Thermal properties of $$\pi $$ and $$\rho $$ meson

We computed the pole masses and decay constants of $$\pi $$ π and $$\rho $$ ρ meson at finite temperature in the framework of Dyson–Schwinger equations and Bethe–Salpeter equations approach. Below transition temperature, pion pole mass increases monotonously, while $$\rho $$ ρ meson seems to be temperature independent. Above transition temperature, pion mass approaches the free field limit of screening mass $$\sim 2\pi T$$ ∼ 2 π T , whereas $$\rho $$ ρ meson is about twice as large as that limit. Pion and the longitudinal projection of $$\rho $$ ρ meson decay constants have similar behaviour as the order parameter of chiral symmetry, whereas the transverse projection of $$\rho $$ ρ meson decay constant rises monotonously as temperature increases. The inflection point of decay constant and the chiral susceptibility get the same phase transition temperature. Though there is no access to the thermal width of mesons within this scheme, it is discussed by analyzing the Gell-Mann-Oakes-Renner (GMOR) relation in medium. These thermal properties of hadron observables will help us understand the QCD phases at finite temperature and can be employed to improve the experimental data analysis and heavy ion collision simulations.

Dispersion relations for hadronic light-by-light 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, namely hadronic vacuum polarization (HVP) and hadronic lightby-light (HLbL) contributions. Especially the latter is emerging as a potential roadblock for a more accurate determination of (g−2)µ. The main focus here is on a novel 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 $ \alpha _\mu ^{\pi {\rm{ - box}}} = - 15.9(2) \times {10^{ - 11}} $. 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 $ \alpha _\mu ^{\pi {\rm{ - box}}} + \alpha _{\mu ,J = 0}^{\pi \pi ,\pi {\rm{ - pole}}\,{\rm{LHC}}} = - 24(1) \times {10^{ - 11}} $.

Exploratory studies for the position-space approach to hadronic light-by-light scattering in the muon g - 2

The well-known discrepancy in the muon g − 2 between experiment and theory demands further theory investigations in view of the upcoming new experiments. One of the leading uncertainties lies in the hadronic light-by-light scattering contribution (HLbL), that we address with our position-space approach. We focus on exploratory studies of the pion-pole contribution in a simple model and the fermion loop without gluon exchanges in the continuum and in infinite volume. These studies provide us with useful information for our planned computation of HLbL in the muon g − 2 using full 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].

Hadronic light-by-light scattering contribution to the muon g – 2 on the lattice

We briefly review several activities at Mainz related to hadronic light-by-light scattering (HLbL) using lattice QCD. First we present a position-space approach to the HLbL contribution in the muon g̅2, where we focus on exploratory studies of the pion-pole contribution in a simple model and the lepton loop in QED in the continuum and in infinite volume. The second part describes a lattice calculation of the double-virtual pion transition form factor Fπ0γ*γ* (q21; q21) in the spacelike region with photon virtualities up to 1.5 GeV2 which paves the way for a lattice calculation of the pion-pole contribution to HLbL. The third topic involves HLbL forward scattering amplitudes calculated in lattice QCD which can be described, using dispersion relations (HLbL sum rules), by γ*γ* → hadrons fusion cross sections and then compared with phenomenological models.

Neutral Pion Pole Mass Calculation in a Strong Magnetic Field: Lattice QCD Versus NJL Model

Within the framework of cold magnetized SU(2) Nambu-Jona-Lasinio model we evaluate the [Formula: see text] and [Formula: see text] pole mass, as well as, [Formula: see text], [Formula: see text] at zero baryon density. We employ a magnetic field dependent coupling, [Formula: see text], fitted to reproduce lattice QCD results for the quark condensates. In particular, we find that the [Formula: see text] meson mass systematically decreases when the magnetic field increases, in good agreement with recent lattice calculations.