In this talk I present recent developments in chiral dynamics of hadrons and
hadrons in a medium addressing the following points: interaction of the octet
of pseudoscalar mesons with the octet of baryons of the nucleon, showing recent
experimental evidence on the existence of two $\Lambda(1405)$ states, the
interaction of the octet of pseudoscalar mesons with the decuplet of baryons of
the $\Delta$, with particular emphasis on the $\Lambda(1520)$ resonance,
dynamically generated by this interaction. Then I review the interaction of
kaons in a nuclear medium and briefly discuss the situation around the claims
of deeply bound states in nuclei. The large renormalization of the
$\Lambda(1520)$ in the nuclear medium is shown as another example of successful
application of the chiral unitary techniques.Comment: Talk at the Fifth International Conference on Perspectives in
  Hadronic Physics: Particle-Nucleus and Nucleus-Nucleus Scattering at
  Relativistic Energies, Trieste, May 200

A. Ramos

Agnello

Akaishi

Bernard

E. Oset

Ecker

H. Toki

Hirenzaki

Hyodo

Jido

Kaskulov

Kolomeitsev

L. Roca

Lutz

M. Kaskulov

M.J. Vicente Vacas

Magas

Mast

Meissner

Oller

Oset

Prakhov

Ramos

Roca

S. Sarkar

Sarkar

V.K. Magas

Nuclear Physics A

English

arXiv

In this talk I present recent developments in chiral dynamics of hadrons and hadrons in a medium addressing the following points: interaction of the octet of pseudoscalar mesons with the octet of baryons of the nucleon, showing recent experimental evidence oil the existence of two Lambda(1405) states, the interaction of the octet of pseudoscalar mesons with the decuplet of baryons of the Delta, with particular emphasis on the Lambda(1520) resonance, dynamically generated by this interaction. Then I review the interaction of kaons in a nuclear medium and briefly discuss the situation around the claims of deeply bound states in nuclei. The large renormalization of the Lambda(1520) in the nuclear medium is shown as another example of successful application of the chiral unitary techniques

Oset Báguena, Eulogio

Sarkar, S.

Vicente Vacas, Manuel José

Kaskulov, Murat M.

Roca Zamora, Luis

Magas, Volodymyr

Ramos Gómez, Àngels

Toki, Hiroshi

Repositori d'Objectes Digitals per a l'Ensenyament la Recerca i la Cultura

arXiv:nucl-th/0607051v1  24 Jul 2006Recent developments in chiral dynamics of hadrons and hadrons in anuclear mediumE. Oset a, S. Sarkar a, M. J. Vicente Vacas a, M. Kaskulov a, L. Roca a, V.K. Magas b,A. Ramos b and H. Toki caDepartamento de Fisica Teorica e IFIC, Centro Mixto Universidad de Valencia-CSIC,Institutos de Investigacion de Paterna, Apdo 22085, 46071 Valencia, SpainbDepartament d’Estructura i Constituents de la Materia, Universitat de Barcelona,SpaincRCNP, Osaka University, JapanIn this talk I present recent developments in chiral dynamics of hadrons and hadrons ina medium addressing the following points: interaction of the octet of pseudoscalar mesonswith the octet of baryons of the nucleon, showing recent experimental evidence on theexistence of two Λ(1405) states, the interaction of the octet of pseudoscalar mesons withthe decuplet of baryons of the ∆, with particular emphasis on the Λ(1520) resonance,dynamically generated by this interaction. Then I review the interaction of kaons in anuclear medium and briefly discuss the situation around the claims of deeply bound statesin nuclei. The large renormalization of the Λ(1520) in the nuclear medium is shown asanother example of successful application of the chiral unitary techniques.1. IntroductionChiral theory has caught up as an important tool to deal with hadron reactions atlow and intermediate energies, accounting for the underlying basic QCD dynamics. Byintroducing chiral Lagrangians where the explicit fields are mesons and baryons, a per-turbative expansion in powers of momenta is done, leading to chiral perturbation theory(χPT ) which has allowed great progress in hadron physics. A very important developmentin this direction is done with the introduction of unitarity in coupled channels which hasallowed to extend the predictions of chiral theory at higher energies than is possible withchiral perturbation theory. A review of the basic ideas can be found in [ 1]. One of theimportant issues of this unitarized theory is that it allows to deal with resonances, someof which appear necessarily as a consequence of the dynamics of the chiral Lagrangians, ina similar way as bound states or resonances appear in potential theory in Quantum Me-chanics. We call these resonances dynamically generated and by now about 10-15 percentof the particles in the PDG can qualify for this nature, meaning that the meson- mesoncloud, or meson-baryon cloud, becomes the basic part of the wave function overriding therelevance of the primary building blocks: constituent qq¯ or three q for the case of mesonsor baryons, respectively. I shall mention here some of these cases.2 E. OsetThe findings about the nature of some resonances have also consequences in nuclearphysics, since basic features associated to the chiral dynamics of the resonances show upin interesting ways in nuclear processes which can then be used to stress the nature ofthese resonances. I shall also give some example of that in this talk. A more extensivedescription of the ideas exposed here can be found in [ 2], but we concentrate here on therecent developments not discussed in [ 2].2. The meson baryon interactionWe skip here details on the chiral lagrangians which can be found in [ 1, 2, 3, 4]and sketchhow unitarity enters the framework. One can find a systematic and easilycomprehensible derivation of the ideas of the N/D method applied for the first time tothe meson baryon system in [ 5], which we reproduce here below and which follows closelythe similar developments used before in the meson meson interaction [ 6]. One defines thetransition T−matrix as Ti,j between the coupled channels which couple to certain quantumnumbers. For instance in the case of K¯N scattering studied in [ 5] the channels with zerocharge are K−p, K¯0n, pi0Σ0,pi+Σ−, pi−Σ+, pi0Λ, ηΛ, ηΣ0, K+Ξ−, K0Ξ0. Unitarity incoupled channels is written asImTi,j = Ti,lρlT∗l,j (1)where ρi ≡ 2Mlqi/(8piW ), with qi the modulus of the c.m. three–momentum, and thesubscripts i and j refer to the physical channels. This equation is most efficiently writtenin terms of the inverse amplitude asIm T−1(W )ij = −ρ(W )iδij , (2)The unitarity relation in Eq. (2) gives rise to a cut in the T–matrix of partial waveamplitudes, which is usually called the unitarity or right–hand cut. Hence one can writedown a dispersion relation for T−1(W )T−1(W )ij = −δij{a˜i(s0) +s− s0pi∫∞sids′ρ(s′)i(s′ − s)(s′ − s0)}+ T −1(W )ij , (3)where si is the value of the s variable at the threshold of channel i and T−1(W )ij indicatesother contributions coming from local and pole terms, as well as crossed channel dynamicsbut without right–hand cut. These extra terms are taken directly from χPT after requiringthe matching of the general result to the χPT expressions. Notice also that the curledbracket, that we call the g(s) function, is the familiar scalar loop integral.One can further simplify the notation by employing a matrix formalism. Introducingthe matrices g(s) = diag (g(s)i), T and T , the latter defined in terms of the matrixelements Tij and Tij , the T -matrix can be written as:T (W ) = [I − T (W ) · g(s)]−1 · T (W ) . (4)which can be recast in a more familiar form asT (W ) = T (W ) + T (W )g(s)T (W ) (5)1-column format camera-ready paper in LATEX 3250200150100500Im zR   [MeV]17001600150014001300Re zR   [MeV] 1390     (I=0)  1426     (I=0) 1680     (I=0) 1580     (I=1) disappear     (I=1)Singlet OctetFigure 1. Trajectories of the poles in the scattering amplitudes obtained by changingthe SU(3) breaking gradually. The symbols correspond to the step size δx = 0.1 with xrunning from 0 to 1 . The results are from [ 8].Now imagine one is taking the lowest order chiral amplitude for the kernel T as donein [ 5]. Then the former equation is nothing but the Bethe Salpeter equation with thekernel taken from the lowest order Lagrangian and factorized on shell, the same approachfollowed in [ 7], where different arguments were used to justify the on shell factorizationof the kernel.The on shell factorization of the kernel, justified here with the N/D method, rendersthe set of coupled Bethe Salpeter integral equations a simple set of algebraic equations.3. Poles of the T-matrixThe amplitudes of the channels discussed above are extrapolated to the complex secondRiemann sheet and we search for poles there. Here I discuss recent finding concerning thetwo poles corresponding to the Λ(1405) resonance. In fig. 1 we can see, from the work of[ 8], the trajectories of the poles when we start from an SU(3) symmetric situation andgo to the real world where this symmetry is broken. This appears because of the differentmasses of the mesons and the baryon in the study of the interaction of the octet of thepion and the octet of the nucleon respectively. The SU(3) symmetric case corresponds tothe poles in the real axis where we have two degenerate octets and a singlet. As soon asSU(3) symmetry starts being broken the degeneracy of the two octets disappears and twobranches for I=0 and for I=1 develop which, at the end of the trajectories that representthe real world, correspond to well know resonances like the Λ(1670) etc.The interesting thing to note is that in the region of the Λ(1405) there are two poles, onefrom the original singlet and another one from one of the branches of the original octet.In practice it is impossible to see two peaks in any reaction because the two resonancesoverlap, but the fact that the two poles couple differently to K¯N and piΣ (the narrowerpole couples strongly to K¯N and the wider one to piΣ) has as a consequence that the4 E. OsetΛ(1405) should show up with quite different shapes in different reactions depending ontheir particular dynamics. This is indeed the case as could be demonstrated recently withthe performance of the K−p → pi0pi0Σ0 [ 9] experiment. This reaction has been studiedin [ 10] and the basic mechanism for the reaction is given by fig. 2 left, where we seethat it is dominated by the K−p→ pi0Σ0 amplitude which has a strong contribution fromthe narrow pole at higher energies. We should then expect that the peak of the Λ(1405)appears at higher energies in this reaction and with a smaller width, and this is the caseas one can see in fig. 2 right by comparing with the standard Λ(1405) extracted fromthe pi−p→ K0piΣ reaction which was studied in [ 11].The two experimental figures for the shapes of the Λ(1405) in both reactions can beseen in Fig. 2 right, giving a strong support to the existence of the two Λ(1405) states.pi0pi0Σ0K−p1.3 1.35 1.4 1.45 1.5 1.5500.511.522.5 x 10−12MI, GeVdσ/d MI, arb. units K− p −−> pi0 pi0 Σ0pi− p −−> K0 pi ΣMΛ=1395 MeVMΛ=1420 MeVFigure 2. Nucleon pole term for the K−p → pi0Σ0 (left) and two experimental shapes ofΛ(1405) resonance (right). See text for more details.4. The interaction of the decuplet of baryons with the octet of mesonsGiven the success of the chiral unitary approach in generating dynamically low en-ergy resonances from the interaction of the octets of stable baryons and the pseudoscalarmesons, in [ 12] the interaction of the decuplet of 3/2+ with the octet of pseudoscalarmesons was studied and shown to lead to many states which were associated to experi-mentally well established 3/2− resonances. One of these would correspond to the Λ(1520).In [ 13, 14] a refinement of the approach discussed above has been done including theK¯N and piΣ decay channels of the Λ(1520) and finetuning the subtraction constants inthe g function, such that a good agreement with the position and width of the Λ(1520)is attained. With this new information one can face the study of the reaction K−p →pi0pi0Λ by using the mechanisms of K−p→ pi0Σ∗0 → pi0pi0Λ which provides the dominantcontribution to the reaction at energies close to the Λ(1520). At higher energies of theexperiment of [ 15] one finds other background mechanisms (dashed line in fig. 3)providing a contribution that helps bring the theory and experiment in good agreement,as we can see in fig. 3. One can see in the figure that up to 575 MeV/c of momentumof the K− the mechanism based on the strong coupling of the Λ(1520) to the piΣ(1385)1-column format camera-ready paper in LATEX 5channel is largely dominant and provides the right strength of the cross section. Obviouslyit would be most interesting to investigate the region of lower energies of the K− in orderto see if the predictions done by the theory are accurate. This could be done for adifferent reaction, the K−p → pi+pi−Λ [ 16], where the cross section is double than forK−p → pi0pi0Λ. As we can see in fig. 3, the predictions of the theory are in goodagreement with the data.350 400 450 500 550 600 650 700q  (MeV)00.20.40.60.811.21.41.61.82 σ(K-p    pi0 pi0 Λ)   (mb)300 320 340 360 380 400 420 440 460q  (MeV)00.511.522.533.54 σ(K-p    pi+pi−Λ)   (mb)Figure 3. Cross section for the K−p→ pi0pi0Λ (left) and K−p→ pi+pi−Λ [ 16] right.5. K¯ in a nuclear mediumThe K¯ interaction in a nuclear medium has been the subject of many studies. In [ 17]a selfconsistent calculation of the K¯ nucleus optical potential is done and the results areconsistent with data of kaonic atoms as shown in [ 18]. This potential has a strength ofabout 50 MeV attraction at normal nuclear matter and an imaginary part of about 50MeV. This leads to deeply bound states in nuclei of about 30 MeV binding and widths ofaround 100 MeV. It was hence surprising to find other potentials where, with only threenucleons, the K¯ potential reaches a strength of about 650 MeV at the center for the nucleus[ 19]. A closer inspection shows that the huge results come from several approximationsamong them the lack of selfconsistency in the calculations that, according to [ 20], leads tomeaningless results, plus the shrinking of the nucleus to attain ten times nuclear matterdensity at the center of the nucleus. Based on this potential, some peaks seen at KEKin the proton spectra following the absorption of K− on 4He were interpreted as a signalof deeply bound kaonic states. Recently, it was shown in [ 21] that the peaks of theexperiments could be easily interpreted in terms of K− absorption by pairs of nucleonsleading to Σp or Λp without further interaction of the baryons with the nucleus. Thisclaim has been recently reinforced by an experiment at FINUDA [ 22] where the protonspectra is also studied following K− absorption in different nuclei and the same peaks areseen. An additional measurement of pions in coincidence shows that they come from thedecay of the Σ for the peak at lower proton momentum, hence, confirming the claims of[ 21].6 E. OsetThe FINUDA collaboration has another paper [ 23] in which a wider peak has been seenin the invariant mass of pΛ measured back to back following K− absorption in differentnuclei and which was claimed to correspond the a K−pp bound state. In another recentpaper [ 24] it has been shown that such a peak appears unavoidably as a consequence of themechanism of K− absorption by a pair of nucleons going to pΛ, followed by rescatteringof the p or the Λ in the nucleus. Thus, the claims made for deeply bound kaons in nucleiwith binding energies of about 200 MeV and narrow widths are unfounded and this wasthe conclusion of a recent meeting explicitly devoted to this issue in ECT ∗ Trento [ 25].6. Λ(1520) in a nuclear mediumWithin these techniques there is work done in η selfenergy in the medium, ρ and φrenormalization in nuclei and others, but I shall concentrate here on the latest issuewhich has connections with section 4, where we studied the interaction of the decupledof baryons with the octet of nucleons. The Λ(1520) is one of the resonances dynamicallygenerated with the channels piΣ(1385) and KΞ. Actually, this picture is only qualitativesince the Λ(1520) couples also to the piΣ and K¯N channels to which it decays. Thestudy done in [ 14] including these channels finds that the coupling of the resonance tothe piΣ(1385) is the strongest of all, as if it kept memory of what would happen in asimplified ideal world.Λ∗ Λ∗Ν−Λ∗ Λ∗Σ(1189)Λ∗ Λ∗Ν−Σ(1189) Σ(1189)Λ∗ Λ∗Ν−Λ∗ Λ∗ Λ∗ Λ∗Ν−Λ∗ Λ∗Ν−Λ∗ Λ∗ Λ∗ Λ∗Ν−Σ (1385)∗ Σ (1385)∗ Σ (1385)∗Κ−Κ− Κ− Κ− Κ−pi piΝpipi piΝ Ν Νpi piΝpipi pi∆∆(1232)Σ(1189),Λ(1115) Σ(1385)a) b) c)d) e) f)g) h) i)Figure 4. Diagrams for the Λ(1520) selfnergy in the nuclear mediumEven if the Λ(1520) couples strongly to the piΣ(1385) channel, it does not decay intothis state because it is below the threshold of piΣ(1385). However, in a nucleus the pion1-column format camera-ready paper in LATEX 7can easily excite a ph which has energy starting from zero. Thus we gain 140 MeV phasespace for the decay and this leads to a width in the medium from only this channel whichis already bigger than the 14 MeV free width of the Λ(1520). This is not the only source ofmedium modification for the resonance, since the other decay channels are also modifiedin the medium. A detailed study has been done [ 26] (see diagrams in fig. 4 ) and wepresent the results in fig. 5.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2ρ/ρ00102030405060708090100Γ Λ(1520) [MeV]0.8 0.85 0.9 0.95 1 1.05 1.1 1.15PΛ(1520) [GeV]1020304050Re[δΣ]Λ(1520) [MeV]δρ0δρ0/2δρ0/40.85 0.9 0.95 1 1.05 1.1 1.15PΛ(1520) [GeV]0102030405060708090100-Im [Σ] Λ(1520) [MeV]ρ0ρ0/2ρ0/4a) b) c)Figure 5. Results for the Λ(1520) selfenergy as a function of the nuclear density andΛ(1520) momentum.7. ConclusionsThe use of chiral Lagrangians for the meson baryon interaction and the unitary exten-sions of chiral perturbation theory have allowed to face a large amount of problems whichwere barred to standard perturbation techniques. It has opened the door to the studyof many baryonic resonances which qualify neatly as dynamically generated resonances,or quasibound states of meson baryon. Thanks to this, a quantitative description of themeson baryon interaction at intermediate energies is now possible and with this, an im-portant systematics has been introduced in the many body problem to face issues on therenormalization of hadron properties in the nuclear medium. The constructed scheme israther powerful and allows to make predictions which consecutive experiments are prov-ing right. Two of these predictions, the two states for the Λ(1405), and the nature ofthe Λ(1520) roughly as a quasibound state of piΣ(1385), have found strong support fromtwo very recent experiments. The spectacular change of the width of the Λ(1520) in themedium is partly due to the strong coupling of the resonance to the piΣ(1385) as predictedby chiral unitary dynamics. Finally, we also discussed that chiral theory, implementingselfconsistency in the many body calculation, leads to a moderate attraction for K¯ innuclei, and that recents claims for deeply bound kaon states, which would require a hugeK¯ optical potential, were a consequence of an incorrect identification of some peaks forwhich a natural conventional explanation has been just found.8 E. OsetAltogether, one is seeing through all this work that chiral dynamics is a key ingredientthat allows a unified description of much of the hadronic world at low and intermediateenergies.8. AcknowledgmentsThis work is partly supported by the Spanish CSIC and JSPS collaboration, the DG-ICYT contract number BFM2003-00856, and the E.U. EURIDICE network contract no.HPRN-CT-2002-00311. This research is part of the EU Integrated Infrastructure Initia-tive Hadron Physics Project under contract number RII3-CT-2004-506078.REFERENCES1. J. A. Oller, E. Oset and A. Ramos, Prog. Part. Nucl. Phys. 45 (2000) 157.2. E. Oset, D. Cabrera, V. K. Magas, L. Roca, S. Sarkar, M. J. Vicente Va-cas and A. Ramos, Lectures at Puri Hadron Workshop, Pramana 66 (2006) 731[arXiv:nucl-th/0504033].3. U. G. Meissner, Rep. Prog. Phys. 56 (1993) 903; V. Bernard, N. Kaiser and U. G.Meissner, Int. J. Mod. Phys. E4 (1995) 193.4. G. Ecker, Prog. Part. Nucl. Phys. 35 (1995) 1.5. J. A. Oller and U. G. Meissner, Phys. Lett. B 500 (2001) 2636. J. A. Oller and E. Oset, Phys. Rev. D 60 (1999) 074023.7. E. Oset and A. Ramos, Nucl. Phys. A 635 (1998) 99.8. D. Jido, J.A. Oller, E. Oset, A. Ramos, U.G. Meissner, Nucl. Phys. A 725 (2003) 181.9. S. Prakhov et al. [Crystall Ball Collaboration], Phys. Rev. C 70 (2004) 034605.10. V. K. Magas, E. Oset and A. Ramos, Phys. Rev. Lett. 95 (2005) 052301.11. T. Hyodo, A. Hosaka, E. Oset, A. Ramos and M. J. Vicente Vacas, Phys. Rev. C 68(2003) 065203.12. E. E. Kolomeitsev and M. F. M. Lutz, Phys. Lett. B 585 (2004) 243.13. S. Sarkar, E. Oset and M. J. Vicente Vacas, Nucl. Phys. A 750 (2005) 294.14. L. Roca, S. Sarkar, V. K. Magas and E. Oset, Phys. Rev. C 73 (2006) 045208.15. S. Prakhov et al., Phys. Rev. C 69 (2004) 042202.16. T. S. Mast, M. Alston-Garnjost, R. O. Bangerter, A. Barbaro-Galtieri, F. T. Solmitzand R. D. Tripp, Phys. Rev. D 7 (1973) 5.17. A. Ramos and E. Oset, Nucl. Phys. A 671 (2000) 481.18. S. Hirenzaki, Y.Okumura, H. Toki, E. Oset and A. Ramos, Phys. Rev. C61 (2000)055205.19. Y. Akaishi, A. Dote and T. Yamazaki, Phys. Lett. B 613 (2005) 140.20. M. Lutz, Phys. Lett. B426 (1998) 12.21. E. Oset and H. Toki, Phys. Rev. C, in print. arXiv:nucl-th/0509048.22. M. Agnello et al., arXiv:nucl-ex/0606021.23. M. Agnello et al. [FINUDA Collaboration], Phys. Rev. Lett. 94 (2005) 212303.24. V. K. Magas, E. Oset, A. Ramos and H. Toki, arXiv:nucl-th/0601013.25. http://www.itkp.uni-bonn.de/percent7Erusetsky/TRENTO06/trento06.html26. M. Kaskulov and E. Oset, Phys. Rev. C 73 (2006) 045213.

Recent developments in chiral dynamics of hadrons and hadrons in a nuclear medium

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Recent developments in chiral dynamics of hadrons and hadrons in a
  nuclear medium

Recent developments in chiral dynamics of hadrons and hadrons in a nuclear medium

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Repositori d'Objectes Digitals per a l'Ensenyament la Recerca i la Cultura

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