Searching for long-lived axion-like particles via displaced vertices at the HL-LHC

Axion-like particles (ALPs) are well-motivated extensions of the standard model (SM) that appear in numerous new physics scenarios. In this paper, we concentrate on searches for long-lived ALPs predicted by the photophobic scenario at the HL-LHC with the center-of-mass energy $\sqrt{s}=14$ TeV and the integrated luminosity $\mathcal{L}=$ $3$ ab${}^{-1}$. We consider the process $pp\to \gamma a$ with the ALP $a$ decaying into a pair of displaced charged leptons and perform a detailed analysis of two types of signals: ${\pi }^{+}{\pi }^{-}\gamma E{\mathrm{/}}_T$ and ${\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}\gamma E{\mathrm{/}}_T$. For the ${\pi }^{+}{\pi }^{-}\gamma E{\mathrm{/}}_T$ signal, we find that the prospective sensitivities of the HL-LHC can reach $g_{aWW}\in [8.72\times {10}^{-3},6.42\times {10}^{-2}]$ TeV${}^{-1}$ for the ALP mass $m_a\in [4,10]$ GeV. While for the ${\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}\gamma E{\mathrm{/}}_T$ signal, the HL-LHC can probe a broader parameter space, with the sensitivities covering $m_a\in [4,10]$ GeV and $g_{aWW}\in [4.17\times {10}^{-3},2.00\times {10}^{-1}]$ TeV${}^{-1}$. These long-lived searches complement some previous prompt decay studies from LEP and LHC experiments, extending the parameter space explored by the LHCb collaboration. Our results show that the HL-LHC has significant potential to probe long-lived ALPs via their displaced vertex signatures.