First measurement of the $$C\!P$$ C P -violating phase in $${{B} ^0_{s}} \!\rightarrow {{J /\psi }} ($$ B s 0 → J / ψ ( $$\rightarrow $$ → $$e ^+e ^-$$ e + e - ) $$\phi $$ ϕ decays

A flavour-tagged time-dependent angular analysis of $${{B} ^0_{s}} \!\rightarrow {{J /\psi }} \phi $$ decays is presented where the $${J /\psi }$$ meson is reconstructed through its decay to an $$e ^+e ^-$$ pair. The analysis uses a sample of pp collision data recorded with the LHCb experiment at centre-of-mass energies of 7 and $$8\text {\,Te V} $$ , corresponding to an integrated luminosity of $$3 \text {\,fb} ^{-1} $$ . The $$C\!P$$ -violating phase and lifetime parameters of the $${B} ^0_{s} $$ system are measured to be $${\phi _{{s}}} =0.00\pm 0.28\pm 0.07\text {\,rad}$$ , $${\Delta \Gamma _{{s}}} =0.115\pm 0.045\pm 0.011\text {\,ps} ^{-1} $$ and $${\Gamma _{{s}}} =0.608\pm 0.018\pm 0.012\text {\,ps} ^{-1} $$ where the first uncertainty is statistical and the second systematic. This is the first time that $$C\!P$$ -violating parameters are measured in the $${{B} ^0_{s}} \!\rightarrow {{J /\psi }} \phi $$ decay with an $$e ^+e ^-$$ pair in the final state. The results are consistent with previous measurements in other channels and with the Standard Model predictions.