Probing for chiral $Z^{\prime }$ gauge boson through scattering measurement experiments

Motivated by the observation that tiny neutrino mass cannot be explained within the framework of the Standard Model, we consider extra gauge extended scenarios in which tiny neutrino masses are generated through the seesaw mechanism. These scenarios are equipped with a beyond the Standard Model neutral gauge boson called $Z^{\prime }$ in the general $U(1{)}_X$ symmetry, which is a linear combination of $U(1{)}_Y$ and $U(1{)}_{B-L}$. In this case, left- and right-handed fermions interact differently with the $Z^{\prime }$. The $Z^{\prime }$ gives rise to different processes involving neutrino-nucleon, neutrino-electron, electron-nucleus, and electron-muon scattering processes. By comparing with proton and electron beam-dump experiment data, recast data from searches for the long-lived and dark photon at BABAR, LHCb, and CMS experiments, the electron and muon $g-2$ data, and the data of the dilepton and dijet searches at the LEP experiment, we derive bounds on the gauge coupling and the corresponding gauge boson mass for different $U(1{)}_X$ charges and evaluate the prospective limits from the future beam-dump scenarios at DUNE, FASER (2), and ILC. We conclude that large parameter regions could be probed by scattering, beam-dump, and collider experiments in the future.

Figure 1

Number of muon neutrinos pass through the $\mathrm{FASER}\nu$ (left) and SND@LHC (right) detectors. Thirty energy bins are defined uniformly on the logarithmic scale in $[10,{10}^4]\mathrm{GeV}$.

Figure 2

The neutrino-proton scattering cross section ${\sigma }_{\nu p}$ divided by the incoming neutrino energy $E_{\nu }$. The gauge coupling $g_X$ is set to unity.

Figure 3

The muon neutrino spectra at the $\mathrm{FASER}\nu$ (top), $\mathrm{FASER}\nu 2$ (middle) and SND@LHC (bottom) detectors.

Figure 4

Left: the total cross section for the bremsstrahlung $Z^{\prime }$ production. Right: normalized $E_{Z^{\prime }}/E_0$ distribution for different $Z^{\prime }$ masses. $E_0=100\mathrm{GeV}$ is the electron beam energy.

Figure 5

Top-left: the distribution of the number of events contributed only by the SM particles in MUonE. Top-right, bottom-left, and bottom-right panels: the distributions of the deviation of the number of events in MUonE from that contributed only by the SM particles: $\delta N_i/N_i^{\mathrm{SM}}\equiv (N_i^{\mathrm{SM}+Z^{\prime }}-N_i^{\mathrm{SM}})/N_i^{\mathrm{SM}}$ for $(M_{Z^{\prime }}/\mathrm{GeV},g_X)=({10}^{-3},{10}^{-3}),({10}^{-1},{10}^{-3}),(10,{10}^{-3})$, respectively.

Figure 6

Limits on $g_X–M_{Z^{\prime }}$ plane for $x_H=-2$ [upper, $U(1{)}_R$ case] and $x_H=-1$ (lower) taking $x_{\mathrm{\Phi }}=1$ considering ${10}^{-3}\le M_{Z^{\prime }}\le 150\mathrm{GeV}$. For $x_H=-2$ we show the region sensitive to the MUonE experiment. Recasting the data we compare the parameter region with those we estimated from LEP, dark photon searches at BABAR, LHCb, and CMS (CMS Dark), and different beam-dump experiments at Orsay, KEK, E137, CHARM, NOMAD, $\nu$-cal, E141, E774, NA64, NA62, FASER, and involving prospective bounds from FASER(2), DUNE, and ILC-BD, respectively, from theoretical analyses. For $x_H=-1$ we show the regions sensitive to $\mathrm{FASER}\nu$, $\mathrm{FASER}\nu 2$, SND@LHC, $\mathrm{NA}64(eN)$, and JSNS2 experiments. We compare our results recasting limits from LEP, CHARM-II, GEMMA, BOREXINO, COHERENT, TEXONO, dark photon search at BABAR [visible (vis) and invisible (invis)], LHCb, and CMS (CMS Dark), and different beam-dump experiments at Orsay, KEK, E137, CHARM, NOMAD, $\nu$-cal, E141, E774, NA64, and involving prospective bounds from FASER(2), DUNE, and ILC, respectively. In this case, the MUonE bound cannot be calculated because $e_R$ does not interact with the $Z^{\prime }$.

Figure 7

Limits on $g_X–M_{Z^{\prime }}$ plane for $x_H=-0.5$ (upper) and $x_H=0$ (lower, $B-L$ case) taking $x_{\mathrm{\Phi }}=1$ considering ${10}^{-3}\le M_{Z^{\prime }}\le 150\mathrm{GeV}$, showing the regions sensitive to $\mathrm{FASER}\nu$, $\mathrm{FASER}\nu 2$, SND@LHC, $\mathrm{NA}64(eN)$, and JSNS2 experiments. Recasting the existing results in our case, we compare parameter regions obtained from LEP, dark photon searches at BABAR (vis and invis), LHCb, and CMS(CMS Dark), scattering experiments CHARM-II, GEMMA, BOREXINO, COHERENT, TEXONO, and different beam-dump experiments from Orsay, KEK, E137, CHARM, NOMAD, $\nu$-cal, E141, E774, NA64, NA62, FASER involving prospective bounds from FASER(2), DUNE, and ILC(ILC-BD), respectively, from theoretical analyses.

Figure 8

Limits on $g_X–M_{Z^{\prime }}$ plane for $x_H=0.5$ (upper) and $x_H=1$(lower) taking $x_{\mathrm{\Phi }}=1$ considering ${10}^{-3}\le M_{Z^{\prime }}\le 150\mathrm{GeV}$ showing the regions sensitive to $\mathrm{FASER}\nu$, $\mathrm{FASER}\nu 2$, SND@LHC, $\mathrm{NA}64(eN)$, and JSNS2 experiments. Recasting the existing results in our case, we compare parameter regions obtained from scattering experiments at LEP, CHARM-II, GEMMA, BOREXINO, COHERENT, TEXONO, dark photon searches at BABAR (vis and invis), LHCb, and CMS(CMS Dark) experiments, and different beam-dump experiments at Orsay, KEK, E137, CHARM, NOMAD, $\nu$-cal, E141, E774, NA64, NA62, FASER involving prospective theoretical bounds from FASER(2), DUNE, and ILC(ILC-BD), respectively.

Figure 9

Limits on $g_X–M_{Z^{\prime }}$ plane for $x_H=2$ taking $x_{\mathrm{\Phi }}=1$ considering ${10}^{-3}\le M_{Z^{\prime }}\le 150\mathrm{GeV}$, showing the regions sensitive to $\mathrm{FASER}\nu$, $\mathrm{FASER}\nu 2$, SND@LHC, $\mathrm{NA}64(eN)$, and JSNS2 experiments. Recasting the existing results in our case, we compare parameter regions obtained from the scattering experiments at LEP, CHARM-II, GEMMA, BOREXINO, COHERENT, TEXONO, dark photon searches at BABAR (vis and invis), LHCb, and CMS(CMS Dark), and different beam-dump experiments at Orsay, KEK, E137, CHARM, NOMAD, $\nu$-cal, E141, E774, NA64, NA62, and FASER, and involving prospective bounds from FASER(2), DUNE, and ILC(ILC-BD), respectively.