A method to identify hadronic molecules in the particle spectrum is reviewed
and the conditions for its applicability discussed. Special emphasis is put on
the discussion of molecule candidates in the baryon spectrum.Comment: Talk presentent at NSTAR 2007, 5 - 8 September 2007, Bonn, German

Baru

C. Hanhart

Doring

Faessler

Hanhart

Jido

Jones

Kaiser

Kolomeitsev

Krehl

Morgan

Roca

Sarkar

Schutz

Weinberg

Weinstein

Yao)

English

arXiv

A method to identify hadronic molecules in the particle spectrum is reviewed and the conditions for its applicability discussed. Special emphasis is put on the discussion of molecule candidates in the baryon spectrum

Hanhart, C.

Juelich Shared Electronic Resources

arXiv:0711.0578v1  [hep-ph]  5 Nov 2007EPJ manuscript No.(will be inserted by the editor)How and when can one identify hadronic molecules in the baryonspectrumC. HanhartInstitut fu¨r Kernphysik (Theorie), Forschungzentrum Ju¨lich, D-52425 Ju¨lich, GermanyReceived: date / Revised version: dateAbstract. A method to identify hadronic molecules in the particle spectrum is reviewed and the conditionsfor its applicability discussed. Special emphasis is put on the discussion of molecule candidates in the baryonspectrum.PACS. PACS-key discribing text of that key – PACS-key discribing text of that key1 IntroductionIf we want to deduce any information about quark con-finement from the hadron spectrum, it is necessary to dis-entangle those states that exist due to inter–quark (orquark–gluon or gluon–gluon) interactions from those thatexist due to hadron–hadron interactions. The latter I willcall hadronic molecules, the former elementary states (some-times I will also use the notion quark states, however, itshould become clear that the method outlined only al-lows one to quantify the molecular component of a stateand not to draw any conclusion on the composition ofthe elementary part, which might be a conventional me-son/baryon or diquark–antidiquark/pentaquark or con-tain valence gluons). Since also the individual hadrons aremade of quarks and gluons this distinction sounds quiteacademic. However, this is not the case. In this presen-tation I will first discuss under which circumstances wehave a chance to identify hadronic molecules in a modelindependent way. After this, the conditions are checked forvarious baryons that are candidates for molecules in thespectrum. Then the example of the Λ(1520) is discussedin some detail.Before going into details some general remarks are use-ful. What we call a hadronic molecule1 is an object thatexists as the result of non–perturbative hadron–hadron in-teractions. For the considerations below it is not necessaryto assume a particular mechanism for the hadron–hadroninteraction. All that will be needed is that this interac-tion is attractive and sufficiently strong to form a boundstate — the latter property will be parameterized by an ef-fective coupling constant. To understand under which cir-cumstances it is possible to disentangle hadronic moleculesand quark states, let us look at the analytic properties ofa general loop digram with either of these degrees of free-1 In Ref. [1] the same objects are baptized extraordinaryhadrons.qq¯= (Polynomial in E)h1h2={iµ√Eµ+ (Pol. in E); E > 0−µ√−Eµ+ (Pol. in E); E < 0Fig. 1. Illustration of the essential difference between hadronloops (or loops of colour neutral objects) and quark–loops(or loops of coloured objects): only the former have non–analyticities.dom as possibilities for the essential building block of aparticular state (for simplicity, in this section we discussthe case of mesons only — the generalization of the argu-ment to baryons is straightforward). Since quarks can notgo on–shell, the corresponding loop integral needs to leadto a function analytic in the energy. On the other hand, inaddition to an analytic part, the hadronic loop containsalso a non–analytic piece that originates from the unitar-ity cut. This piece is genuine to the two–hadron loop. Thissituation is illustrated in Fig. 1. Thus, if we can identifysituations where this non–analytic piece gives the mostprominent contribution for molecules, we should have achance to disentangle model independently hadronic fromquark loops or, better, hadronic molecules from elemen-tary states. In the next section we will briefly sketch howthis argument can be made quantitative.2 FormalismThe analysis is based on a series of papers by S. Wein-berg that allowed him to deduce that the deuteron can be2 C. Hanhart: How and when can one identify hadronic molecules in the baryon spectrumviewed as a proton–neutron bound state [2]. The formal-ism can be applied, if the binding momentum γ =√2µǫis much smaller than any other intrinsic scale of the prob-lem. Here, ǫ denotes the binding energy with respect to thenearby continuum channel characterized by its reducedmass µ. Especially, γ ≪ β is a necessary condition, whereβ denotes the inverse of the range of forces. Then the lowenergy scattering parameters — or equivalently the effec-tive coupling constant, geff , of the physical state to thecontinuum — provide a direct measure of the molecularcomponent of the state. It was shown that (in the normal-isation of Ref. [3])g2eff4π= 16(m1 +m2)(1−Z)√2µǫ≤ 16(m1 +m2)√2ǫµ .where Z is a direct measure of the nature of the state:Z = 1 for a purely elementary state and Z = 0 for amolecule. For a short derivation of the above result seeRef. [3]. In Ref. [4] it was argued that the same formalismcan also be used in the presence of inelastic channels, aslong as the corresponding thresholds are sufficiently faraway and the states are narrow. It can be shown [4] thatthe results described are equivalent to those of Refs. [5]derived from the theory of scattering off a potential.When this formalism was applied to the scalar mesonsa0(980) and f0(980) it was found from an analysis of a se-ries of reactions [9] that the latter is indeed predominantlyof molecular nature, in line with the results of Refs. [10],while the former did not give results that point at anunambiguous interpretation. This might either point ata prominent non–molecular contribution to the a0 struc-ture, or the a0 is not a bound state, but a virtual state.In Ref. [6] the same ideas were applied to an analysis ofthe decays of the Ds(2317) viewed as a KD–molecule.The relation of Eq. (1) was confirmed in a microscopicmodel [7]. In the same spirit, in Ref. [8] the data on thehidden–charm resonanceX(3872) was shown to be consis-tent with an interpretation as a virtual state in the D∗D¯system.In the rest of this paper we discuss the possibilitiesof the application of the method to the baryon spectrum,which was not yet done in detail.3 Application to the baryon spectrumRecently a sizable number of baryon resonances was iden-tified as candidates for hadronic molecules. We will now gothrough some examples and check for the relevant scales ofthe individual problems to see to what extend the methoddescribed in the previous section is applicable.Probably the classic example for a dynamically gener-ated baryon state is the Λ(1405) — proposed to originatefrom meson–baryon dynamics as early as 1977 [11]. It islocated quite close to the ΛK threshold (ǫ ∼ 30 MeV),however, also the πΣ threshold is nearby (ǫ ∼ 70 MeV).In addition, recently this state was re-investigated withinthe chiral unitary approach [12] with the result that itis supposedly composed of two nearby singularities. Thisintroduces a new, small parameter into the system. Forthese two reasons the formalism of the previous sectioncan not be applied.The next state of possible dynamical origin is the πNresonance S11(1535) [13]. This state is known to couplestrongly to the ηN–channel. However, it is only a reso-nance in this channel since it is located above the ηNthreshold — mη +MN = 1487 MeV — and it is thereforeunlikely to be a dynamical ηN state (see also Ref. [14]). InRef. [13] the binding is provided in the strangeness chan-nels KΣ and KΛ— however, those are further away fromthe pole position of the S11(1535) — mK +MΣ = 1687MeV and mK +MΛ = 1614 MeV — than the inelasticchannel ηN . Thus the method of the previous section cannot be applied.Another state that is a constant problem for quarkmodels is the Roper resonance P11(1440). In Ref. [15] itwas proposed as a candidate for a dynamical σN state— where σ denotes the very broad lowest isoscalar me-son resonance (f0(600) in the particle data booklet [16]).However, due to the large width of the σ not even a welldefined threshold can be identified.However, there are two promising candidates, namelythe Λ(1520), proposed to be a πΣ(1385)∗ bound state,and the ∆(1700), proposed to be a η∆(1232) molecule(although the KΣ(1385)∗ channel plays a very importantrole) [17,18]. In what follows we will briefly discuss theformer example.The important parameters to be extracted from thedata are pole positions and residues. Those can not betaken directly from the data but theory is needed forthe analytic continuation from the physical axis into thecomplex plain where the poles are located. Thus what isneeded for the analysis are not only exclusive data fromvarious probes in many channels that allow one to fix theparameters of the theoretical models. The requirement tothese models is a consistency with analyticity that the an-alytic continuation can be performed. The chiral unitaryapproach meets this requirement and therefore calcula-tions based on it will be used for the arguments below.Let us now focus on the Λ(1520). Please note that theΣ∗(1385) is not stable but has a decay width of 30 − 40MeV (depending on the charge state [16]). It is not clearhow to take this into account in the relation of Eq. (1).In the following we will therefore only make a qualitativecomparison with the arguments of Sec. 2 by adopting thata large effective coupling can be interpreted as an indica-tion of a large molecular component.In Ref. [18] the Λ(1520) is investigated within the chi-ral unitary approach. The channels considered are πΣ∗(1385)and KΞ∗(1530). Thus, with respect to the former channelthe binding energy is only 5 MeV (if we take the centralvalue of the mass for the Σ and ignore its width), whilethe second channel is more than 500 MeV away. Thus thesituation seems ideal. The inelastic channels of relevanceare K¯N and πΣ, both more than 100 MeV away.C. Hanhart: How and when can one identify hadronic molecules in the baryon spectrum 3The analysis revealed [18,20] that, within the presentapproach, indeed the by far largest coupling of the Λ(1520)to a continuum channel is to the πΣ∗ channel. Neverthe-less the model is still consistent with a branching ratio ofonly 10 % of the Λ(1520) to ππΛ (Λπ is with 88% the mostimportant decay channel of the Σ∗), as a result of the lim-ited phase space for πΣ∗. To test this approach it needsto be applied to various reactions. So far a fair descrip-tion of the data was found for the reactions K−p→ Λππ,γp→ K+K−p, γp→ K+π0π0Λ and π−p→ K0K−p [19].In Ref. [20] an additional measurement of the reactionspp → pK+K−p and pp → pK+π0π0Λ was proposed (thecalculation needs additional input, e.g. on baryon–baryonfinal state interactions, and was performed on the basis ofthe formalism of Ref. [21]). In Ref. [22] the radiative decaysΛ(1520) → γΣ were studied, however, sizable discrepan-cies to the data were observed. Thus the model discussedso far might not be complete yet.Eventually the model described will be improved suf-ficiently that it is consistent with all the available data.Then the effective coupling constants can be extractedand be compared to Eq. (1), once it is understood howto generalize this equation for unstable decay particles —then a solid conclusion can be drawn on the nature ofthe Λ(1520), however, already now evidence points at aprominent molecular component.4 SummaryAs soon as a physical state is located very close to a contin-uum threshold it is possible to extract information on themolecular component of that state almost directly fromthe data. So far this program was applied in much de-tail to the light scalar mesons, however, also investiga-tions of heavier systems have started. The central resultof this part was that a large effective coupling constant ofa resonance to a nearby continuum channel shows a largemolecular component of that state. Especially, the effec-tive coupling constant gets maximal for a pure moleculeand its value can be calculated solely in terms of the bind-ing energy and the masses of the continuum particles.In this note for the first time possibilities of a studyof the baryon system were discussed. It is argued that theconditions for the applicability of the above mentionedformalism are not met for most of current molecule can-didates. However, the Λ(1520) and the ∆(1700), both al-ready studied within dynamical models, were identifiedas promising candidates and the former was discussed insome detail. Since it is not known yet how to include afinite width of one of the continuum particles into the for-malism mentioned in the previous paragraph, so far noquantitative conclusions regarding the molecular compo-nent of the Λ(1520) can be drawn, however, qualitativelya consistent picture emerges where it appears as a stategenerated dynamically in the πΣ∗ channel.References1. R. L. Jaffe, arXiv:hep-ph/0701038.2. S. Weinberg, Phys. Rev. 130, 776 (1963); 131, 440 (1963);137 B672 (1965).3. C. Hanhart, Eur. Phys. J. A 31 (2007) 543[arXiv:hep-ph/0609136].4. V. Baru et al., Phys. Lett. B 586, 53 (2004).5. D. Morgan, and M.R. Pennington, Phys. Rev. D 35, 1633(1987); D. Morgan, Nucl. Phys. A543, 632 (1992); N.To¨rnqvist, Phys. Rev. D 51, 5312 (1995); M. Boglione andM.R. Pennington, Phys. Rev. D 65, 114010 (2002).6. A. Faessler, T. Gutsche, V. E. Lyubovitskij and Y. L. Ma,Phys. Rev. D 76 (2007) 014005 [arXiv:0705.0254 [hep-ph]].7. D. Gamermann, L. R. Dai and E. Oset, arXiv:0709.2339[hep-ph].8. C. Hanhart, Yu. S. Kalashnikova, A. E. Kudryavtsevand A. V. Nefediev, Phys. Rev. D 76 (2007) 034007[arXiv:0704.0605 [hep-ph]].9. C. Hanhart, Yu. S. Kalashnikova, A. E. Kudryavtsevand A. V. Nefediev, Phys. Rev. D 75 (2007) 074015[arXiv:hep-ph/0701214]; Yu. Kalashnikova, A. E. Kudryavt-sev, A. V. Nefediev, J. Haidenbauer and C. Hanhart,Phys. Rev. C 73 (2006) 045203 [arXiv:nucl-th/0512028];Yu. S. Kalashnikova, A. E. Kudryavtsev, A. V. Nefediev,C. Hanhart and J. Haidenbauer, Eur. Phys. J. A 24 (2005)437 [arXiv:hep-ph/0412340].10. J. Weinstein and N. Isgur, Phys. Rev. Lett. 48, 659 (1982);Phys. Rev. D 27, 588 (1983); Phys. Rev. D 41, 2236 (1990);G. Janssen et al., Phys. Rev. D 52 (1995) 2690; J. A. Ollerand E. Oset, Nucl. Phys. A 620 (1997) 438 [Erratum-ibid.A 652 (1999) 407]; J. R. Pelaez, Phys. Rev. Lett. 92 (2004)102001 [arXiv:hep-ph/0309292].11. M. Jones, R. H. Dalitz and R. R. Horgan, Nucl. Phys. B129 (1977) 45.12. D. Jido, J. A. Oller, E. Oset, A. Ramos and U. G. Meissner,Nucl. Phys. A 725 (2003) 181 [arXiv:nucl-th/0303062].13. N. Kaiser, T. Waas and W. Weise, Nucl. Phys. A 612(1997) 297 [arXiv:hep-ph/9607459]; J. C. Nacher, A. Par-reno, E. Oset, A. Ramos, A. Hosaka and M. Oka, Nucl. Phys.A 678 (2000) 187 [arXiv:nucl-th/9906018]; M. F. M. Lutzand E. E. Kolomeitsev, Nucl. Phys. A 700 (2002) 193[arXiv:nucl-th/0105042].14. C. Schutz, J. Haidenbauer, J. Speth and J. W. Durso,Phys. Rev. C 57, 1464 (1998).15. O. Krehl, C. Hanhart, S. Krewald and J. Speth, Phys. Rev.C 62 (2000) 025207 [arXiv:nucl-th/9911080].16. W. M. Yao et al. [Particle Data Group], J. Phys. G 33(2006) 1.17. E. E. Kolomeitsev and M. F. M. Lutz, Phys. Lett. B 585(2004) 243 [arXiv:nucl-th/0305101];18. S. Sarkar, E. Oset and M. J. Vicente Vacas, Nucl.Phys. A 750 (2005) 294 [Erratum-ibid. A 780 (2006) 78][arXiv:nucl-th/0407025].19. L. Roca, S. Sarkar, V. K. Magas and E. Oset, Phys. Rev.C 73 (2006) 045208 [arXiv:hep-ph/0603222].20. L. Roca, C. Hanhart, E. Oset and U. G. Meissner, Eur.Phys. J. A 27 (2006) 373 [arXiv:nucl-th/0602016].21. C. Hanhart, Phys. Rept. 397 (2004) 155[arXiv:hep-ph/0311341].22. M. Doring, E. Oset and S. Sarkar, Phys. Rev. C 74 (2006)065204 [arXiv:nucl-th/0601027].

How and when can one identify hadronic molecules in the baryon spectrum

EDP Sciences OAI-PMH repository (1.2.0)

Crossref

How and when can one identify hadronic molecules in the baryon spectrum⋆

http://juser.fz-juelich.de/record/3259/files/0711.0578v1.pdf

How and when can one identify hadronic molecules in the baryon spectrum

Abstract

Similar works

Full text

Available Versions

Juelich Shared Electronic Resources

EDP Sciences OAI-PMH repository (1.2.0)

Juelich Shared Electronic Resources

Crossref