Dispersive analysis of the γγ∗→ππ\gamma\gamma^{*} \to \pi \pi process

We present a theoretical study of the $\gamma\gamma^{*} \to \pi^+\pi^-, \pi^0\pi^0$ processes from the threshold through the $f_2(1270)$ region in the $\pi\pi$ invariant mass. We adopt the Omn\`es representation in order to account for rescattering effects in both s- and d-partial waves. For the description of the $f_0(980)$ resonance, we implement a coupled-channel unitarity. The constructed amplitudes serve as an essential framework to interpret the current experimental two-photon fusion program at BESIII. They also provide an important input for the dispersive analyses of the hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment.Comment: 8 pages, 4 figures (journal version

Coupled-channel dynamics in mesonic systems

Quantum chromodynamics (QCD) is the SU(3) color gauge theory, which describes strong interactions. At high energies QCD possesses a remarkable property of asymptotic freedom which allows the use of the standard perturbation theory. At low energies, however, the running coupling becomes strong and the associated confinement makes perturbative calculations impossible. To overcome this problem one has to apply nonperturbative methods like QCD sum rules or lattice simulations. Another powerful theoretical framework is chiral Perturbation Theory (ChPT) which is connected with spontaneous chiral symmetry breaking of QCD. According to the Goldstone theorem, this breakdown leads to the appearance of an octet of Goldstone bosons which are identified with pseudo-scalar mesons (π, K, η). An analysis of the low energy region is conducted in terms of experimentally detected hadrons rather than explicit quark-gluon degrees of freedom. A systematic expansion of matrix elements is performed in terms of masses of the light quarks and small momenta. However, ChPT leads to controlled results in the close to threshold region only and a generalization to resonance region is desirable. In order to extend the validity of ChPT to higher energies we include light vector degrees of freedom into the chiral Lagrangian according to hadrogenesis conjecture and take into account nonperturbative effects by the novel unitarization technique. The latter is based on micro-causality and coupled-channel unitarity constraints and also preserve the electromagnetic gauge invariance property. In this work, first we apply the novel unitarization scheme to Yukawa interactions of various strengths and ranges. This analysis helps us to realize the usefulness of the new approach and to what extend it is valid. The typical case of a superposition of strong short-range and weak long-range forces is investigated. Then we study Goldstone boson scattering based on the flavor SU(3) chiral Lagrangian with dynamical light vector mesons as formulated within the hadrogenesis conjecture. A coupled-channel computation is confronted with the empirical s- and p-wave phase shifts up to 1.2 GeV. In the isoscalar and isovector isospin sectors the f0(980) and a0(980) resonances are dynamically generated. In the p-wave scattering, vector mesons are described as Castillejo-Dalitz-Dyson poles. Then we extend our analysis to the photon-fusion reactions which are very sensitive to hadronic final-state interaction. In this case the Lagrangian contains few unknown coupling constants parameterizing the interaction terms with two vector meson fields. These parameters are fitted to photon fusion data γγ->π0π0, π+π- and to the decay η->π0γγ. Based on our parameter sets we predict the γγ->K0K0, K+K- and ηη cross sections

Исследования возможностей использования математического моделирования для оценки энергоэффективности асинхронных двигателей

The theoretical analysis of the γγ → π0η process is presented within the energy range up to 1.4 GeV. The S -wave resonance a0(980) is described involving the coupled channel dispersive framework and the D-wave a2(1320) is approximated as a Breit-Wigner resonance. For the a0(980) the pole is found on the IV Riemann sheet resulting in a two-photon decay width of Γa0 → γγ = 0.27(4) keV. The first dispersive prediction is provided for the single-virtual γγ*(Q2) → π0η process in the spacelike region up to Q2 = 1 GeV2

Dispersive analysis of the γγ → DD¯ data and the confirmation of the DD¯ bound state

In this paper, we present a data-driven analysis of the γγ → D+ D− and γγ → D0D¯ 0 reactions from threshold up to 4.0 GeV in the DD¯ invariant mass. For the S-wave contribution, we adopt a partial-wave dispersive representation, which is solved using the N/D ansatz. The left-hand cuts are accounted for using the model-independent conformal expansion. The D-wave χc2(3930) state is described as a BreitWigner resonance. The resulting fits are consistent with the data on the invariant mass distribution of the e+e− → J/ψ DD¯ process. Performing an analytic continuation to the complex s-plane, we find no evidence of a pole corresponding to the broad resonance X(3860) reported by the Belle Collaboration. Instead, we find a clear bound state below the DD¯ threshold at √sB = 3695(4) MeV, confirming the previous phenomenological and lattice predictions

A dispersive estimate of scalar contributions to hadronic light-by-light scattering

We consider the contribution of scalar resonances to hadronic light-by-light scattering in the anomalous magnetic moment of the muon. While the f0(500)has already been addressed in previous work using dispersion relations, heavier scalar resonances have only been estimated in hadronic models so far. Here, we compare an implementation of the f0(980)resonance in terms of the coupled-channel S-waves for γ∗γ∗→ππ/ ̄KKto a narrow-width approximation, which indicates aHLbLμ[f0(980)] =−0.2(2) ×10−11. With a similar estimate for the a0(980), the combined effect is thus well below 1 ×10−11in absolute value. We also estimate the contribution of heavier scalar resonances. In view of the very uncertain situation concerning their two-photon couplings we suggest to treat them together with other resonances of similar mass when imposing the matching to short-distance constraints. Our final result is a refined estimate of the S-wave rescattering effects in the ππand ̄KKchannel up to about 1.3GeV and including a narrow-width evaluation of the a0(980): aHLbLμ[scalars] =−9(1) ×10−11