English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We propose an $A_4$ modular invariant flavor model of leptons, in which bothCP and modular symmetries are broken spontaneously by the vacuum expectationvalue of the modulus $\tau$. The value of the modulus $\tau$ is restricted bythe observed lepton mixing angles and lepton masses for the normal hierarchy ofneutrino masses at $3\sigma$ confidence level. The predictive Dirac CP phase$\delta_{CP}$ is in the ranges $[0^\circ,50^\circ]$, $[170^\circ,175^\circ]$and $[280^\circ,360^\circ]$ for ${\rm Re}\, [\tau]<0$, and$[0^\circ,80^\circ]$, $[185^\circ,190^\circ]$ and $[310^\circ,360^\circ]$ for${\rm Re}\,[\tau]>0$ at $3\sigma$ confidence level. The sum of three neutrinomasses is predicted in $[60, 84]$ meV, and the effective mass for the$0\nu\beta\beta$ decay is in [0.003, 3] meV. On the other hand, there is noallowed region of the modulus $\tau$ for the inverted hierarchy of neutrinomasses at $3\sigma$ confidence level. The modulus $\tau$ links the Dirac CPphase to the cosmological baryon asymmetry (BAU) via the leptogenesis. Due tothe strong wash-out effect, the predictive baryon asymmetry $Y_B$ can be atmost the same order of the observed value. Then, the lightest right-handedneutrino mass is restricted in the range of $M_1 =[1.5,\,6.5] \times 10^{13}$GeV. We find the correlation between the predictive $Y_B$ and the Dirac CPphase $\delta_{CP}$. Only two predictive $\delta_{CP}$ ranges,$[5^\circ,40^\circ]$ (${\rm Re}\,[\tau]>0$) and $[320^\circ,355^\circ]$ (${\rmRe}\,[\tau]<0$) are consistent with the BAU.

Modulus $\tau$ linking leptonic CP violation to baryon asymmetry in $A_4$ modular invariant flavor model