Muonic hydrogen cascade time and lifetime of the short-lived $2S$ state

Metastable ${2S}$ muonic-hydrogen atoms undergo collisional ${2S}$-quenching, with rates which depend strongly on whether the $\mu p$ kinetic energy is above or below the ${2S}\to {2P}$ energy threshold. Above threshold, collisional ${2S} \to {2P}$ excitation followed by fast radiative ${2P} \to {1S}$ deexcitation is allowed. The corresponding short-lived $\mu p ({2S})$ component was measured at 0.6 hPa $\mathrm{H}_2$ room temperature gas pressure, with lifetime $\tau_{2S}^\mathrm{short} = 165 ^{+38}_{-29}$ ns (i.e., $\lambda_{2S}^\mathrm{quench} = 7.9 ^{+1.8}_{-1.6} \times 10^{12} \mathrm{s}^{-1}$ at liquid-hydrogen density) and population $\epsilon_{2S}^\mathrm{short} = 1.70^{+0.80}_{-0.56}$ % (per $\mu p$ atom). In addition, a value of the $\mu p$ cascade time, $T_\mathrm{cas}^{\mu p} = (37\pm5)$ ns, was found.