Antonio Marrone

We show that solutions to the strong CP problem based on modular invariance can be extended to incorporate features that appear in string compactifications: quarks with mostly positive modular weights and non-trivial gauge kinetic functions. This requires assuming that singularities and zeroes only appear at special points, such as decompactification limits. We discuss the impact of these assumptions on string gauge unification.

We perform an updated global analysis of the known and unknown parameters of the standard three-neutrino ( 3 ν ) framework, using data available at the beginning of 2025. The known oscillation parameters include three mixing angles ( θ 12 , θ 23 , θ 13 ) and two squared mass gaps, chosen as δ m 2 = m 2 2 − m 1 2 > 0 and Δ m 2 = m 3 2 − 1 2 ( m 1 2 + m 2 2 ) , where the discrete parameter α = sign ( Δ m 2 ) distinguishes normal ordering (NO, α = + 1 ) from inverted ordering (IO, α = − 1 ). With respect to our previous 2021 update, the combination of accelerator, reactor, and atmospheric neutrino data leads to appreciably reduced uncertainties for θ 23 , θ 13 , and | Δ m 2 | . In particular, | Δ m 2 | is the first 3 ν parameter to enter the domain of subpercent precision (0.8% at 1 σ ). We underline some issues about common systematics in combined fits that might affect (and possibly weaken) this error estimate. Concerning oscillation unknowns, we find a relatively weak preference for NO versus IO (at 2.2 σ ), for C P violation versus conservation in NO ( 1.3 σ ), and for the first θ 23 octant versus the second in NO ( 1.1 σ ). We discuss the current status and qualitative prospects of the mass ordering hint in the plane charted by the mass parameters ( δ m 2 , Δ m e e 2 ) , where Δ m e e 2 = | Δ m 2 | + 1 2 α ( cos 2 θ 12 − sin 2 θ 12 ) δ m 2 , to be jointly measured by the JUNO experiment with subpercent precision. We also discuss upper bounds on nonoscillation observables, including the effective ν e mass m β in β decay, the effective Majorana mass m β β in 0 ν β β decay, and the sum of neutrino masses Σ in cosmology. We adopt m β < 0.50 eV ( 2 σ ) from current H 3 data and report m β β < 0.086 eV ( 2 σ ) from a combined Ge 76 , Te 130 , and Xe 136 data analysis, accounting for parametrized nuclear matrix element covariances. Concerning Σ , current results show tensions within the standard Λ cold dark matter ( Λ CDM ) cosmological model, pulling Σ toward unphysical values and suggesting possible model extensions. We discuss representative combinations of data, with or without augmenting the Λ CDM model with extra parameters accounting for possible systematics (lensing anomaly) or new physics (dynamical dark energy). The resulting 2 σ upper limits are roughly spread around the bound Σ < 0.2 eV within a factor of 3 (both up- and downward), with different implications for NO and IO scenarios. Bounds from oscillation and nonoscillation data are also discussed in the planes charted by pairs of ( m β , m β β , Σ ) parameters.

In a predictive modular invariant theory of flavor there should exist correlations between the quark and lepton observables, induced by the common modulus, by joint experimental constraints and possibly, in grand unified theories (GUTs), by common gauge multiplets. So far, in non-GUT bottom-up modular flavor models, these observables have been analyzed separately, making it impossible to investigate their interconnections. We perform a joint analysis of quark and lepton observables (22 altogether, 18 being measured) and of their correlations in a modular flavor model of the indicated class. The model is based on 2 O flavor symmetry and, within its class, it is characterized by the minimal number of free parameters (14 real constants). The joint analysis shows that the model is in good agreement with the experimental data for normal neutrino mass ordering, while predicting the leptonic Dirac C P -violating ( C P V ) phase ( δ C P ), the two Majorana C P V phases ( η 1 , η 2 ), the lightest neutrino mass ( m 1 ) and the effective neutrino masses probed by beta and neutrinoless double beta decay ( m β and m β β ). A detailed comparison of the separate (lepton-only and quark-only) and combined (lepton and quark) fit results shows differences in best-fit values and jointly allowed regions, that reflect a nontrivial interplay between quark and lepton observables in the model. Most importantly, our analysis highlights the existence of significant correlations between various pairs of such observables. For instance, the ratio of the strange and bottom quark masses, r s b , is strongly negatively correlated with each of the three lepton mixing angles and with δ C P , m 1 , m β , and m β β , while being positively correlated with η 1 and η 2 . These findings, that are missed in separate analyses of quark and lepton flavor sectors, as well as in (GUT and non-GUT) models with a relatively large number of free parameters, fall within ranges that can be tested by current and future experiments.