Bai-Long Hoid

We present a dispersive amplitude analysis of the low-energy π 0 π 0 system in the radiative decay J / ψ → γ π 0 π 0 , using the mass-independent BESIII 0 + + and 2 + + intensities, the total spectrum, and the measured 0 + + − 2 + + E 1 phase difference. The isoscalar S -wave is described by a coupled-channel π π / K K ¯ Muskhelishvili–Omnès representation, which implements the strong final-state interactions associated with the f 0 ( 500 ) and f 0 ( 980 ) . The D -wave is treated with a single-channel π π Muskhelishvili-Omnès representation, where we identify all kinematic constraints of helicity amplitudes before transforming them to the experimental E 1 , M 2 , and E 3 multipoles. Smooth short-distance production of a pseudoscalar-meson pair is encoded in subtraction polynomials, while left-hand-cut effects are estimated and found to be numerically subleading. We identify the negative solution of the BESIII 0 + + − 2 + + E 1 phase ambiguity, after using the modulo- π freedom of production amplitudes, as the phase solution compatible with unitarity constraints, showing that the measured phase information can be accommodated with the Omnès phase motion without requiring large additional phases. By normalizing the BESIII intensities with the extracted branching fraction, we fix the absolute scale of the fitted amplitudes, making them suitable as input for future dispersive studies of two-pion contributions to gravitational form factors.

We present an analysis of the radiative decay ϕ → γ π 0 π 0 in a dispersive framework, where the two-pion subsystem undergoes strong final-state interactions that cover the f 0 ( 500 ) and f 0 ( 980 ) regions. We employ a coupled-channel Muskhelishvili-Omnès framework that allows for a consistent treatment of two scalar resonances and crossed-channel singularities induced by the Born and vector-meson exchanges. We explicitly verify the equivalence between the modified and standard Muskhelishvili-Omnès representations for vector-meson pole contributions when the isoscalar Omnès matrix is chosen asymptotically bounded, and we adopt the standard representation in decay kinematics. This yields, for the first time, a parameter-free dispersive prediction for the kaon Born rescattering, which provides a dominant contribution. To obtain a good fit to the KLOE and SND data, we employ a once-subtracted coupled-channel dispersion relation with heavier left-hand cut contributions and two unknown subtraction constants. The results demonstrate the consistency among the data for π π scattering, γ γ fusion, and ϕ radiative decay, thereby validating the underlying dispersive formalism and the input used for the hadronic Omnès matrix and left-hand cuts.

A bstract: The rare decays η ^{( ′ )} → ℓ ⁺ ℓ ⁻ , ℓ ∈ { e , μ }, are highly suppressed in the Standard Model, both by their chirality structure and the required loop attaching the lepton line to the η ^{( ′ )} → γ ^∗ γ ^∗ matrix element. The latter is described by a single scalar function, the transition form factor, which has recently been studied in great detail for η ^{( ′ )} in the context of the pseudoscalar-pole contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon. Based on these results, we evaluate the corresponding prediction for the η ^{( ′ )} dilepton decays, supplemented by an improved evaluation of the asymptotic contributions including pseudoscalar mass effects. In particular, the dispersive representation for the η ^{( ′ )} transition form factors allows us, for the first time, to perform a robust evaluation of the imaginary parts due to subleading channels besides the dominant two-photon cut. Our final results are Br[ η → e ⁺ e ⁻ ] = 5.37(4)(2)[4] × 10 ⁻⁹ , Br[ η → μ ⁺ μ ⁻ ] = 4.54(4)(2)[4] × 10 ⁻⁶ , Br[ η ^′ → e ⁺ e ⁻ ] = 1.80(2)(3)[3] × 10 ⁻¹⁰ , and Br[ η ^′ → μ ⁺ μ ⁻ ] = 1.22(2)(2)[3] × 10 ⁻⁷ , where the errors refer to the uncertainty in the normalized branching fraction, the one propagated from Br[ η ^{( ′ )} → γγ ], and the total uncertainty, respectively. The branching fraction for η → μ ⁺ μ ⁻ exhibits a mild 1.6 σ tension with experiment, and we explore the bounds that can be derived on physics beyond the Standard Model.

A bstract: An efficient numerical algoritm is proposed for the calculation of the modified Lüscher zeta-function in the presence of a long-range force. Using the formalism developed in ref. JHEP05(2024)168 for the analysis of synthetic data on the finite-volume energy levels in a toy model, it is demonstrated that, in contrast to the standard Lüscher approach, the truncation of the higher partial waves has very little effect on the final result. Furthermore, the regularization and renormalization of the modified Lüscher zeta-function is discussed in detail, as well as the problems arising within the cutoff regularization. It is shown that, using the renormalization scheme proposed in the present paper, one obtains modified effective range expansion parameters of natural size in all partial waves.

The kaon physics programme, long heralded as a cutting-edge frontier by the European Strategy for Particle Physics, continues to stand at the intersection of discovery and innovation in high-energy physics (HEP). With its unparalleled capacity to explore new physics at the multi-TeV scale, kaon research is poised to unveil phenomena that could reshape our understanding of the Universe. This document highlights the compelling physics case, with emphasis on exciting new opportunities for advancing kaon physics not only in Europe but also on a global stage. As an important player in the future of HEP, the kaon programme promises to drive transformative breakthroughs, inviting exploration at the forefront of scientific discovery.

An efficient numerical algoritm is proposed for the calculation of the modified Lüscher zeta-function in the presence of a long-range force. Using the formalism developed in Ref.~\cite{Bubna:2024izx} for the analysis of synthetic data on the finite-volume energy levels in a toy model, it is demonstrated that, in contrast to the standard Lüscher approach, the truncation of the higher partial waves has very little effect on the final result. Furthermore, the regularization and renormalization of the modified Lüscher zeta-function is discussed in detail, as well as the problems arising within the cutoff regularization. It is shown that, using the renormalization scheme proposed in the present paper, one obtains modified effective range expansion parameters of natural size in all partial waves.

A bstract: The strength of the interaction of three pions and a photon, F _{3 π} is predicted by the axial anomaly in terms of the pion decay constant, a relation that is frequently used to constrain low-energy radiative processes involving pions, but only tested experimentally at the 10% level. Here, we present a new avenue to test this prediction, via a fit of a dispersive description of the γ ^∗ → 3 π amplitude to data for e ⁺ e ⁻ → 3 π . From the global fit to SND, CMD-2, and BaBar data we obtain F _{3 π} = 33.1(1.7) GeV ⁻³ , in agreement with the chiral prediction at the level of 5%. We also consider dispersive fits to the recent data by Belle II, in which case we observe tensions with the dispersive constraints, the width parameters of ω and ϕ , and the chiral anomaly.