Modular S 3 flavored Pati-Salam model with a two family seesaw mechanism

We present a unified model of quarks and leptons with modular <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>S</a:mi> <a:mn>3</a:mn> </a:msub> </a:math> flavor symmetry, where the two lightest family masses are naturally suppressed via a Pati-Salam version of the type I seesaw mechanism, mediated through heavier vectorlike fermions. Majorana neutrino masses are further suppressed through a double seesaw mechanism. The viable parameter space has a preferred range of the modulus field with <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>Im</c:mi> <c:mo stretchy="false">(</c:mo> <c:mi>τ</c:mi> <c:mo stretchy="false">)</c:mo> <c:mo>∼</c:mo> <c:mn>2</c:mn> </c:math> , leading to successful fermion masses and mixing. The prediction for neutrinoless double beta decay is partly within the reach of the nEXO experiment. In particular, the Dirac <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:mi>C</g:mi> <g:mi>P</g:mi> </g:mrow> </g:math> violating neutrino oscillation phase is predicted to lie in the range <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msubsup> <i:mi>δ</i:mi> <i:mrow> <i:mi>C</i:mi> <i:mi>P</i:mi> </i:mrow> <i:mi>ν</i:mi> </i:msubsup> <i:mo>∼</i:mo> <i:mn>270</i:mn> <i:mi>°</i:mi> <i:mo>−</i:mo> <i:mn>360</i:mn> <i:mi>°</i:mi> </i:math> .