Real and complex singlet-scalar benchmarks with a vector-like down quark for B→ Xₛγ and Bₛ-B̄ₛ mixing

We study a simple extension of the Standard Model with a vector-like down-type quark D and a neutral singlet scalar S=SR,Φ S = S R , Φ . The scalar is considered in two forms, a real field SR=SR^ S R = S R † and a complex field Φ ≠ Φ ^ Φ ≠ Φ † . The interaction -λ ᵢSD̄L dRi+h.c. - λ i S D ¯ L d Ri + h . c . generates the radiative transitions b→ sγ b → s γ and b→ sg b → s g at one loop. Since S S has no electric charge or color, the gauge boson is emitted from the internal D line, giving C7γNP/C8GNP=QD=-1/3 C 7 γ NP / C 8 G NP = Q D = - 1 / 3 at the matching scale for Δ B=1 Δ B = 1 dipole transitions. For MD=mS=1~TeV M D = m S = 1 TeV