Extracting the f0(980) signal from the photoproduced π+ π- spectrum

We present a phenomenological analysis of the π + π - photoproduction data obtained by the CLAS collaboration at the Thomas Jefferson Laboratory. A special emphasis is put on the interference pattern observed in the moments of angular distribution for the π + π - efective masses around 1 GeV. This pattern is attributed to the photoproduction of the scalar-isoscalar resonance f 0 (980). By fitting the model parameters to the data we obtain the strengths of the resonant and nonresonant parts of the S-wave photoproduction amplitude. We calculate the f 0 (980) photoproduction cross section which is smaller than previous estimations by a factor of about 5. A new estimation of the product of the σ meson couplings to nucleon and to the γρ system |g NNσ g γρσ | is given.


Introduction
Reactions induced by electromagnetic probes are good sources of information on the inner structure of scalar mesons. In the radiative decays of the ρ mesons into γπ + π − and the φ mesons into γKK or into γπη, the isoscalar mesons f 0 (500) and f 0 (980) or the isovector meson a 0 (980) play a substantial role. Photoproduction reactions like γp → π + π − p [1] or γp → K + K − p are valuable alternatives. These processes are, however, plagued by the relatively small values of the scalar meson photoproduction cross sections, thus making their observation in π + π − and K + K − mass distributions very difficult. Nevertheless the strength of the S − wave amplitude can be determined by analysing its interference with the dominant P-wave. Such an approach has been already successfully applied to determine the S -wave component in the γp → K + K − p reaction [2].

Model description
We adopt the mechanisms commonly used to describe the π + π − photoproduction like the diffractive ρ(770) photoproduction, Fig. 1(a) and the photon dissociation into pair of pions with pion-nucleon rescattering (the Drell mechanism), Fig. 1(b) [3]. This standard approach is extended, however, by taking into account the photoproduction of the scalar-isoscalar mesons treated as resonances created dynamically through final state pion-pion interactions, Fig. 1(c). Our model includes also the ρ photoproduction amplitudes generated by the π, σ and f 2 exchanges which are important at low photon energies [4,5], Fig. 1(d).
We define the moments of the pion angular distribution in the s-channel helicity system as  where Ω is the π + solid angle, L and M are the angular momentum of the pion and its projection on the direction opposite to the recoil proton momentum, A P , A π , A σ and A f 2 are the pomeron, π, σ and f 2 exchange amplitudes, respectively; A D is the Drell amplitude in which the πp scattering amplitudes are parameterised using the phase shifts and inelasticities from the SAID database [6]. The form of the resonant S -wave amplitude A f 0 is whereV is the Born amplitude,t is transition matrix between the intermediate mm states (ππ or KK) and the final π + π − state [7] and κ ′ (κ) is CM momentum of the two-meson system in the intermediate (final) state. The F(κ, κ ′ ) form factor is used to regularize the divergent mesonic loop of the diagram 1(c).

Moments
For the meson exchange amplitudes (Fig. 1(d)) we use the same values of the coupling constants and form factor range parameters as in Ref. [5]. However, due to substantial discrepancies concerning the σ meson couplings we treat the product g σργ g σNN as a free parameter which we fit to mass distributions obtained by CLAS for the photon energy E γ =3.3 GeV [1]. Our result |g σργ g σNN |=15.12±1.53 can be compared with the values between 2.55 and 35.9 calculated from the couplings given in Ref. [5].
In order to fit the moments Y 1 0 and Y 1 1 we introduced correction phases and scale parameters to individual partial waves. As seen in Fig. 2 a good description of these moments for the effective masses around 1 GeV is obtained. High L moments are not discussed here since in these moments the S -wave which is of interest to us interferes with higher partial waves of much smaller intensities than that of the dominant P-wave. 09009-p.2

Mass distribution
By fitting the moments with L 1 we have determined the absolute strength of the resonant ( f 0 (980)) S -wave amplitude and were able to calculate the corresponding mass distributions. The t-integrated mass distribution (Fig. 3) can be compared with previos calculations performed for the photon energies of 1.7 GeV [8] and 5 GeV [9], respectively. Assuming the ρ-type Regge energy dependence of the total S -wave cross section we find our result below those of [8] and [9] (Scenario II) by a factor of about 5.

Summary and outlook
The model provides a good description of the moments of the pion angular distribution in the reaction γp → π + π − p for the π + π − effective masses around the mass of the scalar-isoscalar resonance f 0 (980). We found the resonant S -wave cross section to be remarkably smaller than the values previously calculated using the chiral unitary model [8] and the quark model [9].