Comprehensive amplitude analysis ofγγ→π+π−,π0π0and

L. Dai

¹

,

M.R. Pennington

²

Abstract

In this paper we perform an amplitude analysis of essentially all published pion and kaon pair production data from two-photon collisions below 1.5 GeV. This includes all the high statistics results from Belle, as well as older data from Mark II at SLAC, CELLO at DESY, and Crystal Ball at SLAC. The purpose of this analysis is to provide as close to a model-independent determination of the γγ to meson pair amplitudes as possible. Having data with limited angular coverage, typically j cos θj < 0.6-0.8, and no polarization information for reactions in which spin is an essential complication, the determination of the underlying amplitudes might appear an intractable problem. However, imposing the basic constraints required by analyticity, unitarity, and crossing symmetry makes up for the experimentally missing information. Above 1.5 GeV multimeson production channels become important, and we have too little information to resolve the amplitudes. Nevertheless, below 1.5 GeV the two-photon production of hadron pairs serves as a paradigm for the application of S-matrix techniques. Final state interactions among the meson pairs are critical to this analysis. To fix these, we include the latest ππ → ππ, KK scattering amplitudes given by dispersive analyses, supplemented in the KK threshold region by the recent precision Dalitz plot analysis from BABAR. With these hadronic amplitudes built into unitarity, we can constrain the overall description of γγ → ππ and KK data sets, both integrated and differential cross sections, including the high statistics charged and neutral pion, as well as K s K s , data from Belle. Since this analysis invokes coupled hadronic channels, having data on both ππ and KK reduces the solution space to essentially a single form in the region where these channels saturate unitarity. For the ππ channel, the separation of isospin-0 and -2 and helicity-0 and -2 components is complete. We present the partial wave amplitudes, show how well they fit all the available data, and give the two-photon couplings of scalar and tensor resonances that appear. These partial waves are important inputs into forthcoming dispersive calculations of hadronic light-by-light scattering. PHYSICAL REVIEW D 90, 036004 (2014) 036004-2 LING-YUN DAI AND M. R. PENNINGTON PHYSICAL REVIEW D 90, 036004 (2014) 036004-4 FIG. 8 (color online). Fit to the γγ → π þ π − differential cross section of CELLO experiment. Here, Cello1 is from Harjes [3] and Cello2 from Behrend et al. [4]. The numbers give the central energy in GeV of each angular distribution listed in order of the cross section at z ¼ 0, where z ¼ cos θ. COMPREHENSIVE AMPLITUDE ANALYSIS OF … PHYSICAL REVIEW D 90, 036004 (2014) 036004-15 FIG. 9 (color online). Fit to the γγ → π þ π − differential cross section of the Belle experiment [13]. The numbers give the central energy in GeV of each angular distribution listed in order of the cross section at z ¼ 0, where z ¼ cos θ. The data are normalized so that the integrated cross section is just a sum of the differential cross sect...

Electromagnetic trace anomaly in a generalized linear sigma model

“…However, our results show that mixing among two-and four-quark components is essential for understanding the experimental data on decay width of f 0 ð980Þ to two photons, hence, providing an indirect probe of the quark substructure of the light scalar mesons. In summary, the lower bound of 0.5 KeV for the decay width of f 0 ð500Þ to two photons obtained in this analysis (within the leading order of the generalized linear sigma model) is qualitatively consistent with other estimates [37][38][39][40]. A more precise prediction is expected when higher-order effects are taken into account.…”

“…2. Considering the acceptable ranges of τ 2 ≥ 0.7 and τ 2 ≤ −0.8, the prediction of this decay width shows the lower bound of approximately [40] found this decay width to be 2.05 AE 0.21 KeV. They also found Γ½f 0 ð980Þ → γγ ¼ 0.32 AE 0.05 KeV.…”

A chiral covariant approach to $$\varvec{\rho \rho }$$ ρ ρ scattering

“…This simple qq picture for the tensor f 2 (1270) resonance has been recently validated by the analyses performed in Ref. [20] of the high-statistics Belle data [21][22][23][24][25] on γ γ → ππ in both the neutral and the charged pion channels. Another point of importance in support of the qq nature of the f 2 (1270) is Regge theory, since this resonance lies in a parallel linear exchange-degenerate Regge trajectory with a "universal" slope parameter of around 1 GeV [26][27][28][29][30].…”

Dispersion relation for hadronic light-by-light scattering: two-pion contributions

“…The essential features of the generalization towards the doubly-virtual case, i.e. the appearance of anomalous thresholds for time-like kinematics [57] and the modifications to tensor basis and kernel functions [28,31], have already been laid out in previous work, but the practical implementation involves a number of challenges: due to the strong coupling between the ππ/KK channels in the isospin-0 S-wave a single-channel analysis is limited to rather low energies [54,56,117,118], assumptions for the LHC and number of subtractions need to be carefully studied to reliably assess the sensitivity to the high-energy input in the dispersive integrals [55], a full analysis of the generalized Roy-Steiner equations [28,31,55] involves solving coupled S-and D-wave systems of various helicity projections, and last but not least constraints on the γ * γ * → ππ amplitudes from asymptotic behavior and the sum rules derived in section 2.4.3 need to be incorporated. A full analysis along these lines will be left for future work.…”

“…In the on-shell case, available data on γγ → ππ [104][105][106][107][108][109] (in combination with γγ → KK [110][111][112][113][114][115][116]) are now sufficient to perform a partial-wave analysis [117], but such an approach appears unrealistic to control the dependence on the photon virtualities. However, approaches that exploit more comprehensively the analytic properties of the amplitude, see [54,55,118] for on-shell photons, can be extended towards the off-shell case with limited data input required to determine parameters, as demonstrated for the singly-virtual process in [56].…”