Properties of the baryon antidecuplet

Abstract

We study the group structure of baryon anti-decuplet containing the Θ + . We derive the SU(3) mass relations among the pentaquark baryons in the anti-decuplet, when there is either no mixing or ideal mixing with the pentaquark octet, as advocated by Jaffe and Wilczek. This constitutes the Gell-Mann-Okubo mass formula for the pentaquark baryons. We also derive SU(3) symmetric Lagrangian for the interactions of the baryons in the anti-decuplet with the meson octet and the baryon octet. Our analysis for the decay widths of the anti-decuplet states suggests that the N (1710) is ruled out as a pure anti-decuplet state, but it may have anti-decuplet component in its wavefunction if the multiplet is mixed with the pentaquark octet. The recent discovery of the Θ + baryon by LEPS Collaboration at SPring-8 [1], which has been confirmed by several groups [2], initiated a lot of theoretical works in the field of exotic hadrons. Experimentally, the Θ + is observed to have a mass of 1540 MeV and a decay width of < 25 MeV. Because of its positive strangeness, the Θ + baryon is exotic since its minimal quark content should be uudds. Other states that have positive strangeness but different charges are not observed, which suggests that the Θ + is an isosinglet. The existence of such an exotic state with narrow width was first predicted by Diakonov et al. [3] in the chiral soliton model, where the Θ + is a member of the baryon anti-decuplet. Although it should be confirmed by other experiments, the recently discovered Ξ −− 3/2 baryon [4] strongly supports the anti-decuplet nature of pentaquark baryons. The discussion on the existence of a baryon anti-decuplet has a longer history going back to the early 1970's [5], and in the Skyrme model [6]. Pentaquark states with a heavy antiquark (uuddc, uuddb) were also predicted in the Skyrme model. Here an important issue is whether such nonstrange heavy pentaquark states are stable against strong decays [7,8,9,10,11]. Subsequent theoretical investigations on the Θ + include approaches based on the constituent quark model [12,13,14], Skyrme model [15,16,17,18,19], QCD sum rules [20,21], lattice QCD [22], chiral potential model [23], large N c QCD [24], and Group theory approach [25]. The production of the Θ + was also discussed in relativistic nuclear collisions [26], where the number of the anti-Θ + (1540) produced are expected to be similar to that of the Θ + (1540).Several pressing issues that should be clarified are whether the Θ + has positive or negative parity, and whether the Roper N (1710) is included in the baryon anti-decuplet with the Θ + . As for the spin-parity of the Θ + , several works claim that J P = 1 2 − is more natural [13,21,22], which, however, is in contrast to the prediction of the soliton models, where the relative orbital angular momentum plays an important role 10

Pentaquark Θ+(1540) production in γN→KK¯N reactions

“…In Ref. [122], however, it was pointed out that the N(1710) should be excluded as a pure antidecuplet state. This is because, within SU(3) symmetry, antidecuplet does not couple to decuplet and meson octet, whereas N(1710) has a large branching ratio into π∆ channel.…”

Photoproduction of Θ+ and other pentaquark states

“…[15,16,17] implicitly constrains these to be g 2 ΘN K * = 3g 2 ΘN K and |κ * θ | = 0. Note that this will enhance the strength of the K * exchange since most of the previous literature [19,20,21,22,25,26] assume…”

“…Several phenomenological studies of γN → KΘ + have been proposed in the literature [18,19,20,21,22,23,24,25,26]. Although these give quite different predictions in detail due to their varied underlying assumptions, they share certain essential common features that enable robust constraints to be placed on the relative production rates for various pentaquarks.…”

“…The differing output of the calculations in Refs. [18,19,20,21,22,23,24,25,26] for magnitudes and energy dependences are due to their various assumptions on the magnitudes of, e.g., g ΘN K , g ΘN K * , the role of the contact term and importance of s : u channels. However, some qualitative features can be immediately understood, which are sufficient for the generalisations in this present paper.…”

“…The general assumption subsumed in Refs. [18,19,20,21,22,23,24,25,26] is that for γn → K − Θ + , four transition amplitudes labelled by the Mandelstam variables contribute in the Born approximation limit. These are shown by diagrams in Fig.…”