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Flavor violating signatures of lighter and heavier Higgs bosons within the Two Higgs Doublet Model Type-III at the LHeC

We analyze the prospects for observing the CP-even neutral Higgs bosons (h and H) in their decays into flavor violating $b \bar s+ c.c.$ channels at the proposed LHeC, with $\sqrt s \approx 1.3$ TeV, in the 2HDM Type-III, assuming a four-zero texture in the Yukawa matrices and a general Higgs potential. We consider theoretically consistent scenarios in agreement with current experimental data from flavor and Higgs physics. We investigate the charged current production process $ν_e ϕq$ in presence of flavor violating decays of the Higgs bosons, that lead to a 3-jets + $E\!\!\!\!/_T$ signature. We demand exactly two jets, one tagged $b$-jet and one light-flavor jet, all in the central rapidity region. The remaining jet (originated by the remanent quark $q$) is tagged in the forward or backward regions and this together with a central jet veto (not more than one light-flavor jet) are essential criterions to enhance the signal--to--background rates. We consider the most relevant Standard Model (SM) backgrounds, treating $c$-jets separately from light-flavor and gluon ones, while allowing for mis-tagging. We find that the SM-like Higgs boson, $h$, would be accessible within several parameter configurations of our model at approximately the 1-2$σ$ level with 100 fb$^{-1}$ of data. We also find that the heaviest neutral Higgs boson, $H$, with mass up to 150 GeV, would have a 1$σ$ significance for the same data sample. At the end of the LHeC running, one would have ten times data accumulation and for all the Higgs masses the significances are enhanced so as to allow for detection of both the $h$ and $H$ state. Hence, one of the most viable extensions of 2HDMs with FCNC's generated at tree level but controlled by a four-zero texture approach in the Yukawa matrices, as opposed to the adoption of ad hoc discrete symmetries, could be put under scrutiny at a future LHeC.