Compton scattering off pions and electromagnetic polarizabilities

The electric [Formula: see text] and magnetic [Formula: see text] Compton polarizabilities of both the charged and the neutral pion are of fundamental interest in the low-energy sector of quantum chromodynamics (QCD). Pion polarizabilities affect the shape of the [Formula: see text] Compton scattering angular distribution at back scattering angles and [Formula: see text] absolute cross sections. Theory derivations are given for the [Formula: see text] Compton scattering differential cross section, dispersion relations, and sum rules in terms of the polarizabilities. We review experimental charged and neutral polarizability studies and theoretical predictions. The [Formula: see text] polarizabilities were deduced from DESY Crystal Ball [Formula: see text] data, but with large uncertainties. The charged pion polarizabilities were deduced most recently from (1) radiative pion Primakoff scattering [Formula: see text] at CERN COMPASS, (2) two-photon pion pair production [Formula: see text] at SLAC Mark II, and (3) radiative pion photoproduction [Formula: see text] from the proton at MAMI in Mainz. A stringent test of chiral perturbation theory (ChPT) is possible based on comparisons of precision experimental charged pion polarizabilities with ChPT predictions. Only the CERN COMPASS charged pion polarizability measurement has acceptably small uncertainties. Its value [Formula: see text] agrees well with the two-loop ChPT prediction [Formula: see text], strengthening the identification of the pion with the Goldstone boson of chiral symmetry breaking in QCD.

Dispersion relations for hadronic light-by-light scattering and the muon g – 2

The largest uncertainties in the Standard Model calculation of the anomalous magnetic moment of the muon (g – 2)μ come from hadronic effects, and in a few years the subleading hadronic light-by-light (HLbL) contribution might dominate the theory error. We present a dispersive description of the HLbL tensor, which is based on unitarity, analyticity, crossing symmetry, and gauge invariance. This opens up the possibility of a data-driven determination of the HLbL contribution to (g – 2)μ with the aim of reducing model dependence and achieving a reliable error estimate. Our dispersive approach defines unambiguously the pion-pole and the pion-box contribution to the HLbL tensor. Using Mandelstam double-spectral representation, we have proven that the pion-box contribution coincides exactly with the one-loop scalar-QED amplitude, multiplied by the appropriate pion vector form factors. Using dispersive fits to high-statistics data for the pion vector form factor, we obtain [see formula in PDF]. A first model-independent calculation of effects of ππ intermediate states that go beyond the scalar-QED pion loop is also presented. We combine our dispersive description of the HLbL tensor with a partial-wave expansion and demonstrate that the known scalar-QED result is recovered after partial-wave resummation. After constructing suitable input for the γ*γ* → ππ helicity partial waves based on a pion-pole left-hand cut (LHC), we find that for the dominant charged-pion contribution this representation is consistent with the two-loop chiral prediction and the COMPASS measurement for the pion polarizability. This allows us to reliably estimate S-wave rescattering effects to the full pion box and leads to [see formula in PDF].

Exotic meson decays and polarization asymmetry in hadron environment with chiral imbalance

The possibility of the formation of a local parity breaking in a quark-hadron medium is described as a result of a violation of chiral symmetry, i.e, the difference between the average numbers of right and left -handing quarks in the fireball after HIC.The phenomenology of LPB in the fireball induces the introduction of a topological charge and, accordingly, a topological (chiral) chemical potential. Using the effective meson Lagrangian motivated by QCD in the chiral medium the properties of light scalar and pseudoscalar mesons are analyzed. It is establish that exotic decays of scalar mesons arise as a result of mixing of π and a0 vacuum states in the presence of chiral imbalance. The pion electromagnetic formfactor obtains a parity-odd supplement which generates a photon polarization asymmetry in pion polarizability. We consider that the above-mentioned properties of LPB can be revealed in experiments on LHC, RHIC, CBM FAIR and NICA accelerators.