Can transverse mass scaling shed light on the event-activity dependence of $\Upsilon$-meson production at the LHC?

Measurements by the CMS experiment [S. Chatrchyan (CMS Collaboration), J. High Energy Phys. 04 (2014) 103; A. M. Sirunyan (CMS Collaboration), J. High Energy Phys. 11 (2020) 001] reveal a deficit of charged particle tracks in events with higher <math display="inline"><mrow><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mi>nS</mi><mo stretchy="false">)</mo></mrow></math> states. This observation is suggested to be a manifestation of the excited bottomonia suppression in <math display="inline"><mi>p</mi><mi>p</mi></math> interactions. Transverse mass (<math display="inline"><msub><mi>m</mi><mi mathvariant="normal">T</mi></msub></math>) 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 <math display="inline"><msub><mi>m</mi><mi mathvariant="normal">T</mi></msub></math>-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 <math display="inline"><msub><mi>m</mi><mi mathvariant="normal">T</mi></msub></math>-scaling assumption to the excited bottomonia states, it is observed that the measured cross sections of <math display="inline"><mrow><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>2</mn><mi mathvariant="normal">S</mi><mo stretchy="false">)</mo></mrow></math> and <math display="inline"><mrow><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>3</mn><mi mathvariant="normal">S</mi><mo stretchy="false">)</mo></mrow></math> 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 <math display="inline"><mrow><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mi>nS</mi><mo stretchy="false">)</mo></mrow></math> meson states.