Murayama [arXiv:2601.02465] proposed a GeV-scale axion theory where the up-quark mass term is generated dynamically by the QCD chiral condensate, spontaneously breaking a Peccei-Quinn symmetry. It predicts a too large mass splitting between neutral and charged pions. Trying to solve this problem we explore extensions. Despite some partial improvements, we identify a structural obstruction: the new Peccei-Quinn spurion breaks the accidental isospin symmetry of the chiral Lagrangian, leading to an enhanced higher-order operator. As a consequence, pion scatterings too are distorted. We also examine the limit where the axion becomes light, finding that it is excluded by fifth-force constraints.

Italy

Luca Luzio

Michele Redi

Alessandro Strumia

Andrea Tesi

Arsenii Titov

The too visible QCD axion

We show that baryogenesis can arise from the cosmological evolution of a scalar field that governs CP-violating parameters, such as the Yukawa couplings and the theta terms of the Standard Model. During the big bang, this scalar may reach a CP-violating minimum, where its mass can be comparable to the inflationary Hubble scale. Such dynamics can emerge in theories featuring either a spontaneously broken local U(1) symmetry or modular invariance. The latter arises naturally as the effective field theory capturing the geometric origin of CP violation in toroidal string compactifications. Modular baryogenesis is compatible with the modular approach to resolving the strong CP problem.

Mateusz Duch

Baryogenesis from cosmological CP breaking

A correction to this paper has been published: https://doi.org/10.1007/JHEP05(2025)238

Spain

Rebeca Beltrán

Chile

Giovanna Cottin

Germany

Julian Günther

Martin Hirsch

China

Zeren Wang

Erratum to: Heavy neutral leptons and top quarks in effective field theory

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.

Ferruccio Feruglio

Antonio Marrone

Solving the strong CP problem in string-inspired theories with modular invariance

We study the phenomenology of heavy neutral leptons (HNLs) at the LHC in effective field theory, concentrating on $\textit{d}$ = 6 operators with top quarks. Depending on the operator choice and HNL mass, the HNLs will be produced either from proton-proton collisions in association with a single top, or via non-standard decays of top quarks. For long-lived HNLs we estimate the sensitivity reach of different detectors to various operators with top quarks and the HNLs for the high-luminosity phase of the LHC. For certain operators, ATLAS and some far detectors (MATHUSLA and ANUBIS) will be able to probe the associated new-physics scale as large as 12 TeV and 4.5 TeV, respectively, covering complementary HNL-mass ranges.

Heavy neutral leptons and top quarks in effective field theory

We propose a theory that preserves spin-summed scattering and decay rates at tree level while affecting particle spins. This is achieved by breaking the Lorentz group in a non-local way that tries avoiding stringent constraints, for example leaving unbroken the maximal sub-group SIM(2). As a phenomenological application, this new physics can alter the spins of top-antitop pairs (and consequently their entanglement) produced in collisions without impacting their rates. Some observables affected by loops involving top quarks with modified entanglement receive corrections.

New physics in spin entanglement

We formulate general conditions under which the strong CP problem is solved by spontaneous CP violation. Quark-mass matrix elements are polynomials in the CP-breaking order parameters, engineered such that their determinant is a real constant. This scheme permits only a limited number of textures. These conditions can be realized in supersymmetric theories with CP as an anomaly-free local flavor symmetry, suggesting a unified solution to the strong CP problem and the flavor puzzle. Our solution can be implemented using either modular invariance or a local U(1) symmetry. We present modular-invariant realizations where matter fields are assigned small modular weights ±2 (±1), utilising higher levels $\textit{N}$ = 2 ($\textit{N}$ = 3). Heavy quarks are in general not required, but their presence allows for models where colored particles fill non-singlet representations of the flavor group.

Matteo Parriciatu

Solving the strong CP problem without axions

In the framework of the low-energy effective theory containing, in addition to the Standard-Model fields, heavy neutral leptons (HNLs), we compute the decay rates of neutral and charged kaons into HNLs. We consider both lepton-number-conserving and lepton-number-violating four-fermion operators, taking into account also the contribution of active-heavy neutrino mixing. Assuming that the produced HNLs are long-lived, we perform simulations and calculate the sensitivities of future long-lived-particle (LLP) detectors at the high-luminosity LHC as well as the near detector of the Deep Underground Neutrino Experiment (DUNE-ND) to the considered scenario. When applicable, we also recast the existing bounds on the minimal mixing case obtained by NA62, T2K, and PS191. Our findings show that, while the future LHC LLP detectors can probe currently allowed parameter space only in certain benchmark scenarios, DUNE-ND should be sensitive to parameter space beyond the current bounds in almost all the benchmark scenarios, and, for some of the effective operators considered, it can even probe new-physics scales in excess of 3000 TeV.

Taiwan

Zeren Simon Wang

Heavy neutral leptons from kaons in effective field theory

We consider the dipole portal to sterile neutrinos, also called heavy neutral leptons (HNLs). The dipole interaction with the photon leads to HNL production in meson decays as well as triggers the HNL decay into an active neutrino and a photon. HNLs with masses of the order of 0.01–1 GeV are naturally long lived if the dipole coupling is sufficiently small. We perform Monte Carlo simulations and derive the sensitivities of the proposed FASER2 and FACET long-lived particle experiments to HNLs produced via the dipole operator in meson decays at the high-luminosity LHC. Our findings show that these future detectors will be complementary to each other, as well as to existing experiments, and will be able to probe new parts of the parameter space, especially in the case of the dipole operator coupled to the tau neutrino.

Daniele Barducci

Wei Liu

Yu Zhang

Probing the dipole portal to heavy neutral leptons via meson decays at the high-luminosity LHC

String compactifications on an orbi-folded torus with complex structure give rise to chiral fermions, spontaneously broken CP, modular invariance. We show that this allows simple effective theories of flavour and CP where: i) the QCD angle vanishes; ii) the CKM phase is large; iii) quark and lepton masses and mixings can be reproduced up to order one coefficients. We implement such general paradigm in supersymmetry or supergravity, with modular forms or functions, with or without heavy colored states.