We explore a scenario of new physics entering the description of

B \to K^{(*)} μ μ

decay through couplings to the operators

O_{9, 10}^{'}

, satisfying

C_{9}^{'} = - C_{10}^{'}

. From the current data on

B (B_{s} \to μ μ)

and

B (B \to K μ μ)_{[15, 22] {GeV}^{2}}

, we obtain constraints on

Re C_{10}^{'}

and

Im C_{10}^{'}

which we then assume to be lepton specific, and find

R_{K} = B (B \to K μ μ) / B (B \to K μ μ)_{[1, 6] {GeV}^{2}} = 0.88 (8)

, consistent with the recent value measured at the LHCb. A specific realization of this scenario is the one with a scalar leptoquark state

Δ

, in which

C_{10}^{'}

is related to the mass of

Δ

and its Yukawa couplings. We then show that this scenario does not make any significant impact on

B_{s} - {\bar{B}}_{s}

mixing amplitude or on

B (B \to K ν \bar{ν})

. Instead, it can modify

R_{K^{*}} = B (B \to K^{*} μ μ) / B (B \to K^{*} μ μ)_{[1, 6] {GeV}^{2}}

, which will soon be experimentally measured, and we find it to be

R_{K^{*}} = 1.11 (8)

, while

R_{K^{*}} / R_{K} = 1.27 (19)

. A similar ratio of forward-backward asymmetries also becomes lower than in the Standard Model.

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