Tri-resonant leptogenesis in a non-holomorphic modular A$$_4$$ scotogenic model

Abstract We investigate low-scale baryogenesis via tri-resonant leptogenesis within the scotogenic model with a scalar dark matter embedded in non-holomorphic modular $$A_4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:math> symmetry framework. The model naturally accommodates three nearly degenerate right-handed (RH) neutrinos when they are assigned to the triplet representation of $$A_4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:math> . The near degeneracy originates from treating the symmetric contribution to the Majorana mass matrix, arising from the $$\textbf{3}\otimes \textbf{3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>⊗</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> decomposition of $$A_4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:math> , as a small perturbation to the dominant singlet contribution. For inverted hierarchy (IH), the predicted $$3\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>3</mml:mn> <mml:mi>σ</mml:mi> </mml:mrow> </mml:math> range of $$\theta _{23}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>θ</mml:mi> <mml:mn>23</mml:mn> </mml:msub> </mml:math> lies in the lower octant close to maximal value while Dirac CP phase $$\delta _{\textrm{CP}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>δ</mml:mi> <mml:mtext>CP</mml:mtext> </mml:msub> </mml:math> and the Majorana phase $$\alpha _{21}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>α</mml:mi> <mml:mn>21</mml:mn> </mml:msub> </mml:math> are predicted to lie close to $$0^\circ $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>0</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:math> or $$360^\circ $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>360</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:math> . Also, in this case, predicted values of $$m_{ee}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:mrow> <mml:mi>ee</mml:mi> </mml:mrow> </mml:msub> </mml:math> and $$\sum _i m_i$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mo>∑</mml:mo> <mml:mi>i</mml:mi> </mml:msub> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>i</mml:mi> </mml:msub> </mml:mrow> </mml:math> can be tested and constrained by future neutrinoless double beta decay $$(0\nu \beta \beta )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mi>ν</mml:mi> <mml:mi>β</mml:mi> <mml:mi>β</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> experiments, as well as by cosmological observations, particularly DESI+CMB and Planck data. In fact DESI+CMB disallows IH in the model. We further show that successful baryogenesis can be achieved for both normal hierarchy (NH) and inverted hierarchy (IH) of light neutrino masses with RH neutrino masses as low as $$537~\textrm{GeV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>537</mml:mn> <mml:mspace/> <mml:mtext>GeV</mml:mtext> </mml:mrow> </mml:math> rendering this scenario experimentally testable. For NH, RH neutrino mass degeneracy of $$\mathcal {O}(10^{-7}\!-\!10^{-6})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow>