Heavy neutrino production via $Z^{\prime }$ at the lifetime frontier

We investigate the pair production of right-handed neutrinos from the decay of an additional neutral $Z^{\prime }$ boson in the gauged $B-L$ model. Taking into account current constraints on the $Z^{\prime }$ mass and the associated gauge coupling $g_1^{\prime }$, we analyse the sensitivity of proposed experiments at the lifetime frontier, FASER 2, CODEX-b, MATHUSLA as well as a hypothetical version of the MAPP detector to a long lived heavy neutrino $N$ originating in the decays of the $Z^{\prime }$. We further complement this study with determining the reach of LHCb and a CMS-type detector for the high-luminosity LHC run. We demonstrate that in a backgroundfree scenario with $g_1^{\prime }={10}^{-3}$ near the current limit, FASER 2 is sensitive to the active-sterile neutrino mixing down to $V_{\mu N}\approx {10}^{-4}$, while a reach of $V_{\mu N}\approx {10}^{-5}$ can be obtained for CODEX-b and LHCb, in a mass regime of $m_N\approx 5–20\mathrm{GeV}$ and $m_{Z^{\prime }}\approx 20–70\mathrm{GeV}$. Finally, MATHUSLA can probe $V_{\mu N}\approx {10}^{-7}$ and cover the mixing regime expected in a canonical seesaw scenario of light neutrino mass generation.

Figure 1

Production cross section of $pp\to Z^{\prime }$ at $\sqrt{s}=14\mathrm{TeV}$ for $g_1^{\prime }={10}^{-3}$ (left). Branching ratios of $Z^{\prime }$ to various final states; here $\nu \overline{\nu }$ and $NN$ represent the sum over all three light and heavy neutrinos in the corresponding final states (right).

Figure 2

Existing limits on the $g_1^{\prime }\text{−}{m}_{Z^{\prime }}$ parameter space using Darkcast. Constraints derived from decays to SM final states for a $B-L$ model containing three generations of heavy neutrinos (left). Constraints derived from $Z^{\prime }$ decays to heavy neutrino final states assuming that the heavy neutrinos are stable.

Figure 3

Projected sensitivity of displaced vertex detectors in the heavy neutrino mass $m_N$ and neutrino mixing $V_{\mu N}$ parameter plane. The $U(1{)}_{B-L}$ gauge coupling and the $Z^{\prime }$ mass are chosen as $g_1^{\prime }={10}^{-3}$ and $m_{Z^{\prime }}=3.33\times m_N$, respectively. The displaced vertex detectors are CMS (HL-LHC), LHCb, MATHUSLA, FASER 2, MAPP* and CODEX-b as indicated, at 14 TeV and using projected future luminosity as detailed on the text. In the left plot, we assume no background to displaced vertex searches whereas in the right plot, we scale current background limits for CMS and LHCb to the luminosity used. The red curves denote the proper decay length of the heavy neutrino $N$ and the horizontal band indicates the preferred parameter region where the light neutrinos acquire a mass between ${10}^{-2}\mathrm{eV}$ and 0.3 eV in a canonical seesaw mechanism.

Figure 4

Distribution of the heavy neutrino decay length in the laboratory system for $m_N=5\mathrm{GeV}$, $m_{Z^{\prime }}=17\mathrm{GeV}$ (left) and $m_N=15\mathrm{GeV}$, $m_{Z^{\prime }}=50\mathrm{GeV}$ (right). The active-sterile neutrino mixing is set at $V_{\mu N}={10}^{-4.5}$. The three histograms represent the distributions of all events (fiducial) as well as those passing the angular acceptance criteria of FASER and CODEX-b. The vertical lines show the approximate distance from the interaction point at which FASER and CODEX-b are located. For CODEX-b, the two lines shown represents the depth of detector.

Figure 5

Projected sensitivity of lifetime frontier detectors in the heavy neutrino mass $m_N$ and neutrino mixing $V_{\mu N}$ parameter plane as in Fig. 3 (left) but for a series of fixed values of $m_{Z^{\prime }}$ and $g_1^{\prime }$ as indicated. The background is assumed to be zero for all detectors.

Figure 6

Left: The distribution of the momentum and its angle between the beam line $\theta$ of the heavy neutrino N, with $m_N=3\mathrm{GeV}$ and $m_{Z^{\prime }}=10\mathrm{GeV}$. Right: Same but $m_{Z^{\prime }}=50\mathrm{GeV}$. Up: The distribution at parton level. Bottom: The distribution at hadronization/shower level. The solid purple line corresponds to $p_T=p\sin \theta =m_{Z^{\prime }}/2$. The horizontal lines indicate the decay length in lab frame when $V_{lN}$ is fixed at ${10}^{-3}$ for FASER 2 (480 m), LHCb ($\sim 1\mathrm{m}$) and MATHUSLA ($\sim 200\mathrm{m}$) which are taken as representative examples, while the vertical lines show $\theta$ range for FASER 2 ($\theta <{10}^{-2.7}$), LHCb (${10}^{-2.0}<\theta <{10}^{-0.5}$) and MATHUSLA ($\theta <{10}^{-0.5}$).