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The ratio of the $B^0_s$ and $B^0$ fragmentation fractions, $f_s/f_d$, inproton-proton collisions at the LHC, is obtained as a function of $B$-mesontransverse momentum and collision centre-of-mass energy from the combinedanalysis of different $B$-decay channels measured by the LHCb experiment. Theresults are described by a linear function of the meson transverse momentum, orwith a function inspired by Tsallis statistics. Precise measurements of thebranching fractions of the $B^0_s \to J/\psi \phi$ and $B^0_s \to D^-_s \pi^+$decays are performed, reducing their uncertainty by about a factor of two withrespect to previous world averages. Numerous $B^0_s$ decay branching fractions,measured at the LHCb experiment, are also updated using the new values of$f_s/f_d$ and branching fractions of normalisation channels. These resultsreduce a major source of systematic uncertainty in several searches for newphysics performed through measurements of $B^0_s$ branching fractions.

Precise measurement of the $f_s/f_d$ ratio of fragmentation fractions and of $B^0_s$ decay branching fractions