Starting from a consistent SU(6) extension of the Weinberg-Tomozawa (WT)
meson-baryon chiral Lagrangian (Phys. Rev. D74 (2006) 034025), we study the
s-wave meson-baryon resonances in the strangeness S=-3 and negative parity
sector. Those resonances are generated by solving the Bethe-Salpeter equation
with the WT interaction used as kernel. The considered mesons are those of the
35-SU(6)-plet, which includes the pseudoscalar (PS) octet of pions and the
vector (V) nonet of the rho meson. For baryons we consider the 56-SU(6)-plet,
made of the 1/2+ octet of the nucleon and the 3/2+ decuplet of the Delta.
Quantum numbers I(J^P)=0(3/2^-) are suggested for the experimental resonances
Omega*(2250)- and Omega*(2380)-. Among other, resonances with I=1 are found,
with minimal quark content sss\bar{l}l', being s the strange quark and l, l'
any of the the light up or down quarks. A clear signal for such a pentaquark
would be a baryonic resonance with strangeness -3 and electric charge of -2 or
0, in proton charge units. We suggest looking for K- Xi- resonances with masses
around 2100 and 2240 MeV in the sector 1(1/2^-), and for pi Omega- and K- Xi*-
resonances with masses around 2260 MeV in the sector 1(3/2^-).Comment: 3 pages, 1 Postscript figure, 7 table

Aston

Biagi

C. Garcıa-Recio

Garcia-Recio

J. Nieves

Kaiser

Kolomeitsev

L. L. Salcedo

Nieves

Yao)

English

arXiv

C.  Garcıa-Recio

Crossref

Meson-baryon s-wave resonances with strangeness -3

Starting from a consistent SU(6) extension of the Weinberg-Tomozawa (WT) meson-baryon chiral Lagrangian ( Phys. Rev. D 74, 034025 (2006)), we study the s-wave meson-baryon resonances in the strangeness S = - 3 and negative-parity sectors. Those resonances are generated by solving the Bethe-Salpeter equation with the WT interaction used as kernel. The considered mesons are those of the 35-SU(6)-plet, which includes the pseudoscalar (PS) octet of pions and the vector (V) nonet of the rho-meson. For baryons we consider the 56-SU(6)-plet, made of the 1/2+ octet of the nucleon and the 3/2+ decuplet of the Delta. Quantum numbers I(J
P) = 0(3/2-) are suggested for the experimental resonances Ω
*(2250)- and Ω
*(2380)-. Among other, resonances with I = 1 are found, which minimal quark content is sss¯l', being s the strange quark and l, l' any of the the light up or down quarks. A clear signal for such a pentaquark would be a baryonic resonance with strangeness -3 and electric charge -2 or 0, in proton charge units. We suggest looking for K
-
Ξ
- resonances with masses around 2100 and 2240MeV in the sector 1(1/2-), and for π
±
Ω
- and K
-
Ξ
*- resonances with masses around 2260MeV in the sector 1(3/2-)

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Starting from a consistent SU(6) extension of the Weinberg-Tomozawa (WT) meson-baryon chiral Lagrangian (Phys. Rev. D 74, 034025 (2006)), we study the s-wave meson-baryon resonances in the strangeness S = -3 and negative-parity sectors. Those resonances are generated by solving the Bethe-Salpeter equation with the WT interaction used as kernel. The considered mesons are those of the 35-SU(6)-plet, which includes the pseudoscalar (PS) octet of pions and the vector (V) nonet of the rho-meson. For baryons we consider the 56-SU(6)-plet, made of the 1/2(+) octet of the nucleon and the 3/2(+) decuplet of the Delta. Quantum numbers I(J(P)) = 0(3/2(-)) are suggested for the experimental resonances Omega*(2250)(-) and Omega*(2380)(-). Among other, resonances with I = 1 are found, which minimal quark content is sss(l)over bar>l', being s the strange quark and l, l' any of the the light up or down quarks. A clear signal for such a pentaquark would be a baryonic resonance with strangeness -3 and electric charge -2 or 0, in proton charge units. We suggest looking for K(-)Xi(-) resonances with masses around 2100 and 2240 MeV in the sector 1(1/2(-)), and for pi(+/-)Omega(-) and K(-)Xi(*-) resonances with masses around 2260 MeV in the sector 1(3/2(-))

García Recio, Carmen

Nieves Pamplona, Juan Miguel

Salcedo, Lorenzo Luis

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

arXiv:hep-ph/0610353v1  26 Oct 2006EPJ manuscript No.(will be inserted by the editor)Meson-Baryon s–wave Resonances with Strangeness –3C. Garc´ıa-Recio, J. Nieves, and L. L. SalcedoDepartamento de F´ısica Ato´mica, Molecular y Nuclear, Universidad de Granada, E-18071 Granada, SpainReceived: date / Revised version: dateAbstract. Starting from a consistent SU(6) extension of the Weinberg-Tomozawa (WT) meson-baryonchiral Lagrangian (Phys. Rev. D74 (2006) 034025), we study the s–wave meson-baryon resonances in thestrangeness S = −3 and negative parity sectors. Those resonances are generated by solving the Bethe–Salpeter equation with the WT interaction used as kernel. The considered mesons are those of the 35-SU(6)-plet, which includes the pseudoscalar (PS) octet of pions and the vector (V) nonet of the rho meson.For baryons we consider the 56-SU(6)-plet, made of the 1/2+ octet of the nucleon and the 3/2+ decuplet ofthe Delta. Quantum numbers I(JP ) = 0(3/2−) are suggested for the experimental resonances Ω∗(2250)−and Ω∗(2380)−. Among other, resonances with I = 1 are found, which minimal quark content is sssl¯l′,being s the strange quark and l, l′ any of the the light up or down quarks. A clear signal for such apentaquark would be a baryonic resonance with strangeness −3 and electric charge of −2 or 0, in protoncharge units. We suggest looking for K−Ξ− resonances with masses around 2100 and 2240 MeV in thesector 1(1/2−), and for pi±Ω− andK−Ξ∗− resonances with masses around 2260 MeV in the sector 1(3/2−).PACS. 11.30.Hv Flavor symmetries – 11.30.Ly Other internal and higher symmetries – 11.10.St Boundand unstable states; Bethe–Salpeter equations – 11.30.Rd Chiral symmetries – 11.80.Gw Multichannelscattering1 IntroductionUsing a spin-flavor-SU(6) extended Weinberg-Tomozawa(WT) meson-baryon interaction1 [1], we study the s-waveresonances with strangeness S = −3, isospin I=0, 1 andspin-parity JP = 1/2−, 3/2−, 5/2−. The resonances aregenerated by solving the Bethe–Salpeter equation with theextended WT meson-baryon interaction used as a kernel.In this model, the involved mesons are those of the 35-SU(6)-plet=81⊕83⊕13, which includes the PS meson octetof the pions, (pi, η, K, K¯) ∈ 81 and the V nonet of the rhomeson, (ρ, ω, φ, K∗, K¯∗)∈ 83⊕13. We approximate the ηmeson as the isospin singlet state of the PS SU(3)-octet.For the ω and φ vector mesons, we assume ideal mixingamong the V singlet and octet mesons. The baryons arethose of the 56-SU(6)-plet=82 ⊕ 104, which contains the1/2+ octet of the N (N, Λ, Σ, Ξ) and the 3/2+ decupletof the ∆ (∆, Σ∗, Ξ∗, Ω). Masses, widths and couplingsof the resonances found are calculated and, when possible,comparison with experimental ones is attempted.Unitary extensions of chiral perturbation theory tostudy meson-baryon interactions using a coupled chan-nel scheme were introduced some time ago [3]. They havebeen successfully applied in the theoretical microscopi-cal description of meson-baryon scattering and of wellSend offprint requests to:1 This WT interaction has also been extended to arbitrarynumber of colors and flavors in ref. [2]known lowest lying baryon resonances, which were shownto be dynamically generated. Thus different JP = 1/2−s−wave resonances ( ⊂ 8pi×8N , made of PS mesons ofthe pion octet and of the baryons of the nucleon octet)like N∗(1535), Λ(1405), Λ(1670),Σ(1620) and Ξ(1620) [4]and, more recently, the JP = 3/2− d−wave resonances (⊂ 8pi×10∆, made of PS mesons of the pion octet and of thebaryons of the delta decuplet) like Λ(1520), Σ(1670) andΞ(1820) [5] have been found and their properties stud-ied. Those previous chiral Bethe-Salpeter coupled chan-nels unitary approaches using the WT kernel have in-cluded hadron multiplets belonging to the flavor SU(3)irreducible representations. In the case of mesons, the onlyingredient has been the octet of PS mesons.2 ModelMotivations for extending the previous SU(3) based mod-els to a SU(6) extended model are the following. First,in the large Nc limit, 8N and 10∆ are degenerated andform a 56-multiplet of spin–flavor SU(6). Second, vectormesons do exist, interact and couple to baryons. Third,there are baryonic resonances decaying to a PS meson anda baryon, but also to a V meson and a baryon, for instance,the strangeness –3 resonanceΩ∗(2380)−decays toK−Ξ∗0and to K¯∗0Ξ− with similar strengths and of the same or-der as the other known decay mode (K¯−pi0Ξ−) [8]. All ofthese call for a ’SU(6)’ model which deals all together with2 C. Garc´ıa-Recio et al.: Meson-Baryon s–wave Resonances with Strangeness –3the 56-baryons and 35-mesons like that of ref.[1]. We con-sider this spin–flavor symmetric scenario as a reasonablefirst approach. In the ’SU(6)’ approach the interacting ker-nel V IY J for a sector with hypercharge Y (strangenessplus one for baryons), isospin I and spin J is given by:〈mi, Bi|V IY J (s)|mj , Bj〉 = DIY Jij2√s−MBi −MBj4 f2mi,mj ∈ 35, Bi, Bj ∈ 56, DIY J =∑νλ¯ν PˆIY Jνλ¯56 = −12, λ¯70 = −18, λ¯700 = 6, λ¯1134 = −2,Pˆ IY Jν is the projector of the meson-baryon into the ν–SU(6)-representation, and ν runs over 56, 70, 700, 1134because 35⊗56= 56⊕ 70⊕ 700⊕ 1134.The λ¯ν positive (negative) means that in channel ν themeson-baryon interaction is repulsive (attractive). Whenthis kernel is restricted to mi,mj being only PS mesons,it coincides with the ’SU(3)’ lowest order WT kernels pre-viously used in refs.[4,5].Note that D is SU(6) invariant, this symmetry being ex-plicitly broken by the different masses of baryons andmesons. In addition we replace the f2 of the interaction byfmifmj for the ij matrix element. We use fpi = 92.4 MeV,fK = 1.15fpi, fη = 1.2fpi [7], and fK∗ = fK , fρ = fpi,fω = fφ = fη. This interaction is used to solve the Bethe–Salpeter coupled channel equation for the meson-baryonT−matrixT−1(s) = V −1(s) − J(s) (1)where J(s) is the diagonal matrix of the meson-baryonloop functions [4,5]. For each channel (mi, Bi) it is ultra-violet regularized by subtracting a constant so thatJ(s = mmi2 +MBi2)= 0.We test that the inclusion of the new ’SU(6)’ channels(those involving V mesons not included in the ’SU(3)’calculations) does not spoil previous results which weresuccessful. See ref. [6] for comparison in the sector (S =−1, I = 0, JP = 1/2−).3 ResultsWe solve the coupled–channel Bethe–Salpeter equationand look for the T−matrix poles in the second Riemannsheet. Close to a pole the T−matrix behaves asTij ∼ gigj√s− (MR − iΓR/2) (2)and the position of the pole and its residue define themassMR, width ΓR and complex coupling constants gi todifferent i channels of the found resonance.All the calculations are done neglecting the widths ofthe baryons of the decuplet and of the V mesons. Whenthe orbital angular momentum of the meson-baryon sys-tem is zero, the odd parity S = −3 resonances formed bycoupling 35-mesons to 56-baryons can have the follow-ing I(JP ) quantum numbers: 0(1/2−), 0(3/2−), 0(5/2−),1(1/2−), 1(3/2−) and 1(5/2−). The mass, width and ab-solute values of the coupling constants of the resonancesfound for each of those sectors are shown in tables 1, 2,3, 4, 5 and 6, respectively. Resonances with width below125 MeV are displayed in fig. 1.Several (S = −3, I = 1) resonances have been found(tables 4, 5 and 6 and full symbols in fig. 1).These reso-nances have, at least, three s quarks to provide strangenessS = −3 and a pair of light (u or d) quark-antiquark toachive isospin I = 1 quantum number. Hence, those dy-namically generated (S = −3, I = 1) resonances are pen-taquarks and in principle they could be empirically spot-ted very easily. A clear signal of them would be a resonancewith strangeness S = −3 and electric charge Q = −2 (thisis Iz = −1) with minimal quark content sssdu¯. Anotherclear signature would be a S = −3 and Q = 0 resonancewith a minimal quark content of sssud¯. From the tables,the best ways for observing pentaquarks would be, in thesector I(JP ) = 1(1/2−) looking for K−Ξ− resonanceswith masses around 2100 and 2240 MeV, and in the sec-tor I(JP ) = 1(3/2−) looking for pi±Ω− and K−Ξ∗− res-onances with masses around 2260 MeV.All the experimentally known Ω∗ resonances are listed intable 7. Tentatively, we identify the experimental isoscalarΩ∗(2250)− to the theoreticalΩ∗(2265)− of sector 0(3/2−),because of the relative closeness of masses and widths and,also, of observed decay channels. Likewise, the experimen-tal Ω∗(2380)− could be assigned to the found Ω∗(2343)−of sector 0(3/2−). We do not find a clear assignment forthe experimental Ω∗(2470) because it decays to Ω−pi+pi−,and the resonances that we find around that energy havenot the possibility of decaying to such channel.More details will be given elsewhere. 0 20 40 60 80 100 120 1400  1600  1800  2000  2200  2400Γ R  [MeV]MR  ±  ΓR / 2  [MeV] I=1, 1/2- (JP) I=1, 3/2- I=1, 5/2- I=0, 1/2- I=0, 3/2- I=0, 5/2-Exp Ω∗Fig. 1. Spin–parity JP = 12−, 32−and 52−resonance propertiesin the I = 0 (empty symbols) and I = 1 (filled symbols), S =−3 (Y = −2) sectors. The points with error-bars are definedfrom the masses (MR) and widths (ΓR) of the found resonancesas (MR ± ΓR/2, ΓR). The experimental Ω∗ resonance massesand widths with their error bars are from refs. [7,8,9,10]C. Garc´ıa-Recio et al.: Meson-Baryon s–wave Resonances with Strangeness –3 3Table 1. Masses, widths and absolute values of coupling con-stants for each channel, in the sector I = 0, JP = 1/2− andS = −3. The underlining indicates open channels. ’SU(6)’stands for the full 35×56 result. ’SU(3)’ for the 8×8 result.I = 0, JP = 1/2−, ’SU(6)’MR ΓR |gi|[ MeV ] K¯Ξ K¯∗Ξ K¯∗Ξ∗ ωΩ φΩ1309 00 1.22 0.61 3.27 0.17 5.781871 70 1.57 3.63 4.17 1.39 3.232201 2.8 0.22 1.63 2.36 0.48 1.382334 44 0.76 0.37 0.66 3.44 1.082454 33 0.38 0.22 0.97 0.18 4.32- - - ’SU(3)’Table 2. Same as Table 1 for the sector I = 0, JP = 3/2−.I = 0, JP = 3/2−, ’SU(6)’MR ΓR |gi|[ MeV ] K¯Ξ∗ K¯∗Ξ ηΩ K¯∗Ξ∗ ωΩ φΩ1969 0 1.78 2.43 2.37 1.44 0.00 2.512265 82 1.19 0.34 0.28 3.71 1.21 0.552343 36 0.42 0.84 0.04 1.01 3.31 0.162437 80 0.07 0.09 1.19 0.12 0.00 4.382051 86 1.97 3.34 ’SU(3)’Table 3. Same as Table 1 for the sector I = 0, JP = 5/2−.I = 0, JP = 5/2−, ’SU(6)’MR ΓR |gi|[ MeV ] K¯∗Ξ∗ ωΩ φΩ2376 00 1.41 2.78 0.00Table 4. Same as Table 1 for the sector I = 1, JP = 1/2−.I = 1, JP = 1/2−, ’SU(6)’MR ΓR |gi|[ MeV ] K¯Ξ K¯∗Ξ K¯∗Ξ∗ ρΩ2100 118 1.47 3.39 1.1 2.12241 63 0.88 0.87 1.67 3.87- - - ’SU(3)’We acknowledge discussions with Drs. Angels Ramos and ManuelJ. Vicente-Vacas. This work was supported by DGI, FEDER,UE and Junta de Andaluc´ıa funds (FIS2005-00810, HPRN-CT-2002-00311, FQM225).References1. C. Garcia-Recio, J. Nieves and L. L. Salcedo, Phys. Rev. D74 (2006) 034025.Table 5. Same as Table 1 for the sector I = 1, JP = 3/2−.I = 1, JP = 3/2−, ’SU(6)’MR ΓR |gi|[ MeV ] piΩ K¯Ξ∗ K¯∗Ξ K¯∗Ξ∗ ρΩ2018 267 2.19 1.64 2.14 1.75 0.252258 101 0.54 1.23 0.13 3.19 2.332288 32 0.33 0.17 0.93 2.29 3.112146 359 2.30 2.47 ’SU(3)’Table 6. Same as Table 1 for the sector I = 1, JP = 5/2−.I = 1, JP = 5/2−, ’SU(6)’MR ΓR |gi|[ MeV ] K¯∗Ξ∗ ρΩ2324 0 1.79 3.09Table 7. Experimentally known Ω∗ resonances [7,8,9,10].The branching ratios are relative.Resonance Mass Width Decay BranchingI(J)P [ MeV ] modes ratiosΩ∗(2250)− 2252 ± 9 55± 18 Ξ−pi+K− 10(??) *** Ξ∗0K− 0.7± 0.2Ω∗(2380)− 2384 ± 13 26± 23 Ξ−pi+K− 1?(??) ** Ξ∗0K− < 0.4Ξ−K¯∗00.5± 0.3Ω∗(2470)− 2474 ± 12 72± 33 Ω−pi+pi−?(??) **2. C. Garcia-Recio, J. Nieves and L. L. Salcedo, Phys. Rev. D74 (2006) 036004; Ibidem, hep-ph/0610204.3. N. Kaiser, P. B. Siegel and W. Weise, Nucl. Phys. A 594(1995) 325; N. Kaiser, T. Waas and W. Weise, Nucl. Phys. A612 (1997) 297; E. Oset and A. Ramos, Nucl. Phys. A 635(1998) 99; J. A. Oller and U. G. Meissner, Phys. Lett. B 500(2001) 263.4. J. Nieves and E. Ruiz Arriola, Phys. Rev. D 64 (2001)116008; T. Inoue, E. Oset and M. J. Vicente Vacas, Phys.Rev. C 65 (2002) 035204; D. Jido et al, Nucl. Phys. A 725(2003) 181; C. Garcia-Recio et al, Phys. Rev. D 67 (2003)076009; C. Garcia-Recio, M. F. M. Lutz and J. Nieves, Phys.Lett. B 582 (2004) 49; J. A. Oller, arXiv:hep-ph/0603134.5. E. E. Kolomeitsev and M. F. M. Lutz, Phys. Lett. B 585(2004) 243; S. Sarkar, E. Oset and M. J. Vicente Vacas, Nucl.Phys. A 750 (2005) 294; S. Sarkar, E. Oset and M. J. VicenteVacas, Eur. Phys. J. A 24 (2005) 287; L. Roca, S. Sarkar,V. K. Magas and E. Oset, Phys. Rev. C 73 (2006) 045208.6. C. Garcia-Recio, J. Nieves and L. L. Salcedo,arXiv:hep-ph/0610127.7. W.-M. Yao et al. (Particle Data Group), J. Phys. G 33(2006) 1.8. S. F. Biagi et al., Z. Phys. C 31 (1986) 33.9. D. Aston et al., Phys. Lett. B 194 (1987) 579.10. D. Aston et al., Phys. Lett. B 215 (1988) 799.

Meson-baryon s-wave resonances with strangeness-3

Meson-Baryon s-wave Resonances with Strangeness -3

Meson-Baryon s-wave Resonances with Strangeness -3

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