Lopsided texture compatible with thermal leptogenesis in partially composite Pati--Salam unification

Abstract

In this paper, we consider a lopsided flavor texture compatible with thermal leptogenesis in partially composite Pati--Salam unification. The Davidson--Ibarra bound $M_{\nu R1}\gtrsim 10^9$ GeV for the successful thermal leptogenesis can be recast to the Froggatt--Nielsen (FN) charge of the lopsided texture. We found the FN charge $n_{\nu 1}$ of the lightest right-handed neutrino ${\nu }_{R1}$ can not be larger than a upper bound, $n_{\nu 1}\lesssim 4.5$. From the viewpoint of unification, the FN charges of the neutrinos $n_{\nu i}$ should be the same to that of other SM fermions. Then, two cases $n_{\nu i}=n_{qi}=(3,2,0)$ and $n_{\nu i}=n_{li}=(n+1,n,n)$ are considered. Observations of PS model shows that the case of $n=0$, $n_{li}=n_{di}=(1,0,0)$ will be the simplest realization. To decrease the FN charges of these fermions from the GUT invariant FN charges $n_{qi}=(3,2,0)$, we utilize the partial compositeness. In this picture, the hierarchies of Yukawa matrices are a consequence of mixings between massless chiral fermions $f_L,f_R^{\prime }$ and massive vector fermions $F_{L,R},F_{L,R}^{\prime }$. This is induced by the linear mixing terms ${\lambda }^f{\bar{f}}_L{F}_R$ and ${\lambda }^{f^{\prime }}{\bar{F}}_L^{\prime }{f}_R^{\prime }$. As a result of the partial compositeness, the decreases of FN charges require fine-tunings between mass and Yukawa matrices either for the increases of ${\lambda }^{f,f^{\prime }}$ or for the decreases of $M_{F,F^{\prime }}$. Therefore, the case for $n=2$ and $n_{di}=n_{li}=(3,2,2)$, which requires only increases of FN charges will be appropriate to build a natural model.

arXiv comment17 pages, 4 tables, substantially modified from the first version

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