FZJ–IKP(TH)–2003–17 How to measure the parity of the Θ + in pp

Triggered by a recent paper by Thomas, Hicks and Hosaka, we investigate which observables can be used to determine the parity of the Θ from the reaction ~p~ p → ΣΘ near its production threshold. In particular, we show that the sign of the spin correlation coefficient Axx for small excess energies yields the negative of the parity of the Θ. The argument relies solely on the Pauli principle and parity conservation and is therefore model–independent. 1. There is increasing experimental evidence for an exotic baryon with strangeness S = +1, the Θ(1540), see e.g. [1,2,3,4,5], preceded and complemented by a flurry of theoretical activity, see e.g. [6,7,8,9,10]. Experimental activities are now trying to pin down the quantum numbers of the Θ; in particular the parity π(Θ) of this state is so far not determined experimentally, and the theoretical predictions allow for both possibilities. For example the chiral soliton model points at a positive parity state [7,8] whereas lattice calculations indicate a negative parity state for the pentaquark ground state [10], just to name a few. It is thus of utmost importance to determine π(Θ) to further constrain the internal dynamics and structure of this exotic state. The determination of the internal parity of a state is in general difficult, for any signal gets distorted by the interference of the resonance amplitude with the background [11]. Thus, in order to unambiguously pin down the parity of a state from an angular distribution, one needs to know the background rather precisely. This makes it difficult to get model–independent results. A way to Preprint submitted to Elsevier Science 12 March 2008 minimize the impact of the background would be to also measure the polarization of the decay products of the resonance as proposed in Ref. [12], however, these are extremely difficult measurements. In a recent work, Thomas, Hicks and Hosaka have proposed an alternative method to unambiguously determine the parity of the Θ by looking at ~p~p → ΘΣ close to the production threshold [13]. The idea relies only on the conservation of total angular momentum and parity in strong interactions and is therefore completely independent of the reaction mechanism. In this paper we will discuss this proposal in more detail. To be specific we will supply first a discussion of the most relevant observable including its angular structure and energy dependence in the near threshold regime, and second a brief discussion of its experimental boundary conditions as well as its feasibility. Let us start, however, with a repetition of the argument by Thomas et al. It is well known that the Pauli principle closely links spin and parity of a two nucleon state, since the relation (−) = −1 holds, where T denotes the total isospin of the two nucleon system (for pp T = 1), L the angular momentum and S the total spin. Thus, a spin triplet (singlet) pp pair has to be in an odd (even) parity state. As a consequence, selecting the spin of a pp state implies preparing its parity. From the argument given it also follows that the corresponding reaction from a pn initial state does not allow to prepare the initial parity, for a pn state is an admixture of T = 1 and T = 0 states. Close to the production threshold only s–waves are kinematically allowed in the final state. Consequently, a negative parity Θ can only originate from a spin triplet initial pp state while a positive parity Θ can only stem from a spin singlet pp state. In Refs. [14,15,16] it was shown, that a measurement of the spin correlation parameters Axx, Ayy, Azz as well as the unpolarized cross section allows to project on the individual initial spin states. More precisely 1σ0= σ0(1− Axx −Ayy − Azz) , 3σ0= σ0(1 + Axx + Ayy − Azz) , 3σ1= σ0(1 + Azz) , (1) where the spin cross sections are labeled following the convention of Ref. [14] as 2S+1σMS , with S the total spin of the initial state and MS its projection; σ0 denotes the unpolarized cross section. Therefore, if only Σ Θ s–waves contribute and the Θ has positive parity, only σ0 would be non–vanishing. Unfortunately, longitudinal polarization (needed for Azz) is not easy to prepare. However, the following linear combination projects on spin triplet initial states and no longitudinal polarization is needed: