tetraquark model for the new X ( 1576 ) K + K − resonance

We discuss the likely tetraquark interpretation of the X(1576) KK isovector resonance recently reported by BES with J = 1. We point out that if this interpretation as a four-quark state is correct, the sus̄d̄ tetraquark decays might have striking signatures. We also provide predictions for possible analogous tetraquarks involving heavy quarks – cqc̄q̄ and bqb̄q̄. e-mail: [email protected] e-mail: [email protected] 1 I. THE NEW ISOVECTOR KK RESONANCE We have noticed with interest the new KK resonance [1] with J = 1 , and a pole mass at 1576 −55(stat) +98 −91(syst) − i ( 409 −12(stat) +32 −67(syst) ) MeV which seems to be a four-quark state. Since it is produced with a pion from the isoscalar J/ψ, which has odd G-parity it must be isovector and have even G-parity. Since no nonstrange even-G vector resonances like ρ−ρ or π−π have been reported in this mass range the new KK resonance seems to contain a strange quark pair. An isovector particle containing a strange quark pair must necessarily contain an additional isovector nonstrange pair to make an isovector. Thus this new state must contain a minimum of two quark-antiquark pairs. It is also worth noting that this state cannot be a s̄s hybrid, since a state of a strange quark pair and gluons is isoscalar and cannot be isovector. A recent examination of four-quark (tetraquark) states [2] has emphasized the states including heavy quarks near the two-meson threshold may well exist as bound tetraquarks. Applying this approach to the two-kaon system gives two diquark-antidiquark configurations with masses above the two-kaon threshold with ratios of masses to the mass of two kaons of 1.21 and 1.16 respectively. These results are for S-wave systems and neglect spin dependence. They are therefore lower than the mass of the new state which must have a P -wave to explain the negative parity. They are therefore in a reasonable ball park, since experimentally mX/(2mK) ≈ 1.6. In contrast with the 1 state reported by BES [1], the S-wave tetraquark with these flavor quantum numbers probably breaks up so fast that it is too broad to be seen. At this stage any further calculation of orbital and spin effects will be highly model dependent and unreliable. However, the diquark-antidiquark model [2] makes clear flavor predictions that are easily tested in experiment. We consider here predictions relating the decays of the new X(1576) resonance. Although only X has been observed experimentally, existence of X and X follows from X having I = 1. Since decays involving charged pions in the final state are much easier to observe, we focus on these: We first note that the dominant decay mode of a tetraquark is the “fall-apart mode” in which the two quarks and two antiquarks rearrange into two mesons and separate. No new quark-antiquark pairs are created or destroyed. This immediately leads to a selection rule for a diquark(us)-antidiquark(d̄s̄) model for the new X(1576) resonance. BR(X → ππ) = 0 (1) This selection rule provides the crucial distinction between tetraquark and qq̄ models. A positively charged qq̄ must be in an octet of SU(3)flavor . The ππ decay amplitude is required by SU(3) symmetry to be proportional to the same reduced matrix element as the KK̄ and cannot vanish for a hadron decaying into KK̄. A further prediction for the tetraquark model is obtained by noting that there are two ways in which a us diquark and a d̄s̄ antidiquark can rearrange to make two mesons