$B$-jet fragmentation with $B^{\pm} \to J/ψK^{\pm}$ 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 $J/\psi (\to \mu^{+} \mu^{-}) K^{\pm}$ decay channel using the 2016-2018 $\sqrt{s} = 13$ TeV proton-proton collision data collected with the LHCb detector. 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.