Predictions for $h_c$ and $h_b$ production at the LHC

The production cross sections of $h_c$ and $h_b$, the ${}^1P_1$ quarkonia can be predicted in Non-Relativistic Quantum Chromodynamics (NRQCD) using heavy quark symmetry. Our study includes predictions for both the integrated cross-section and the transverse momentum ($p_T$) distribution of $h_c$ ($h_b$) production at the Large Hadron Collider (LHC), using the decay process $h_c (h_b) \rightarrow \eta_c (\eta_b) + \gamma$, $\eta_c (\eta_b) \rightarrow p \overline{p}$. We demonstrate substaintial discrepancies in integrated cross-section and the $p_T$ distribution of ${}^1P_1$ quarkonia production at the LHC using Colour-Singlet Model (CSM), NRQCD and modified NRQCD. Measuring these resonances at the LHC could discriminate between these models, thereby offering further insights into the dynamics of quarkonium production. In addition, we compare the recent LHCb data for the integrated cross-section of $h_c$ production at $\sqrt{s}$ = 13 TeV in the kinematic range 5.0 $<$ $p_T$ $<$ 20.0 GeV and 2.0 $<$ $y$ $<$ 4.0 with the theoretical predictions using NRQCD and modified NRQCD. Modified NRQCD gives an agreement with the recent LHCb experimental data.