!p ! !0")

!(K!p ! neutral states)

threshold branching ratios

2.36 ± 0.04

0.66 ± 0.01

0.19 ± 0.02

0.64

2.36

0.18

kaonic hydrogen shift & width theory (WT) exp.

!E (eV)

! (eV)

288

567

PRELIMINARY

f!, fK

fit achieved with

scattering length a(K!p) = !0.57 ± 0.26 i [fm]

280 ± 35

520 ± 80

!2/d.o.f. ! 1.2

Chiral SU(3) dynamics: predicted cross sections [mb] with Weinberg - Tomozawa termsplus subtraction constants constrained by threshold observables

UPDATED ANALYSIS of K!p THRESHOLD PHYSICS

0

20

40

60

80

100

120

140

50 100 150 200 250

(mb)

Plab(MeV)

K-p -> 0 0

5

10

15

20

25

30

35

50 100 150 200 250

(mb)

Plab(MeV)

K-p -> 0

0

50

100

150

200

250

50 100 150 200 250

(mb)

Plab(MeV)

K-p -> + -

K!p ! K!p K!p ! !+!! K!p ! !

0!0

K!p ! !!!+ K!p ! !

0!K!p ! K0n

0

10

20

30

40

50

60

50 100 150 200 250

(mb)

Plab(MeV)

K-p -> barK0n

0

10

20

30

40

50

60

70

80

50 100 150 200 250

(mb)

Plab(MeV)

K-p -> - +

0

50

100

150

200

250

300

50 100 150 200 250

(mb)

Plab(MeV)

K-p -> K-p

T. Hyodo, Y. Ikeda, W.W. (2010) PRELIMINARY

5.3. Results 135

-2

0

2

4

0

1

2

3

4

5

6

-0.5

0

0.5

1

0

0.5

1

1.5

1.32 1.35 1.38 1.41 1.44

-1

0

1

2

1.32 1.35 1.38 1.41 1.44-3

-2

-1

0

Ref (

I=

0)[fm

]

KN ! KN

!! ! !!

KN ! !!

"s [GeV]

Imf (

I=

0)[fm

]

"s [GeV]

Figure 5.11: Real (left panel) and imaginary part (right panel) of the I = 0 KN and!! amplitudes in the WT approach. The best fit is represented by the solid lines whilethe bands comprise all fits in the 1" region. The !! and KN thresholds are indicatedby the dotted vertical lines.

Chiral SU(3) Coupled Channels Dynamics

Relevant amplitudes, subthreshold extrapolations and uncertainty analysis R. Nissler PhD thesis (2008)

B. Borasoy, R. Nissler, W. W. : Eur. Phys. J. A25 (2005) 79

notedisplacement !

B. Borasoy, U.-G. Meissner, R. Nissler, Phys. Rev. C74 (2006) 055201

increased accuracy to be expected in view of new SIDDHARTA data

SPECTRAL

DISTRIBUTIONS

3.

Implications of two-poles scenario

Photoproduction vs. absorption and proton-proton induced reactions

!!

K!

MASS SPECTRA !!

Chiral SU(3) dynamics with uncertainty analysis

5.3. Results 129

0

50

100

150

200

0

50

100

150

1.35 1.40 1.45

0

50

100

150

0

10

20

30

0

10

20

30

1.35 1.40 1.45

0

10

20

30

arbit

rary

unit

s

arbit

rary

unit

s

!s [GeV]

!s [GeV]

WT

WTB

full

WT

WTB

full

Figure 5.7: Left: !!!+ event distribution for the three di"erent approaches comparedto data from [182] (which have been supplemented by statistical errors following [194]).The best fits are represented by the solid lines while the shaded areas indicate the 1"confidence regions. Right: !0!0 event distribution as predicted by the chiral unitaryapproaches compared to the recent data from [183] which were not included in the fit;only an overall normalization constant was adjusted to the data.

5.3. Results 129

0

50

100

150

200

0

50

100

150

1.35 1.40 1.45

0

50

100

150

0

10

20

30

0

10

20

30

1.35 1.40 1.45

0

10

20

30

arbit

rary

unit

s

arbit

rary

unit

s!

s [GeV]!

s [GeV]

WT

WTB

full

WT

WTB

full


!!

!+

5.3. Results 129

0

50

100

150

200

0

50

100

150

1.35 1.40 1.45

0

50

100

150

0

10

20

30

0

10

20

30

1.35 1.40 1.45

0

10

20

30

arbit

rary

unit

s

arbit

rary

unit

s

!s [GeV]

!s [GeV]

WT

WTB

full

WT

WTB

full


5.3. Results 129

0

50

100

150

200

0

50

100

150

1.35 1.40 1.45

0

50

100

150

0

10

20

30

0

10

20

30

1.35 1.40 1.45

0

10

20

30

arbit

rary

unit

s

arbit

rary

unit

s

!s [GeV]

!s [GeV]

WT

WTB

full

WT

WTB

full


!0!

0

ANKE data (COSY / Jülich)

I. Zychor et al. Phys. Lett. B660 (2008) 167

R. Nissler, PhD thesis (2008)

“old” dataR.J. Hemingway,

Nucl. Phys. B253 (1985) 742

agreement of two Σ+channels

Invariant Mass [GeV]! "1.3 1.4 1.5

/dM

[ar

bit

rary

sca

le]

#d

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6<2.23$1.99<E

2.15<W<2.25

-! 0! p % -! +"-! +! n % -! +"

weighted average

PDG Breit-Wigner

Preliminary

K. Moriya (CMU) CLAS Λ(1405) February 2010 1 / 2

MASS SPECTRA (contd.)!!

K. Moriya, NFQCD Kyoto (2010)

!(1405) (CLAS @ JLAB)

! p ! K+!

+"!

K. Moriya, R. Schumacher HYP-X Conference (2009)

Nucl. Phys. A 835 (2010) 231

Note: upward shift of spectrum compared to “standard” PDG!(1405)

. !(1405)

!p

!

K+

K!

!

Photoproduction of

D. Jido, E. Oset, T. SekiharaarXiv:1008.4423 [nucl-th]


!(1405)Antikaon-induced production on deuteron target

downward shift of by final state interactions ?


pp ! pK+{!±!!}

!(1405)

J. Siebenson, E. Epple, L. Fabbietti, et al. (2010)

preliminary

T. Hyodo, T. Uchino, M. Oka (2010)

News from HADES

model calculation of !!N potential

based on chiral SU(3) coupled channelsand boson exchange

[MeV]

r [fm]

dynamics of the system ?( talk by Avraham Gal )

K+!!N

Antikaon-Nuclear Clusters:Prototype System K pp-4.

3-Body (Faddeev)Calculations Variational Calculations

Issues in both approaches:energy dependence of basic input amplitudes,subthreshold / off-shell extrapolations, necessary approximations, . . .

OVERVIEW

{K[NN]T=1}I=1/2Binding energies and widths of quasibound

48 61

20 ± 3 40 ! 70

40 ! 80 40 ! 85

phenomenological potential(energy independent)

chiral SU(3) dynamics

coupled channels phenomenological (incl. p wave)

[1]

[2]

[3]

50 ! 70


90 ! 110

45 ! 80 45 ! 70

14 58

phenomenological

!) !)

!)

(energy independent)

(energy dependent)

[4]

[5]

[6]KbarNN pole position

B [MeV] !

B [MeV] !

Variational

Faddeev

two-body input:

two-body input:3-body coupled channels

[1] T. Yamazaki, Y. Akaishi Phys. Lett. B535 (2002) 70

Phys. Rev. C76 (2007) 045201

[2] A. Doté, T. Hyodo, W. W. Nucl. Phys. A804 (2008) 197

Phys. Rev. C79 (2009) 014003

[3] S. Wycech, A.M. Green Phys. Rev. C79 (2009) 014001

[4] N.V. Shevchenko, A. Gal, J. MaresPhys. Rev. Lett. 98 (2007) 082301(+ J. Révay) Phys. Rev. C76 (2007) 044004

[5] Y. Ikeda, T. SatoPhys. Rev. C76 (2007) 035203Phys. Rev. C79 (2009) 035201

[6] Y. Ikeda, H. Kamano, T. Sato arXiv:1004.4877 [nucl-th] (2010)

OVERVIEW


50 ! 70


90 ! 110

45 ! 80 45 ! 70

14 58

phenomenological

!) !)

!)


(energy dependent)

[4]

[5]


B [MeV] !

B [MeV] !

Variational

Faddeev

two-body input:



Phys. Rev. C76 (2007) 045201


Phys. Rev. C79 (2009) 014003





48 61

20 ± 3 40 ! 70

40 ! 80 40 ! 85




[1]

[2]

[3]

energy independent

OVERVIEW


50 ! 70


90 ! 110

45 ! 80 45 ! 70

14 58

phenomenological

!) !)

!)


(energy dependent)

[4]

[5]


B [MeV] !

B [MeV] !

Variational

Faddeev

two-body input:



Phys. Rev. C76 (2007) 045201


Phys. Rev. C79 (2009) 014003





48 61

20 ± 3 40 ! 70

40 ! 80 40 ! 85




[1]

[2]

[3]

energy dependent

K pp System: Coupled-Channels Faddeev Approach

-

Y. Ikeda, H. Kamano, T. Sato: arXiv:1004.4877 [nucl-th]

Recent advanced calculation:Importance of full, energy dependent

interactingpair

spectator

KN and !! interactions

Two-pole structure also seen in 3-body amplitude

based on chiral SU(3) dynamics

K pp System: Coupled-Channels Faddeev Approach

- (contd.)

Search for 3-body resonanceson physical sheetKNN

Energy dependent interactions

two poles in 3-body amplitude

Full

I

II

[MeV]

KNN

!!N

implications for spectral functions ? weak binding

Y. Ikeda, H. Kamano, T. Sato arXiv:1004.4877 [nucl-th]

.p

!K+ !

p

p

Y

!

!"#$%&'()*+),-%./,0%1-).,/0%!2*3'%3!*4'%&)3+/)51+),-

!"#$%&!

'(

About DISTO

“antikaon-less” ( ) 3-body coupled-channels scenario ?

!p

!0!p, !

+!n

!!N

Open questions:

T. Yamazaki et al. Phys. Rev. Lett. 104 (2010) 132502

How to make sure that K pp is dominant component of measured DISTO spectrum ?

-

M(!

!p)

=2.189

M. Maggiora et al. Nucl. Phys. A835 (2010) 43

!YN

!0p

!+n

p p ! K+ !p (2.85 GeV)

Strong energy dependence ?

(no DISTO effect seen at 2.5 GeV ?)

Low-Energy QCD: spontaneous chiral symmetry breaking scenario established

Summary

Chiral SU(3) x SU(3) Effective Field Theory : Successful framework for low-energy hadron physics with s-quarks

Structure of !(1405) governed by (chiral) SU(3) coupled-channelsdynamics and two-poles scenario

KNN quasibound systems ?

Weak binding + large width from chiral SU(3) dynamics

DISTO (and FINUDA) signals not understood in terms ofdeeply bound state

KNN states ( ! !YN dynamics ?)high-precision KN threshold data

much improved !! mass spectra

Needed and/or in progress:

KNN

Antikaons in interaction

Extrapolations to far-subthreshold region still an issue

!anks to :

Bugra Borasoy Akinobu Doté Tetsuo Hyodo

Yoichi Ikeda Norbert Kaiser Robin Nissler

"e End

antikaon nuclear few body systems - theory … · antikaon-nuclear few-body systems - theory status...

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