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Strange mesons in nuclei. S=-1 mesons: - K ( J p =0 - ) - K* ( J p =1 - ). A. Ramos University of Barcelona (JPS+SPHERE meeting, Vila Lanna , Prague 4-6 September, 2010). in collaboration with : V.K. Magas , E. Oset , R. Molina, L . Tolós , J. Yamagata- Sekihara , S. Hirenzaki.

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Strange mesons in nuclei

S=-1 mesons:

- K (Jp=0-)

- K* (Jp=1-)

A. Ramos

University of Barcelona

(JPS+SPHERE meeting, Vila Lanna, Prague 4-6 September, 2010)

in collaboration with :

V.K. Magas, E. Oset, R. Molina, L. Tolós,

J. Yamagata-Sekihara, S. Hirenzaki

PseudoscalarK mesons in nuclei
  • Understanding the properties of Kbar mesons has been one of the major goals in strange nuclear physics.
  • How attractive is the Kbar-nucleus optical potential?
  • May kaon condensation occur in neutron star interiors?
  • Phenomenological fits to kaonic atom data preferred UK(r0) ~ -200 MeV


  • Self-consistent theoretical calculationsthat use realisticKbar N interactions
  • (KN data reproduced, chiral dynamics) obtain UK(r0) ~ -50 to -70 MeV


  • Evidences of deeply bound K- nuclear states (BK ~ 100 MeV) from slow kaon reactions on nuclei has been claimed
The observed peaks in nuclear reactions using slowkaons:
  • (K-stop, p) (bump)
  • (K-stop, Lp)
  • (K-stop, Ld)
  • can be explained in terms of conventional input that combines:
  • an absorption mechanism
    • K-NN  LN (in 1. and 2.)
    • K-NNN  Ld (in 3.)
  • nuclear medium effects:
  • Fermi motion/recoil
  • (direct reaction peaks broaden)
  • FSI of the emitted particles (if daughter nucleus is big enough)
  • ( secondary peaks/structures may appear)

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

T. Suzuki et al., Mod. Phys. Lett. A23, 2520 (2008)

M. Agnello et al. Phys. Lett. B654, 80 (2007)

T. Suzuki al. Phys. Rev .C76, 068202 (2007)

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

V.K. Magas, E. Oset and A. Ramos, Phys. Rev C77, 065210 (2008)

V.K. Magas, E. Oset, A. Ramos and H. Toki, Nucl.Phys. A804, 219 (2008)

V.K. Magas, E. Oset, A. Ramos and H. Toki, Phys. Rev. 74 (2006) 025206

Another “evidence” for a very deeply attractive K- nucleus potential:

The (K-,p) reaction on 12C at KEK

T. Kishimoto et al., Prog. Theor. Phys. 118 (2007) 181

pK = 1 GeV/c

  • in-flight kaons
  • forward nucleons

qp < 4.1o

(the most energetic)

plus “coincidence requirement”:

(at least one charged particle in decay counters surrounding the target)

claimed not to affect the spectrum shape

Analysis of T. Kishimoto et al., Prog. Theor. Phys. 118 (2007) 181
  • Process: quasielastic scattering K- p  K- p in nuclei
  • Green’s function method
  • Normalization: fitted to experiment
  • Background: fitted to experiment

Re UK=−60 MeVIm UK=−60 MeV

Re UK=−190 MeVIm UK=−40 MeV

Re UK=−160 MeVIm UK=−50 MeV

The only mechanism for fast proton emission in the Green’s function method is

the quasielastic process K- p  K- p where the low-energy kaonin the final statefeels a nuclear optical potential and can occupy stable orbits (no width) , unstable orbits, or be in the continuum (quasifree process)

However, there are other mechanisms that can contribute:

  • Multistep processes:
  • K- and/or N undergo secondary collisions as they leave the nucleus
  • One-nucleon absorption:
  • K- N  p L and K- N  p S
  • followed by decay of L or S into pp
  • Two-body absorption:
  • K- N N S N and K- N N L N
  • followed by hyperon decays

Taken from J. Yamagata and S. Hirenzaki,

Eur. Phys. J. A 31, 255{262 (2007)

We implement these processes in a Monte Carlo simulation of K- absorption in nuclei

Monte Carlo simulation

(details in next talk by V. Magas)

  • Thenucleusisdescribedby a nuclear densityprofiler(r)
  • Theincoming K- willexperience a certainprocess (quasielastic,
  • one-nucleonortwo-nucleonabsorption) at a pointrwith a probability
  • givenbysqerdl, s1Nrdl ors2Nrdlwheredlis a typicalstepsize.
  • Once a process has beendecided, we determine the local momenta
  • of theemittedparticlesaccordingtophasespace
  • Furthercollisions of theemittedparticles as theycrossthenucleus.
  • Wefollow: theK-untilitleavesthenucleusorgets absorbed
  • allenergeticp and n(untiltheyleavethenucleus)
  • allenergeticL and S(untiltheyleavethenucleusand decayintopN)
  • Finally, werepresentthespectra of theemergingprotons
Proton spectrum

V.K. Magas, J. Yamagata-Sekihara, S. Hirenzaki, E. Oset and A. Ramos, Phys. Rev. C81, 024609 (2010).

No coincidence


1N-absorption, rescattering

2N absorption, rescattering

 Oursimulationshouldconsider the coincidence requirement of KEK-PS E548

“The experiment measures the proton PLUS at least one charged particle in the decay counters surrounding the target”

The simulation of such coincidence requirement is tremendously difficult, because it would imply keeping track of all charged particles coming out from all possible scatterings and decays.

The best we can do is to eliminateprocesses that, for sure, cannot have a coincidence: quasi-elastic K- p  K- p events where neither the p nor the K-suffer secondary collisions. (In this type of processes the fast p moves forward and the K- escapes undetected through the back).

 minimal coincidence requirement

Comparison with KEK data:

The coincidence requirement removes a substantial fraction of events and changes the shape of the spectrum drastically

Comparison with KEK data:

Supp. ~ 1.0

Supp. ~0.7

Low energy p – multiparticle final states

 should be less supressed!

The results of the in-flight 12C(K-,N) reaction at KEK (PS-E548) can probably be
  • explained with a conventional kaonoptical potential(UK(r0) ~ -60 MeV)
  • We have seen that the coincidence requirement introduces a non-negligible
  • distortion in the spectrum
  • This distortion is comparable in size (even bigger) than that produced by using a
  • different kaon optical potential.
Vector K* mesons in nuclei

 From (K-,K*-) reaction in nuclei

(see V. Magas’ talk)

The study of vector meson properties in the nuclear medium has received a lot of attention, since they are tied to fundamental aspects of QCD

ρ meson: KEK325, CLAS-g7, CERES, NA60

ω meson: NA60, CBELSA/TAPS

ϕ meson: KEK325, LEPS, COSY-ANKE

Less attention has been paid to the K* meson!

(probably because it does not decay into dileptons).



K* N interaction in free space:

(coupled-channels model)

E. Oset, A. Ramos, Eur.Phys.J. A44 (2010) 431



ωΛ, ωΣ

ρΛ, ρΣ

ϕΛ, ϕΣ


Tij = Vij + Vil GlTlj

transition potential

 From local hidden gauge formalism

Bando et al. Phys. Rev. Lett. 54, 1215 (85); Phys. Rep. 164, 217 (88)

  • Deals simultaneously with vector and pseudoscalarmesons
  • Implements chiral symmetry naturally
  • Leads to the same lowest order Lagrangian for pseudoscalarmesons
  • Reproduces all the empirically successful low-energy relations of the rmeson (KSFR) relation, vector meson dominance,…)
transition potential VB->VB


Bando et al, PRL 112 (1985)

and Phys. Rep. 164 (1988) 217

 KSFR relation

BBV vertex

Klingl, Kaiser, Weise,

NPA 624 (1997) 527

(same s-wave amplitude as in P B  P B S-wave scattering)

Loop function G incorporates mass distribution (width) of vector meson



1783, Γ=9


Λ(1690) 3/2-

Λ(1800) 1/2-

1830, Γ=42


Σ(1750) 1/2-

Our resonances are narrower than

known PDG states because coupling

to pseudoscalar-baryon channels is

not included

K* self-energy in the medium

a) K*  K p and medium modifications

free decay : G = -ImP/MK*= 50 MeV

medium corrections (absorption)


N, D

vertex corrections

The K* width increases substantially (factor 2)

due to pion self-energy in nuclear matter




Tij = Vij + Vil GlTlj



Tij(r) = Vij + VilGl(r)Tlj(r)

b) K* N interaction in the medium:

q.e. process K*N  K*N ,

and also new absorption processes: K*N  pKN, K*NN  KNN

Free space

meson dressing


Pauli blocking


baryon dressing




DressedK* meson:

L. Tolos, R. Molina, E. Oset, and A. Ramos,

arXiv:1006.3454 [nucl-th].

K* self-energy in the medium

K* width at normal nuclear matter density (r0) is 5-6 times larger than in free space!!

Can it be checked by some reaction in nuclei?? (V. Magas, next talk )