  Measurements by the CMS experiment [CMS Collaboration, JHEP04 (2014) 103; CMS
Collaboration, JHEP11 (2020) 001] reveal a deficit of charged particle tracks
in events with higher $\Upsilon$(nS) states. This observation is suggested to
be a manifestation of the excited bottomonia suppression in $pp$ interactions.
Transverse mass ($m_{\mathrm{T}}$) scaling can be implied to check this
assumption in an independent way. The scaling has been observed for a wide
range of particle species in proton-proton collisions at various energies from
the SPS to RHIC and the LHC. The observed scaling is known to be different for
baryons and mesons, and this work presents a comprehensive study of the
$m_{\mathrm{T}}$-scaling of mesons at LHC energies with a focus on heavier
mesons. The study demonstrates patterns in the scaling properties of mesons,
which are related to the particle quark content. In particular, light species
and ground-state quarkonia obey the same scaling, whereas open-flavor particles
deviate from it because their spectra are significantly harder. The magnitude
of deviation depends on the flavor of the heaviest quark in the meson. By
extending the $m_{\mathrm{T}}$-scaling assumption to the excited bottomonia
states, it is observed that the measured cross sections of $\Upsilon$(2S) and
$\Upsilon$(3S) are reduced by factors of 1.6 and 2.4 compared to the
expectation from the scaling. This observation is consistent with recently
observed differences between the event-activity dependence of different
$\Upsilon$(nS) meson states.
