A first search for the lepton-flavour violating decays B0 → K*0τ±μ∓ is presented. The analysis is performed using a sample of proton-proton collision data, collected with the LHCb detector at centre-of-mass energies of 7, 8 and 13 TeV between 2011 and 2018, corresponding to an integrated luminosity of 9 fb−1. No significant signal is observed, and upper limits on the branching fractions are determined to be $$ \mathcal{B}\left({B}^0\to {K}^{\ast 0}{\tau}^{+}{\mu}^{-}\right)<1.0(1.2)\times {10}^{-5} $$
B
B
0
→
K
∗
0
τ
+
μ
−
<
1.0
1.2
×
10
−
5
and $$ \mathcal{B}\left({B}^0\to {K}^{\ast 0}{\tau}^{-}{\mu}^{+}\right)<8.2(9.8)\times {10}^{-6} $$
B
B
0
→
K
∗
0
τ
−
μ
+
<
8.2
9.8
×
10
−
6
at the 90% (95%) confidence level.
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