Flavor puzzle in three-Higgs-doublet models: Insights from Branco-Grimus-Lavoura and lessons from flavor data

We study a variant of the three-Higgs-doublet model (3HDM), referred to as the Branco-Grimus-Lavoura–(BGL-)3HDM, incorporating a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>1</a:mn><a:msub><a:mo stretchy="false">)</a:mo><a:mn>1</a:mn></a:msub><a:mo>×</a:mo><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>1</a:mn><a:msub><a:mo stretchy="false">)</a:mo><a:mn>2</a:mn></a:msub></a:math> symmetry, which can distinguish the primary sources of mass for different fermion generations. In the version considered here, the Yukawa matrices in the down-quark and charged lepton sectors are diagonal, thereby eliminating tree-level flavor changing neutral currents (FCNCs) in these sectors. FCNC interactions mediated by neutral nonstandard Higgses are confined to the up-quark sector only. No new Beyond-Standard-Model parameters are introduced by the Yukawa sector of the model, making it as economical as the natural flavor conservation (NFC) versions of 3HDM with a <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>U</g:mi><g:mo stretchy="false">(</g:mo><g:mn>1</g:mn><g:msub><g:mo stretchy="false">)</g:mo><g:mn>1</g:mn></g:msub><g:mo>×</g:mo><g:mi>U</g:mi><g:mo stretchy="false">(</g:mo><g:mn>1</g:mn><g:msub><g:mo stretchy="false">)</g:mo><g:mn>2</g:mn></g:msub></g:math> symmetry in terms of the number of free parameters. However, even in the down-quark and in the charged lepton sectors, flavor diagonal but nonuniversal Higgs couplings set this model apart from the NFC versions of the 3HDM.