$B$-jet fragmentation with $B^{\pm }\to J\mathrm{/}\psi K^{\pm }$ decays in $\sqrt{s}=13$ TeV $pp$ collisions at LHCb

The collinear and transverse-momentum-dependent jet fragmentation function and the radial profile for $B^{\pm }$ mesons in jets are measured. The $B^{\pm }$ mesons are reconstructed through the $J\mathrm{/}\psi (\to {\mu }^{+}{\mu }^{-})K^{\pm }$ decay channel using proton-proton collision data collected during 2016-2018 with the LHCb detector at a center-of-mass energy of $\sqrt{s}=13$ TeV, corresponding to an integrated luminosity of $5.4$ fb${}^{-1}$. The results complement recent measurements of jet fragmentation functions for heavy-flavor hadrons and suggest a growing contribution of gluon fragmentation to $B^{\pm }$ mesons as the jet transverse momentum increases.