Article

# Improved dispersion relations for γγ→ππ

• ##### Carlos Schat
Departamento de Física, Universidad de Murcia, E-30071 Murcia, Spain; CONICET and Departamento de Física, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria, Pab. 1, (1428) Buenos Aires, Argentina
Physics Letters B (Impact Factor: 4.57). 01/2008; 659(1-2):201-208. DOI: 10.1016/j.physletb.2007.11.030
Source: arXiv

ABSTRACT We perform a dispersive theoretical study of the reaction
γγ→ππ emphasizing the low
energy region. The large source of theoretical uncertainty to calculate
the γγ→ππ total cross
section for s≳0.5 GeV within the dispersive approach is removed.
This is accomplished by taking one more subtraction in the dispersion
relations, where the extra subtraction constant is fixed by considering
new low energy constraints, one of them further refined by taking into
consideration the f(980) region. This allows us to make
sharper predictions for the cross section for s≲0.8 GeV, below the
onset of D-wave contributions. In this way, were new more precise data
on γγ→ππ available one
might then distinguish between different parameterizations of the
ππ isoscalar S-wave. We also elaborate on the width of the σ
resonance to γγ and provide new values.

0 Bookmarks
·
34 Views
• Source
##### Article: MO analysis of the high statistics Belle results on γ γ→π + π −, π 0 π 0 with chiral constraints
[Hide abstract]
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 low-energy 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 left-hand 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 left-hand cut are found to be numerically important. We perform fits to the data imposing chiral constraints, in particular, using a model independent sum-rule 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 70(1-2). · 5.25 Impact Factor
• Source
##### Article: Roy–Steiner equations for γγ→ππ
[Hide abstract]
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 high-energy input, we also consider once- and twice-subtracted 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 isospin-two S-wave, which, together with chiral constraints, produces an improved prediction for the charged-pion 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 two-photon coupling of the σ-resonance Γ σγγ . The twice-subtracted version predicts a correlation between this width and the isospin-zero pion polarizabilities, which is largely independent of the high-energy 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 71(9). · 5.25 Impact Factor
• Source
##### Article: S-wave {gamma}{gamma}{yields}{pi}{pi} and f{sub 0}(980){yields}{pi}{pi}
[Hide abstract]
ABSTRACT: We report on a dispersion relation for the {gamma}{gamma}{yields}({pi}{pi}){sub I} S-wave in isospin I emphasizing the low energy region. The f{sub 0}(980) signal that emerges in {gamma}{gamma}{yields}{pi}{pi} is also discussed. Our results could be used to distinguish between different {pi}{pi} isoscalar S-wave parameterizations. We also calculate the width of the {sigma} resonance to {gamma}{gamma} and obtain the value {gamma}({sigma}{yields}{gamma}{gamma}) (1.68{+-}0.15)KeV. Finally, we elaborate on the size of the f{sub 0}(980) coupling to {pi}{pi} and show that its smallness compared to the KK-bar one is not related to the OZI rule.
AIP Conference Proceedings. 08/2008; 1030(1).