K- bound states? A theoretical view V. Magas, A. Ramos (University of Barcelona) E. Oset (University...

K- bound states? A theoretical view

V. Magas, A. Ramos (University of Barcelona)E. Oset (University of Valencia)H. Toki (RCNP,Osaka University)

International Conference on Hypernuclear and Strange Particle Physics, HYP06Mainz, September 10-14, 2006

HYP06, K- bound states? 2

In recent years, there has been a lot of activity in studying the interaction of antikaons with nucleons

K N scattering: a lively topic

K N scattering in the I=0 channel is dominated by the presence of the (1405), located only 27 MeV below the K N threshold

Already in the late sixties, Dalitz, Wong and Rajasekaran [Phys. Rev. 153 (1967) 1617] obtained the (1405) as a KN quasi-bound state in a potential model (Scrhoedinger equation).


The study of KN scattering has been revisited more recently from the modern view of chiral Lagrangians. The presence of a resonance makes PT not applicable non-perturbative techniques implementing unitarization in coupled channels are mandatory!

Since the pioneering work of Kaiser, Siegel and Weise [Nucl. Phys. A594 (1995) 325] many other chiral coupled channel models have been developed.

E. Oset and A. Ramos, Nucl. Phys. A635 (1998) 99J.A. Oller and U.G. Meissner, Phys. Lett. B500 (2001) 263M.F.M. Lutz, E.E. Kolomeitsev, Nucl. Phys. A700 (2002) 193C.Garcia-Recio et al., Phys. Rev. D (2003) 07009 M.F.M. Lutz, E.E. Kolomeitsev, Nucl. Phys. A700 (2002) 193

more channels,next-to-leading order,Born terms beyond WT (s-channel, u-channel),fits including new data…B.Borasoy, R. Nissler, and W. Weise, Phys. Rev. Lett. 94, 213401 (2005); Eur. Phys. J. A25, 79 (2005)

J.A. Oller, J. Prades, and M. Verbeni, Phys. Rev. Lett. 95, 172502 (2005)J. A.Oller, arXiv:hep-ph/0603134.B. Borasoy, U. G. Meissner and R. Nissler, arXiv:hep-ph/0606108.


K in a nuclear medium:The presence of the (1405) resonance makes the in-medium KN interaction to be very sensitive to the particular details of the many-body treatment.

we’d better do a good job! (SELF-CONSISTENCY)

Pauli blocking

free(repulsive)

medium(attractive)

Self-consistent kaon dressing

pion and kaon dressing

K

K

K

K

K

K

Weise, Koch

Ramos,Oset

Lutz


A moderate attraction of about -40 MeV at 0 is obtained

A. Ramos, E. Oset, Nucl. Phys. A671, 481 (2000)L. Tolós, A. Ramos, E. Oset, Phys. Rev. C (2006)

Akaishi and Yamazaki:

Phenomenological KN- potential:

+ many-body treatment (self-consistency ignored) deep optical potential

+ shrinkage effect ((0)~100!) + extra tuning: strongly bound kaonic states: BK = 169 MeV in ppn-K- (T=0) BK = 194 MeV in pnn-K- (T=1)

Other shallow optical potentials:

J. Schaffner-Bielich, V.Koch, M. Effenberber, Nucl. Phys. A669, 153 (2000)A.Cieply, E.Friedman, A.Gal, J.Mares, Nucl. Phys. A696, 173 (2001)

Y.Akaishi, T.Yamazaki, Phys.Rev.C65,044005 (2002)

Y.Akaishi, A. Dote, T.Yamazaki, Phys.Lett.B613, 140 (2005)

see, however: Shevchenko, Gal, Mares, nucl-th/0610022 !


The KEK proton missing mass experiment:

T. Suzuki et al., Phys. Lett. B597, 263 (2004)

S0 is a tribaryon with S = -1 and T = 1

If interpreted as a pnn-K- bound system… BK = 197 MeV

formation rate: 1% per absorbed K-


Oset-Toki’s view:

K- absorption by two nucleons leaving the other nucleons as spectators

E. Oset, H. Toki, Phys. Rev. C74, 015207 (2006)

do not absorbe energy nor momentum from the probe

some Fermi motion broadening is possible, it would explain the ~60 MeV/c peak spreading

p

-

d

NO! This configuration (phase-space-like)would produce more broadening


The FINUDA proton missing mass experiment:

M. Agnello et al, Nucl. Phys. A775, 35 (2006)

This view is consistent with the observation bythe FINUDA collaboration of a peak in the proton missing mass spectrum at ~ 500 MeV/c(from K- absorbed in 6Li)

A study of the angular correlations (p and - are emitted back-to-back) allow them to conclude that the reaction:

in 6Li is the most favorable one to explain their signal

6Li4He


The FINUDA (p) invariant mass experiment M. Agnello et al. Phys. Rev. Lett. 94, 212303 (2005)

But here both emitted particles are detected! (not just the proton)

the invariant mass of the p pair is measured, Mp

The same elementary reaction takes place: K- p p p (select p > 300 MeV/c to eliminate K- N

A peak for the transition to the g.s. of the daugther nucleus should be observed at:

Nuclei:


Transition to the g.s. of daughter nucleus

Interpreted by the FINUDA experiment

as a (K-pp) bound state

M. Agnello et al. Phys. Rev. Lett. 94, 212303 (2005)

Our view:Final State Interactions (FSI) of the primary and p (produced after K- absorption) in their way out of the daughter nucleus!


Our calculation

Monte Carlo simulation of K- absorption by pp and pn pairs in nuclei

For each nucleus, the K- is absorbed mainly from the lowest atomic orbit for which the energy shift has been measured

Primary and N emitted according to phase space:

The K- is absorbed by two nucleons with momenta randomly chosen within the local Fermi sea:

Further collisions of and N as they cross the nucleus according to a probability per unit length with ~2N/3

Finally, the invariant p mass is reconstructed from the final events


Nuclear density profile and overlap

p

p

p


First (narrow) peak: formation of the g.s. of the daughter nucleus

How much strength?Formation probability (FP) x Survival probability (PS)

In light nuclei: FP ~ | 0.3 - 0.7 |2 = 0.1 – 0.5 and PS ~ 0.6 6 - 30% (ex: 7Li (pp)-1 5H)

In heavier nuclei: FP increases but PS decreases also below 30%

for the light nuclei

The largest part of the K- absorption events go into nuclear excitations, mostly to the continuum. Where is this strength located? Obviously at smaller invariant p masses


Second (wider) peak: Quasi-elastic peak (QEP) after K- absorption

A peak is generated in our Monte Carlo simulations when the

primary and p (produced after K- absorption) undergo quasi-elastic collisions with the nucleus, exciting it to the continuum.

This is the analogue of the quasi-elastic peak (QEP) observed in nuclear inclusive reactions using a variety of different probes: (e,e’), (p,p’), (’),…(The QEP comes mostly from one collision of the particles exciting the nucleus to the continuum).

The QEP accounts for the second peak of the FINUDA experiment!


Invariant mass distribution (one-collision)


Allowing up to three collisions


Angular correlations


Mixture of the light targets


Peak does not move with size of nucleus Cannot be a bound K- nuclear state!


Can the peak be due to other processes?

followed by

This peaks around 2170 MeV (where there is indeed a small thirdpeak in the experiment) and has a smaller strength than

A)

B)

followed by

located in the region of the QEP and all events back-to-back,but strength is small, ~ 10-30% of events


Conclusions

The p invariant mass distribution of the FINUDA p invariant massexperiment is naturally explained in terms of thereaction followed by further interactions of the or the N in the daughter nucleus.

E. Oset and H. Toki, Phys. Rev. C74, 015207 (2006)V. K. Magas, E. Oset, A. Ramos and H. Toki, Phys. Rev. C74, 025206 (2006)

The recent experiments of proton missing mass spectra (at KEK and FINUDA) can be explained in terms of K- absorption by two nucleons. The remaining residual system is left in a bound (ground) state.

In summary, present data can be interpreted without the need ofinvoking exotic mechanisms, like the formation of deeply bound K- nuclear states!


We give a conventional explanation: Final State Interactions (FSI) of the primary and p (produced after K- absorption) as they cross the daughter nucleus!

M. Agnello et al. Phys. Rev. Lett. 94, 212303 (2005)

(Discarded in the experimental analysis on the basis of back-to-back correlations)

K- bound states? A theoretical view V. Magas, A. Ramos (University of Barcelona) E. Oset (University...

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