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An amplitude analysis of $B^0 \to J/\psi \phi K_S^0$ decays is performedusing proton-proton collision data corresponding to an integrated luminosity of9 ${\rm fb}^{-1}$, collected with the LHCb detector at centre-of-mass energiesof 7, 8 and 13 TeV. Evidence with a significance of $4.0$ standard deviationsof a structure in the $J/\psi K_S^0$ system, named $T_{\psis1}^{\theta}(4000)^0$, is seen, with its mass and width measured to be$3991~_{-10}^{+12}~^{+\phantom{0}9}_{-17}$ MeV and$105~_{-25}^{+29}~^{+17}_{-23}$ MeV, respectively, where the first uncertaintyis statistical and the second systematic. The $T_{\psi s1}^{\theta}(4000)^0$state is likely to be the isospin partner of the $T_{\psi s1}^{\theta}(4000)^+$state, previously observed in the $J/\psi K^+$ system of the $B^+ \to J/\psi\phi K^+$ decay. When isospin symmetry for the charged and neutral $T_{\psis1}^{\theta}(4000)$ states, is assumed, the signal significance increases to$5.4$ standard deviations.

Evidence of a $J/\psi K_S^0$ structure in $B^0 \to J/\psi \phi K_S^0$ decays