Lattice Study of the ExoticS=+1Baryon

Abstract

We propose S=+1 baryon interpolating operators, which are based on an exotic description of the antidecuplet baryon like diquark-diquark-antiquark. By using one of the new operators, the mass spectrum of the spin-1/2 pentaquark states is calculated in quenched lattice QCD at β = 6/g 2 = 6.2 on a 32 3 × 48 lattice. It is found that the J P assignment of the lowest Θ(uudds) state is most likely (1/2) − . We also calculate the mass of the charm analog of the Θ and find that the Θc(uuddc) state lies much higher than the DN threshold, in contrast to several model predictions.PACS numbers: 11.15. Ha, 12.38.Gc, 12.39.Mk, 14.20.Lq Recently, LEPS collaboration at Spring-8 has observed a very narrow resonance Θ + (1540) in the K − missingmass spectrum of the γn → nK. A remarkable observation is its strangeness is S=+1, which means that the observed resonance must contain a strange antiquark. Thus, the Θ + (1540) should be an exotic baryon state with the minimal quark content uudds. This discovery is subsequently confirmed in different reactions by several other collaborations [2]. It should be noted, however, that the experimental evidence for the Θ + (1540) is not very solid yet since there are a similar number of negative results to be reported [3].Theoretically the existence of such a state was predicted long time ago by the Skyrme model [4]. However, the prediction closest in mass and width with the experiments was made by Diakonov, Petrov and Polyakov using a chiral-soliton model [5]. They predicted that it should be a narrow resonance and stressed that it can be detected by experiment because of its narrow width. In a general group theoretical argument with flavor SU (3), S=+1 pentaquark state should be a member of antidecuplet or higher dimensional representation such as 27-plet or 35-plet. Both the Skyrme model and the chiral-soliton model predict that the lowest S=+1 state appears in the antidecuplet, I=0, and its spin and parity should be (1/2) + [4,5]. Experimentally, spin, parity and isospin of the Θ + (1540) are not determined yet. After the discovery of the Θ + (1540), many model studies for the pentaquark state are made with different spin, parity and isospin.Lattice QCD in principle can determine these quantum numbers of the Θ + (1540), independent of such arbitrary model assumptions or the experiments. We stress that there is substantial progress in lattice study of excited baryons recently [6]. Especially, the negative parity nucleon N * (1535), which lies close to the Θ + (1540), has become an established state in quenched lattice QCD [6,7]. Here we report that quenched lattice QCD is capable of studying the Θ + (1540) as well.Indeed, it is not so easy to deal with the qqqqq state rather than usual baryons (qqq) and mesons (qq) in lattice QCD. The qqqqq state can be decomposed into a pair of color singlet states as qqq and qq, in other words, it can decay into two-hadron states even in the quenched approximation. For instance, one can start a study with a simple minded local operator for the Θ + (154...

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