Article
Improved dispersion relations for γγ→ππ
Departamento de Física, Universidad de Murcia, E30071 Murcia, Spain
Physics Letters B (Impact Factor: 6.02). 01/2008; 659(12):201208. DOI: 10.1016/j.physletb.2007.11.030 Source: arXiv

Article: Roy–Steiner equations for γγ→ππ
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ABSTRACT: Starting from hyperbolic dispersion relations, we derive a system of Roy–Steiner equations for pion Compton scattering that respects analyticity, unitarity, gauge invariance, and crossing symmetry. It thus maintains all symmetries of the underlying quantum field theory. To suppress the dependence of observables on highenergy input, we also consider once and twicesubtracted versions of the equations, and identify the subtraction constants with dipole and quadrupole pion polarizabilities. Based on the assumption of Mandelstam analyticity, we determine the kinematic range in which the equations are valid. As an application, we consider the resolution of the γγ→ππ partial waves by a Muskhelishvili–Omnès representation with finite matching point. We find a sum rule for the isospintwo Swave, which, together with chiral constraints, produces an improved prediction for the chargedpion quadrupole polarizability $(\alpha_{2}\beta_{2})^{\pi^{\pm}}=(15.3\pm3.7)\times 10^{4}$ fm5. We investigate the prediction of our dispersion relations for the twophoton coupling of the σresonance Γ σγγ . The twicesubtracted version predicts a correlation between this width and the isospinzero pion polarizabilities, which is largely independent of the highenergy input used in the equations. Using this correlation, the chiral perturbation theory results for pion polarizabilities, and our new sum rule, we find Γ σγγ =(1.7±0.4) keV.European Physical Journal C 09/2011; 71(9). · 5.44 Impact Factor  [Show abstract] [Hide abstract]
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, Crystal Ball at SLAC. The purpose of this analysis is to provide as close to a modelindependent determination of the $\gamma\gamma$ to meson pair amplitudes as possible. Having data with limited angular coverage, typically $\cos \theta < 0.60.8$, 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 crossingsymmetry makes up for the experimentally missing information. Final state interactions among the meson pairs are critical to this analysis. To fix these, we include the latest $\pi\pi\to\pi\pi$, ${\overline K}K$ scattering amplitudes given by dispersive analyses, supplemented in the ${\overline K}K$ 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 $\gamma\gamma\to\pi\pi$ and $\overline{K}K$ datasets, both integrated and differential crosssections, including the high statistics charged and neutral pion, as well as $K_sK_s$ data from Belle. Since this analysis invokes coupled hadronic channels, having data on both $\gamma\gamma\to\pi\pi$ and $\overline{K}K$ reduces the solution space to essentially a single form. 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 lightbylight scattering.04/2014; 
Article: MO analysis of the high statistics Belle results on γ γ→π + π −, π 0 π 0 with chiral constraints
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ABSTRACT: We reconsider Muskhelishvili–Omnès (MO) dispersive representations of photon–photon scattering to two pions, motivated by the very high statistics results recently released by the Belle collaboration for charged as well as neutral pion pairs and also by recent progress in the determination of the lowenergy π π scattering amplitude. Applicability of this formalism is extended beyond 1 GeV by taking into account inelasticity due to $K\bar{K}$ . A modified MO representation is derived which has the advantage that all polynomial ambiguities are collected into the subtraction constants and have simple relations to pion polarizabilities. It is obtained by treating differently the exactly known QED Born term and the other components of the lefthand cut. These components are approximated by a sum over resonances. All resonances up to spin two and masses up to ≃1.3 GeV are included. The tensor contributions to the lefthand cut are found to be numerically important. We perform fits to the data imposing chiral constraints, in particular, using a model independent sumrule result on the p 6 chiral coupling c 34. Such theoretical constraints are necessary because the experimental errors are dominantly systematic. Results on further p 6 couplings and pion dipole and quadrupole polarizabilities are then derived from the fit. The relevance of the new data for distinguishing between two possible scenarios of isospin breaking in the f 0(980) region is discussed.European Physical Journal C 11/2010; 70(12). · 5.44 Impact Factor
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