We employ a bottom-up and model-independent technique to search for non-Abelian discrete flavour symmetries capable of predicting viable CKM and PMNS matrices alongside of special patterns of leptoquark couplings. In particular, we analyze patterns de- rived when an ultra-violet flavour theory is assumed to break to global Abelian symmetries in Standard Model fermion masses and new Yukawa-like terms sourced by the leptoquark representation. The phenomenology of different classes of these ‘simplified models’ can be explored without reference to explicit model-building assumptions, e.g. the nature of flavour symmetry breaking or any additional field content associated to it, and are also capable of explaining hints of lepton non-universality in $$ {\mathcal{R}}_{K^{\left(\ast \right)}} $$ . Assuming experimentally interesting CKM and PMNS matrix elements, our algorithm finds an abundance of predictive non-Abelian flavour groups and therefore provides promising directions for future model building in the flavoured leptoquark space, regardless of whether the anomalous $$ {\mathcal{R}}_{K^{\left(\ast \right)}} $$ measurements withstand further experimental scrutiny.
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"value": "We employ a bottom-up and model-independent technique to search for non-Abelian discrete flavour symmetries capable of predicting viable CKM and PMNS matrices alongside of special patterns of leptoquark couplings. In particular, we analyze patterns de- rived when an ultra-violet flavour theory is assumed to break to global Abelian symmetries in Standard Model fermion masses and new Yukawa-like terms sourced by the leptoquark representation. The phenomenology of different classes of these \u2018simplified models\u2019 can be explored without reference to explicit model-building assumptions, e.g. the nature of flavour symmetry breaking or any additional field content associated to it, and are also capable of explaining hints of lepton non-universality in <math> <msub> <mi>R</mi> <msup> <mi>K</mi> <mfenced> <mo>\u2217</mo> </mfenced> </msup> </msub> </math> $$ {\\mathcal{R}}_{K^{\\left(\\ast \\right)}} $$ . Assuming experimentally interesting CKM and PMNS matrix elements, our algorithm finds an abundance of predictive non-Abelian flavour groups and therefore provides promising directions for future model building in the flavoured leptoquark space, regardless of whether the anomalous <math> <msub> <mi>R</mi> <msup> <mi>K</mi> <mfenced> <mo>\u2217</mo> </mfenced> </msup> </msub> </math> $$ {\\mathcal{R}}_{K^{\\left(\\ast \\right)}} $$ measurements withstand further experimental scrutiny."
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