Systematic study of bottomonium production in proton-proton collisions at LHC energies

Abstract

We present a comprehensive study of $\Upsilon(nS)$ ($n$ = 1, 2, 3) production in proton-proton ($pp$) collisions at various LHC energies and rapidity ranges within the framework of leading order non-relativistic quantum chromodynamics (NRQCD) factorization. The transverse momentum ($p_{\rm T}$)-dependent production cross-sections are calculated, incorporating both direct and feed-down contributions. Specifically, feed-down from $\Upsilon(2S)$, $\Upsilon(3S)$, $\chi_{bJ}(1P)$, and $\chi_{bJ}(2P)$ states to $\Upsilon(1S)$ is included, while $\Upsilon(2S)$ receives contributions from $\Upsilon(3S)$ and $\chi_{bJ}(2P)$. No significant feed-down is considered for $\Upsilon(3S)$. The computed cross-sections and cross-section ratios among different $\Upsilon$ states are compared with experimental measurements from ALICE, ATLAS, CMS and LHCb. It is found that the experimental cross-sections and cross-section ratios are well described within the theoretical uncertainties arising due to the choices of the factorization and renormalization scales for $p_{\rm T}$ $>$ 4 GeV and $p_{\rm T}$ $>$ 0 GeV, respectively. Furthermore, the cross-section ratios exhibit a clear saturation behavior beyond $p_{\rm T}$ $\approx$ 40 GeV.