Flavored QCD axion and Modular invariance

TL;DR

This paper develops a string-inspired supergravity model incorporating modular invariance and anomaly cancellation, predicting specific axion properties, neutrino masses, and flavor structures consistent with current experimental data.

Contribution

It introduces a novel effective model with modular invariance that constrains flavor structures, axion properties, and neutrino masses, linking string theory to observable phenomenology.

Findings

Predicts axion mass around 0.009 eV and photon coupling ~1.7×10^{-13} GeV^{-1}

Reproduces quark and lepton data with flavor-violating couplings suppressed

Yields normal neutrino hierarchy consistent with oscillation and cosmological data

Abstract

A four-dimensional effective model with $G_{\rm SM}\times SL(2,\mathbb{Z}) \times U(1)_X$ is proposed in string-derived supergravity framework, where $G_{\rm SM}$ is the Standard Model (SM) gauge group and $U(1)_X$ is gauged. We show $SL(2,\mathbb{Z})$- and $U(1)_X$-mixed anomalies should vanish. Anomalies induced by K{\"a}hler transformations match those from gaugino chiral rotations. When SM fermions transform nontrivially under $SL(2,\mathbb{Z})$, and with vanishing gaugino contributions, the anomaly-free conditions are powerful enough to determine the quark and lepton flavor structures, set scales for $U(1)_X$ breaking, and ensure the strong CP phase remains unmodified. While the Green-Schwarz coefficient $\delta^{\rm GS}_X$ is generically non-zero, vanishing $U(1)_X$ anomalies cause gauge boson decoupling and $\delta^{\rm GS}_X\rightarrow 0$, yielding a massless global $U(1)_X$ without a Nambu-Goldstone mode. We show that the modulus vacuum expectation value stabilizes near $\langle\tau\rangle \approx i$, where exact $SL(2,\mathbb{Z})$ ($T$-duality) is spontaneously broken, removing residual modular symmetry. The framework predicts seesaw-generated neutrino masses and flavored axion properties, with all Yukawa coefficients constrained to unit-magnitude complex numbers. Our model reproduces current quark and lepton data, predicts an axion mass $m_a\approx0.9\times10^{-2}$ eV and photon coupling $|g_{a\gamma\gamma}|\approx1.7\times10^{-13}\,{\rm GeV}^{-1}$, and unlike the ordinary case, suppresses flavor-violating axion couplings to $s,d$ quarks and $\mu,e$ leptons to $\mathcal{O}(\lambda^4)$ (with $\lambda$ the Cabibbo angle). It also yields normal neutrino mass hierarchy consistent with oscillation data, $0\nu\beta\beta$-decay rate, and cosmological and astrophysical measurements.