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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 $pp \to γa$ with the ALP $a$ decaying into a pair of displaced charged leptons and perform a detailed analysis of two types of signals: $π^+ π^- γE\mkern-10.5 mu/_T $ and $\ell^+ \ell^- γE\mkern-10.5 mu/_T $. For the $π^+ π^- γE\mkern-10.5 mu/_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 $\ell^+ \ell^- γE\mkern-10.5 mu/_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.